University of Southern California Dissertations and Theses

Cardiorespiratory interactions in sleep apnea: A comprehensive model

(USC Thesis Other)

Cardiorespiratory interactions in sleep apnea: A comprehensive model

PDF

Download

Open document

Flip pages

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content CARDIORESPIRATORY INTERACTIONS IN SLEEP APNEA: A COMPREHENSIVE MODEL by Hsing-Hua Fan A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BIOMEDICAL ENGINEERING) August 2002 Copyright 2002 Hsing-Hua Fan R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UMI Number: 3094335 UMI UMI Microform 3094335 Copyright 2003 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90089-1695 This dissertation, written by J k i V t ^ - f - iu .f r Tar) _ _ _ _ _ _ under the direction o f h )S dissertation committee, and approved by all its members, has been presented to and accepted by the Director o f Graduate and Professional Programs, in partial fulfillment o f the requirements for the degree of DOCTOR OF PHILOSOPHY Director Date 4 X________ Dissertation Committee /\&{stL -0~ 4A fCfw=> Chair R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Dedication To my parents for their unconditional love and support. To my sisters for their uninterrupted encouragement. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Acknowledgements I wish to express my gratitude to my advisor, Dr. Michael C. K. Khoo for his continuous guidance and advice. His endless patient has helped me tremendously in solving problems encountered in my research. Thank you Dr. Khoo! I want to thank Dr. David Z. D ’Argenio and Dr. Dennis P. O’Leary for serving in my thesis defense committee and for their time and guidance. I want to thank all my labmates: Vasily, Smita, Javier, Anna and Edwin for sharing their experiences with me and exchanging interesting personal thoughts with me. Most of all, I want to thank them for listening my long discussions on my research. I want to thank my good friends, Emil, Luan, Stephanie and Bob for their encouragements. Most of all, I want to thank my parents and my sisters for their support throughout my graduate study R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table of Contents Dedication........................................................................................................................... ii Acknowledgements...........................................................................................................iii List of Figures.................................................................................................................... vi List of Tables......................................................................................................................x Abstract............................................................................................................................... xi 1. In tro d u ctio n ..................................................................................................................l 1.1 Objective....................................................................................................................1 1.2 Organization of the Thesis...................................................................................... 5 2. L iterature R eview ....................................................................... 7 2.1 Cardiovascular Modeling Overview...................................................................... 7 2.2 Respiratory Mechanics Modeling Overview....................................................... 10 2.3 Circadian Rhythm....................................................................................................1 3 2.4 Sleep Architecture....................................................................................................14 2.5 Obstructive Sleep Apnea Syndrome......................................................................1 9 3. Model Description.................................. .23 3.1 Cardiovascular System...........................................................................................23 3.1.1 Reflexes...............................................................................................................24 3.1.2 SA Node.............................................................................................................. 28 3.1.3 Total Peripheral Resistance............................................................................. 31 3.1.4 Stroke V olum e...................................................................................................32 3.1.5 Circulatory M echanics..................................................................................... 33 3.2 Respiratory System .................................................................................................36 3.2.1 Inspiratory Muscle A ctivity............................................................................37 3.2.2 Gas Exchange and Transport..........................................................................46 3.3 Neural Control..........................................................................................................58 3.3.1 Autorhythmicity................................................................................................58 3.3.2 Ventilatory Drive.............................................................................................. 59 3.3.3 Neuromuscular Drive........................................................................................62 3.3.4 Autonomic Efferent Activity........................................................................... 63 3.4 Cardiorespiratory Interactions Summary............................................................. 67 3.5 Sleep Mechanism and Assisted Ventilation.........................................................69 3.5.1 Mechanical Ventilation................................................................................... 69 iv R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.5.2 Sleep Mechanism and Upper Airway Mechanism..................................... 70 3.6 Model Graphics..................................................................................................... 78 4. SimulinkImplementation.................................. 87 4.1 Compartments Summary...................................................................................... 87 4.2 Simulink Diagram.................................................................................................102 5. Simulation Results........................................... — 129 5.1 Simulation Descriptions...................................................................................... 129 5.2 Simulation Results................................................................................................138 6. Discussion and Conclusion ....... 154 References......................................................................................................................... 162 Bibliography......................................................................................................................179 v R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Figures F igu re 2.1: Respiratory M echanics........................................................................................................................... 13 F igure 3.1: (a) Carotid baroreceptors characteristic, (b) Parasympathetic activity modulated by barorecptors. (c) Sympathetic activity modulated by the com bined inputs from baroreflex, chem oreflex, central RSA and lung stretch recep tors......................................................................................... 78 F igure 3.2: A utonom ic control response. The parasympathetic nerves response faster than the sym pathetic nerves, (a) parasympathetic frequency response, (b) beta-sym pathetic frequency response, (c) alpha-sympathetic frequency response...........................................................................................79 F igure 3.3: Peripheral resistance change. Top page show s the general m echanism for hypotension that invokes vasoconstriction. Bottom graphs show the peripheral resistance change with the application o f a negative pressure. Top panel is the pressure drop applied. The middle panel is the Arterial B lood Pressure and the bottom panel is the Alpha-Sym pathetic activities. 80 F igu re 3.4: Interaction between A BP and pleural pressure. Pleural pressure has a negative effect on A BP. Top panel show s the A B P before any pleural influence. The second panel show s the pleural pressure. The third graph overlaps the effect o f pleural pressure on A BP. The dash line is the ABP before pleural influence and the solid line is the after result. The bottom panel show s the final ABP signal to be sent into the baroregulation....................................................................................................................81 F igu re 3.5: Respiratory modulation on the heart rate and A BP from spontaneous breathing. RSA causes changes in heart rate through the autonom ic control. ABP varies from the pleural effect and from baroregulation. (a) tidal volum e in liters, (b) changes in heart rate, (c) change in A B P 82 F igure 3.6: Stroke V olum e. V enous Return and Heart Contractility are affected by Arterial Blood Pressure changes, (a) V enous Return dynam ics (b) Heart Contractility dynam ics (c) exam ple o f increasing A BP affecting Stroke V olum e by decreasing V enous Return......................................................83 F igu re 3.7: Neurom uscular Drive, N t for each breath is contributed from the V entilatory Drive, D T. (a) D T and N t increase due to hypercapnia. (b) D T and Nt decrease due to w akefulness stimulus withdraw in sleep .............................................................................................................................................. 84 F igure 3.8: Carbon D ioxide and O xygen D issociation. Carbon D ioxide is represented as in concentration, w hile O xygen is displayed based on the saturation level. Both dissociations are affected by both C 0 2 and 0 2 partial pressures, (a) dissociation curve for [C 0 2]. C 0 2 concentration is in ml o f C 0 2 per ml o f w hole blood, (b) saturation curve for O xygen. Saturation is in percentage. .......................... ~...................................................... 85 F igu re 3.9: Sleep M echanism , (a) Circadian Rhythm and Sleep Propensity, (b) Slow W ave A ctivity (SW A ), (c) Rapid Eye M ovem ent (REM ) stage in sleep ................................................................... 86 F igu re 4.1: Cardiorespiratory M o d e l......................................................................................................................102 F igu re 4.2: Cardiovascular S y ste m ........................................................................................................................ 103 F igure 4.3: Cardiovascular System - Baroreceptor F igure 4.4: Cardiovascular System - C hem oreflex.......................................................................................... 104 vi R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. F igu re 4.5: Cardiovascular System - Lung Stretch Receptors R eflex F igu re 4.6: Cardiovascular System - SA Mode F igu re 4.7: Cardiovascular System - SA N ode modulated by P-sym pathetic nerves.........................105 F igure 4.8: Cardiovascular System - SA N ode modulated by parasympathetic nerves F ig u r e 4.9: Cardiovascular System - Stroke V olum e F igu re 4.10: Cardiovascular System - T PR ........................................................................................................ 106 F igure 4.11: Cardiovascular System - TPR modulated by a-sym pathetic nerves F igu re 4.12: Cardiovascular System - Circulatory M echanics.....................................................................107 F igure 4.13: Respiratory System ..............................................................................................................................108 F igure 4.14: Respiratory System - Respiratory M echanics F igure 4.15: Respiratory System - Respiratory M uscle A ctivity.................................................. 109 F igure 4.16: F igure 4.17: Respiratory System - Respiratory M uscle Reaction Respiratory System - Flow Generation......................................................................... 110 F igure 4.18: Figure 4.19: F igure 4.20: Respiratory System - Pleural Pressure Respiratory System - A lveolar Pressure Respiratory System - Chest Wall Pressure................................................................... 111 F igu re 4.21: Respiratory System - Gas Exchange and Transport................................................ 112 F igure 4.22: F igure 4.23: F igu re 4.24: Respiratory System - Dead Space Respiratory System - Total Dead Space for C 0 2 Respiratory System - Dead Space Compartment for C 0 2..................................... 113 F igu re 4.25: Figure 4.26: F igure 4.27: Respiratory System - Total Dead Space for 0 2 Respiratory System - Dead Space Compartment for 0 2 Respiratory System - Gas Exchange in the L ungs.................................................... 114 Figure 4.28: F igure 4.29: Figure 4.30: Respiratory System - C 0 2 Gas Exchange in the Lungs Respiratory System - 0 2 Gas Exchange in the Lungs Respiratory System - Cardiovascular M ixing and C onvection............................ 115 F igure 4.31: F igure 4.32: F igure 4.33: Respiratory System - Cardiovascular M ixing and C onvection for C 0 2 Respiratory System - Cardiovascular M ixing and C onvection for 0 2 Respiratory System - B ody T issu es................................................................................ 116 Figure 4.34: F igure 4.35: F igure 4.36: Respiratory System - C 0 2 Exchange in B ody Tissues Respiratory System - 0 2 Exchange in Body Tissues Respiratory System — D issociation.................................................................................. 117 F igu re 4.37: Figure 4.38: Respiratory System - Brain Region Respiratory System - Cerebral F low .............................................................................. 118 Figure 4.39: F igure 4.40: Neural Control - Central N eurom uscular Drive Neural Control - V entilatory D rive................................................................................. 119 F igure 4.41: F igure 4.42: Neural Control - A utonom ic Control External Pressure M odule................................................................................................... ............ 120 vii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. F igure 4.43: Respiratory System - State Dependent Upper Airway M echanism 121 F igu re 4.44: Sleep M echanism 122 F igu re 4.45: Sleep M echanism - Slow W ave Activity 123 F igu re 4.46: Main Control GUI panel 124 F igu re 4.47: Constant Parameters GUI panel 125 F igu re 4.48: Initial Conditions GUI panel 126 F igu re 4.49: Adjustable Inputs GUI panel 127 F igu re 4.50: External Interventions GUI panel 128 F igu re 5.1: Sim ulation under normal conditions for approxim ately 60 seconds. The w hole panel consists o f the total ventilatory drive / chem ical drive, state-related drive, tidal volum e, heart rate, arterial blood pressure, pleural pressure, oxygen saturation, carbon dioxide partial pressure, circadian sleep process signals respectively. CH igi, and CL ow are upper and lower circadian threshold F igure 5.2: Simulation o f 600 seconds o f Isocapnic H ypoxia case. H ypoxia is induced by low ering the inspiratory 0 2 partial pressure to 60m m H g. Isocapnia is maintained by increasing 20m m H g o f inspiratory C 0 2 partial pressure. Both added 0 2 and C 0 2 partial pressure changes are fixed during the isocapnic hypoxic sim ulation period. “Start” marks the beginning o f the hypoxic event and “R elease” show s the end o f the event. With the increase in respiratory effort, there is an increase in heart rate and the arterial blood pressure rises due to the chem ical built u p .............................................139 F igure 5.3: Simulation o f 600 seconds o f hypercapnic hypoxia case. Hypoxia is induced by low ering the inspiratory 0 2 partial pressure to 60m m H g. Hypercapnia is introduced by increasing 40m m H g o f inspiratory C 0 2 partial pressure. Both added 0 2 and C 0 2 partial pressure changes are fixed during the isocapnic hypoxic sim ulation period. “Start” marks the beginning o f the hypoxic event and “R elease” show s the end o f the event. With even more respiratory effort than isocapnic case, the heart rate increases more. The arterial blood pressure rises and more fluctuation per breath due to higher respiratory effect................................................................................................................................... 140 F igure 5.4: Experimental vs. Simulated data for M ueller and Breath H olding maneuvers, (a) Simulated M ueller maneuver. Because o f high negative pleural pressure produced from the inspiration, the arterial blood pressure drops, (b) Breath H olding. N o visible change in heart rate and very sm all increase in arterial blood pressure, (c) Left colum n is the adapted drawings o f experimental data from Morgan et al. [1 85], Right side is the simulated data from the m odel. Solid line represents the M ueller maneuver and dashed line represents the Breath Hold maneuver. A ll panels are com posite graphs o f both m aneuvers for com parison.................................................................. 142 F igu re 5.5: Experimental vs. Simulated V alsalva m aneuver. At the onset o f the expiratory straining, there is an initial increase in the arterial blood pressure and follow ed by a recovery period during straining. At the end o f the straining, a decrease in the arterial blood pressure can be seen and there is an elevation in the blood pressure after the maneuver. Top figure is the experim ental data recording from Dr. V asily B elozeroff and is show n here with his perm ission. Bottom figure is the simulated data using our m odel............................................................................................................................ 143 hold for the sleep process 138 V lll R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. F igu re 5.6: Simulation o f the w hole night o f sleep. With sleep onset there is a decrease in heart rate and blood pressure. Normal sleep takes about 8 hours.....................................................................................144 F igu re 5.7: Simulation o f the w hole night sleep with O SA during both N R E M and REM stages. The interrupted sleep with repetitive arousal lengthens the sleep time. Norm al sleep lasts about 8 hours w hile the sleep period for O SA subject prolongs to about 8 hours and 40 minutes as shown from the last panel in the graph. This O SA simulation is using the same NREM /R EM period as for normal sleep ......................................................................................................................................................................145 F igure 5.8: Simulated O SA episodes during N REM and REM stages. This is taken from a segm ent o f the w hole night O SA simulation. With greater reduction in hypoxic ventilatory response in REM stage, about 50% compared to NREM stage and with low er arousal threshold value, the ventilatory drive attenuates. H owever, the obstructive period in REM sleep is shorter than in NREM stage. The arousal period is longer than in NREM stage...............................................................................................146 F igure 5.9: The sudden surge in blood pressure upon arousal can be caused by high alpha- sym pathetic activity. From our simulation, w e can observe the sudden increase in sympathetic activity at arousal caused by the increase in ventilatory drive both at NREM and REM stages....................................................................................................................................................................................147 F igu re 5.10: OSA patient is som etim es given oxygen treatment to replenish the oxygen desaturation. In our sim ulation, inspiratory 0 2 partial pressure is increased by 30m m H g more during the oxygen application period. It show s that each obstruction lengthens and with less oxygen desaturation....................................................................................................................................................................... 148 F igure 5.11: CPAP machine is usually prescribed by the doctor to OSA patient as a treatment. Our m odel can simulate the administration o f CPAP and prevent the occurrence o f upper airway obstruction. 10 cm H 20 o f positive pressure is applied to the upper airw ay.................................................................................................................................................................................. 149 F igure 5.12: Severe C ongestive Heart Failure (CHF) can produce apnea in sleep. From our simulation, it show s that with the decrease in blood flow and the increase in transporting tim e to chem oreceptors apnea can be induced in sleep. With the large periodic breathing, arousal takes place. The cardiac output is reduced by 80% and the transport delay is increased to about 4 0 -5 0 seconds from the normal 6 second in the sim ulation to generate the period breathing in sleep 150 F igure 5.13: A segm ent o f the simulated periodic breathing in sleep for CHF patient which show s the crescendo-decrescendo breathing pattern in more detail............................................................................151 F igure 5.14: O xygen treatment is som etim es used for CHF patient to lessen the apnea in sleep. We simulate the case for both oxygen and carbon dioxide treatment, (a) Separate oxygen and carbon dioxide treatment during sleep, (b) C 0 2 treatment in sleep with the disappearance o f the apnea and regaining normal sleep. Inspiratory C 0 2 partial pressure is increased by 40m m H g during the application period, (c) O xygen treatment in sleep with attenuation in periodic breathing but still triggering arousals. Inspiratory 0 2 partial pressure is increased by 40m m H g during the application period................................................................................................................................................................................... 152 F igure 6.1: Cardiorespiratory Simulator / Predictor.........................................................................................161 ix R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Tables T ab le 2.1: EEG Frequency B and...............................................................................................................................17 T able 2.2: Different sleep stages and characteristics..........................................................................................18 T able 4.1: Baroreceptors T ab le 4.2: C hem oreflex T able 4.3: Lung Stretch Receptors R eflex.............................................................................................................. 88 T ab le 4.4: S A N o d e .........................................................................................................................................................89 T able 4.5: Stroke Volume T ab le 4.6: T PR ..................................................................................................................................................................90 T ab le 4.7: Circulatory M echanics............................................................................................................................. 91 T ab le 4.8: M uscle Reaction T able 4.9: Respiratory M uscle Interaction............................................................................................................92 T able 4.10: Flow T able 4.11: Pleural Pressure........................................................................................................................................93 T able 4.12: Dead Space T able 4.13: Lung............................................................................................................................................................. 94 T able 4.14: Cardiovascular Interaction T able 4.15: B ody T issu es.............................................................................................................................................95 T able 4.16: D issociation .............................................................................................................................................96 T able 4.17: Brain............................................................................................................................................................. 97 T able 4.18: Central N eurom uscular Drive T able 4.19: Ventilatory D rive.................................................................................................................................... 98 T able 4.20: A utonom ic Efferent A ctivity..............................................................................................................99 T able 4.21: Sleep M echanism .................................................................................................................................. 100 x R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Abstract The dynamic interactions among the peripheral inputs that originate from the chemoreflexes, baroreflexes and pulmonary stretch receptors, together with central autonomic coupling between respiratory and cardiovascular efferents, play important roles in determining the physiological effects that accompany sleep apnea such as Obstructive Sleep Apnea. However, previous modeling studies have focused primarily on specific regions of interest. The purpose of this study is to integrate the key features of existing cardiovascular and respiratory models into a comprehensive model that is capable of simulating the dynamics of cardiorespiratory control during wakefulness and sleep. The model allows the simulation of important cardiorespiratory interactions that occur during obstructive sleep apnea, such as the differential effects of apnea and arousal on heart rate and blood pressure. For instance, the model is capable of simulating the hypoxia- induced bradycardia that is unmasked by the absence of vagal feedback from the lung stretch receptors during apnea. As well, the model incorporates a realistic simulation of the wake-sleep cycle and allows changes in sleep-wake state to interact with the respiratory and cardiovascular subsystems. The comprehensive cardiorespiratory model is implemented using SIMULINK® (The Mathworks, Natick, MA), a graphical environment that allows the user to easily convert control block diagrams into networks of blocks of mathematical functions. The advantages of this form of implementation lie in: (1) the modularity of its various components; xi R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (2) the flexibility with which changes can be made to selected portions of the program; and (3) transportability of the model across different computer platforms and operating systems. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1. Introduction 1.1 Objective Obstructive Sleep Apnea Syndrome (OSAS) presents an alarming health problem today. About 2 to 4% of the general population suffers OSA, mostly in men [1], OSA patient who meets the criteria usually shows loud and irregular snoring and snorts during nighttime and displays excessive sleepiness or fatigue in daytime. It poses a personal and a societal risk such as the higher potential to cause an automobile accident while driving on the road. Prolongation of this disorder can lead to cardiovascular disease such as heart failure or stroke which can become a real threat to life. The etiology and the pathophysiology of OSA have been studied extensively. Cardiorespiratory changes in OSA have also been noted from experimental data [2-6]. Visible cardiorespiratory traits in OSA episode are the pause in breathing, bradycardia during apnea followed by tachycardia and the surge of arterial blood pressure upon arousal. To understand and to capture these dynamic changes better, we can use computer modeling as an assistive tool. Many cardiovascular models already exist in publications [8-26]. The complexities of these models vary in accordance to the purpose of each study. The structures of these models reflect the author’s interest in the specific region of the system. Early cardiovascular models dealt with the vascular system and its properties. More recent models start to include the central nervous system and peripheral reflexes [27-39]. 1 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Early studies on respiratory mechanics were focused on predicting the ventilatory response to added mechanical loads. However, the intrinsic behavior of the respiratory muscles has not been explored much. More recent model developments have been able to separate the respiratory mechanics into the pulmonary and chest compartment [40-55], But, the majority of these models do not deal with the relationship between the neural activity of the respiratory muscles and the mechanical output that generates the airflow and the lung volume. Since breathing is a neurally driven event, a neurally controlled model can provide us with more accurate descriptions on the respiratory mechanics. This will give us a better characterization on the interaction between the respiratory muscles and the neural control center. Even though there exists several individual cardiovascular and respiratory models, relatively little effort has been made to integrate these two systems together to describe the dynamical interactions between them [27, 56]. But interactions such as the respiratory sinus arrhythmia (RSA) which shows the respiratory modulation on heart rate regulation, the effect of intrathoracic pressure on the left ventricle, the ventilatory response to the heart rate and the blood pressure and the change in cardiac output to the blood flow regulation for gas exchange and transport all cannot be neglected. These modulations are very important in cardiorespiratory regulation. By incorporating these interactions, a more realistic cardiorespiratory model can be utilized to study the cardiorespiratory dependencies. Furthermore, modeling work in cardiorespiratory responses in sleep 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. is even more limited. Therefore, a comprehensive cardiorespiratory model with sleep mechanism can help us to better understand those mechanisms which contribute to the cardiorespiratory changes in OSA episodes. If too many components are used in a model, it defeats the purpose of modeling which is to extract the essential features that characterize the system structurally and functionally. Therefore it is crucial to devise a model that captures the major reflexes and controls such as the baroreflex, chemoreflex, lung stretch receptors reflex coupled with central respiratory modulation, most importantly a sleep mechanism and still retain the computation speed for simulation. By integrating the cardiovascular and the respiratory system and the sleep mechanism together, cardiorespiratory changes in sleep apnea can be simulated from the model. The differential effects of apnea and arousal on the cardiovascular system in OSA episodes constitute the primary focus of this study. The purpose of this study is to develop a neurally driven cardiorespiratory model that serves as a framework to piece together existing results or models from both cardiovascular and respiratory studies. On top of that the incorporation of the sleep mechanism in the model will widen the range of applicability of the cardiorespiratory model. In this study, we have implemented our model using the Matlab/Simulink software environment.. The advantages for using this package are its portability and modularity. Matlab and Simulink are available in many computer platforms: Unix, PC and Mac. Therefore, our model can easily run on various computers while sharing the same source code. This bypasses the hassle of 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. recompiling the computer source code for each platform. The graphich user interface, (GUI) panels implemented with this model will allow the user to vary parameter values and make it easier to operate. The graphic friendly feature in Simulink allows the user to put together the model from built-in blocks or user- defined functions. With this building block concept, it optimizes the exchangeability of our model. This comprehensive model will help us to understand better on influences between the cardiovascular and the respiratory system and their regulations in sleep. Most importantly, we want to be able to obtain a better description on the behavior of this cardiorespiratory model in the case of Obstructive Sleep Apnea. We want to see if we can explain some of the cardiorespiratory interactions that cause the changes in heart rate and blood pressure. We also want to expand our simulation to other sleep apnea. From the standpoint of design, we want to make this toolbox robust and friendly enough so that we can interchange components with newer models that either suit for our own study or other users who are interested in this toolbox. By implementing our model using Simulink, we can achieve the modularity and the flexibility we desired and integrate our model into a useful tool. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1.2 Organization of the Thesis In chapter 2, we will summarize some of the cardiovascular and the respiratory models from the literatures. We will mention the sleep architecture and take a brief look at circadian rhythm and different sleep stages. Last, we will describe some of the characteristic of obstructive sleep apnea syndrome. In chapter 3, we describe each compartment in our model in details with both physiological background and model equations. Characteristics of some components are also shown in graphs. Basically we divide our model into 3 major systems: cardiovascular system, respiratory system and neural control center. The cardiorespiratory interactions which are the baroreflex, the chemoreflex and the lung stretch receptors reflex coupled with central respiratory modulation are summarized here. The pleural pressure effect and the cardiac output influence are addressed as well. The upper airway and the sleep mechanism are described separately. But the cardiorespiratory changes in sleep are mentioned when we describe the three major systems. In chapter 4, we provide the Simulink schematic diagrams of our model. A brief description of each compartment is added along with a table o f nominal parameter values. This will give us and other people a better idea on what we have included in our model and how we have implemented our components. In chapter 5, we test our model by simulating Valsalva and Mueller maneuvers and hypoxia cases. We also perform simulation on obstructive sleep 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. apnea and periodic breathing in Congestive Heart Failure (CHF) patient. The simulated result and notable cardiorespiratory changes are shown in this chapter. In chapter 6, we summarize the compartments in our comprehensive cardiorespiratory model. We discuss those cardiorespiratory changes occurred in obstructive sleep apnea and the mechanisms contributed to those changes from our simulation. We then suggest future improvements and studies for this research. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2. Literature Review 2.1 Cardiovascular Modeling Before the advancement of the computer, complex modeling of the cardiovascular system posed a tremendous challenge to researchers. The focus of most studies was primarily on the circulation. The most prominent representation of hemodynamics was Windkessel theory. In Windkessel theory, the arteries are viewed as a network of interconnected tubes that are capable for fluid storage. At one end of the tube, the fluid is pumped in with a pulsatile fashion while the outflow at the other end keeps relatively constant due to the peripheral resistance regulation. The capacity to store blood is contributed by the elasticity of the tube. Windkessel model remains a good candidate to be used for arterial modeling in the cardiovascular system. Aside from the Windkessel model which is designed based on the hydrodynmic theory, the advancement of the electric circuit theory has enabled the circulation to be modeled as a combination of many transmission lines. The early stage of the cardiovascular modeling was more mechanical orientated than neurally driven. Several hydrodynamic models were published from the mid 1800s to the mid 1900s. These mechanical closed loop models included left side of the heart, the aorta, the peripheral resistance and the veins with appropriate valves. In these models, the resistance, the compliance and the contraction frequency can be adjusted. Most of these models were designed mainly for teaching purpose [7]. 7 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. As mathematical modeling evolved, more detailed mathematical descriptions of the heart were developed. These developments showed a change from a mechanical design point of view to an electrical design aspect with linear resistors and capacitors. The early electrical models were used to describe the circulation changes for infants rather than for adults. In 1959, Grodin introduced a more sophisticated electrical model for the circulatory system. In his model, he derived the expression for the heart using Starling’s Law. In the model, he used 23 simultaneous equations that could be solved using the analog computer [16]. However this and previous models lacked the triggering mechanism of the heart, the atrioventricular and sinoatricular activity. With the ubiquity of the computer, the development of cardiovascular modeling has been transformed from crude approximations to more realistic approaches. One of the newer additions is myocardiac contraction, especially in the ventricular region that are modeled using the force-volume properties of the skeletal muscles. The increase in the capability of the computer has also enabled the study of the effects of some feedback controls, such as the control of cardiac output under different conditions and the regulation of the heart rate. One important control mechanism introduced is the baroreceptors in the carotid sinus. Firings from the baroreceptors regulate the vagal and the sympathetic nerves which control the heart rate and the peripheral resistance. At this stage of the development, the nervous control has been incorporated into the overall 8 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. cardiovascular model along with the early development of the arterial tree hemodynamic [80-83]. One of the areas of concentration in cardiovascular system modeling has been the characterization of the heart as a pump, particularly the left ventricle. The left ventricular activity closely correlates with the arterial blood pressure and the cardiac output. The simple scheme that describes the response follows the Starling Law where the systolic pressure, the peripheral resistance, the heart rate and the cardiac contractility are held at constant values. However, this does not adequately capture the pumping action of the heart. The better model shows the ventricle as a contracting chamber which can generate responses under varies conditions in preload such as the diastolic volume or afterload i.e. the peripheral resistance and the arterial impedance [14, 15, 18, 22, 36, 39]. As the cardiovascular modeling progresses, an overall model can be separated under four major components, namely the arterial tree, the venous return, the cardiac pump and the reflex control system driven by the central nervous system. In the early models, neurogenic regulation was not incorporated because the focus was on the hydraulic aspects of the system. With the accumulation of more experimental evidence on the reflex control mechanism, some initial models characterized the direct baroreceptor feedback on the systemic pressure as a sigmoidal curve or considered the CNS to be a single integrator of different afferent inflows that produces one outflow as the representation of the CNS stimulation to efferent sites. 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Newer developments in reflex control studies have enabled more detailed modeling for these feedback controls. More recent models contain separate controls for the heart rate, the cardiac contractility, the arterial resistance and the venous tone. These controls are based on experimental data correlating the input and the output variable for each reflex system. One example of the reflex system is the carotid baroreceptor control of the heart rate. These advancements provide us with more realistic descriptions in creating a better cardiovascular model. In our model, we want to piece together these optimal modules that describes the cardiovascular system and generates output signals that correlate with experimental recordings. 2.2 Respiratory Mechanics Modeling Modeling in the respiratory system has focused more on the mechanical properties of the system, mainly the lungs and the chest wall [42, 51]. Since most interests have been on the whole respiratory mechanics, the upper airway structure has usually been a minor consideration. The most commonly used model for the respiratory system is a simple two elements model. One element represents the elastance like a ballon and the other describes the resistance like a pipe of the system. To better capture those mechanical properties, more numbers of elements can be incorporated into the model. One type of these two compartment models emphasize the gas distribution throughout the lungs. Assuming inhomogeneity in gas distribution, parallel 10 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. alveolar compartments that are connected by separate airways to the trachea have been proposed. Alternative serial configurations have also been used which represent a homogeneous alveolar compartment connecting to the trachea along with a compliant airway tree as shown in Fig 2.1 [53]. Another extension of the single compartment model deals with the mathematical formulation of the viscoelastic or the plastoelastic properties of lung tissue. These models compose of a parallel structure of an airway resistance component, a static elastic component and a viscoelatstic or plastoelastic element. The viscoelastic element is usually represented in terms of springs and dashpots such as a Maxwell body (see appendix). This accounts for the slower part of the respiratory responses. The plastoelastic element characterizes the quasi-static pressure-volume hysteresis. The dashpot in the viscoelastic element is substituted with a Coulomb element for the plastic element. However experimental data show that this hysteresis is minimal in human at rest. Thus the viscoelastic element better describes the behavior of respiratory mechanics. [48-50] The viscoelastic approach has been used to model the lungs and the chest wall dynamics. A generalized scheme for the respiratory mechanics consists of an airway resistance in parallel with a Kevin body which is a parallel configuration of a static elastance and a Maxwell body. The same arrangement applies to the chest wall as for the lungs. The distance between the parallel configuration of the system will be the lung volume and the tension between them will be the pressure which is usually the pressure measured at the airway opening [54-55]. 11 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Values for these parameters are usually measured from the flow interruption or from the airway occlusion method. These methods can obtain the total resistance of the respiratory system and the interrupter resistance reflects the airway resistance. The lungs and the chest wall resistance can then be computed from those values. The elastances can also be derived from those occlusion pressure measurements [43]. The generalized model has been used to study the respiratory mechanical behavior for normal subject. More importantly, it has been applied to investigate and to understand the response in severe obstructive respiratory disease such as the chronic obstructive pulmonary disease (COPD) that requires mechanical assisted ventilation. These diseases greatly affect the lungs and the chest wall fuction [45- 47, 52]. Through modeling, these mechanics can be better represented. 12 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. P a ra lle l g a s d is trib u tio n S e r ia l g a s d istrib u tio n p la s to e la tic m o d e l w ith C o u lo m b , C e le m e n t CllltWlI -IT I L ung a n d C h e s t W all m e c h a n ic s u sin g v is c o e la s tic e m o d el w ith K elvin Body F igure 2.1: Respiratory M echanics 2.3 Circadian Rhythm Human’s behavioral and physiological activities are generally governed by an internal time cue, known as the circadian rhythm. One prominent example is the wake/sleep cycle that we experience everyday. The rhythm usually matches the 24 hours day-night cycle. But experiments have shown that without the light information the sleep/wake cycle shifts and extends to about 25 hours. Therefore the circadian rhythm can be modified by the external factor such as lights. It has been shown that hormonal changes in our body affect this rhythm also. 13 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. One possible area for circadian rhythm generation is the hypothalamus. Experiments have shown that by stimulating the hypothalamus particularly in the suprachiasmatic nuclei (SON), there are significant impacts on the circadian rhythm. Under free running conditions, circadian rhythm is mostly correlated with our body temperature which extends over 25 hours. But with our daily working schedule, the circadian rhythm we followed has been entrained by the light-dark cycle of the 24-hour day. However, both the free running and entrained circadian systems are simultaneously running in our body. Therefore, internal desynchronization can occur because of the difference in periodicity of these nonlinear systems. In awake state, there is high level of catecholamine activity. While in sleep, there is an increase in serotonin concentration which helps the slow wave generation. 2.4. Sleep Architecture Sleep can be described as a state change from consciousness to partial unconsciousness. During sleep, the more common physical characteristics in sleep are postural recumbency, quiescence and closed eye. Generally sleep can be separated into two groups, NREM and REM. As the person falls asleep, the electroencephalogram (EEG) shifts to a lower frequency region and these high voltage slow waves can be seen in NREM sleep. NREM sleep has been 14 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. conventionally divided into four stages which correlates with the depth of the sleep. During this state, the respiratory movement, heart rate and blood pressure are generally below awake state. There is an overall decline in muscle tone. Contrast to NREM sleep, the slow wave activities are replaced by EEG patterns resembled to arousal state in REM or paradoxical sleep. Because of the episodic bursts of rapid eye movement, the stage is usually referred to as REM stage. The first REM sleep usually occurs after 80 to 100 minutes after sleep onset. The alternation between NREM and REM stage is known as ultradian rhythm. One of the possible sites that induce the REM sleep is locus caeruleus located in the Pons. Overall body muscle tones are also reduced in REM sleep. In REM sleep, muscle activities are more suppressed than in NREM and most of the time atonia occurs. Postsynaptic inhibition of the alpha motor neurons is believed to be the cause of the reduction in the muscle tone. Breathing and heart rate become irregular and blood pressure varies in REM sleep. Dreaming usually occurs in this stage. In normal circumstance, sleep onset takes place in NREM sleep. At sleep onset, the electromyogram (EMG) level is reduced. Electro-oculogram (EOG) shows slow and asynchronous eye movement (SEM). Also during the onset, periodic breathing can be frequently observed. The oscillation in breathing lasts throughout most of the transition from wake to stage 2. It frequently disappears once a stable stage 2 is achieved. The EEG wave shifts from a clear alpha wave to a mixed frequency pattern as it enters stage 1 NREM sleep. During stage 1, arousals are more frequent because the arousal threshold is low and it serves as the 15 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. transitional stage throughout the night. In stage 2, K complexes or sleep spindles appear frequently. Some would qualify the occurrence of the stage 2 patterns as the end of sleep onset. As stage 2 progresses, slow wave activity (SWA) stalls to appear in EEG pattern and it becomes more prominent by the time it reaches stage 3. In stage 3, SWA accounts for more than 20% but less than 50% in EEG recordings. In stage 4, the SWA appears more frequently, accounting for more than 50% of each epoch. In stage 3 and 4, larger stimuli are needed for arousal. The last two stages are usually referred as delta sleep or slow wave sleep. During slwo wave sleep, breathing is very regular with small variability. Experiments have shown that in awake state, low frequency electrical stimulation of the medullary reticular formation in particular the dorsal reticular formation and the solitary tract nucleus can produce cortical activity similar to slow wave sleep which makes those two the possible places for slow wave generation. As the stable sleep progresses, there is a shift back to the light sleep stage again before it makes the transition from NREM to REM sleep. REM sleep usually does not last long in the early cycles and lengthens towards the later cycles in the night. The arousal threshold in REM sleep varies but experimental data have shown that the overall threshold is lower than in NREM sleep. Minute ventilation, tidal volume and respiratory rate during REM only show very small difference than in NREM sleep. The ultradian rhythm repeats several times throughout the whole sleep period. As REM sleep becomes longer throughout the night, stage 3 and 4 sleep become shorter and stage 2 sleep may take over the whole NREM sleep in the 16 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. later stage of the night. NREM sleep tends to dominate the first one third of the night from the initiation of the sleep while REM sleep is the strongest at last portion of the night. Generally speaking, the length of sleep is correlated with the circadian rhythm but external factors such as sleep deprivation can also affect the amount of sleep needed. NREM sleep is also age related. At younger age, slow wave sleep is very prominent in sleep and it starts to diminish as a person grows older. REM sleep remains relatively consistent throughout lifetime. Arousals occur more frequently as a person becomes older. Below is a tabulated summary of the distinct characteristics of each sleep stages [180], T able 2.1: EEG Frequency Band Frequency Band Frequency Range (H z) Alpha (a ) 8-13 Beta (|3) >13 Delta (8) <4 Theta (0) 4-7 17 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. T able 2.2: Different sleep stages and characteristics Sleep Stages Characteristics R elaxed W akefu ln ess EEG — alpha activity shift to low voltage m ix frequency. EOG - rapid eye m ovem ent, blinks when open. Few or no eye m ovem ent w hen closed. Slow eye m ovem ents when transit to stage 1 sleep EMG - high activity N R E M Stage 1: EEG - low voltage m ix frequency. Burst o f high voltage synchronous theta activity. EOG - slow eye m ovem ent EMG - low m uscle activity. A graduate diminution o f EMG amplitude from wake to sleep. Stage 2: EEG - mix frequency as the background. Sporadic K -com plex and sleep spindle. 3-8 spindles per minute. Each K -com plex last 0.5 sec. 1 com plex per 3 minutes. EMG - active but at a lower amplitude than w akefulness. Stage 3 & 4: EEG - high voltage slow w ave activity. 20 to 50% per epoch for stage 3. > 50% per epoch for stage 4. EOG - no m ovem ent EMG - tonically active but m ay be low and close to REM stage. R E M EEG - Low voltage m ixed frequency. Theta and alpha range activities can be seen as well. EOG — activated or desynchronized, burst o f rapid eye m ovem ent. EMG - suppressed tonically. 18 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.5 Obstructive Sleep Apnea Syndrome Obstructive Sleep Apnea Syndrome is commonly characterized by the recurrent episodes of apnea due to the complete or partial upper airway blockage during sleep. The cessation of the airflow with the continuation of the respiratory effort marks the initiation of the apnea. During sleep, there is a decrease in upper airway respiratory muscle tone, making the upper airway more prone to collapse. With the combination of the muscle tone change during sleep and the generally narrower upper airway in OSA patients, at the onset of the inspiration the upper airway can easily collapse and obstruct the incoming air. But the upper airway obstruction does not diminish the respiratory pump drive. Therefore, the respiratory effort persists and other respiratory muscles continue to contract during apnea. As the obstruction of the upper airway lengthens, asphyxia starts to occur due to the lack of fresh air. When the chemical level reaches the threshold, the whole episode of the apnea is terminated by a brief arousal. During this period, the upper airway regains its patency and the airflow resumes as the OSA patient drifts back to sleep. The recurrent arousal episodes repeat for hundreds of times in an apnea patient each night and can be seen clearly in experimental recordings. This disruption of the continuity of overnight sleep affects the daily performance and creates health problems for the apnea patient. One of the possible causes for the initiation of OSA is the instability of the respiratory regulation. From the sleep study recordings, apnea patients display a period of decrease or absent ventilatory response followed by a period of excess 19 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. ventilation during their sleep. This periodic breathing resembles the pattern of Cheyne-Stokes respiration that is generally associated with neurological lesions or cardiac or pulmonary dysfunction. These lesions can cause an alteration in the chemosensitivity or prolong the blood transit time between the lungs and the brain. These variations can create instability in the respiratory control and produce episodic apnea [1, 57, 59]. Even though OSA is primarily caused by the collapse of the upper airway, the initial triggering mechanism may be centrally influenced. The difference in timing between the drive to the diaphragm muscles and to the upper airway dilator muscles has also been postulated as the cause for the instability in the respiratory regulation. If inspiration occurs before the activation of the upper airway dilator muscles, then there is a risk for the closure of the upper airway by the suction. The exact site for the obstruction in OSA varies from one patient to another. Generally it occurs in the pharynx, usually the oropharyngeal region. During inspiration, inspiratory muscles create a negative intrathorascic pressure. Around the pharyngeal region, this subatmospheric pressure can cause the upper airway to collapse. To prevent any collapse, dilator muscles are activated around that region. The upper airway is also enlarged reflexively by activating the palatal and the tongue muscles. Studies have shown that there is a reduction in the size of the oropharyngeal lumen for OSA patient and this relates to higher pharyngeal compliance for these patients and higher potential for the obstruction. 20 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In the transition from wakefulness to sleep, there is a reduction in upper airway muscle activity. This reduction in the muscle tone makes the upper airway more passive and floppy. Because of the structural difference in the oropharyngeal lumen for the OSA patient plus the reduction of the muscle tones in sleep, the upper airway becomes easier to collapse with the negative pressure from inspiration. The decrease in the upper airway muscle tones is more visible during REM sleep stage. This is the probable cause for the first occurrence of OSA and during this stage the obstruction is more severe than in other stages [62-64, 71, 73], Once the upper airway is obstructed, asphyxia starts to develop. The oxygen saturation decreases as the blockage continues and at the same time the carbon dioxide content increases. These changes will stimulate the chemoreceptors and increase the ventilatory drive. When the chemical change reaches a threshold, arousal takes place. The patient temporarily awakens and upper airway patency is restored, allowing normal airflow to occur. After this short arousal, there is a rapid transition back to sleep and the obstruction starts over. For OSA patient, the periodic wake and sleep alternations continue throughout the whole sleeping period. It diminishes the quality of sleep, causing daytime sleepiness and working performance degradation [68]. For normal people, during sleep there is a fall in ventilation and decreases in the heart rate and blood pressure. For OSA patient, at the onset of the obstruction the ventilation ceases because of the upper airway blockage. During the apnea, the blood pressure decreases initially because of the negative pleural 21 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. pressure but as the blood oxygen continues to decrease, arterial pressure starts to increase. At the same time, vagally mediated bradycardia can be seen in the apneic episode. At the termination of the apnea, the blood pressure falls toward normal and the heart rate accelerates. However in the case of the rapid succession of apneas the blood pressure does not return to normal and an elevation in the pressure can be observed over the course of the night [58, 60, 65-67, 69-70, 72, 74-76, 78], The cardiac output does not seem to vary much during the apnea even though the heart rate decreases. This is due to the increase in stroke volume and vasoconstriction. The stroke volume increases initially because of the negative pleural pressure that will increase the venous return. Follow the arousal, since there is an increase in heart rate, an increase in cardiac output occurs. One of the chronic hemodynamic effects of OSA is systemic hypertension. The patient who suffers OSA usually has the symptom of hypertension. Long term increases in the ventricular stroke due to pulmonary and systemic hypertension pose the risk of the left and right ventricular failure. Reports have shown that with the successful treatment for OSA, systemic hypertension can be reduced [61, 77, 79], 2 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3. Model Description: 3.1 Cardiovascular System Cardiovascular system can be viewed as a transport system for the whole body. The arteries carry necessary nutrients to the body tissues and the brain. The veins then take back metabolized by-products from the body. These substances are transported with the blood as the medium. The delivery of these nutrients to the body and the removal of these chemicals from the tissues are accomplished by two circulatory systems: the systemic circulation and the pulmonary circulation. The systemic circulation distributes the blood to the whole body tissues and the brain and takes up the waste. The pulmonary circulation connects both the heart and the lungs so that the by-product can be expired out from the lungs while new nutrients can come in and replenish the body tissues. The heart and the vessels are both innervated. These nerve fibers control the muscle contraction and the vessel constriction or dilation. These regulations are controlling by several reflexes. Our current model for the cardiovascular system simulates the beat to beat or the R-R interval dynamic of the heart rate. Since we are interested in the long term effects of the cardiovascular system reflecting in OSA, this heart period approach suits our interest of study. Therefore, the intra-beat characteristic or the pulsatile dynamic will not be considered in the model. We have designed our model to have common output measurements as those used in actual experiments such as the heart rate and the blood pressure. The major reflexes and the control 23 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. systems implemented in this model are the baroreflex, chemoreflex, lung stretch receptors reflex, the heart rate and the peripheral resistance regulations and the circulation. 3.1.1 Reflexes Baroreceptors Baroreceptors are located in the carotid sinus where the common arteries divide into the internal and the external carotid arteries and also in the aortic arch. These stretch receptors are stimulated by the arterial pressure change. Impulses from baroreceptors travel to the medulla region and regulate the cardiac activities and vasomotor activities accordingly. Most studies have been focused on the carotid baroreceptors. The baroreceptors from the aortic arch have not been examined much. The baroreflex can be characterized as a negative-feedback system for maintaining a relatively constant arterial blood pressure from disturbances to the cardiovascular system. Most baroreflex experiments are performed on animals because it is difficult to do invasive procedures on human subjects. There are a few studies performed on humans using neck suction to stimulate the baroreceptors. The corresponding response in cuff pressure is then correlated with the heart rate to get some characteristics of the baroreflex. In animal experiments, the carotid sinus is surgically exposed to record the firing activity and catheters are placed in the carotid artery to obtain the carotid sinus pressure [83-94], 24 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Experimental data show a nonlinear relationship between the intra-sinus blood pressure and the sinus firing. A lower threshold region, a linear and an upper saturation region can be seen from the recording. This behavior can be modeled using a sigmoidal function, shown in equation 1. Experimental recordings during sleep also show a change in the arterial blood pressure and the heart rate responses from awake to sleep state. Upon sleep onset, the baroreflex sensitivity (BRS), as measured by the sequence method increases [97-100], One of the possible factors contributed to this change is the resetting of the baroreceptors which neutralizes the change in the blood pressure and maintains the operation in the linear region of the baroresponse. There is also the factor of increases in parasympathetic tone and the decreases in sympathetic activity [95,96], We incorporate these factors in equations derived by Ursino et al. [36], as shown in equation 1, 7, 9 and 12. where f cs is the firing rate from the baroreceptor, fcs,min and fcs,max are the lower and upper threshold of the sigmoidal function, P is the arterial pressure, Pn is the central pressure of the sigmoidal function and kc s is the parameter that controls the slope of the function. 0P and 9cs are constant parameter adjusting the baroreflex sensitivity during sleep. Responses from stimulating the sympathetic and the parasympathetic nerve fibers in the carotid sinus exhibit an opposing effect between each other. fc s ~ fc s, min + fc s, max ®exP (1) ( p - p _f) x i r n Op 1+exp ------------------ n u p 25 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Experiments show that with higher stimulation rate in the carotid sinus, there is a reduction in the sympathetic firing but an increase in the parasympathetic activity. This antagonistic behavior helps to regulate the heart rate [101-110]. The decrease in the sympathetic activity can be modeled using a negative monotonic static exponential function, as shown in equation 90 and 91. The monotonic increasing trend between the parasympathetic and the carotid sinus also exhibits an upper saturation. We can use a sigmoidal function to obtain this effect as seen in first part of equation 89. Chemoreceptors The central and the peripheral chemoreceptors are mainly involved with respiratory regulation but in the peripheral site there is also the influence to cardiac activities. The peripheral chemoreceptors are located in the aortic arch and in the carotid body at the branching of the common carotid arteries. These receptors are sensitive to arterial oxygen, carbon dioxide and blood PH changes. Stimulation of the carotid chemoreceptors site usually induces a decrease in the heart rate and an increase in the vasomotor tone. However these changes are often masked by the lung stretch reflex. The P0 2 response can be characterized by a sigmoidal function under constant Pco2 conditions. The Pcm static response with normoxia can be reproduced by a logarithmic curve. The nonlinear dynamic between P 0 2 and Pco2 are incorporated as the multiplicative interactions between the two. A time 26 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. adjustment is included to reflect the delay from the chemo-stimulations to the cardioresponses. Model equations for chemoreflex mechanism is from Ursino et al. [Ill] , as shown in equation 2-4. fchem o,m in + fchem o.m ax exP ^chem oiPaO i ■ > ? aC O i) P gq1 - P a o - , kchemo 1 + exp PaO 2 - Pa02 K ® In ( X p«co2 + f V PaC 02 (2) ^cherno ) K - kh Kh -\2\ Po q j - 80 30 K H -1 .6 dfchemo ■ if Pao2 > 80 if 40 < Pao2 = 5 8 ° if P a g 2 < 40 (3) '( fchem o + < Pchemo) (4) dt Tchemo where fchem o,m in and fchemo,max are the lower and upper saturation for the sigmoidal function, PaQ 2 is the center point of the sigmoidal function, kC h e m o controls the slope of the function, Pa£Q 2 is the normalizing value, Kh and f are constant values for the static response, xC he m o is the time constant for the chemoreflex. Luns Stretch Receptors Reflex Stretch receptors located on the lungs have shown to influence the cardiovascular regulation. Moderate lung inflation can accelerate the heart rate. Therefore the lung volume can be correlated for stretch receptors influence on cardiovascular changes, shown in equation 5 and 6. 27 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Piling ~ G[ung V f (5) (6) where Giu n g is a constant gain, xiu n g is the time constant for the response and Vx is the tidal volume. Equation 5 and 6 are from Ursino et al. [111], 3.1.2 SA Node The sinoatrial(SA) node is known as the natural pacemaker of the heart. Under the normal condition, both divisions of the autonomic nervous system influence the activity of the SA node. These influences include the regulation of the heartbeat, the systolic contractile force, and the velocity of the atrioventricular conduction. The sympathetic system accelerates the rhythmicity of the pacemaker while the parasympathetic system has the inhibitive response to it. Therefore, an increase in the heartbeat is governed both by a diminution of the parasympathetic activity and a rise in the sympathetic firing. The slowdown of the heart rate is usually caused by reversal actions from these mechanisms. The parasympathetic fibers originate from the medulla. From the medullary center, the vagus nerves pass through in close proximity to the carotid arteries and to the postganglionic cells in the heart. Most of these postganglionic cells are located in SA or AV node. The parasympathetic nerves mediate changes in heart rate by the chemical transmitter, acetylcholine. Activation of the parasympathetic nerves slows down the heartbeat. 28 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The sympathetic fibers originate from the upper segment of the thoracic and the lower segment of the cervical segments of the spinal cord. These fibers exit from the spinal column and enter the paravertebral chain of ganglia. The sympathetic nerves influence the heart by the chemical transmitter, noradrenalin. Stimulation of the sympathetic nerves will speed up the heart rate. The parasympathetic and the sympathetic fibers join together to form a complex network in the heart. When both the parasympathetic and the sympathetic nerves are stimulated at the same time, the parasympathetic branch usually have the dominant effect. Experiments have been performed on the effect of each pathway to the heart rate regulation using pharmacological blockade to inhibit any response from the other pathway. They have shown that by stimulating either autonomic branch, there is a delayed response to the heartbeat. The delay associated with vagal stimulations is very short compared to sympathetic stimulation. The time constant associated with parasympathetic control is also shorter than the sympathetic response. In the case of hypertension, the activation of the parasympathetic nerves dominates the mediation process that slows down the heart rate. In the sympathetic pathway, there is a higher response in the low firing frequency and then a decline and a more flatten output as the frequency increases. 29 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Sympathetic Response For sympathetic part, it is modeled with a pure latency, a logarithmic static function and a low-pass first-order filter, shown in equations 7 and 8. , , _ ,a b s^ b s ^n\-ftbs(t ~ D tb s)~ ftb s ,m in + 1 ] ‘ f ftb s - f b s ,m in sq\ i f ftb s < fb s,m m ( 7 ) d9 1 s S 9 ... = - i - [ - A Ts (/) + o T s (/)] (8 ) dt r bs where gts is the output from the log static function, D|,s is the time delay, fbS ,m in is the lower limit, T bS is the time constant and otbS is the scaling factor for tone change between awake and sleep states. Parasympathetic Response The parasympathetic part can be modeled by incorporation of a pure latency, a constant gain and a first order dynamics: (Jfp (t) = a p a ra G p a ra fp {* ~ D p a ra ) (9) ^ ^ f A 7> (0 + o7>(0] (10) d t r para where c t t p is the output from the static function, Dp ara is the time delay, Tp ara is the time constant and a p ara is the scaling factor for tone change between awake and sleep states. Equation 7-10 are from Ursino et al. [36]. 30 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Heart Period In the model we used, the heart period is the summation of the response from the sympathetic, the parasympathetic nerves in the SA node and a basal level that denotes the heart period in the situation of the cardiac denervation. Th p = ATs + ATv +T0 (11) 3.1.3 Total Peripheral Resistance Total peripheral resistance refers to the overall resistance of the systemic circulation. The peripheral resistance modulates vascular changes that alter the blood pressure by vasodilation or vasoconstriction. The change in the total peripheral resistance affected by the alpha-sympathetic nerve can be modeled in a way similarly to the beta-sympathetic response to the SA node. As the beta- sympathetic model, the alpha-sympathetic model consists of a pure latency, a log static function and a low-pass first-order filter shown in equations 12, 13, 14. ,a a s ^ a s + 'l tf f t a s - f t a s , min °7 > (0 = {n i f f u l J Jtas^Jtax,mm ^ W = J_[_A 7> (0 + o7>(/)] (13) dt ras a TPR = ATr +«TPR, 0 (14) where c x t p r is the total peripheral resistance, ATr is resistance change, ajpR,o is the nominal TPR change, Da s is the time delay and r a s is the time constant, fas,m in is the lower limit and a a s is the scaling factor for tone change between awake and sleep states. Equations 12-14 are from Ursino et al. [36], 31 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.1.4 Stroke Volume The heart operates like a pump that draws the blood from the veins and pushes it out into the arteries. Even though the heart consists of four chambers, in the model we consider the heart as one big Starling chamber with more focus on the left ventricular function since stroke volume is defined by the output from the left ventricle during each heartbeat. Each heart period consists of two phases: diastole and systole. The closing of the aortic valve marks the beginning of the ventricular diastolic phase. During the early diastolic phase, left ventricle relaxes and ventricular pressure decreases. Upon the opening of the atrioventricular (AV) mitral valve, blood flows in from the atria and ventricular volume increases along with the residual volume in the ventricle. With the increment of the volume, ventricular pressure starts to build up as it prepares for the ejection. Once the pressure reaches the threshold, the semilunar valve between the left venticle and the aorta opens up as the heart pumps the blood out to the arteries and goes through the systemic circulation. The stroke volume is maintained at a relatively constant volume within the normal blood pressure range but with adjustments from the influence of venous return, heart period and contractility [112,113]. The stroke volume equations are shown in equations 15-20 which are derived from TenVoorde’s paper [113]. SV(t) = 8(t)VR(t) + CT(t) (15) S(t) = 0.5+ 0.5 THP (16) 32 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A VR(t) = ------[-^VR(t) + GvR(PABP 0 ~ pABP(l ~ d VR)1 (17) tvr VR(t)=VR0 +&VR(t) (18) ACT(t) = -^— [-ACT(t) + G c T ( pABP 0 - pA B P ^ ~ DCT H 0 ^ ) r ct CT{t) = CT0 + ACT(t) (20) Where SV is the stoke volume, VR is the venous return, CT is the heart contractility and 8 is the left ventricular filling factor. The filling factor is affected partially by the heart period, T h p- The venous return, VR is determined by a gain, Gvr, a time constant, tvr, a time delay, D vr and a constant venous return, VRq. The heart contractility, CT shares the same characteristics as the venous return with a gain, G c t, a time constant, t c t, a time delay, D c t, and a constant contractility term, CT0. 3.1.5 Circulatory Mechanics The circulatory system functions as a means for transporting oxygenated blood to the rest of the body and to the brain. It also carries deoxygenated blood to the lungs. Thus the circulation encompasses both the cardiovascular and the respiratory systems. The arterial trees are tubes that carry the oxygen rich blood to the body while the veins transport the carbon dioxide filled blood to the heart and to the lungs for gas exchange. The capillaries distribute oxygen to all tissues in the body and the brain and take up by-products from them. This is done in the systemic circulation. In the pulmonary circulation, carbon dioxide is exchanged R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. with the oxygen in the lungs from the fresh air breathed in and the oxygenated blood is then carried to the heart. The whole process starts from the left ventricle where the clean blood pumps out to the aorta and distributes to the body through the arteries and the capillaries. The deoxygenated blood is carried back through the veins and into the right atrium. The carbon dioxide filled blood is then sent to the lungs from the right ventricle through the pulmonary arteries. After gas exchange, the oxygenated blood exits from the lungs back to the left atrium through the pulmonary veins. The process repeats again starting from the left ventricle. Circulatory flow is determined by the stroke volume and by vascular regulation. The arterial blood pressure interacts with the baroreceptors in the carotid sinus. Through the baroregulation, the left ventricular reaction and the vascular change are modulated. The regulations of heart contraction and the vessel resistance affect circulatory flow rate. The vessel resistance also helps to maintain a continuous blood flow in the body from the intermittent behavior of the heart. The simplest model for characterizing arterial hemodynamics is the Windkessel model. Some researchers combine several Windkessel models together to depict different segments in the arterial circulation. For our model, we will only use a two element Windkessel model to represent overall circulatory mechanics. The Windkessel model consists of a resistor representing the peripheral resistance in parallel with a capacitor characterizing the arterial compliance. Through the autonomic control in our model, changes to the peripheral resistance can be 34 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. modulated to the resistance in the Windkessel model. The arterial compliance remains constant at this stage. Therefore, the arterial blood pressure is obtained by the interactions between the cardiac output, the peripheral resistance and the arterial compliance in the Windkessel model, shown in equation 21. ’ = 7-------- ^ — 77; l(a TPR r TPR M O - Rabp 0 )1 (21) dt {apPR RTPR )Can where Pab p is the arterial pressure generated from the circulation, Rtpr and c c t pr are the peripheral resistance and change, Cart is the arterial compliance, and Q(t) is the cardiac output. Parameter values for equation 21 are taken from Cavalcanti et al. [28]. Arterial blood pressure is a useful quantitative measurement for the diagnosis in most patients. It provides an indication for the cardiovascular regulation. The change in the arterial blood pressure depends on both the cardiac output and the peripheral resistance. 35 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.2 Respiratory System In order for the cells to metabolize normally, a continuous oxygen uptake and waste removal is essential. The whole process of transporting nutrients from the oxidative breakdown to be utilized by cells and carrying out by-products from the metabolism, mainly the carbon dioxide is enabled by the ventilation. The rate of ventilation can be influenced by the alteration of the metabolic rate, the modification in the respiratory mechanics or the environmental changes from the outside. Ventilation can then be adjusted accordingly through feedback control. Gas exchange is also influenced by blood flow from the cardiovascular system. From a control system point of view, the respiratory system can be divided as a controller and a plant. The controller consists of two major components, the central neural control and different types of receptors. The respiratory neural center in the controller determines respiratory muscle activities. The receptors, mainly the central and the peripheral chemoreceptors affect the ventilatory drive from the neural center. The plant part composes of the lungs, the chest wall, other respiratory muscles and necessary blood components for gas exchange and transport. The respiratory mechanics in our model is closely similar to the model proposed by Younes et al. [151, 154, 155]. We have used the Younes model as a base and have made modifications to this base model [148-150, 152, 153]. A more detailed description of the base model will be explained in the following few sections. 36 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.2.1 Inspiratory Muscle Activity Muscle Reaction Time Since we are studying the active inspiratory response, all activities will be represented as the value above the FRC. When the inspiratory muscle neurons are activated, a short period of time is required for the muscle to react. It takes approximately 60 ms for the muscle to contract and generate the pressure. The output pressure shows an exponential increase with the inspiratory muscle activity. To accommodate the constant change of the muscle during breathing, the relationship between the output pressure and the neural activity will have to be modified to reflect the muscle reaction time. The output pressure can be generated by a convolution (represented by symbol *) between the neuromuscular drive profile and the response time constant. where N(t) is the inspiratory muscle neural profile and P(t) is the isometric pressure and RC is the response time constant. Pressure Loss The pressure generated from the inspiratory muscle decreases as the lung volume increases. This takes the form of a curvilinear relationship between the output pressure and the volume. The decline in the pressure is also affected by the level of the neural activity. It becomes steeper with an increase in the activity. So, (22) 37 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the pressure decay is both volume and neural related. It is modeled with relation to both the inspiratory activity and the lung volume. pv = m e - vt /028vc (23) where P(t) is the isometric pressure in time and V is the lung volume and VC is the vital capacity of the lungs. Pressure output and flow In isolated skeletal muscle, the interaction between the force and the velocity has been described as curvilinear. Hill has characterized the response in frog’s sartorius using a hyperbolic equation. Researchers have been using this equation to describe the response in a variety of skeletal muscles and none has been proven to behave differently. Human’s diaphragm has shown a similar behavior accordingly and can be describe using the Hill’s equation, equation 24. (P + a)(v + b) = (P0 + a)b (24) where P is the tension when shortening, v is the velocity of the shortening, P q is the isometric tension, a and b are both constants. To use this model for the respiratory muscle activities, it is necessary to obtain the values for constant a and b. From experimental data, it has shown that the parameter a is a constant fraction to the isometric tension, Pq. a = 0.25Po (25) On the other hand, parameter b appears to be more variable. From the experimental approximation, it shows that at a constant flow (1.6VC/s), the 38 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. pressure generated is exponentially related to the lung volume and proportionally with the isometric pressure, equation 23. P = Py (0.69-0A2le~Vtl025VC) (26) If we substitute the flow rate v and the relationship between the output pressure and the isometric pressure into Hill’s equation, we can obtain the approximation for the parameter b as shown in equation 27, 28 and 29. jj = v(p + a) n j \ (Pq - P ) _ 1,6F C [/f/(0.94 - 0.12le ~ ^ 7 0-25KC))] P y (0.31+ 0.12\e~Vt /Q25VC)) , L 6 V C (7 .7 7 -e ~ Vt l 0 -25VC )) (2.56 + e - Vt /025VCh Now that we have the values for parameter a and b, we can substitute them back into the Hill’s equation to predict the inspiratory pressure generated in relation with the airflow, shown below. P = bP° - al (30) v + b (31) (1)+*) Flow Equation Since our study is for normal breathing, we neglect expiratory muscle activity in our analysis. The airflow will be derived based on the inspiratory 39 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. muscle activity where the expiratory muscle pressure will be zero. The net dynamic muscular pressure will be the difference between the inspiratory muscle pressure and the expiratory muscle pressure. Pm u s =Pi -P e (32) substituting Pj into the equation 32 and we obtain the muscular pressure related to the lung volume and the airflow, shown blow: PVt {hV -0.25 Vf ) f M U S ‘ ~ ------------------— PE (33 ) (K, + < / ) From equation 33, we have the relationship between the pressure at a given volume and the isometric pressure. The net dynamic pressure can then be expressed in term of the isometric pressure as shown in equation 34. P (t)e -V /0 2 8 V C (bV -0.25Vt ) PMUS = -------------------------------------------- PE (34) (V, + b V ) The total driving pressure for each breath is not just restricted to the net dynamic muscular pressure. It can be a combined effort from the respiratory muscle and from an external pressure such as coming from a mechanical ventilator. In this case, the total driving pressure will be the summation from both pressures. PfJRY = PMUS + pAO (35) During inspiration, the total driving pressure has to overcome the elastic, flow-resistive and inertial forces from the different components of the respiratory 40 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. system. However, the inertial force is usually small during physiological conditions and can be neglected. PDRV = Vt E + vtR (36) where E is the passive elastance and R is the flow resistance. By substituting equations 35 and 36 into equation 37, we can compute the airflow. . P{t)e-Vt l0.2WC{bV ^ 25V ) V t E + Vt R = ^ ---------------- 1 -------------i±_pE+PA0 (37) (V t + b V ) By expanding equation 37 and we obtain the quadratic equation that allows us to solve for the airflow: ( IV ) 2 R + V ;( 0 .2 5 P ( t ) e ~ V 1 / 0 - 28 VC + b v R + V fE + PE - P A0 ) (38) kV - v t / 0.28 PC 1 / C p ^ p i n - b (P(t)e t - V t E - P E + P ao ) = 0 The airflow equation is from Younes et al. [155, 156]. In equation 38, the resistance R is used. But in the case of the obstructive sleep apnea, when the upper airway is blocked, this resistance will become infinite. This can complicate the computation used in model simulation. So, instead of working with resistance, we introduce the conductance. Therefore, when the airway is completely obstructed, the conductance assumes a value of zero. The conductance is the inverse of the resistance. G-1/R (39) 41 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. When we substitute equation 39 into equation 37, we obtain a new quadratic equation in terms of the conductance: (V,)2 + V((0.25GP(t)e~Vt /0 -28f/C + bV + GV,E + GPE - GPA 0 ) (4Q) - b V {GP (t)e~Vt 1Q'n V C - GVt E - GPE + GPAO ) = 0 To obtain the airflow value, we simply solve the quadratic equation. The result formula to calculate the airflow is shown below. V t = -0,5 * ( 0.25GP(t)e~~Vt /0 2 W C + bv + GV,E + GPg - GPa o ] + 0,5 * J(025G P (t)e~ V tl0 2 W C + bV + GVt E + GPE - GPA O )2 + 4bV (GP(t)e~Vt /a2 8 F C - GVt E - GPE + GPA O ) ^ ^ Volume The lung volume is approximated using the Euler-Cauchy method from the flow value, shown below. Vt+ i ^ V t + A tV t (42, 43) A t Vt + \ = V t + ~ { V t + \ + Vt ) each integration step is determined from the integration step in the simulation. Pleural Pressure The pleural cavity is bounded by the visceral and the parietal pleura. The pressure difference between the pressure generated within that space and the atmospheric pressure is know as the pleural pressure. The pleural pressure varies during each respiration. During inspiration, the pleural pressure decreases more as the lung and the chest cavity expand. The pressure will climb back to the resting 42 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. level during the expiratory phase. Since the pressure in the pleural cavity is lower than the atmospheric pressure outside, the pleural pressure is represented as a negative pressure. In the normal environment, the pleural pressure is the opposing force of the dynamic respiratory muscular pressure and the recoil and the viscoelastic pressure from the chest wall as shown in equation 44 [52]. Stress adaptation of the chest wall can be modeled by a Voigt Body which is a springboard and a dashpot in parallel [43, 45, 47, 54], This mechanical scheme can be converted into an equivalent RC circuit which is a resistor in series with a capacitor. The pressure generated can be expressed in terms of R, C and the flow, shown below. Pew = RCW v + - 1 „ v (45) CC W S Instead of using the compliance for our model, we use the elastance to describe the chest wall mechanics. Elastance is the inverse of the compliance. ECW = -~ -— (46) CCW Substituting that into equation 45 and we have equation 45 in term of the resistance and the elastance of the chest wall. In the regular environment the pleural pressure can be modeled by the addition of both the muscular pressure and the chest wall pressure, shown below. pPL - pCW + PMUS = 0 (44) pCW = RCW vt + ECW vt (47) 43 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. P y (b V - 0 . 2 5 Vt ) (48) PPL = ~ P C W v t + E C W v t + V During the mechanical ventilation, the dynamic muscular pressure disappears because the respiration has been taken over by the external assistance. If sufficient ventilation is provide by the ventilator, the natural chemoreflex mediated ventilatory response will disappear. However, airflow will still continue due to the artificial ventilation provided by the external device. Under such conditions, the pressures that contribute to pleural pressure are the alveolar pressure and the chest wall pressure. Respiratory muscle drive will be zero. During inspiration, air flows into the lungs and this creates a pressure drop across the airway. This pressure drop is modeled using Rohrer’s equation, show in equation 49 [52], Since we can calculate the pressure drop across the airway, the alveolar pressure is the difference betweent the external pressure and the pressure drop across the airway. Combining the alveolar pressure with the original pleural pressure equation will give us a modified equation that incorporates the effects on the pleural pressure of using the mechanical ventilator as shown in equation 51. During mechanical ventilation, the pleural pressure will be positive rather than be negative. APA w = & \,A W + k 2,A W v t vt (49) p A (M ech Vent) = p A O ~ a p A W (50) 44 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. During normal breathing, the thoracic cavity expands which decreases the pleural pressure which enables the lungs to expand. However, in the case of mechanical ventilation, lung expansion is produced by the externally applied pressure. This causes an increase in the pleural pressure. Therefore, the pleural pressure becomes more positive compared to the atmospheric pressure. pPL = pA(Mech Vent) - PMUS + PCW ( 5 1 ) If we expand all pressures contribute to the pleural pressure, we can get the following equation to calculate the pleural pressure in our model, shown in equation 52. pPL ~ pAO ~ & p AW k \,A W + p 2 ,AW \ Vt vt J Pyt (b Vt - 0 . 2 5 V,) (F; + by‘ ) < 52> - pE - R CW vt~ P CW vt Pleural Pressure and Arterial Blood Pressure The variation in pleural pressure affects the cardiovascular system. When pleural pressure decreases during the inspiration, the left ventricular stroke volume decreases and the arterial blood pressure changes due to the reduction. During the inspiratory phase, the arterial blood pressure decreases. It returns back to normal at the end of the expiration [114-126]. In our respiratory model, the pleural pressure is given in the units of cmHiO but the arterial blood pressure in the cardiovascular system is in units of mmHg. A unit conversion is used to match the transmission of changes in pleural pressure to corresponding changes in arterial blood pressure. 45 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 mniHg = \ 36mmH 2O (53) The negative pleural pressure affects the arterial blood pressure linearly in our model. When the pleural pressure becomes more negative, the arterial pressure decreases as well. ABP - A BP hem 0dynam ic + P pl (54) where A B P i ie m o d y n a m ic is the arterial blood pressure from the circulation in the cardiovascular system and Ppi is the pleual pressure from the respiratory system. 3.2.2 Gas Exchange and Gas Transport Gas exchange and gas transport involve two types of process, diffusion and convection. Diffusion covers the short distance exchange of the Cb and CO2 while convection is used for long distance transportation. Diffusion process does not require any energy from the cellular metabolism. It is just a passive transfer from a higher concentration to a lower concentration or from a higher pressure to a lower pressure. The whole exchange and transport process starts from the inspired gas entering the upper airway. The freshly inspired air transports from the upper airway to the lungs through the convection process. At the alveolar, the exchange between the alveolar air and the pulmonary capillaries occurs by diffusion. Then the O2 enriched blood is pumped from the left ventricle to be distributed to the tissues and the brain by the convection process because of the long distance 46 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. transport. The uptake of the O2 and the removal of the CO2 from the tissues and the brain are assumed to be affected by diffusion. The by-products from the metabolism is carried back to the lungs by the convection process. The CO2 filled air is then breathed out from the lungs to the outside through convection. The same cycle repeats at the next breathing cycle. Blood is the main medium that helps carrying the oxygen from the lungs to the tissues and the brain and takes the CO2 from the body back to the lungs. O2 is transported in the blood mainly by chemically combined with the hemoglobin. Only a small quantity is dissolved in the physical solution in the plasma. CO2 is carried both by the chemical combination (carbaminohemoglobin) and in the physical solution in the plasma. It is mainly in the form of bicarbonate, HCO^ . The gas exchange model follows the basic dynamics as the model proposed by Grodins et al. [127], The model we have employed is a modification of the Grodins model by Khoo et al. [142,143]. Dead Space When we inspire, the air enters through the airway into the lungs as it prepares for the gas exchange in the alveoli. As we breathe out, the reverse process occurs. The volume of the inspired or the expired gas that takes no part in the gas exchange is considered as the dead space. In an average man, the anatomical dead space is about 150 ml. Even though it seems that the dead space is useless in the gas exchange it plays an important role in the heat and water exchange. The 47 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. inspired air is humidified and adjusted to the body temperature as it runs through the dead space. Also, the dead space partially cleans out small particles, dust and bacteria before it reaches to the more delicate gas-exchange surfaces. In our model, the dead space consists of five equal-sized compartments. The dead space volume remains constant in each breathing cycle. According to Henry-Dalton Law, each gas in a mixture corresponds to a partial pressure proportional to the concentration of that gas. Therefore, most measures are represented as partial pressures. The O2 and CO2 partial pressure in the dead space can be represented using the law of mass, shown below. Since the inspired air has very small amount of CO2 concentration, the inspired Pco2 is zero. Equations for dead space as shown below are from Khoo et al. [142], C 0 2: During inspiration ( V > 0) vd(\)Pd(])co2 = V[P'C 0 2 ~ Pd0 )C O 2 ] (55) i'd(i) Pd{i)co2 ~ V{pd { i- \) C 0 2 Pd(i)C 0 2 ^ 2 < i <5 (56) During expiration ( V < 0) vd(i) Pd(i)co2 ~ vlpd(i+l)co2 P d(0cO2 ^ 1 < i < 4 (57) vd(5) pd(5)co2 ~ V\- P Aco2 P d(5)C02 ^ (58) 48 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Vd(i) is the dead space volume in z'th compartment. P d(i)C 02 is the CO2 partial pressure in the z'th dead space compartment. Pic-02 is the CO2 partial pressure from the inspired air. PAC02. is the CO2 partial pressure in the alveolar. 02: During inspiration ( V > 0) vd{\) Pd(\)o2 = nPlo2 - pd{\)o2 ] P d(i) Pd(i)()2 - V[Pd{i-\) qj ~ Pd(i)o7 1 2<i<5 During expiration ( V < 0 ) vd(i) Pd(i)o2 = VlPd(M )cb ” Pd(i)ch 1 1 < / < 4 Y d(5)p d(5)o2 = v lpA o 2 - Pd{S)o2 ] Vd(i) is the dead space volume in zth compartment. Pd(i)0 2 is the O2 partial pressure in the zth dead space compartment. P102 is the O2 partial pressure from the inspired air. P a o 2 is the O2 partial pressure in the alveolar. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Gas Exchange in the Lungs Gas exchange occurs in the alveoli in the lungs by diffusion. From Fick’s law of diffusion, to make an effective exchange a large surface area is needed. This makes the alveoli a good candidate. The total surface area of the alveoli has been ■ y estimated to be about 50-80 m“ and the pulmonary capillaries is separated from a thin sheet of tissue to the space inside the alveoli. When blood passes through the pulmonary capillary bed, fresh O2 is added to the blood from the alveolar air while C 0 2 is removed from the blood and introduced to the alveolar air. The whole diffusion path extends over about 1 pm. To model the gas exchange in the lungs, we use a single homogeneous alveolar compartment. In the body, C 0 2 can be stored in many places. It is mainly stored in the form of bicarbonate compound in the blood and the tissues. It also keeps its gaseous form in the lungs and in the body fluids. But, oxygen only exists in smaller quantity in the alveolar gas, in the physical solution and in combination with the hemoglobin and myoglobin. Therefore in this compartment, the effective C 0 2 storage space is larger than the gaseous 0 2 volume. For a healthy person, the partial pressure in the arterial blood is practically identical to those in the alveoli in the lung. Equations for C 0 2 and 0 2 partial pressures are from Khoo et al. [142], as shown below: Inspiration (V > 0): ^ c o j P A cc>2 = [8 6 3 Q ( C VCq 2 ~ Coco 2 ^+ t/ A(F‘ d(5)cc>2 PAco2^ (6j ) 50 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Fq 2 P ^°2 ~ [86j Q(Cvc>2 Cac > 2 ) + PA (pd(5)o2 PA o 2 ^ (64) Expiration (V < 0): V C 02 P Aco2 -[863g(CV C 0 2 ^aco 2 ^ (65) V 02 p Ao2 =[863 Q(CV01 - Cac>2 ^ (66) Paco2 and Pao2 are the alveoli CO2 and O2 partial pressure. VC0 2 and V 0 2 are lung storage volume for CO2 and O2. Cvco2 and Cvo2 are mixed venous blood CCb and O2 concentration. Caco2 and Ca o2 are arterial blood CO2 and O2 concentration. Q is the blood flow. Va is the alveolar ventilation. Body Tissue Compartment After gas exchange in the lungs, the arteries carry the oxygenated blood to the brain and the body tissues. CO2 and O2 transport across the tissue-capillary membrane by diffusion. Generally, the tissue and the capillary Pco2 reach equilibrium rapidly. The same applies to the oxygen partial pressure. The metabolism controls the O2 uptake and the CO2 removal in the exchange process. In the resting condition, both the CO2 metabolic production rate and the 0 2 consumption rate are constant. In sleep both O2 and CO2 metabolic change decrease which reflects in the equations below [128]. The CO2 and O2 51 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. concentration in the venous blood indicate the amount of the oxygen been used by the body and the CO2 produced by the metabolism, shown in equation 67 and 68. Equations for metabolism are from Khoo et al. [142]. ^CC> 2 CVCO2 = \ - a awake / sleepMRcC> 2 + aCC> 2 ~ VCO2 ^ (67) ^02 2 = \.~a awake/ sleepMR()2 + Q ^ a O 2 _< -'K02 ^ (68) Cyco2 and CV02 are mixed venous blood CO2 and O2 concentration. Caco2 and Ca o2 are arterial blood CO2 and O2 concentration. Vtco2 and Vto2 are the body tissue storage volumes for CO? and O2. MRco2 and MR0 2 are the metabolic production rate for CO2 and consumption rate for O2 . Q is the blood flow. o taw ak e/sieep state related scaling factor for metabolic change. Cardiovascular Mixing and Convection Effects Chemical control of the ventilation is mediated by the chemoreceptors. Thus, the time delay from the pulmonary capillaries to these receptors affects the chemoreflex ventilatory response. To model this compartment, we use the transfer function derived by Lange et al. [129], shown in equation 69. It describes the effect of the circulatory mixing and the delay between the arterial blood from the lungs to the chemoreceptors. 52 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. p, aco 2 P, (69) PA co2 PA o2 (1 + s T \ ) Q + s T2) From the Laplace transform equation, we can obtain the second order differential equation of this model. Experiments show that T2 « 2Ti. PaC02 and Pa o2 are the arterial CO2 and O2 partial pressure. P a c o 2 and P a o 2 are the alveolar CO? and O2 partial pressure. Ta is the time delay from the lung to chemoreceptors. Tp is the peripheral delay constant. Q is the blood flow. Tj and T2 are the circulatory mixing time constant. Oxygen and Carbon Dioxide dissociation In the red blood cell, most of the oxygen is transported by being bound to hemoglobin and assuming the form of oxyhemoglobin. The amount of the oxygen bounded with the hemoglobin depends on the oxygen partial pressure. Each hemoglobin can bind with up to four oxygen molecules. However, when pH decreases, there is a reduction in the affinity of the oxygen molecule for the P a C ° 2 = ( j X* t 2 ) ^P A C 02 (T i + T2) P a C 0 2 ~ Pa C 0 2 1 (70) Pao2 “ 7 7 fr^fzz\.pAoo (t-T a )-(T\ + T2) P ao2 ~Pao2 J {1 I I Z) (71) (72) 53 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. hemoglobin. This is known as Bohr effect and it facilitates the uptake of oxygen in the lungs and assists the exchange of oxygen into the tissue. According to Henry-Dalton law, the concentration of the dissolved gas in a physical solution is determined by the partial pressure of the gas and the solubility of the gas, a. l ^ ] ^ P gas (73) Therefore, the concentration of the O2 dissolved in physical solution is proportional to the 0 2 partial pressure. The total oxygen concentration in the blood is the sum of the 0 2 dissolved in the physical solution and the 0 2 combined with the hemoglobin. The percentage of the hemoglobin in the form of the oxyhemoglobin is used as the oxygen saturation. The arterial oxygen saturation at the chemoreceptor site takes into the effect of the cardiovascular convection. Carbon Dioxide is carried in the blood in three forms: dissolved in the physical solution, as bicarbonate and as a carbamino compound. The amount of the C 0 2 in the physical solution depends on the carbon dioxide partial pressure. C 02 is more soluble than 0 2. The formation of bicarbonate from C 0 2 is accelerated in the red blood cell. Another way that C 0 2 can be transported is by direct combination with the protein compound of the hemoglobin and forming carbhemoglobin. Similar to 0 2, the concentration of CO? is related to the partial pressure of the C 02. Therefore the total C 0 2 content in the blood consists of both the physically dissolved and the chemically bounded reaction. The chemically combined content includes the standard bicarbonate, the hemoglobin and 54 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. oxyhemoglobin and the carbhemoglobin that takes into the Haldane effect. The Haldane effect shows that the amount of the CO2 binding depends on the degree of the oxyhemoglobin. The pH of the blood is based on the Henderson-Hasselbalch equation, shown in equation 76. It depends on the CO2 partial pressure and the carbamate content. The CO2 concentration is also been affected by the oxygen saturation and pH balance. where pK is the logarithm of the equilibrium constant, [HA] is a weak acid and [A‘] is the conjugated base from the dissociation. Both oxygen and carbon dioxide concentrations are influenced by the partial pressure of both gases. The dissociation and oxygen saturation equations are from Spencer et al. [130], as shown below: CO2 dissociation (75) ^Aco2 (' + P2^Ao2 ) C °2 KlO + a 2PAo2 1 (76) O2 dissociation (77) 55 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. ^Ao2 f + P\ ^co2 ) ° 2 K \(\ + a \P A c 0 2 ) (78) Oxygen Saturation Xl00% (79) Cac02 and Ca02 are the arterial carbon dioxide and oxygen concentration. C ac02 C a02 are the maximum concentration. aj, a2, Ki, K .2, e sq , 0.2, Pi,and P2 are parameters to fit the data. Paco2, Paco2 and SA are alveoli carbon dioxide, oxygen partial pressures and oxygen saturation. Brain Compartment The central chemoreflex response is a function of the Pco2 in brain tissue. The cerebral vessels are very sensitive to the CO2 pressure. The increase in Pa co2 marks a visible vasodilation and a 7% CO2 inhalation doubles the cerebral flow. The opposite occurs when the CO2 tension decreases. One unique feature about the cerebral circulation is that it all lies within the same uncompressible rigid structure, the cranium. With an increase in the arterial flow, there has to be a comparable increase in the venous outflow. The reciprocal change happens to both the blood and the extravascular fluid. The dynamic change of Pco2 in the tissues around the region of the medullary chemoreceptors depends on the CO2 production rate and the CO2 flow 56 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. rate. With an elevation in Pco2, the cerebral blood flow progressively increases and alters the CO2 flow rate. Same as with body tissues, the metabolic change of CO2 decreases in sleep. We employ the dynamic equation derived by Read and Leigh for the CO2 partial pressure change in the brain chemoreceptors, shown in equation 80. The cerebral blood flow depends on Pbco2 and the equation is derived from the empirical results obtained during steady-state CO2 inhalation study as seen in equation 81 [131-133]. SbCC > 2 PbCC> 2 = ia a w ake / sleepM R bC C > 2 + Qb ^ C 0 2 ^ a C 0 2 ~ ^ b C O j ) — N (8b) Qb2 -[\ + 0.03(Pbco2 -40)]O/,0 Qb +0.03(MRbcO2 -h)Q b0/S C O 2 =0 (81) Sbco 2 = Brain tissue CO2 dissociation slope SC02 = Blood CO2 dissociation slope Pbco 2 = Brain CO2 partial pressure Paco 2 = Arterial O2 partial pressure MRbco2 = Metabolic CO2 production rate in the brain tissues Q b = Cerebral blood flow Q b 0 = Nominal cerebral blood flow The central chemoreflex response, Pbco2, and the peripheral chemo- responses, Paco2 and SA0 2 contribute to the ventilatory response. It governs the neuromuscular drive for the inspiratory muscles. 57 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.3 Neural Control In our implementation, we have created a neural control compartment to govern and to adjust respiratory and cardiovascular activities. In this compartment, the respiratory rhythm combined with the ventilatory drive determines the neuromuscular drive. The ventilatory drive is established by both the central and peripheral chemoreflex components. Autonomic responses from the baroreceptors, chemoreceptors, central respiratory and lung stretch receptors are integrated together here which then regulate the heart rate and the peripheral vasculatures. 3.3.1 Auto rhy thmicity Normal spontaneous breathing occurs as a result of respiratory autorhythmicity. The central respiratory mechanism that generates this rhythm is located within the medulla. Studies show that the respiratory periodicity still exists even in the absence of connections from both central and peripheral reflexes. The respiratory center consists of two neuronal groups, one inspiratory and one expiratory in function. These cells distribute in the medullary and part of the pontine reticular fomation. The inspiratory center is located at the caudal third and dorsolateral portion of the bulbopontine region. Stimulations to the inspiratory neurons can produce maximal inspiratory effort. This effort can be sustained as long as the stimulation exists. The expiratory center is concentrated in the middle third of the 58 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. bulbopontine region. Stimulation of this region do not necessarily produce a sustained exhalation effort but it can initiate expiration and inhibit inspiration.[134] In the current model, respiratory autorhythmicity is assumed to be an “on and o ff’ switching action. During inspiratory phase, inspiratory neurons are being excited and inhalation occurs. The inspiratory phase is terminated by the off switch mechanism. During the expiratory phase, the off switch mechanism inhibits firings from the inspiratory neurons and delays the occurrence of the next inhalation. In eupnea, inspiration is a neurally mediated response while expiration is just a passive action. The respiratory periodicity can be influenced by afferent nerve fibers from the lungs or the central and the peripheral chemoreceptors. To create the respiratory periodicity, we use a simple square wave function to generate the on and off respiratory pattern which can be seen in equation 82. Respiratory Autorhythmicity = SquareFunciTl, TT) (82) where TI is the time for the inspiratory phase and TT is the time for each breathing period. 3.3.2 Ventilatory Drive The change in the respiratory activity is mainly modulated by the chemoreflex. The chemoreceptors influence the ventilation based on the degree of the alternation in the CCb partial pressure, the Cb partial pressure and the pH balance in the arterial blood. The chemoreceptors exist both in the central and in the peripheral region. The central chemoreceptors are located in the medulla. The 59 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. peripheral chemoreceptors are found in the paraganglia of the carotid sinus and the aortic arch. An increase in CO2 partial pressure causes an increase in the ventilation. Over a wide range, the increase between the CO2 partial pressure and the ventilation is virtually linear. But as the CO2 partial pressure reaches a certain threshold, it presents a plateau region and as the pressure increases more, a decrease in ventilation occurs because of the inhibition in the respiratory center from a higher concentration of CO2. The pH effect on the ventilation is more or less coupled with the effect from the CO2 partial pressure. When the pH value in the arterial blood drops below the normal 7.4 value, an increase in the respiration takes place. Studies have shown that about 60% of the CO2 ventilatory response is contributed by CO2 directly and approximately 40% is due to the alteration of H+. When the O2 partial pressure falls, the ventilation increases. Arterial hypoxia usually happens either in higher altitudes or causes by some pulmonary malfunctions. The relationship between O2 partial pressure and the ventilation is hyperbolic rather than the more linear characteristic between the CO2 partial pressure and the ventilation. Under normal conditions, at high O2 partial pressure, the effect on the ventilation is small. Only when in the state of considerable hypoxia can a visible influence be detected. However, in the case of the severe pulmonary malfunction, the change in breathing is contributed by arterial hypoxia rather than by hypercapnia. 60 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Central chemoreflex is influenced primarily by CO2 partial pressure and pH balance. Peripheral chemical control is influenced by the O2 and the CO2 partial pressure and the pH value. CO?, and O2 interact multiplicatively in the carotid and aortic bodies. The ventilatory response to hypoxia seems to be enhanced by the change in CO2 partial pressure and at the same time the effect of hypercapnia on peripheral chemoresponse is accentuated by hypoxia. To characterize the ventilatory response from the chemical control, both central and peripheral influences have to be included. The central chemoreflex drive depends mainly on the CO2 partial pressure from the brain. The peripheral chemical influence on the ventilation is the interaction between the arterial CO2 partial pressure and the oxygen saturation. So we include this factor in the peripheral gain [135-141], The ventilatory drive from the chemoreflex will be the combination of the central and the peripheral drive as shown in equation 83, 84 and 85. These equations are from Khoo et al. [142]. Dvent ~ Dc + D p (8j ) J a c lP bC02 -lc] Dei 0 [ 0 e lse ' n fa R E M G P[(pa C 0 2 - / P ) ( 102-4- S A 0 2 )] D P > 0 D' ’ to ,85) where Dv en t is the total ventilatory drive, Dc and Dp are the central and the peripheral ventilatory drive. Gc and Gp are the central and the peripheral gains. Ic and Ip are threshold values for the central and the peripheral apnea [143,144]. a re m is the scaling factor during REM stage. 61 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Besides the influence from the chemoreflex, the ventilatory drive is also affected by the state-related drive. This state drive is contributed by the wakefulness control. In sleep this drive decreases the ventilatory response. Therefore, the total ventilatory drive is the combination of both the chemical drive and the state drive, shown blow: Dtotal = a awake / sleep invent + D state ) (86) a awake / sleep ~ ' - state (87) 3.3.3 Neuromuscular Drive The inspiratory neuromuscular drive has been a difficult task for researchers to measure because this drive is an integration of activities from various muscles. Central neural drive is distributed to various components such as the diaphragm, the abdominal muscles and the upper airway muscles. Also, it is more complicated to gather data in conscious animals and humans because of the interference from the expiratory muscle and other accessory muscles. But, in anesthetized animals, the overall neural drive can be characterized by the integrated phrenic efferent discharge and the diaphragmatic electrical activity. This represents some neural activities of the respiratory muscle. A more popular method introduced to estimate the neuromuscular drive is the airway occlusion pressure. The airway occlusion pressure has been a useful index to capture the total neuromuscular drive. In anesthetized animals and humans, the neural output from the occlusion or regular environment generally are the same. While measuring at 62 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the relaxed FRC (Functional Residual Capacity), the net elastic recoil of the respiratory system is zero. Therefore, the measurement will be the net pressure developed by the inspiratory muscle. The shape of the occlusion pressure provides some characterization of the neuromuscular drive that controls the respiratory muscle activity [145-147], The respiratory muscles are controlled by the respiratory center. The neural activity is affected by the ventilatory drive contributed by the chemoreflex and the state drive. To generate a similar shape as the occlusion pressure in our model, we integrate the ventilatory response in the inspiratory phase. Since the expiration is a passive action during normal breathing, the neural drive remains inactive for that period. The muscular drive for each breathing period is shown in equation 88. N (t) = ° total dt 0 < t < Tj (88 ) [0 Ti < t < T f where Dto ta i is the total ventilatory drive, TI is the inspiration period and T j is the breathing period. 3.3.4 Autonomic Efferent Activity The autonomic nervous system regulates the heart rate, cardiac contractility and peripheral resistance. Both sympathetic and the parasympathetic pathways control the heart rate. The sympathetic nerves increase heart rate while the parasympathetic nerves slow down the heart beat. However, changes in cardiac contractility and peripheral resistance are only mediated by the sympathetic branch of the autonomic nervous system. Several reflexes can affect activities in these 63 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. pathways to adjust heart rate changes. In our model, we have included four effects, the respiratory sinus arrhythmia, the baroreflex, the chemoreflex and the pulmonary stretch reflex. The respiratory sinus arrhythmia (RSA) originates from both central and peripheral mechanisms. RSA has been characterized as the variation in the heart rate modulated by the respiratory activity. The heart rate accelerates with the inspiration and falls at the expiration. During the inspiration, there is an increase in the sympathetic and a decrease in the parasympathetic activity that cause the speedup in the heart rate. The opposite effect takes place during the expiration as the heartbeat slows down. This antagonistic effect between sympathetic and parasympathetic controls has been used as an index for assessing autonomic regulation [56, 91, 101, 108, 167]. The baroreflex effects on the autonomic pathways have been mentioned in the previous section. Changes in the arterial blood pressure will stimulate the baroreceptors which will alter the heart rate. As we inspire, the intrapleural pressure becomes more negative which increases the venous return and thus decreases the arterial blood pressure. This respiratory modulation on the arterial blood pressure can change the heart rate through the baroreflex. The chemical effects on the cardiovascular system can be seen in situations such as hypoxia, hypercapnia and sleep, etc. In hypoxia and in hypercapnia, tachycardia usually occurs but when carotid body is stimulated alone, then 64 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. bradycardia shows up. Therefore, the chemoreflex slows down the heart rate but increase the peripheral resistance to induce higher blood pressure [156-166], The pulmonary stretch reflex can be seen more visibly during the mechanical ventilation. If an appropriate respiratory frequency and sufficiently high tidal volume are applied externally, after a period of the time the intrinsic ventilatory drive is eliminated and the external ventilation takes over. Studies show that respiratory variation in the heart rate still exists even without central respiratory drive. This is contributed by the pulmonary stretch receptor on the lungs [168, 169], The stretch reflex also modulates variations in sympathetic activity. Experimental data show that the muscle sympathetic activity displays the same trend in the situation of the normal breath and in mechanical ventilation. The maximal activity occurs at the end of the expiration and at the end of the inspiration, it has the lowest activity. Because the muscle sympathetic activity still exists in the absence of the central neural control, respiratory modulation of the peripheral sympathetic response is not mainly controlled by the central nervous system but rather by the pulmonary stretch receptors [170-174]. To incorporate these modulations, we integrate those signals from all these reflexes to obtain the total effects on the parasympathetic and the sympathetic pathway for the heart regulation and the peripheral resistance change, show in equation 89-91. 65 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (89) + Gchemofchemo + G lung flung ^^RSA^t ftbs ~fs,<x> +Us,0 fs, co)® (90) exp[A ® (~ Gbaro, bs fcs + ^ chemo, bs fchemo + &lung, bs flung + & RSA, bs^ t)] ftas ~ ~ fs,< x > + Us,0 fs,o o ) • (91) exp[*s * (“ Gbaro,asfcs + ^chemo, as fchemo + &lung,as flung + ^RSA,as^t) ] where fbaro,o and fb aro .o , are the lower and upper threshold for the sigmoidal function, fcs.o is the central point in the function and kp controls the slope, fS jo and fS i 0 D are the lower and the upper limits of the exponential decay, fcs, fC h em o, flung, Nt are the neural firings from carotid sinus, from peripheral chemoreceptors and from lung stretch receptors and from respiratory rhythm, GC h em o ,p, Gk m g ;P , GR S a,p, Gb aro ,b S , G ohem o,bs, GiU n g ,b s, GR S A .b s, Gb aro ,as, Gc hem o ,as, Giung ,a s and GR S A ,a s are constant gains for baroreflex, chemoreflex, lung stretch receptors reflex and RSA modulation to parasympathetic, ^-sympathetic and a-sympathetic nerves, ftp, ftb s and fta s are total neural responses for parasympathetic, (3-sympathetic and a-sympathetic activities. 66 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.4 Cardiorespiratory Interaction Summary More detailed cardiorespiratory interactions have been described in previous sections. We briefly summarize those interactions implemented in our model. In our model, we have included both respiratory effects on the cardiovascular system and the cardiovascular influence in the respiratory system. Even though both systems interact with each other to function, the respiratory system exerts more influence on the cardiovascular system than vice versa. The respiratory system affects the cardiovascular system through both central and peripheral mechanisms. Respiratory to Cardiovascular effect: Central respiratory neurons influence the heart rate variation known as the respiratory sinus arrhythmia. They modulate both the parasympathetic and the beta-sympathetic nerves. The effect on the alpha-sympathetic nerves is very small. Chemoreflex influences the ventilatory response in breathing and it also affects the heart rate through the autonomic control. Stimulation to the carotid body shows a show down in the heart rate and an increase in blood pressure. Pulmonary stretch reflex from the lungs acts as a peripheral reflex to the heart rate change. This reflex modulates the parasympathetic nerves, the alpha and the beta- sympathetic nerves. This reflex can be seen more visibly when the central respiratory neurons cease to fire and the external assisted ventilation takes place. 67 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Pleural pressure affects the venous return which in turn influences the arterial blood pressure. During inspiration, the pleural pressure becomes more negative and decreases the arterial blood pressure. The pleural pressure returns back to the original pressure as the expiration ends. During each breath, the arterial blood pressure varies on each heartbeat. C ardiovascular to Respiratory effect: The Baroreflex regulates blood pressure. Blood pressure affects venous return which in turn influences stroke volume and cardiac output. Cardiac output modulates the blood flow in the body. The gas exchange and transport are influenced by the flow rate. How rapidly the oxygenated blood can be delivered to the body tissues and the brain or how quickly the by-product wastes can be removed from the body depend primarily on the blood flow. In this way cardiac output exerts significant effects on gas exchange. 68 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.5 Sleep Mechanism and Assisted Ventilation 3.5.1 Mechanical Ventilation Patients on ventilatory assistance usually receive control mode ventilation (CMV). In this controlled environment, the positive-pressure breath will automatically start by some timing mechanism. The pressurized breath will then be administrated to the patient at a preset time interval. The timing can be adjusted on the machine. To simulate the positive pressure waveform, we use a approach similar to what we have employed to model spontaneous respiration. The unit square function which represents the on and off pattern of the respiratory authorhythmicity is integrated. As a result, the output waveform from this takes on the form of a triangular ramp. We want to make the inclined waveform a curved line instead of a straight line because it is closer to the real positive pressure waveform. To achieve this, we take the square root of the signal. The output signal can then be scaled to the pressure value we want. The equation to generate the external pressure is shown in equation 92. where K is the scaling value and the integration is between the inspiration period and zero for the expiration time. P M ech Vent 0 < t < T i (92) 6 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. For CPAP simulation, a continuous positive pressure value can be added to the external pressure variable, P a o in the respiratory muscle equation. p AO = a C PA PpCPAP (93) where o c c p a p is a scaling factor and P c p a p is the CPAP pressure. 3.5.2 Sleep Mechanism and Upper Airway Mechanism In awake state, ventilation is controlled by three mechanisms: chemoreflex control, behavioral control and sleep-wake state. The chemical effects are determined by the central and the peripheral chemoreflexes. A fall in P0 2 or a rise in Pco2 will alter the ventilatory response to correct the chemical imbalance in the blood. The relationship between P<x> 2 and the ventilation is close to linear. The ventilatory dependence on P0 2 takes on a hyperbolic shape [175, 176]. Behavioral control is more difficult to measure or to document. Some of these behaviors are swallowing, crying, phonation, etc. These actions can override chemical control on respiration for short periods of time regardless o f the metabolic demands of the body. However our knowledge of this particular drive is fragmented because it is difficult to perform experiments that can precisely control it. Respiratory changes influenced by this drive can be found in patients with brain defects. 70 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The last influence on the respiratory control is the “wakefulness stimulus”. Even though the exact location or the particular mechanism that contributes to this wakefulness stimulus is still debatable, it has been shown that with the removal of almost all metabolic stimulation, ventilation still exists due to this wakefulness stimulus. Studies show that human patients with defective chemoreceptors fail to breath only during sleep. It has been shown that one possible location of the source of this stimulus is the reticular formation. Another possibility for this wakefulness stimulus is it arises from the integration of tonic input from non-respiratory sensors such as sight or hearing. In general, during sleep the wakefulness stimulus I inhibited. Ventilation falls in the transition from awake to sleep state. During non-REM sleep, both the wakefulness stimulus and the behavior control disappear. In non-REM sleep stage, ventilation is controlled primarily by the metabolic demand that is determined by the chemoreflex drive from the central and the peripheral chemoreceptors. With the absence of the wakefulness stimulus, ventilation decreases in non-REM sleep. Chemorefelx drive is also reduced during the non-REM sleep. Besides the change in the response slope, the response position also has been shifted at this sleep stage. This likely indicates a higher tolerance for higher Pco2 without much stimulation in the respiratory muscle. Another factor in the ventilatory reduction is the increase in upper airway resistance due to a reduction in upper airway muscle tone in sleep. This alters the normal airflow pattern and produces a small degree of hypoventilation. 71 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Respiratory change in REM sleep is harder to measure because this stage is shorter and harder to achieve when monitoring instruments are attached to the body. However, during this stage, there still exists a reduction in the ventilation. At this stage, chemoreflex control exerts only a minor effect on ventilation. What really controls the respiratory change in REM sleep is not very clear. It has been postulated that behavioral control may contribute to the irregular breathing pattern in REM sleep. Associated with REM sleep are reductions in chemoreflex sensitivity and an increase in upper airway resistance. Studies have shown that in REM sleep, the ventilation has some correlation with the eye movement. It shows a negative association between the frequency of the eye movement and the inhibition in ventilation. The upper respiratory tract includes the external nose, the nasal passage, the pharynx, the mouth and the larynx. While the lower respiratory tract only conducts air from the upper respiratory tract to the alveoli, the upper airway serves more than just an air passage. It modifies the inspired air before it enters the trachea. It functions as a defense barrier against noxious or harmful elements from the inspired air. The upper airway helps us perform some essential activities such as swallowing, speaking, coughing and respiration. The external nose does not appear to contribute any important usage in ventilation except directing the air in and out and for esthetic importance. From the nostril, the cross section of the nasal passage becomes narrower. This increase the resistance for the airflow but due to it structure and geometry, it 72 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. increases its surface area by two-fold. The nasal passage makes an almost sharp right downward turn in the nasopharyngeal region. At this region, the two separate nasal passages combine into one as it travels down. The upper airway ends at the larynx. The shape of the airway between these two regions is determined by the muscle controlled soft palate, the tongue, the pharynx and the larynx. During quiet breathing, the air can get directly to the larynx with only one interruption at the curve of the epiglottis. During inspiration, the tone of the respiratory muscles in the pharynx and the larynx region increases. Inspiration creates a negative transmural pressure in the airway region which acts to collapse the airway. With the increase in muscle tone, patency of the airway against the negative pressure is maintained. During expiration, upper airway muscle tone decreases. This can act as a brake on expiratory airflow. In this way, the muscles of the upper airway are similar to other respiratory muscles. As with the other respiratory muscles, the upper airway muscles are also affected by chemical changes. The wakefulness stimulus diminishes in the transition from wake to sleep state. At the same time, the ventilatory response is reduced during sleep due to loss of voluntary control. These adjustments cause a decrease in the spontaneous activity of the respiratory muscles including the airway muscles. In normal awake state the upper airway muscles are toned to fight the subatmospheric pressure. With the decrease of the muscle tone in sleep, the response of the upper airway muscles to occlusion fades as sleep continues throughout the night. This increases 73 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the collapsibility of the upper airway. With the blockage of the upper airway, obstructive sleep apnea takes place [177]. To incorporate the sleep mechanism in our implementation, we use the sleep model from Borbely et al. [178]. In their design, the total sleep propensity is determined by the combination of two processes: process C and process S. Process C is a sleep independent circadian driven event. Process S is a sleep dependent index governed by the slow wave activity (SWA). For process C, two thresholds are presented to modulate the sleep indication. The high threshold marks the beginning of sleep onset while the lower threshold triggers the termination of sleep. Process S is therefore oscillating between these two thresholds. By varying the interval between those two thresholds, the time length of sleep can be manipulated. Because of this flexibility, not only can the model simulate regular sleep pattern, it can also simulate irregular cases such as sleep deprivation. The Circadian process is described using a skewed sine function which provides the normal 16 hours of awake state and 8 hours of sleep period. The time course of process S is chosen based on experimental data on slow wave recordings. It has been shown that throughout the whole night of sleep, there is an overall decreasing trend in SWA in NREM stages and there is no SWA presented in REM stage. Therefore during sleep, process S is approximated by an exponential decay. The time course for process S activity during awake is described from the interpolation of experimental data points which show an exponential increase with saturation. The SWA in the 74 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. model is affected by the REM stage with a falling and a rising factor [178-180]. Equations for the sleep mechanism are shown in equations 94-98. where A is the amplitude for the circadian process and 0 determines the periodicity of the cycle and X is the offset term. SWA is the slow wave activity and a (c and a rc are the falling and rising factor for SWA during REM stage. S is the signal for process S and REMT is a pulse function trigger between NREM and REM stage. In our model, instead of describing the upper airway resistance, we will be using the upper airway conductance. It is simpler to compute with zero conductance than representing the infinitely large resistance such as in the case of obstructive sleep apnea. We have also convert the respiratory resistance to respiratory conductance in the flow generation equation. The upper airway conductance is represented as the normalized value with one as fully open and zero as completely obstructed. While in the awake state, the conductance remains to be Process q = Ac 0.97(sin 6h)+0.22(sin 20f) + O.O7(sin 30*)1 + 0.03(sin A6t)+ 0.0 l(sin 561) (94) Awake (S(t) ^ Processc low) S(t) = 1 - [l - S(t - u ] e (~-°-0 5 5 13600) (95) Sleep (S(t) < Processcjiigh) dSWA dt = arcS W A » ( l - - a fc SWA » REMT(t) + SWA • n(t) (96) (97) REMT {t) REM NREM (98) 7 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. one, but at the sleep onset, it starts to decrease as the awakefulness stimulus diminishes. Since expiration is a passive action, the conductance will not be affected by the state change. The simple upper airway mechanism in our model is controlled by the state drive and the upper airway sensitivity. The upper airway determines the degree of occlusion during sleep. Therefore the case of partial occlusion and total obstruction can both be achieved. The upper airway conductance is represented as a normalized ratio and is multiplied with the respiratory conductance value, shown in equation 99. where Dstate is the state drive, Sua is the upper airway sensitivity, a m ech is the scaling factor for the external pressure, Pao. During total upper airway obstruction, carbon dioxide starts to build up as the oxygen becomes more desaturated. With the withdraw of the awakefulness stimulus, the total ventilatory drive does not increase as fast as during awake state. When the ventilatory drive reaches a threshold, arousal takes place and the upper airway opens allowing airflow to resume. Experiments have shown that during REM stage, the threshold for arousal is lower than in NREM stage [181-184], In our model, we have set different thresholds between NREM and REM stage. During the arousal period, the wakefulness stimulus reappears and as the ventilatory drive drops back below the theshold, the wakefulness stimulus | T*state i^ua ( ^ state > S sfV A ) + a mechEa o ) t > T i Dtotal > darousal ( REM > N R E M ) Eaw / sleep = * 0 <t<T[ (99) 76 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. disappears once again as sleep continues. The triggering action can be seen in equation 100. SW A D state ~ ‘ sleep onset during sleep ( 100) D total > 6 arousal (REM, NREM) where a is a scaling factor, SWA is the slow wave activity, S is the process S signal and S is the normalized process S. The cyclic alternation between wakefulness and sleep will continue as long as the total ventilatory drive reaches over the threshold. To prevent the occlusion of the upper airway, mechanical ventilator or CPAP can be used to keep the upper airway open during sleep. For our model, the external assistance affects the upper airway sensitivity and maintains the normal upper airway conductance which can be seen in equation 99. Again, external pressure does not interfere with the expiration. 77 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.6 Model Graphs: (a ) (b ) (c ) 35 } - P r essu re (rmmHg) H i" .5 6 .5 5 .5 4 .5 3 Carotid S in u s firing 0 Total Neural firing F igure 3.1: (a) Carotid baroreceptors characteristic, (b) Parasympathetic activity modulated by barorecptors. (c) Sympathetic activity modulated by the com bined inputs from baroreflex, chem oreflex, central R SA and lung stretch receptors. 78 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (a) 1 0.9 0.6 a > c : o 0,6 ^ § 5 1 o 0.5 0.4 0.3 0.7 0.8 0.9 1 0.4 0.5 0.6 0.1 0.2 0.3 0 (b ) 2 O £ o fr e q u e n c y (Hz) (c) c 0.7 fr e q e n c y (Hz) F igure 3.2: A utonom ic control response. The parasympathetic nerves response faster than the sympathetic nerves, (a) parasympathetic frequency response, (b) beta-sym pathetic frequency response, (c) alpha-sympathetic frequency response. 79 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Arterial Pressure I Baroregulation 1 Alpha-sympathetic | ^ V asoconstriction Vascular Resistance ( D O ) C -C O X < D £ 3 E C O ' w < D 0 ) D ( / ) « C l 3 7 3 X O P - £ CD > S < C O < « 1 . c Q . < _ pressure decrease ▼ i I I ! i i I i 0 2 0 4 0 6 0 S O 1 0 0 1 2 0 1 4 0 1 6 0 tim e (sec) ; ( i i i 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 tim e (sec) A ^A m A A A A A A A A A A A A A A A A l I ! ! ^ M a a a a a a a a m a a a a a a m - . . . . ; l i ! 20 4 0 6 0 8 0 1 0 0 tim e (sec) 120 1 4 0 1 6 0 F igure 3.3: Peripheral resistance change. Top page show s the general m echanism for hypotension that invokes vasoconstriction. Bottom graphs show the peripheral resistance change with the application o f a negative pressure. Top panel is the pressure drop applied. The m iddle panel is the Arterial B lood Pressure and the bottom panel is the Alpha-Sym pathetic activities. 80 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. Q . 03 < 9 2 9 0 1 10 15 20 25 30 35 40 45 time (sec) 5 0 ■ 5 0 10 15 25 45 5 20 30 35 40 o O J X E o H H time (sec) 96 94 92 90 10 15 25 0 5 20 30 35 40 45 O ) X CL CQ < time (sec) F igure 3.4: Interaction betw een A B P and pleural pressure. Pleural pressure has a negative effect on A BP. Top panel show s the A B P before any pleural influence. The second panel show s the pleural pressure. The third graph overlaps the effect o f pleural pressure on A BP. The dash line is the ABP before pleural influence and the solid line is the after result. The bottom panel show s the final ABP signal to be sent into the baroregulation. 81 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2 e 0 $ f f i 7 5 h _i ‘ 'w ' D U I C ^ — 0 (1 ) (1 ) D > » , r e J C 0 C L C Q < ^ .£ I < D E ®E * - s -y r e r U 0 ..4 0.2 0 0 1 .5 2 2 .5 3 3 .5 0 .5 time (sec) 4 2 0 0 2 .5 3 3 .5 0 .5 1 .5 2 time (sec) 2 0 ■ 2 0 0 .5 1 .5 2 2 .5 3 3 .5 time (sec) F igure 3.5: Respiratory modulation on the heart rate and A BP from spontaneous breathing. RSA causes changes in heart rate through the autonom ic control. A B P varies from the pleural effect and from baroregulation. (a) tidal volum e in liters, (b) changes in heart rate, (c) change in ABP. 82 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (a) V enous Return (b ) © 0 .! o O .f 0.5 0.4 0.3 0 .5 0.2 0.35 0.45 0.05 0.15 0 .2 5 ( frequency (Hz) 0.3 0.4 H eart Contractility £ 0 .9 © 0.6 < S 0 .' c 0 - 4 0.3 0 .3 5 0.45 0.5 0.05 0 .1 5 0.2 0.3 0.4 0.25 ( frequency (Hz) (c) pressure increase > p o r d > £. OE 80 70 60 50 0 10 20 30 40 60 70 80 90 50 50 tim e (se c ) F igure 3.6: Stroke Volume. Venous Return and Heart Contractility are affected by Arterial Blood Pressure changes, (a) Venous Return dynam ics (b) Heart Contractility dynam ics (c) exam ple o f increasing ABP affecting Stroke Volum e by decreasing Venous Return. 83 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (a) 0.46 0.44 1- 0.42 D 0.4 0.38 0.8 - 0.6 g 0.4 0.2 0 ( (b ) 0.35 Q 0.3 0.25 tim e (sec) 0.6 - 0.4 0.2 0 F igure 3.7: Neurom uscular D rive, N t for each breath is contributed from the V entilatory Drive, D T. (a) D T and Nt increase due to hypercapnia. (b) D T and N t decrease due to w akefulness stimulus withdraw in sleep. 84 _ 1 2 0 1 0 0 tim e (sec) 1 2 0 1 0 0 1 2 0 1 0 0 80 60 1 2 0 1 0 0 tim e (sec) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. F igu re 3.8: Carbon D ioxide and O xygen D issociation. Carbon D ioxide is represented as in concentration, w hile O xygen is displayed based on the saturation level. Both dissociations are affected by both C 0 2 and 0 2 partial pressures, (a) dissociation curve for [C 0 2]. C 0 2 concentration is in m l o f C 0 2 per ml o f w hole blood, (b) saturation curve for O xygen. Saturation is in percentage. 85 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. C ircadian upper threshold JZ A - i > > -C a: c 06 T 3 T O O O I 0 ) S 0.6 f o , Q-0 2 0 ) u- * < D (0 0 Sleep Propensity C ircadian low er threshold 5 10 15 20 25 30 35 40 45 0 1 - £ °-5 tim e (hour) 10 15 20 25 30 tim e (hour) tim e (hour) 0.5 0 5 10 15 20 25 30 35 40 45 35 40 45 F igu re 3.9: Sleep M echanism, (a) Circadian Rhythm and Sleep Propensity, (b) S low W ave A ctivity (SW A ), (c) Rapid Eye M ovem ent (R EM ) stage in sleep. 86 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4. Simulink Implementation 4.1 Com partments Summary Cardiorespiratory Model Figure 4.1 -Cardiorespiratory M odel In our implementation, the cardiovascular system is represented as one subsystem. The respiratory system is implemented as two subsystems: the respiratory mechanics subsystem and the gas exchange and transport subsystem. The respiratory mechanics part generates the breathing movement from the respiratory muscle reactions. The gas exchange and transport determines the level of the blood gases. The central neural control is designed as one subsystem. It receives the ventilatory signal from the respiratory control and determines the neural outputs to both the cardiovascular system and the respiratory mechanics. Values for constant parameters, initial conditions and other adjustments or maneuvers can be modified from the GUI panels. Cardiovascular System Figure 4,2-Cardiovascular System The cardiovascular system includes Reflexes, SA node, TPR, Stroke Volume and Circulatory Mechanics compartments. Heart period, mean arterial blood pressure and cardiac output are the output measurements from this subsystem. Input signals are the central respiratory response, chemical drive, lung stretch receptors reflex and pleural pressure signal from the respiratory system. 87 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Cardiovascular System - Reflexes Figure 4.3-Cardiovascular System - Baroreceptors Figure 4.4- Cardiovascular System - Chemoreflex Figure 4.5- Cardiovascular System — Lung Stretch Receptors Re.flex Baroreflex, chemoreflex, central RSA and lung stretch receptors reflexes contribute to the heart rate and vasculature changes in the cardiovascular system. T able 4.1: Baroreceptors Variables N om inal Values f . A cs.min L ower threshold for fcs 2.52 fcs.max Upper threshold for fcs 47.78 Rs Slope control variable 11.758 P„ Central pressure 90 T able 4.2: C hem oreflex Variables: N om inal Values fchem o.m ax Lower saturation for the sigm oidal function 12.3 fchem o.m in Upper saturation for the sigm oidal function 0.835 P a 0 2 Center point in the sigm oidal function 45 ^chem o Slope control parameter for the sigm oidal function 29.27 P a C 0 2 N orm alizing Pa C 0 2 value 40 f Constant value for the static respoinse 3.6 " L liem o Tim e constant for the chem oreflex 2 T ab le 4.3: Lung Stretch Receptors R eflex Variables: N om inal Values Gjs Constant gain 8.29 Tls Tim e constant 2 88 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Cardiovascular System - SA Node Figure 4.6-Cardiovascular System - SA node Figure 4.7-Cardiovascular System - SA node m odulated by (4-sympathetic nerves Figure 4.8-Cardiovascular System - SA node m odulated by parasym pathetic nerves The sinoatrial node acts as a pacemaker. It regulates the heart rate by the parasympathetic and the beta-sympathetic nerves. Both parasympathetic and sympathetic response can be implemented as a first order system with a gain and a time constant. The parasympathetic and the sympathetic responses from the autonomic control compartment are sent to the SA node. The heart period will be generated from the SA regulation. T ab le 4. 4: SA N ode Variables N om inal V alues To Basal heart period 0.58 Dbs Beta-sym pathetic delay Gbs Beta-sym pathetic gain varied w ith sleep drive -0.01 T b s Beta-sym p tim e constant 2 f|)sjriii: Lower threshold 0.1 Parasympathetic delay 0.25 G ^ara Parasympathetic gain varied with sleep drive 0.06 T p a r a Parasympthetic tim e constant 0.8 89 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Cardiovascular System - Stroke Volume Figure 4.9-Cardiovascular System - Stroke Volume The stroke volume is mostly determined by the venous return and the heart rate. Heart contractility has some contribution to the overall stroke volume. T able 4.5: Stroke Volum e Variables N om inal V alues P a b p o Mean Arterial B lood Pressure 93 VR0 Mean V enous Return 90 G v r Venous Return Gain 5 fVR V enous Return Tim e Constant 30 D vr Venous Return D elay 6 G hc Heart Contractility Gain 0.45 rue Heart Contractility Constant 10 D hc Heart Contractility D elay Cardiovascular System - TPR Figure 4.10-Cardiovctscular System - Total TPR change Figure 4.11-Cardiovascular System - alpha-sym pathetic modulation on TPR change The peripheral resistance controls the vascular action such as vasoconstriction or vasodilation. The TPR change is modulated through the alpha- sympathetic nerves and can be modeled as a first-order system with a gain and a time constant. T ab le 4.6: TPR Variables N om inal Values Ga s A lpha-sym pathetic gain varied with sleep drive -0.03 ^as A lpha-sym pathetic tim e constant 2 Utpr.o N om inal TPR change 1.0 Da s A lpha-sym pathetic tim e delay 4 f . 1asjnm Lower threhold 0.1 90 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Cardiovascular System - Circulatory Mechanics Figure 4.12-Cctrdiovascular System - Circulatory Mechanics The arterial circulation influences the arterial blood pressure from both vascular change and cardiac output. The pleural pressure modulation on the blood pressure is also incorporated in this compartment. A simple two elements Windkessel model is used to characterize the arterial tree. The cardiac output is computed in this compartment and is sent to the respiratory system as the blood flow. T able 4. 7: Circulatory M echanics Variables 1 N om inal V alues R -tpr Total peripheral resistance | 1200/1.333 i r ! ''-'a r t Arterial com pliance | 0.001/1.333 Respiratory System Figure 4.13-Respiratory System Figure 4.14-Respiratory System - Respiratory’ M echanics Figure 4.21-Respiratoiy System - Gas Exchange and Transport The respiratory system contains two major subsystems: the mechanical part and the control part. The respiratory mechanics deals with the interaction between the respiratory muscles and the neural control that generates the airflow. The respiratory control part consists of gas exchange and transport to the whole body. Respiratory System - Muscle Reaction Figure 4.15- Respiratory> System - Respiratory M uscle Reaction From the neural firings to the muscle contraction, a short period of reaction time is needed to generate the pressure. The pressure can be computed using the 91 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. convolution between the neural firing profile and the time constant. The convolution is done using a stepwise solution method. T able 4.8: M uscle Reaction Variables Nom inal V alues RC M uscle response time constant 0.06 d, Integration step time | 0.01 Respiratory System - Muscle Interaction Figure 4.16- Respiratory System - Respiratory M uscles Interaction The relationships between the pressure generated from the respiratory muscles and the airflow can be characterized as a curvilinear response. The variables needed to compute this response are incorporated in this compartment. The lung volume is calculated using the Euler-Cauchy method. T able 4.9: Respiratory M uscles Interaction Variables N om inal V alues j VC Lung vital capacity 5 ! Respiratory System - Flow Figure 4.17-Respiratory System - Flow generation In order to generate the flow, the total driving pressure has to overcome the elastic and the resistive pressure from the respiratory system. By solving the quadratic equation from the muscle pressure and force from the system, the airflow can be calculated in this subsystem. 9 2 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. Table 4.10: Flow Variables Nom inal Values R aw Airway resistance 1.27 Rl Lung resistance 1.69 Rcw Chest Wall resistance 1.03 El Lung elastance A Eqw Chest Wall elastance 5 Respiratory System - Pleural Pressure Figure 4 .18-Respiratory System - Pleural Pressure Figure 4.19-Respiratory System - Airway Pressure Figure 4.20-Respiratory System - Chest Wall Pressure The pleural pressure is the pressure difference between the outside atmosphere pressure and the pressure in the pleural space. The pleural space encircles the thoracic cavity. Therefore, the pleural pressure is the muscular pressure deducts from the elastic and the resistive chestwall pressure. In the event of external pressure such as from a mechanical ventilator, the pleural pressure is mainly contributed from the alveolar pressure and the chestwall pressure because the muscular pressure will be diminished due to the cessation of the neuron firings. The airway pressure in this compartment includes the pressure of the whole airway, including both the upper airway and the rest of the respiratory tract. T ab le 4.11: Pleural Pressure Variables N om inal Values haw. 1 Constant value for airway pressure 1.85 haw.2 Constant value for airway pressure 0.43 93 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Respiratory System - Dead Space Figure 4.22-Respiratory System - D ead Space Figure 4.23-Respiratoiy System - Total D ead Space fo r C 0 2 Figure 4.2 4-Respiratory System ~ D ead Space compartment fo r C 0 2 Figure 4.25-Respiratory System - Total D ead Space fo r 0 2 Figure 4.2 6-Respiratory System - D ead Space compartment fo r 0 2 The dead space is the space for the unmixed gases such as O2 and CO2 before the exchange in the alveolar or the expired gases after the exchange. Each CO2 and O2 consists of five equally divided compartments. T able 4.12: Dead Space Variables N om inal Values Vdfn Dead space volum e ( i = 1 ..5 ) 0.03 P I.C02 Inspiratory C 0 2 partial pressure 0 P[.02 Inspiratory 0 2 partial pressure 150 Respiratory System - Lung Figure 4.27-Respiratory System - Lungs Figure 4.28-Respiratory System — C 0 2 exchange in the lungs Figure 4.2 9-Respiratory System - 0 2 exchange in the lungs The gas exchange in the lungs can be modeled as a first order system for both CO2 and O2. The exchange is affected by the gas concentration in the blood, the gas partial pressure and the blood flow rate. The storage space for CO2 is larger than O2 because it dissolves easier. T ab le 4.13: Lung Variables N om inal V alues Vf02 Storage space for C 0 2 - * * J 5 V0 2 Storage space for 0 2 2.5 94 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Respiratory System - Cardiovascular Interaction Figure 4.3 O-Respiratory System - Cardiovascular M ixing and Convection Figure 4.31-Respiratory System — Cardiovascular M ixing and Convection fo r CO2 Figure 4.32-Respiratory System — Cardiovascular M ixing and Convection fo r 0 2 A short period of time is needed to get the blood from the lung exchange site to the chemoreceptors site. This compartment is modeled using a second order system. T ab le 4. 14: Cardiovascular Interaction Variables N om inal V alues T, Circulatory m ixing tim e constant 1 T, Circulatory m ixing tim e constant 2 T 1 p Peripheral Chemoreceptors D elay Tim e Constant 0.58 Respiratory System - Body Tissues Figure 4.33-Respiratory System -B o d y Tissues Figure 4.34-Respiratory System — Body tissues CO? exchange Figure 4.35-Respiratory System — Body tissues 0 2 exchange As the oxygenated blood travel through the body, the needed oxygen is carried to the tissues for exchange and utilization while the waste product, CO2 diffuses back to the blood and transports back to the lungs for exchange. The O2 used and the CO2 produced are based on the metabolic rate of the tissues. T ab le 4 .1 5 : B ody Tissues Variables N om inal V alues V t.C 0 2 B ody tissue storage volum e for C 0 2 15 Vt,02 Body tissue storage volum e for 0 2 6 MRco2 M etabolic production rate for C 0 2 0.0033 MR0 2 M etabolic consum ption rate for 0 2 0.0038 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Respiratory System - Dissociaton Figure 4.36-Respiratory System — Dissociation The gas concentration in the physical solution is proportional to the partial pressure based on Henry-Dalton law. The arterial O2 and CO2 concentration can be computed from the partial pressure. Each gas concentration depends on both O2 and CO2 partial pressures. The chemoresponse to the oxygen concentration is usually represented based on the oxygen saturation rather than the partial pressure. Oxygen combines with the hemoglobin and forms oxyhemoglobin. So, the percentage of the oxyhemoglobin in the hemoglobin is the oxygen saturation. Oxygen saturation can be extracted from the dissociation equation with the same variable delay as in cardiovascular mixing and convection compartment. T ab le 4. 16: D issociation Variables N om inal Values Z M olar conversion factor 0.0227 C l M axim um concentration o f hem oglobin-bound oxygen 9 C2 M axim um carbon dioxide concentration 87 al Parameter in 0 2 dissociation equation 0.3836 a2 Parameter in C 0 2 dissociation equation 1.819 alpha 1 Parameter in 0 2 dissociation equation 0.02598 alpha2 Parameter in C 0 2 dissociation equation 0.05591 K i Parameter in 0 2 dissociation equation 13 K2 Parameter in C 0 2 dissociation equation 194.4 betal Parameter in 0 2 dissociation equation 0.012275 beta2 Parameter in C 0 2 dissociation equation 0.03255 9 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Respiratory System - Brain Figure 4.37-Respiratory System — Brain Region Figure 4.38-Respiratory System — Cerebral Flow The central chemoreceptors site is located in the medulla region. Since the brain is confined in an enclosed cranium, the cerebral flow links closely to the change of the CO2 tension in the brain. The carbon dioxide tension is controlled by the metabolic rate and the flow rate. T able 4.17: Brain Variables N om inal Values Sb.C02 Brain tissue C 0 2 dissociation slope 0.36 Sc02 B lood C 0 2 dissociation slope 0.0043 MRbco2 Brain metabolic production rate for C 0 2 0.0517 QdBO N om inal cerebral blood flow 0.8333 Neural Control In this compartment, the combination of the respiratory rhythm and the ventilatory drive determines the neuromuscular drive. The ventilatory drive is established by both the central and peripheral chemoresponses from the respiratory system. Autonomic responses from the baroreceptors, chemoreceptors, central respiratory and lung stretch receptors are integrated here as they regulate the heart rate and peripheral vasculatures. 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Neural Control - C entral Neuromuscular Drive Figure 4.39-Neural Control - Central Neuromuscular Drive The intrinsic respiratory rhythm and the ventilatory drive are two main components in the central neural center. The intrinsic rhythm is written as a S- function. The rhythm generator also detects if there is any external pressure present and use it as the primary breathing source. Both the state and the ventilatory drive contribute to the total respiratory response. T ab le 4.18: Central Neuromuscular Drive Variables N om inal Value TI inspiratory tim e 1.5 TT w hole breath time 4 Inhale Boolean variable 1 Neural Control - Ventilatory Drive Figure 4.40-Neural Control ~ Ventilatory Drive The ventilatory drive that determines the degree of breathing is contributed from both the central and the peripheral chemoresponses. The central influence is based on the brain CO2 partial pressure. The peripheral response is a modulation between the arterial CO2 partial pressure and oxygen saturation. T ab le 4.19: Ventilatory Drive Variables N om inal V alues GP Peripheral chem ical gain 0.0063 Gc Central chem ical gain 0.075 h Central apneic threshold 45 h ... Peripheral apneic threshold 38 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Neural Control - Autonomic Efferent Activity Figure 4 .4 1-Neural. Control - Autonomic Control The autonomic control compartment is the whole integration of different neural inputs contributed from both the cardiovascular and the respiratory system. The cardiovascular contribution is from the baroreceptors. The effects from the respiratory system are the central respiratory neural response, the chemoreflex and the lung stretch receptors reflex. Simple linear gains are used in this compartment. T able 4.20: A utonom ic Efferent A ctivity Variables Nom inal Values fb a r o .O Lower threshold o f the parasympathetic baroreflex sigm oidal function 3.2 fiais..' Upper saturation o f the parasympathetic baroreflex sigm oidal function 6.3 hs.O Center point for the sigm oidal function 25 kP Slope control parameter for the sigm oidal function 7.06 Gcrsa.p Central RSA gain for parasympathetic response 2.0 Gch em o,p Chem oreflex gain for parasympathetic response 0.01 G lung,p Lung stretch receptor reflex gain for parasympathetic response 0.4 fs.O Lower limit o f the sym pathetic exponential decay function 16.11 fS ,« Upper saturation o f the sympathetic exponential decay function 2.10 Ks Constant for the exponential function 0.07 GcRSA,bs Central R SA gain for p-sym pathetic response 2.0 G ctienio.bs C hem oreflex gain for P-sym pathetic response 0.006 G iunjf.bs Lung stretch receptor reflex gain for P-sym pathetic 0.25 G baro.bs Baroreflex gain for P-sympathetic 1.0 GcRSA.as Central RSA gain for cc-sympathetic response 2.0 G chem o.as Chem oreflex gain for a-sym pathetic response 5.0 G junp.as Lung stretch receptor reflex gain for a-sym pathetic 0.34 G baro.as Baroreflex gain for a-sym pathetic 1.0 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Assisted Ventilation In the model, external pressure can be applied to the respiratory system that assimilates the case where CPAP or Mechanical Ventilator is used on the patient. Figure 4.42-Assisted Ventilation Sleep Mechanism and Upper Airway Mechanism Figure 4.43-Respiratory System - State Dependent Upper Airw ay M echanism Figure 4.44-Sleep M echanism Figure 4.45-Sleep Mechanism - Slow Wave Activity The sleep mechanism is regulated by two processes: process C and process S. The sleep propensity is determined by the threshold in process C. Process S is affected by the Slow Wave Activity in sleep. The upper airway is modeled with the upper airway sensitivity. The degree of upper airway obstruction is determined by the sensitivity and the sleep state. The triggering threshold for upper airway opening is based on the ventilatory drive. The time required for the transition from wake to sleep is affected by process C. The upper airway sensitivity is also influenced by external pressure, such as from the mechanical ventilator or CPAP. T ab le 4.21: Sleep M echanism Variables N om inal Values A Am plitude o f the skew ed sine function 0.12 e Periodicity o f the circadian rhythm 0 X low Lower circadian threshold 0.17 X high Upper circadian threshold 0.67 Ctrc R ising rate o f Slow W ave A ctivity 0.0033 C C fc Falling rate o f Slow W ave A ctivity 0.0067 C L e0 Constant for sleep decaying 0.000133 O C so Scaling factor for SW A during sleep onset 1.2 SW A0 Initial SW A value 0.007 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. GUI Panels Graphical User Interface (GUI) panels have been created for simulation. Simulations can be controlled from these panels. Main control panel can start, stop or reset the simulation and it also sets the running time, the stopping time, the integration step size and access buttons to other panels: constant parameters, initial conditions, adjustable inputs and external interventions panels. Constant parameters and initial conditions panels are for those variables used in the model. Adjustable inputs panel allows variations of different gains during the simulation. External Interventions panel is used to test some interventions that physician uses in their experiments. Figure 4.46-M ain Control Figure 4.47-Constant Parameters Figure 4.48-Initial Conditions Figure 4.49-Adjustable Inputs Figure 4.50-External Interventions 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2 Simulink Diagrams F igu re 4.1: Cardiorespiratory M odel Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F igu re 4.2: Cardiovascular System Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABP CD - ► C D fcs k_cs Alpha-Symp Integration! G paral - 5 - 5 d > arousai Pn fcs_min fcs_m ax sleep drive F igu re 4.3: Cardiovascular System - Baroreceptor a> To Workspac Logical F igu re 4.4: Cardiovascular System - C hem oreflex 1 0 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fapIC CD- 2 3 .2 9 - 1 5 Gap 1/2 1 /ta u _ a c In te g ra to r F igure 4.5: Cardiovascular System - Lung Stretch Receptors R eflex C D — B eta-Sym p ( ftb s ) ___ arousal G D C Z > - sleep drive C D - Parasym p (ftp) L k jftb s — p aro u sal — W s le e p d r iv e d elta_ H P b s| B eta Sym pj HP change m odulated by beta-sy m p Beta Sym[ l lK jD r aro u sal d e lta HPp sleep drive ftp P ara sy m p HP change m odulated by parasym p - > ( 3 ) Parasym p To W orkspace delta_HPplC To W orkspacel - K D HP F igure 4.6: Cardiovascular System - SA N ode ta u „ b s delta _.HPb ftbs_m if ftb s_ g 8 in b_blocker d e lta JH Pbs_dynam ic Bet a Symp ■ K H Z ) rSZP D D f i Alpha-Sym p Integration G paral F igure 4.7: Cardiovascular System - SA N ode modulated by p-sym pathetic nerves 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ta u _ p ftp _ g ain ftp_delas p_blocker d elta _H Pp_dynam ic ftp S ave Block X 2 ) P arasy m p 0 .0 6 G para 1 -u arousal 0.3 G para _s!eep sleep drive A lpha-Sym p in te g ra tio n G para 1 F igure 4.8: Cardiovascular System - SA N ode modulated by parasympathetic nerves d > To W o rk sp a ce 3 G E> 8 0 +0 2 0 - 8 0 J/ 3 To W orkspac (ABP..O) F ig u r e 4.9: Cardiovascular System - Stroke V olum e To W orkspacel TPR change m odulates by alpha-sym pathetic C D - Alpha Sympl (fas) fas arousal sleep drive alpha_TPR Alpha Symp Alpha Sym ) H K ID arousal C D - sleep drive TPR_0 F igu re 4.10: Cardiovascular System - TPR 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Alph a Sym p > C D ftas_gain del t.a_tpr_ dynam ic C D — r sle e p drive F igu re 4.11: Cardiovascular System - TPR modulated by a-sym pathetic nerves R_TPR ABPIC aipha_TPR To W o rk s p a c e l C a rt A B P_before S tr o k e -\/o lu m e L t o ml 5 2 / 1 .3 3 3 H e a rt-P e r io d ABP 1 / 1.361 Pleural P re s s u re in flu en c e P le u ral P re s s u re U nit C o n v ersio n F igu re 4.12: Cardiovascular System - Circulatory M echanics 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.13: Respiratory System Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Flow C±> PE P leu ral P r e s s u r e (Ppt External Pressure Gain Pleural Pressure Saturation 0.1 To Workspace Pao PleuraL Pressure CD— Respiratory C onductance >g d P tfrc Respiratory m uscles activity F igu re 4.14: Respiratory System - Respiratory M echanics Resp Muscle CZ> —*401 g > ■ K ~ Q F igu re 4.15: Respiratory System - Respiratory M uscle A ctivity 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - ► ( 1 ) P t_frc d > Nt RC P ro d u cts RC F igure 4.16: Respiratory System - Respiratory M uscle Reaction CD- Po_vt -CD Cond CD— — ela sta n ce 1/(R_AW+R_L+R_CW) to ta L re sp c o n d u c tan ce P ro d u ct PE CD CD Pao CD b_yt » C D Flow 1 /2 sq rt F igu re 4.17: Respiratory System - F low Generation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Pm us G > Q } Vt 1 ^ Pleural P ressu re (Ppi) P e w Flow Pew d > Flow Flow C±> Pao P ao F igure 4.18: Respiratory System - Pleural Pressure G > P ao Flow P ro d u c t Abs kaw 2 k aw l F igure 4.19: Respiratory System - A lveolar Pressure R_CW resistance Flow P e w C E > E_CW elastance F igure 4.20: Respiratory System - Chest Wall Pressure Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Q 5 S o F igure 4.21: Respiratory System - Gas Exchange and Transport Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PAC02 PACO 2 'w ' P d 5 C 0 2 r 0 ------------ 1 F low I L C 0 2 DEAD 5PACE Flow P d 5 0 2 Cv PA 02 0 2 DEAD SPACE F ig u re 4.22: Respiratory System - Dead Space puisc C 0 2 P artial P re s s u re ' Pd{1)C 02 C 0 2 A ddition P d (2 )C 0 2 Pd(3)C02 P d (4 )C 0 2 h P d (5 )C 0 2 P d (4 )C 0 2 P d 5 C 0 2 P d (4 )C 0 2 P d (5 )C 0 2 P d (4 )C 0 2 P d (3 )C 0 2 P d (3 )C 0 2 P d(2)C O i PA C 02 P d (5 )C 0 2 F igure 4.23: Respiratory System - Total Dead Space for C 0 2 P IC 0 2 > (T ) P d (1 )C 0 2 1 /V d ea d 1 Flow P d (2 )C 0 2 A bs (v.t) O e a d 1 C 0 2 IC To W o r k s p a c e l F igure 4.24: Respiratory System - Dead Space Com partm ent for C 0 2 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 2 Partial P ressu re P d(1)02 P d (2 )0 2 P d ( 2 ) 0 2 F low P d (3 )0 2 pulse Pd(2)Q 2 P d (4 )0 2 P d (5 )0 ; P d (5 )0 2 P d (4 )0 ; Pd{ 2)02 P d (3 )0 ; F ig u re 4.25: Respiratory System - Total Dead Space for 0 2 P I0 2 >(T) P d (1 )0 2 1/V dead1 F low P d (2 )0 2 D e ad 1 0 2 IC To W o rk s p a c e l Abs (v.t) F igure 4.26: Respiratory System - Dead Space Com partm ent for 0 2 F igu re 4.27: R espiratory System - Gas Exchange in the Lungs 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. P d 5 C 0 2 Flow C V C 0 2 1/s- PA C 02 C a C 0 2 P A C 02IC To W o rk sp ace V LC 02 F igure 4.28: Respiratory System - C 0 2 Gas Exchange in the Lungs 0 s - 0 lam bda* (1 -s ) VL 0 2 -► (?) - M PA02IC To W orkspace F igu re 4.29: Respiratory System - 0 2 Gas Exchange in the Lungs P A C 0 2 0 D Q 0 0 0 D elay C o n s ta n t C 0 2 C a r d io v a s c u la r M ixing a n d C o n v e c tio n E ff e c ts PAC02 Q PaC 02 Peripheral Delay C o n sta n t PA02 Q ^ Peripheral Delay C o n sta n t 0 2 C a rd io v a s c u la r M ixing a n d C o n v e c tio n E f f e c ts — -► (2) F igu re 4.30: Respiratory System - Cardiovascular M ixing and Convection Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To W o rk sp a c e To W o rk s p o c c l P aC O Peripheral Delay C onstant P e r ip h e r a l D elay C o n s t a n t F igure 4.31: Respiratory System - Cardiovascular M ixing and C onvection for C 0 2 Pcfiplwwiil Onlay Cunslnul Peripheral Delay C onstant F igu re 4.32: Respiratory System - Cardiovascular M ixing and C onvection for 0 2 0 « - CvC02 Body Tissues C o m partm ent fo r CQ2 C a C 0 2 C v C 0 2 Q t S t a t e Drivf CaC 02 -<D - 0 -<5 Cv02 Q t C V 02 S t a t e Drivt C a 0 2 Body Tissues C o m p a rtm en t fo r 0 2 - 0 F igu re 4.33: Respiratory System - B ody Tissues 1 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. S ta t e Drive f(u) To W o rk s p a c e 1/V T C 02 C a C 0 2 C v C 0 2 Figure 4.34: Respiratory System - C 0 2 Exchange in Body Tissues S ta te Drive f(u) Cv02IC To W orkspace * 0 CV02 1/V T02 r * . C a02 F igure 4.35: Respiratory System - 0 2 Exchange in Body T issues » m C aC 02 beta; CD- PAC02 SA02_. delayed P eripheral Delay C o n stan t F igure 4.36: Respiratory System - D issociation 117 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. S ta te Drive f(u) P b C 0 2 IC Qb To W orkspace -Kj) P b C 0 2 1/s- S C 0 2 1 /S b C 0 2 P a C 0 2 F igure 4.37: Respiratory System - Brain Region Pbco2 -QdBo .0 3 40 >(T) Q.b u *u -► I |u| j- > sqrt.(u)j M R b C 0 2 4 * 0 .0 3 * Q d B o /S C 0 2 F igu re 4.38: Respiratory System - Cerebral Flow 118 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. S_w ake To W orkspace! CD------ Chemical V entilatory d> j modified resp rhythm Rhythm F igu re 4.39: Neural Control - Central Neurom uscular Drive (u>0)*u 0 .0 7 5 PbC02 G c_blocker Gc Dvent P aC 02 0 .0 0 6 3 Gp_blocker S A 0 2 SWA/S Sleep/A w ake arousal lpC 02 1 -0 .4 * u (u>0)*u — 1 1 -u 1 -u F igu re 4.40: Neural Control - V entilatory Drive 119 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. CD---- C entral R espiratory (u< = 60)'u-*(u> 50)' A lpha-Sym p Integration lung feedback L ung_blockcr G Jung_bsym p •W O QOR ------ G _chem o_bsym p ♦CD ' B eta- (ftbs) (u < = 6 0 ) ’u - * - (u > S O ) ' s-S y m p D eta-sy m p a tb etic j— ► G Jung._para - fe io oi ~ ~ o G _chem o_para — ►CD T otal P arasym p (ftp) (u>=0)"i fcs B arorefiex baro_blocker parasym pathetic b a roresponse F igure 4.41: Neural Control - A utonom ic Control M ech Vent P ressure pulse _ — -♦CD) m ech ver neural O — '--------- m ech ver m echanic s+2.2 P ro d u ct5 M ech_V ent_activation 1/2 pulse CPAP^activation CPAP P ressure F igu re 4.42: External Pressure M odule 120 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. F igure 4.43: Respiratory System - State Dependent Upper A irw ay M echanism R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. F igure 4.44: Sleep M echanism R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 01 *l£>- -4— T S I □ I 0s" I 1 1 V ■ < } x Li CZOI F igure 4.45: Sleep M echanism - Slow W ave A ctivity R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. start tim e erid time P m x T m ax tim e step oT length o t saved 1 fsec! 10 Constant Paametet A d jy s te b i e in p u ts 'r a h a t C sin d ifon ; Intervention' F igure 4.46: Main Control GUI panel 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. •*L2*} S i s , F v » ("so ;{11 75 1_«c ' fv 'v w i' Irajrtas 152, ; g -47.78;' j M l Inhale Tlnwan r T «iea* s 1 5 . | V „fC 3 ",' ~ ( i \ 'i - V C HC f 5 fo o T _lJ 'jvr v < r < s c £ ^ p C 'n ^ * * \ 2 t ? < . < h t f 0.0? ^ v 1 F CV/ £ I h AW ft fW ‘ ^ t = \T * f f w p r fT ~ p ~ p i r fTsTi j < « .m tfte i'. toper* tr a . :ero '_P - Sp_;eTO fp_rf ■ -S.3 | C e a d S fjc e Vdfedl Vde*C Vdsadl Yctead4 Vde-adS i [Tor fc ir f n r f w f r r . 1 1 IlPIfiii .......... h ^ iW p < fe S s v s _ i A U c 'i< , . p § L ) a 2 5 'b_cymp -«h ...ill t p b ipft a ^ P : * co t# mr. - n ~ n ~ r ~ J ^ TPfi_0 . . . . ' / FleStim V fiefcjn V R«*u»< d e * ss> Gain ( w h i ~ • r ~ r ~ i i j ' C j!C il'-ritU‘*f ’ ><eMO Heart Cl fieail O .r • a e k sr G a n ; S a n a r ~ f o i r n r ~ TPS C«r 1.900.2251; .70.001333. v>n3* ou.3 „ r s ~ ; , j Gi dV.-'.rcw's; ‘ 7 mg te k d a ' T1 T2 f * 3 p r | “ i ? a 1 - s lp f e l s i p h d a ? K . 1 —0 ~ f i f g j r p f e i j " J o o s l? fouS af J TiT iC ' betal .'. t*!*2 a ■ 02 n i r r p i r [T k5$ r r f i r ■ ■ > 1 F u J j r -itt. /V T C 02 • VT 0 2 MRC02 MR02 n r 8 j 0GC33 J 0 0038 r f i r r w r r i i i r r i t f F v M nbifi.- -.CfM? 5 0 0 3 r. UdEi. forTT p r r (uTT pH" [uy5~ 1 ,"H i 'V < j * - > — I 3c - IpCO." fp02 f ls f i T fiosi J " “ L l ^ ..rrrrlvefttT T T ; { T tT : E '» < 5 c ’ C w 3 i oil ! » ■ • > ■ P .£ Q 2 J } c 2 ' “ S T ' I 4 0 S~5T 5£S1$ n r RW W : J jm JZ : n r E S JF C i 0251 *.su_C02 f i r : c lc c e F igure 4.47: Constant Parameters GUI panel 125 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Catdwvasufa System H f a - s iC defo>.H PbslC ftp iC defoJ-iPpC- fejC .jbha_TPRC 022133 [34 7927 jTC35T VRIC. V R .deM C HCIC H C jtelsjC ASPIC ■ ■^4 5 5 0" F.e-sp'a'oty Syrtem GWaltC 7HC n r FicrfC Pf itciC I Pi l!c!C 2 M l Dead! 0 2 Dead202 Oead3Q2 Dead40I 1 C :C C 1 C DeadSOi 1 C 1104 363 1 104 225 1104 050 j 1038330 Deadl C G 2 D<?ad2C02 Dead3C02 Dead4C02 DesdSCOI ic - ic ic ic ic [395616" PAO'C PACQT ^a02„delay PAC02_det3y SA32„detay w it. ft. ! l Pa€02ta PaCCS'-econd Pa02fksl Pa02;ecor,d IC I C ■ (C 38.9136 1 j' -0.2465 | 40 3928 [*0355?” C v C O C IC Cvoac P5C02IC yC2!t y C O Z IC ctemo.deiayi: 0 5247 1 0-1639 48.5383 -00018 •0.0251 ciore F igure 4.48: Initial Conditions GUI panel 126 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. m m cm Or RSA G a in T btocte m* A 10 p r ~ p ~ T ~ P r > /> o*feO * jt h fa zte x m m - v a 'p v -a m a x J 7~ \ c'ii foW n m Jffcte Sprnp max p T " Poo* footT a _ _J B in - s w 5 ^ r £ b h * . r 0 1 i f . i tuny ie Mod iwn P.*es;in® max OS 0 j 0.4 m 7 -,' ; , i t: C w d o v a s c u ia i | ,|- ■ i I C j 0 03 j Es'ojy'toij.jn r b lo c * e i : m as< r bwd;ai ra» P U T f T m j 0 j > t * a n fdn r f~ p V « d * * * ff.SX r 01 C s td ^ c O o tp v t .J ~ * :b lO C fc e f.> rriin max r^ * n ~ p— a . ' j a A ? r C H a u .c e p i W a W3* 100 : J-'. R e s p ir a to r I L c C S f c m c 1 - sa c j . . : ■ ■ ■ ■ • • f ~ ~ b to c ^ e r m n sTiax I L >3^ l a " — 1 f~ D fo c fc s r n»n I o ! ° « w - j j ,' jj .ftVi - ■ ■ : ,. •....m ax*-.. • ■ ■ ■ ■ ■ ; pir~ piiisf" p ir V * • ‘ r - . _ j S dtcff' r f o n p r pi?"" p®” a . j . . _ j 025 05 ff-in Ac! i i i , 'ip " * f c ' [ o > s p f n T jlI ' " j a cto * J F igure 4.49: Adjustable Inputs GUI panel 127 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. ■ m m m m U p p e r MW M ech sn i m r hJ p l o c > a g e ita jH s m e j 0 end ifme f g u r n . m a x u u :. . .. . : . > ■ : ■ < ' ■ . r ‘ V » • . ; . . .. .- — ■ ■ Upper | 0 f 0 05 ! 1 A is w * .,, . ' , _ . . ........... Cens#r>.#v , | J , j f~ .d e e p 5 b e p M e c H a n b r e s i « * tfm e M i iiitanstiorrfeie dhobi j 60 .ft-' ^ m a v » < 1 r m j > j j n j T " :s.taft timer' Manoeuvre :- ; f d & a t o p r > ! ! i : r_ T ~ ijrisptraterjfi ■ ■ ; ■ peti&d' : r” \ 4 a b e M a n o e j < • - : s f a it f a e .: . V a b a K a : d u ia iid n ; O il C o r d r e r i ■ ■ Am* time In sp ire d 0 C P u U e P r e * : u e j 0 Im m H J C h d ftp e f , l 5 0 p _ _ d u ra tio n f i r ~ rnn m ax P m r 0 1 1 5 0 J j iD O S C o n fid i \ : lm om d£D ' 2 P y f o P f e f s f e . ^ _ {mmHgS C h a r g e ! 0 H _ ■ ': 'd u f^ ld a .' .. • . 'm ifi;'./ m a y : - / i ^ . ; ■ • - . 1 5 0 150: li I l f External P fs ss ts e : • r CRAP P ressu re j O ' . :crnH20: . ; 1 ? ^ “ .' .duratiotV ipTT"' . ; f~ M reb an ical Ventriakv [ 0 o n H 2 3 I 0 d 'cato i | 0 1 F igure 4.50: External Interventions GUI panel 128 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5. Simulation Results 5.1 Simulation descriptions The cardiorespiratory model is implemented using Simulink from Mathworks. Simulink is an extended package from the popular Matlab. It incorporates general functions from Matlab and it includes extra features for dynamic system simulation. Rather than writing codes or scripts similar to Matlab, Simulink provides the user with graphical blocks. Each block represents a simple function such as a summation, a signal generator and so on. Most complex functions can be constructed from those basic blocks provided in the package. However, the user can also define his or her own function through the block called S-function. The S-function is created using the template provided by Simulink. The user can program within the template. To use Simulink, two main steps are involved. First, the basic outline of the model has to be defined. The model can then be constructed using blocks from the package or from user defined S-functions. After that, the dynamic performance of the implemented system can be simulated using Simulink. The user can set the time length for each simulation. The integration step can be either fixed or varied. The speed of the simulation is mainly influenced by the size of the integration step and the complexity of the model. In our model, we use blocks from the package as well as our own S- functions. To make our model more robust and interchangeable with newer components, we break down our system into as many small compartments as 129 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. possible. The complete schematics are shown in the previous chapter. The integration step size is 50ms for our simulation. We can perform shorter simulation, i.e. hypoxia or longer simulation such as overnight OSA. Due to the initial conditions of the system, the simulation requires a very brief period of time to reach the steady state. We have tested and simulated a few scenarios using our model which we will describe below. Awake sta te: The simulation for normal awake state runs for 500 seconds. This is just to show what our signals look like and these are the signals that we check the most. The result for the normal condition is shown in figure 5.1. Isocapnic Hypoxia and H ypercapnic H ypoxia: Hypoxia usually occurs as the result from cardiorespiratory disorders or from sleep apnea. The cardiorespiratory changes from hypoxia have been studied for many years and the most prominent features are tachycardia and increase in ventilation. It is believed that the chemostimulation is the cause of the increase in the heart rate. However, in obstructive sleep apnea case, even with high ventilatory drive resulted from hypoxia, the heart rate does not increase and some studies show that there is actually a decrease from it. Some people correlate the case in OSA with what known as the “diving reflex” where the heart rate slows down when we hold our breath under water. Experiments have also shown that the heart rate slows down when stimulate the carotid body alone which is the location for peripheral chemoreceptors. Therefore we like to see if our model can produce the general changes in the case of hypoxia. 130 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. We have run two scenarios, one with constant carbon dioxide level and one with higher concentration. Supposedly with both carbon dioxide and oxygen stimulations, there will be higher response from the combinatory contribution from the central and peripheral chemoresponses. Each of our hypoxia stimulations lasts for 600 sec. At the starting of the hypoxia simulation, we decrease the inspiratory O2 partial pressure, P 102 while we increase the inspiratory CO2 partial pressure, Pico2- For isocapnic hypoxia, we decrease the P 102 by 90mmHg throughout the whole hypoxic period. To maintain a relatively constant alveoli CO2 partial pressure, PA co2, we add about 20mmHg of Pico2- For hypercapnic hypoxia, we decrease the P 102 by the same amount as with isocapnic hypoxia. To create the hypercapnia, we increase 40mmHg of Pico2- At the end of the simulation period, all added gas changes are set back to zero. Hypoxic experiements done by Somers et al. [75, 165] show an increase of about 25% in heart rate in both isocapnic and hypercapnic hypoxia cases. Mean arterial pressure increases about 3mmHg in isocpanic hypoxia case and about 1 OmmHg in hypercapnic hypoxia case. From our simulation, we observe the graduate increase in the ventilatory drive. With the increase in the respiratory effort, the tidal volume goes up. We can also see the graduate increase in heart rate and blood pressure. From our simulation, the heart rate increases about 2% for isocapnic hypoxia and about 10% for hypercapnic hypoxia. The mean arterial blood pressure increases about 3mmHg for both isocapnic and hypercapnic hypoxia cases. One major difference from our simulation step and the actual experiment 131 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. protocol is that our simulation is using a fixed breathing period while spontaneous breathing is allowed in experiments. The effect from hypercapnic hypoxia proves to be greater than isocapnic hypoxia with higher increase in heart rate. Simulation for isocapnic hypoxia is shown in figure 5.2 and hypercapnic hypoxia is shown in figure 5.3. M ueller M aneuver and Breath Holding: Both maneuvers are used to test the cardiovascular changes. In Mueller maneuver, the patient inspires through an obstructed upper airway for a period of time and expires quickly afterward. For Breath-Holding, the patient holds breath for the same duration as in Mueller maneuver. We have included an adapted drawing from experimental results from Morgan et al. [185] as shown in figure 5.4(c). From the adapted drawing, during Mueller maneuver, more negative pleural pressure is generated due to the obstructed upper airway. The pleural pressure effect on the blood pressure can be seen from the decrease in arterial blood pressure. Because of this pressure drop, baroreflex is activated which decreases the heart period. At the end of the maneuver, the increase in blood pressure is primarily achieved from chemoreflex. In breath-holding maneuver, both heart period and arterial blood pressure remain relatively constant during the maneuver. The arterial blood pressure increases afterward due to chemoreflex. In our Mueller maneuver simulation, we observe the increase in the arterial blood pressure during the recovery phase caused by pleural pressure change and by chemoreflex. The heart rate decreases during the maneuver because of the central 132 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. respiratory drive, CRSA and also through baroreflex. In breath-holding maneuver, we do not see much change in heart rate and we only observe small increase in arterial blood pressure due to chemoreflex. Again, our simulations are under the fixed breathing period while the actual experiment allows voluntary breathing. Results are shown in figure 5.4. Valsalva M aneuver: This maneuver has been widely used to study the arterial baroreflex [186]. This method is safe and can be performed on patients without sophisticated equipments. The maneuver begins by taking in a full breath of air and then trying to expire with a closed glottis. This straining process lasts for about 10 to 40 seconds. We use 16 seconds for our simulation in comparison with the experimental data. Since we model our respiratory system using the inspiratory muscle activity, the expiratory muscles are not included. During the Valsalva maneuver, the straining creates an increase in the expiratory pressure. To simulate the maneuver, we include a step function for the expiratory pressure. The expiratory pressure remains unchanged in the normal condition. With pennission from Dr. Vasily Belerozoff, experimental data from Dr. Khoo’s lab show all four phases of the maneuver: (1) a rise in the arterial pressure at the onset of the straining, (2) recovery of the arterial pressure during the straining, (3) a reduction in the arterial pressure following the straining and (4) a small sustained elevation in the arterial pressure. Our simulation shows the increase in arterial blood pressure at the initial phase of the straining period. With the decrease in venous return, we can see the graduate decrease in blood pressure. too R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. During this time, the decreasing in heart period can be seen from our simulation which reflects the baroreflex. During releasing period, we see more drop in blood pressure by the change in pleural pressure. In our recovery phase, we do not see the high elevation in blood pressure in our simulation as from experimental data. The simulation result is shown in figure 5.5. N orm al Sleep State: With the sleep mechanism incorporated in our model, sleep onset begins when sleep propensity reaches the upper circadian threshold. From awake to sleep there is a decrease in the ventilatory response due to the disappearance of the wakefulness stimulus. With the reduction in overall ventilatory drive, tidal volume drops slightly. For normal subject, there is also an increase in parasympathetic tone and a decrease in sympathetic tone. In our simulation, we can observe the decrease in the heart rate and arterial blood pressure throughout the night. Normal sleep takes about 8 hours which can be seen from our simulation. The simulation for the whole night can be seen in figure 5.6. Obstructive Sleep Apnea: OSA occurs at the on-set of the inspiration in sleep. During the transition from awake to sleep, the upper airway muscle tone reduces and makes it more collapsible from the sub-atmospheric pressure created from inspiration. In our model, we increase the upper airway sensitivity to simulate OSA case. Combining the state drive and the upper airway sensitivity, the upper airway starts to obstruct during the transition from awake to sleep. Once obstruction occurs, there is no airflow or lung inflation which can be seen in figure 5.7. As asphyxia develops the ventilatory drive increases. Arousal occurs when 134 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the ventilatory response reaches the threshold. The threshold differs in NREM and REM stage. Upon arousal, the upper airway reopens and flow resumes. Since there is more reduction in hypoxic ventilatory response in REM stage, obstruction may last longer in REM stage. Once the ventilatory drive drops below the threshold, sleep takes over again and the obstruction starts as the whole episode repeats. In our OSA simulation, we notice that the sleep period is longer than in normal sleep by about 30 to 45 minutes under the same NREM/REM period conditions. The whole night of OSA simulation is shown in figure 5.7. One segment of the OSA simulation data covering both NREM and REM sleep stage is shown in figure 5.8. The increase in arterial blood pressure upon arousal is contributed by the increase in alpha-sympathetic activity. We have monitored the sympathetic changes in our simulation as well. Figure 5.9 shows the alpha- sympathetic activity during obstruction and arousal with the same sympathetic tone as in normal sleep state. The increase in sympathetic activity upon arousal due to high chemical built up. Sometimes physicians will prescribe oxygen treatment to help with the obstruction because there is a visible oxygen desaturation in OSA case. From our simulation, we have seen that with the increase in oxygen input, the obstruction period lengthens during each episode and this reduces the number of apnea occurrence during sleep. We can also see the reduction in oxygen desaturation. The simulation result is shown in figure 5.10. Our result is comparable to others [187], 135 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. CPAP application during sleep: The most prescribed treatment for OSA is the usage of Continuous Positive Airway Pressure or CPAP machine. Basically a positive pressure air will continuously blow into the upper airway and prevents the upper airway from collapsing. In our model, the flow generation compartment has an external input port which can be used such as in the case of CPAP or mechanical ventilator. From our simulation, we see the disappearance of OSA occurrence during CPAP application. Because of the continuous pressure, the lung residual volume increases since the lungs cannot expires completely. It can be seen in our simulation as well. The simulation result is shown in figure 5.11. P eriodic Breathing: Periodic breathing is usually characterized by the crescendo-decrescendo alteration in the tidal volume. The cyclic breathing pattern in OSA is due to the collapse of the upper airway while other kind of periodic breathing such as central apnea, Cheyne-Stokes, etc are caused by instability of the respiratory control or by cardiovascular conditions. Sleep apnea can be seen in patients with severe Congestive Heart Failure (CHF) [188-195]. With the decrease in cardiac output, the blood flow slows down which can delay the gas transport time from the exchange site in the lungs to the chemoreceptors site in the carotid body. Because the incorrect information is sensed by the receptors, the ventilatory response starts to oscillate and triggers the apnea. In our simulation, we decrease the cardiac output by 80% and increase the chemical delay time to around 40 seconds to create the CHF case. The ventilatory drive starts to oscillate visibly after sleep sets in and apnea takes place as fluctuation increases. With high 136 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. oscillation in ventilatory response, arousal occurs as it continues throughout the night. The simulation for the whole night of apnea in CHF case is shown in figure 5.12. Figure 5.13 is a small segment taken from the whole periodic breathing episode to show the crescendo-decrescendo breathing pattern. Oxygen treatment is sometimes used as the treatment for sleep apnea in CHF patient because of the significant oxygen saturation from apnea. In our simulation, we introduce a period of hyperoxic case and a period of hypercapnic case to the periodic breathing. From our simulation, it shows an attenuation in periodic breathing with the oxygen treatment but arousal still persists but with the carbon dioxide application, apnea disappears and normal sleep continues. The simulations for oxygen and carbon dioxide treatment are shown in figure 5.14. 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2 Simulation Results Aw ake SA02 Sleep Propensity time (sec) F igure 5.1: Sim ulation under normal conditions for approxim ately 60 seconds. The w hole panel consists o f the total ventilatory drive / chem ical drive, state-related drive, tidal volum e, heart rate, arterial blood pressure, pleural pressure, oxygen saturation, carbon dioxide partial pressure, circadian sleep process signals respectively. C Higi, and C Low are upper and lower circadian threshold hold for the sleep process. 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. H ypoxic P erio d £ % £ c (3 Q _ _ 2 m S2 S 5 E ? .S ta rt Release. Awake IM Ii llW ^ T 3 £ O ) •C O = X ° ° « £ **• C L — - £ O 2 3 N 3 J I # $ e (S | M O) o ? o X < £ « £ E £ 5 5 2 120 100 100 200 400 500 300 600 700 -40 100 200 500 300 400 700 600 100 100 200 400 500 300 700 600 High _ 0.5 SA02 PaC02 Sleep Propensity time (sec) F igu re 5.2: Sim ulation o f 600 seconds o f Isocapnic Hypoxia case. H ypoxia is induced by lowering the inspiratory 0 2 partial pressure to 60m m H g. Isocapnia is maintained by increasing 20m m H g o f inspiratory C 0 2 partial pressure. Both added 0 2 and C 0 2 partial pressure changes are fixed during the isocapnic hypoxic sim ulation period. “Start” marks the beginning o f the hypoxic event and “R elease” show s the end o f the event. With the increase in respiratory effort, there is an increase in heart rate and the arterial blood pressure rises due to the chem ical built up. 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. H y p e rc a p n ic H ypoxic P erio d >. 1 0 S T > 5 ■ = C o jn ( 1 ) ■ — it > e £ « e e • 0 3® ■ £ « > £ « T i 2 O ') t O «£SE «m f i 3 <" -i. £ 8 E a . f o < n S i ! ^ O -?o x < £ w « £ E •a < y ai 1 * 1 S ta rt i 100 = X = Re ease 200 “1 — 300 ~1— 400 I 500 I — 600 I — i n H im iH w m m H im u h itm ' h u w ii mhu w n 400 — r ~ 500 z r z 600 m 700 T S le ep P ro p e n s ity 4 tim e (sec) F igure 5.3: Sim ulation o f 600 seconds o f hypercapnic hypoxia case. Hypoxia is induced by lowering the inspiratory 0 2 partial pressure to 60m m H g. Hypercapnia is introduced by increasing 40m m H g o f inspiratory C 0 2 partial pressure. Both added 0 2 and C 0 2 partial pressure changes are fixed during the isocapnic hypoxic simulation period. “Start” marks the beginning o f the hypoxic event and “R elease” show s the end o f the event. With even more respiratory effort than isocapnic case, the heart rate increases more. The arterial blood pressure rises and more fluctuation per breath due to higher respiratory effect. 140 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (a) Mueller Manuever £■ % ! s _. 1 1 1 1 ----------- --------1 ------------------------T*“--------------------1------------------------1 -------------—- i ---------------------- 1....... i........— — r~ ' 1 « ....................... £ 10 20 30 40 50 60 70 60 90 State Drive 10 20 30 40 50 60 70 80 90 . . . ■ M u e l l e r M a n e u v e r *= I 3 A A A A ------------------------ r— A A A A A A A A A . A A / V A A A . 10 20 30 40 60 60 70 80 90 I I I " 1 a. - o.6 c 10 20 30 40 SO 60 70 80 90 I I I ! 5 a s s go c 10 20 30 40 50 60 70 80 90 0 I 5 § -20 3 2 * # " £ L 50 20 30 40 £0 60 70 80 90 O ; 8 f 50 SAOl P aCOZ ________________t________________i_______________ JS.____ __________i________________S ....................____________ ' ......................I,_______________ L______ °0 10 20 30 40 50 SC 70 80 90 t i m e ( s e c ) (b) Breath Hold A. A A A < Breath Hoid ^ A A A A a a a a a t v a .a a a a a tim e ( s e c ) 141 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (c ) 130 IQS * III F igu re 5.4: Experimental vs. Sim ulated data for M ueller and Breath H olding maneuvers, (a) Simulated M ueller maneuver. B ecause o f high negative pleural pressure produced from the inspiration, the arterial blood pressure drops, (b) Breath Holding. N o visible change in heart rate and very sm all increase in arterial blood pressure, (c) Left colum n is the adapted drawings o f experimental data from M organ et al. [185]. Right side is the simulated data from the m odel. Solid line represents the M ueller maneuver and dashed line represents the Breath Hold maneuver. All panels are com posite graphs o f both m aneuvers for comparison. 142 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Valsalva m a n e u v e r: ITV --- ■ ■ " 1 ....... — 1 ....... . strain r e l e a s e R R 1 ! ________________ S B P ......... ......................................................................: I TV (Liter) - / \ / \ ( i i ■ ■ v _ ) 5 1 0 H P (se c ) 15 20 25 30 - ^ _- - ^ ------ ) 5 10 A B P (m m H ^ 20 25 30 f- 1 1 ‘ - — ----------------, ______. ------- - | I ________ — ) 5 10 P p l(cm H 2 d £ 20 25 30 40 - - 2 0 ! R elease - 0 Strain , , i -----------— ------^_ _ i '-------- - ..._ 0 5 10 15 20 2 5 30 tim e (se c ) F igure 5.5: Experimental vs. Sim ulated V alsalva maneuver. At the onset o f the expiratory straining, there is an initial increase in the arterial blood pressure and follow ed by a recovery period during straining. At the end o f the straining, a decrease in the arterial blood pressure can be seen and there is an elevation in the blood pressure after the maneuver. Top figure is the experimental data recording from Dr. V asily B elozeroff and is show n here with his perm ission. Bottom figure is the simulated data using our m odel. 143 Reproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. ai q > j-s 3 5 D 7 5 E S ■ 0 3 ® 0 i ^ F 0.5 0 I 2 1 0 i 90 80 70 ............1 ............ r— .. r” “........1 ! 1 S 1 r --------- r ! 11 i .. i i ....... ....i .,i... .......... Sleep 0 1 2 3 4 5 6 7 8 9 i ‘ f - 0 1 2 3 4 5 6 7 8 9 n 3 | ® ££SS 5 £ D £ £ * * n • — • 120 100 « £ 3 < N = K ^ * 1 § r o i £ Q. £ S5i e 100 SA02 PaC02 Sleep Propensity 0.5 SWA 0 2 1 3 4 5 6 7 8 9 C ■ Sleep Period - time (hour) F igure 5.6: Sim ulation o f the w hole night o f sleep. With sleep onset there is a decrease in heart rate and blood pressure. Normal sleep takes about 8 hours. 1 4 4 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. £ _ o 0) Q ) 5* c o a a - 0 £ o> •c o 5 x «o”E < m £ e * * ■ C l —' :jPS IM »N O) O C o O X < 2^0 £ « £ £ 0 Sleep 1 1 A w ake 100 F SO ; 0 • P aC 02 J __________ P - T * .....I ..........[... ""1 ..................1".... ..."'"I................ T \---- " 1 | 1 I Sleep Propensity rJ f “ --------------------- E - U , . .................................... — OSA Sleep Period - -Normal Sleep Period time (hour) F igure 5.7: Simulation o f the w hole night sleep with O SA during both N REM and REM stages. The interrupted sleep with repetitive arousal lengthens the sleep time. Norm al sleep lasts about 8 hours w hile the sleep period for O SA subject prolongs to about 8 hours and 40 m inutes as shown from the last panel in the graph. This O SA sim ulation is using the sam e N REM /R EM period as for normal sleep. 145 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. - 20 £ □ « 3JI o ? o x <toE « £ E T 3 n j 0 ) ro $ o p a P 5500 T ...... 6500 7000 Sleep 4500 5000 5500 6000 6500 7000 Arousal 1 5 £ 2 X I 3 5 Is • £ fij ^5 ® W « X K « ?*§s 1 2 0 1 0 0 |i 5 m £ £ I 0L i ________________i________________ i ________________i________________i________________i________________ i _____________ tn /W V W W W \A A A /W \A A n /V \A A /V V ^ PaC02 \ t ________ I ________ I ________ I ________ I i — .............. 1 1 ---------------------------L -------------------------- 1 1 V SWA " ' V * Sleep Propensity c L 4500 5000 ------------NREM---------- 6500 7000 REM ---------------- time (sec) Figure 5.8: Sim ulated O SA episodes during N REM and REM stages. This is taken from a segm ent o f the w hole night O SA sim ulation. With greater reduction in hypoxic ventilatory response in REM stage, about 50% compared to NREM stage and with lower arousal threshold value, the ventilatory drive attenuates. H ow ever, the obstructive period in REM sleep is shorter than in N R E M stage. The arousal period is longer than in N REM stage. 146 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 464246024642555555555555 II < / ) < < —1 ______ 4000 3 4500 l l M I i 5000 i l l 1 I i 1 5500 6000 6500 7000 U I l l M A M l A J M i M 4000 4500 5000 5500 6000 6500 7000 ^ -----------------------------------NREM --------------------------------- »» -------------------------------------------------- R E M ------------------------------ ► tim e (sec) F igure 5.9: The sudden surge in blood pressure upon arousal can be caused by high alpha- sympathetic activity. From our simulation, w e can observe the sudden increase in sym pathetic activity at arousal caused by the increase in ventilatory drive both at N REM and REM stages. 147 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. O xygen A pplication <0 03 « - C m Q " 3 i j » tj 3 « 2 1 0 1.2 1.3 0.7 0.8 1 1.1 0.9 Sleep 0.5 A rousal 0.7 1.2 UllllililllUlllhUhiUht 0.7 0.8 0.9 1 1.1 1.2 1-3 « t i £ o •c O = x I 0 8 s ! “ £ & M M M i M J M U J J d J d J d d d d i l w w w v w v w w v v i A n r i y v w i ^ a / v v v I ______ i _______ i ________i ________ i ________i _______i ________i ______ c 0.7 0.8 0.9 1 1.1 1.2 1.3 = t.,j ..............- 1 —------------------1 ------------------------1 — -------------------i ------------------------S ------------------------1 ------------------------! --------------------- - SWA4 c , _ L o w ? time (hour) F igure 5.10: O SA patient is som etim es given oxygen treatment to replenish the oxygen desaturation. In our sim ulation, inspiratory 0 2 partial pressure is increased by 30m m H g more during the oxygen application period. It show s that each obstruction lengthens and with less oxygen desaturation. 148 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. sg 0 Arousal 500 ( J t S i 'O O 3 I ££S£ « e O 2 3 W 3 « X •2 a > £ ^ 120 ■ I 4 4 4 4 - C M Ol i E *1----------- 1 ----------- r — CRAP A pplication............... 8 I _±_ 2500 3000 Sleep 2500 ,------- 1500 2000 4000 -- 3500 4000 3500 4000 SEBEEfinji D 500 1000 1500 2000 2500 3000 3500 4000 "N N SA02'r i 1 I I I PaC02 I y v v u u v v v i 0 500 C H ig h = 1000 1500 2000 2500 3000 3500 4000 - p. Sleep Propensity - 1 , SWA - - B > . . — — s I I I 3 500 1000 1500 2000 2500 time (sec) 3000 3500 4000 \ F igure 5.11: CPAP machine is usually prescribed by the doctor to O SA patient as a treatment. Our m odel can sim ulate the administration o f CPAP and prevent the occurrence o f upper airway obstruction. 10 cm fP O o f positive pressure is applied to the upper airway. 149 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Awake Awake PaC02 S e e p Propensity F igu re 5.12: Severe C ongestive Heart Failure (C H F) can produce apnea in sleep. From our simulation, it show s that with the decrease in blood flow and the increase in transporting tim e to chemoreceptors apnea can be induced in sleep. With the large periodic breathing, arousal takes place. The cardiac output is reduced by 80% and the transport delay is increased to about 4 0 -5 0 seconds from the normal 6 second in the simulation to generate the period breathing in sleep. 150 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. ---------- V .A . A , .A - j V / V 1 0 0 2 0 0 400 500 600 700 ......" H 1 " I " | S le ep I ' ----rp—==i | j A ro u sa l I e = __________ j _______________i .......... ..................i............................ n ______ • - ■ -Jt...... » - .................. 7 5 £ £ ■ o s ® ■ e a * E © IS w I C C r e c a "O ^ D ) •C O = X 5 O * £ 5 C J g £ - ! o g 3 C M = 2 x ® S S a - « ■ o C M C M CJ < S' o E < " 8. E £55 £ 100 200 300 400 500 600 700 800 » • > > A > 100 200 300 400 500 700 800 k — r'A ^ V -— 100 200 300 400 500 600 700 W -.. i 100 200 300 400 500 600 700 800 S e e p P ro p e n sity ~ " T ----- 100 200 300 400 500 600 700 time (sec) F igure 5.13: A segm ent o f the simulated periodic breathing in sleep for CHF patient which show s the crescendo-decrescendo breathing pattern in more detail. 151 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 7 5 - o e« ■ c o j x J»SE t £ ^ f t ■ = “ O 2 3 N 3 8 x z r P = C L C o < s » 2 e = 5 a S « o o SwE D 1 2 3 4 5 6 7 8 S 10 ' ' m ........................................... . ........ i i D 1 2 3 4 5 6 7 8 9 10 - .............................. i i t i i j i i I 1 D 1 2 3 4 5 6 7 8 9 10 ........................... m m n ^ u jg p ,. SA02 = * ------ ^ ^ 1 * 1 i i i l i 1 S 1 PaC02 1 1 ) 1 c u K 2 3 H i g h ......? ,,,y... ;.... — ---- r 4 5 6 7 8 9 10 - m Sleep Propensity D 1 2 3 4 5 6 7 8 9 r 10 L o w time (hour) F igure 5.14: O xygen treatment is som etim es used for CHF patient to lessen the apnea in sleep. We simulate the case for both oxygen and carbon dioxide treatment, (a) Separate oxygen and carbon dioxide treatment during sleep, (b) C 0 2 treatment in sleep with the disappearance o f the apnea and regaining normal sleep. Inspiratory C 0 2 partial pressure is increased by 40m m H g during the application period, (c) O xygen treatment in sleep with attenuation in periodic breathing but still triggering arousals. Inspiratory 0 2 partial pressure is increased by 40m m H g during the application period. 152 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (b) (c) IAAAAAAAAAAAa a a a a a a a a a a a a a a a a a . M ., L - 1 - a 6 0 0 1 0 0 0 1 6 0 0 2 0 0 0 2 6 3 0 3 0 0 0 3 6 0 0 M O O D 4 6 0 0 S O B O K k m m m h ^ A A A M M M M A M M A -------1 -------- 1 -------- ! -------I ” ' ' 1 1 v w w w w v w ......... 1 ......... I 1 ........J L . 0 3 0 0 1 0 0 0 1 3 0 0 2 0 0 0 .........,...... ...... a - "‘ .1 ■ * ' ’ ~ ' B - ....* » 1 " ' " r s ' a T ^ I f \ A A A A A A / V V V V V \ A / W V V i ........ » ...........i ......— « ---------i — — — : — s ----- 2 6 0 0 3 0 0 0 3 6 0 0 4 0 0 0 4 5 0 0 6 0 0 0 --g ---_ ! -------- 1 -------- 1 -------- * -------- » -------- « ----- A S l a e p P r o p a r t s i t y .... 1 ........ * 1 * « 1 2 0 0 0 2 6 0 0 0 0 0 G 3 6 0 0 1 1 I 2 | J 5 e < “ i I IA A A A A A A A A A A a a a a a j ^ 'n a a ^n a i a a a a ^I ’^AAAAAXAAAAJO^a a a a Aa a a a a a a a A jn m " ^ 1 1 1 153 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6. Discussion and Conclusion One way to study cardiorespiratory dynamics is through experiments. But most of the time, this requires invasive procedures. In the case of Obstructive Sleep Apnea, it becomes a difficult task because of the complexity of the processes and their interactions. From the biomedical engineering point of view, an alternative approach for such study is through model simulation. Therefore the aim of this research was to construct a model that simulates cardiorespiratory interactions during wakefulness and sleep. A major goal was to determine whether the model simulation of OSA closely reflect experimental observations. In doing so, we have been able to better understand the cardiorespiratory interactions involved. With this goal in mind, we have carefully selected some of the known cardiovascular and respiratory models and with these components we have successfully implemented a cardiorespiratory model for simulation in Simulink. Since most previous studies were focused on specific regions of interest, by introducing this comprehensive model, we have been able to bridge together two major systems and to explore their interdependencies. Creating a large model always presents the challenge of balancing between the number of components and the computation time. In our model, we have tried to pick out all the essential mechanism so we can minimize the number of components and increase the computation speed but at the same time we can display the general cardiorespiratory changes. 154 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In our model, we have modularized our compartments for future upgradeability and exchangeability. We have divided the model into three major subsystems: the cardiovascular and the respiratory system and the neural control. This approach optimizes the interactions between these systems as well as the independent usage for each subsystem. The known reflexes we incorporated are baroreflex, chemoreflex and the lung stretch receptors reflex. Along with these reflexes, we have also included the central respiratory sinus arrhythmia to the system. The mechanical effect of the pleural pressure to the arterial blood pressure and the influence of the cardiac output to the blood flow have also been addressed. By integrating all of these mechanisms together, we have incorporated detailed cardiorespiratory interactions in our model which most models have lightly touched. With this cardiorespiratory model, we believe our most significant contribution has been to combine it with a sleep mechanism. This expands the scope of the simulation to encompass both wakefulness and sleep. Even though a considerable amount of empirical evidence on sleep has been accumulated, we know of no other comprehensive cardiorespiratory model that has applications in sleep. Some visible changes in sleep are the slowdown in heart rate, the lowering of the arterial blood pressure and the increase in the respiratory load with the decrease in ventilation. Experiments have shown an increase in barosensitivity in sleep. From our model, we find that by increasing the slope of the baroreflex and parasympathetic tone, we obtain a noticeable heart rate change. Some researchers 155 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. postulate that the lowering in the arterial blood pressure is caused by the slowdown of the heart rate which reduces the cardiac output. We notice from our simulation that with just the slow down in the heart rate, the blood pressure drops slightly which is not as visible as in combination with the reduction in the sympathetic tone. Therefore in our model, we have had to reduce the sympathetic tone for the decrease in blood pressure during sleep to attain the levels observed in experimental data. With the decrease in upper airway muscle tone in sleep, the respiratory load increases leading to a decrease in ventilation. In our simulation, we increase the respiratory load by decreasing upper airway conductance in sleep. This increase in respiratory load along with the inhibition of the wakefulness drive leads to the observed reduction in ventilation during sleep. From our simulation, we are able to observe the similar cardiorespiratory changes during each OSA episode compared to experimental recordings. During the apnea phase, we notice a decreasing trend in heart rate and during arousal the heart rate speeds up. The arterial blood pressure starts to increase during apnea and surges during arousal. From our simulation, we observe that during the apnea phase, vagal feedback from the lung stretch receptors is zero. With the dominance of the chemoreflex activity along with the baroreflex, we are able to observe the slowdown of the heart rate. During arousal, with the reappearance of the wakefulness stimulus and the increase in ventilation due to oxygen desaturation and carbon dioxide build-up, tachycardia occurs. This points out the strong influence in heart rate by input from the lung stretch receptors. Along with the sudden increase 156 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. in heart rate, there is a sudden increase in the blood pressure. From our simulation, we believe that the surge in blood pressure is primarily modulated by chemoreflex- mediated alpha-sympathetic activity. Patients with congestive heart failure have been noted to develop sleep apnea. By reducing cardiac output and lengthening the transporting time between the gas exchange sites at the lungs and the chemoreceptors site, we can induce periodic breathing in our model. In our simulation, we notice that apnea only occurs in severe congestive heart failure case. With only a small decrease in the cardiac output, there is some periodic breathing but no apnea. From our simulation, we notice that carbon dioxide treatment seems to be more effective in dampening down the periodic breathing and allowing normal sleep continuity to be preserved for a period of time than oxygen treatment as seen from figure 5.15. So far with the implemented sleep mechanism, we are able to incorporate the overall sleep influence to the cardiovascular and the respiratory system. The sleep module also provides the option of generating the NREM/REM ultradian rhythm. Even though the overall sleep architecture is more defined, REM stage activity is still less clear. From experimental data, it has shown that there is a variation in arousal threshold between NREM and REM stage. There also appears to be a greater reduction in hypoxic ventilatory response in REM stage. We have included these differences in the model. But the potential difference in the metabolic rate, autonomic tone, upper airway resistance and respiratory compliance are still debatable. The relative durations of the NREM and REM stages during 157 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. each sleep cycle are also issues that will have to be addressed to increase the “realism” of our simulation of the sleep mechanism. Another improvement for the sleep mechanism is the arousal response. At the present time, the initiation and the termination of the arousal are determined by a set ventilatory drive threshold. However, the arousal period from our simulation tends to be longer for the upper airway mechanism. The effects from arousal in cardiovascular changes are more abrupt. Therefore more data from studies of the arousal influence will be needed to yield better simulation results. Currently, our cardiovascular subsystem deals with beat-to-beat changes. The intra-beat dynamics has not been studied carefully. But to capture better hemodynamic descriptions, a better circulatory mechanics will be needed. The two element Windkessel model provides a generalized blood pressure response, but it does not yield a very realistic waveform. In cases such as Valsalva maneuver, better representation of the systolic and diastolic pressures can give us better simulation data. There already exists a few pulsatile cardiovascular models with more detailed arterial tree structures. These can be used for future improvement on both stroke volume and circulatory mechanic compartments. With a more dynamic circulatory component, we can also explore the rate dependent and the resetting property of the carotid baroreceptors. The neuromuscular drive profile for the respiratory model gives us reasonably realistic looking airflow and tidal volume waveforms. But we have only focused on modeling inspiratory activity. We can improve the neuromuscular 158 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. profile by incorporating an active component during expiratory activity. In our simulation, we have dealt less with pulmonary dysfunctions. Therefore that will be another area to test the respiratory properties in our model. The gas exchange and transport compartments give us good descriptions of the chemical transfer in our body. But currently, the blood flow regulation to the body tissues and the brain are separately controlled. It will be ideal to have one regulatory mechanism for both regions. One major improvement that will help to simulate the whole OSA process better is to have a more realistic neuromechanical upper airway model. Even though the simple upper airway mechanism in our model is sufficient for producing obstruction for simulation, it does not give us a sense of how the upper airway really obstructs in sleep. With a neuromechanical model and a better arousal mechanism, we can model the start and the termination of the OSA episode more realistically. A neuromechanical upper airway model will also improve our simulation on the respiratory load change in sleep and how it influences the respiratory ventilation. Another improvement that we have been experimented with a little is to have a variable breathing period. In the case of hypoxia or hypercapnia, experimental data have shown a decrease in breathing period. However, in our model, we presently assume a fixed period. This does not fully capture the complete dynamics of respiratory responses. Therefore, we have to be able to change the breathing rate and inspiratory-expiratory ratio to make those cases more 159 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. realistic. Respiratory rhythm generation has been a research topic by itself and there have been a few neural network model proposed. We can test those neural network models on our system and produce more descriptive cardiorespiratory responses. One thing that we are currently unable to do with our simulation model but it will be valuable for future study is the long-term autonomic changes in OSA patients. For now, we can observe the changes in each apnea episode in our model. But for severe OSA case, the patient often develops hypertension which may be the result of long-term alteration in autonomic control. Incorporating long-term effects may help us to gain more insight regarding the chronic effect in OSA. One extension for this research is to expand the sleep simulation study to other cardiorespiratory disorders such as chronic obstructive pulmonary disease (COPD) and asthma to see if there is any correlation between the simulated result with experimental recording and gain more understandings in the cardiorespiratory interactions make more improvements. The other extension can be the modification of this model from a simulator to a predictor or as an assisting procedure to prevent arousal from obstructive sleep apnea patient. From the model, we can generate several noninvasive measurements such as SAO2 , HR, ABP, Tidal Volume, Chest Wall Pressure. So one way can be to input real recording of these signals into the model and compare them with the simulated results and catch the potential of an obstruction and make the necessary preventive steps, shown in figure 6 .1 . 160 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. SA G , HR ABP Tidal Volum e Chest Wall, Patient M onitoring Cardiorespiratory Simulator / Predictor Preventive Steps Rib Cage A ctivity F igu re 6.1: Cardiorespiratory Simulator / Predictor 161 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. References: 1. Thawley, S. E. The Medical Clinics of North America, Symposium on Sleep Apnea Disorders. Philadelphia:W. B. Saunders, 69(6), p.1123- 1152,1985 2. Ballard, R. D. The Sleep Apnea Syndrome: Obstructive and Mixed Apneas. Cardiorespiratory Disorders during Sleep. New York: Futura Publishing. 109-140, 1990. 3. Fairbanks, D. N. F., S. Fujita, T. Ikematsu, and F. B. Simmons. Snoring and Obstructive Sleep Apnea. New York: Raven Press, 1987. 4. Guilleminault C., and M. Partinen. Obstructive Sleep Apnea Syndrome: Clinical Research and Treatment. New York: Raven Press, 1990. 5. Pascualy, R. A., and S. W. Soest. Snoring and Sleep Apnea: personal and family guide to diagnosis and treatment. 2n d ed. New York: Demos Vermande, 1996. 6 . Strohl, K. P. Obstructive Sleep Apnea Syndrome. Sleep Disorders: Diagnosis and Treatment. New Jersey: Humana Press. 117-135, 1998. 7. Noordergraaf, A. Hemodynamics. Biological Engineering. New York:McGraw-Hill. 391-545, 1969. 8 . Arts, T., R. S. Reneman, and P. C. Veenstra. Ann. Biomed. Eng, 7: 299- 318, 1979. 9. Attinger, E. O., and A. Anne. Simulation of the cardiovascular system. Ann.NYAcad, Sci. 128(3):810-829, 1966. 10. Avolio, A. P. Multi-branched model of the human arterial system. Med. Biol. Eng. Comput. 18: 709-718, 1980. 11. Beyar, R., Y. Kishon, S. Sideman, and U. Dinnar. Computer studies of systemic and regional blood flow mechanisms during cardiopulmonary resuscitation. Med. Biol. Eng. Comput. 22:449-506, 1984 12. Boyers, D. G., J. G. Cuthbertson, and J. A. Luetscher. Simulation of the human cardiovascular system: a model with normal responses to change of posture, blood loss, transfustion, and autonomic blockade. Simulation 18: 197-205, 1972. 162 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 13. Braakman, R., P.Sipkeman, and N. Westerhof. A dynamic nonlinear lumped parameter model for skeletal muscle circulation. Ann. Biomed. Eng. 17: 593-616, 1989. 14. Campbell, K., M. Zeglen, T. Kagehiro, and H. Rigas. A pulsatile cardiovascular model for teaching heart-blood vessel interaction. Physiologist 25: 155-162, 1982. 15. Dagan, J. Pulsatile mechanical and mathematical model of the cardiovascular system. Med. Biol. Eng. Comput. 20: 601-607, 1982. 16. DeBoer, R. W., J.M. Karemaker, and J. Strackee. Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am. J. Physiol. 253 (Heart Circ. Physiol. 22): H680-H689, 1987. 17. Grodins, F. S. Integrative cardiovascular physiology: a mathematical synthesis of cardiac and blood vessel hemodynamics. Q. Rev. Biol. 34:93- 116, 1959. 18. Hardy, H. H., and R. E. Collins, and R. E. Calvert. A digital computer model of the human circulatory system. Med. Biol. Eng. Comput. 20: 550- 564, 1982. 19. Jager, G. N., N. Westerhof, and A. Noordergraaaf. Oscillatory flow impedance in electrical analog of arterial system: represenation of sleeve effect and non-Newtonian properties of blood. Circ. Res. 16:121-133, 1965. 20. LaCourse, J. R., G. Mohankrishnan, and K. Sivaprasad. Simulations of arterial pressure pulses using a transmission model. J. Biomech. 19:771- 780, 1986. 21. Mcllroy, M. B., and R. C. Targett. A model of the arterial bed showing ventricular-systemic coupling. Am. J. Physiolog. 25A(Heart Circ. Physiol. 23):H609-H616, 1988. 22. Pickering, W. D., P. N. Nikiforuk, and J. E. Merriman. Analogue computer model of the human cardiovascular control system. Med. Biol. Eng. 7:401-410, 1969. 23. Snyder, M. F., V. C. Rideout, and R. J. Hillestad. Computer modeling of the human systemic arterial tree. J. Biomech. 1:341-353, 1968. 24. Sud, V. K., and G. S. Sekhon. Analysis of blood flow through a model of the human arterial system under periodic body acceleration. J. Biomech. 19: 929-941, 1986. 163 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 25. Wang, J., B. Tie, W. Welkowitz, J. Kostis, and J. Semmlow. Incremental network analogue model of the coronary artery. Med. Biol. Eng. Comput. 27:416-422, 1989. 26. Zagzoule, M., and J.-P. Marc-Vergnes. A global mathematical model of the cerebral circulation in man. J. Biomech. 19:1015-1022, 1986. 27. Bai, J., H. Lu, J. Zhang, and X. Zhou. Simulation Study of the Interaction between Respiration and the Cardiovasculr System. M ethod o f Info in Med. 261-263, 1997. 28. Cavalcanti, S., and E. Bleardinelli. Modeling of Cardiovascular Variability Using a Differential Delay Equation. IEEE Trans. Biomed. Eng. 43:982-989, 1996. 29. Coleman, T. Mathematical Analysis of Cardiovascular Function. IEEE Trans. Biom ed Eng. 32:289-294, 1985. 30. Hammer, P., D. Litvack, and J. P. Saul. Interpreting Open- and Closed- loop Transfer Relations Between Cardiorespiratory Parameters: Lessons Learned from a Computer Model of Beat-to-Beat Cardiovascular Regulation. M ethods o f Information in M edicine. 36(4-5):237-240, 1997. 31. Kitney, R. I., and S. R. Seydnejad. Investigation of HRV by Model Analysis. Frontier o f B lood Pressure and heart Rate Analysis. 67-88, 1997. 32. Madwed, J. B., P. Albrecht, R. G. Mark, and R. J. Cohen. Low-frequency oscillations in arterial pressure and heart rate: a simple computer model. Am. J. Physiolo. 256 (Heart Circ. Physiol. 25): H1573-H1579, 1989. 33. Seydnejad, S. R., and R. I. Kitney. Analysis of HRV and BPV by a Nonlinear Closed Loop Model. M ethodology and Clinical Applications o f B lood Pressure and H eart Rate Analysis. 49-71, 1999. 34. Toska, K„ M. Eriksen, and L. Walloe. Short-term control of cardiovascular function: estimation of control parameters in healthy humans. Am. J. Physiol. 270 (H eart Circ. Physiol. 39): H651-H660, 1996. 35. Ursino, M., M. Antonucci, and E. Belardinelli. Role of active changes in venous capacity by the carotid baroreflex: analysis with a mathematical model. Am. J. Physiol. 267 ( H eart Circ. Physiol. 36): H2531-H2546, 1994. 164 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 36. Ursino, M. Interaction between carotid barorgulation and the pulsating heart: a mathematical model. Am. J. Physiol. 275 {Heart Circ. Physiol. 44) :H1733-H1747, 1998. 37. Vetter, R, P. Celka, J. M. Vesin, G. Thonet, E. Pruvot, M. Fromer, U. Scherrer, and L. Bernardi. Ann. Biomed. Eng. 26:293-307, 1998. 38. Warner, H. R., and A. Cox. A mathematical model of heart rate control by sympathetic and vagus information. J. Appl. Physiol. 17:349-355, 1962. 39. Whittam, A. M., R. H. Clayton, S. W. Lord, J. M. McComb, and A. Murray. Computer Modelling of Heart Rate and Blood Pressure. Comp in Cardio. 25:149-152, 1998. 40. Axen, K., and S. S. Haas. Range of first-breath ventilatory responses to added mechanical loads in naive men. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 46(4): 743-751, 1979. 41. Mount, L. E. The ventilation flow-resistance and compliance of rat lungs. J. Physiol. 127:157-167, 1955. 42. Sharp, J. T., F. N. Johnson, N. B. Goldberg, and P. V. Lith. Hysteresis and stress adaptation in the human respiratory system. J. Appl. Physiol. 23:487-497, 1967. 43. Bates, J. H. T., K. A. Brown, and T. Kochi. Respiratory mechanics in the normal dog determined by expiratory flow interruption. J. Appl. Physiol. 67(6): 2276-2285, 1989. 44. Berger, A. J., R. A. Mitchell, and J. W. Severinghaus. Regulation of Respiration. The N ew England Journal o f M edicine. 297:92-97, 1977. 45. D ’Angelo, E., F. M. Robatto, E. Calderini, M. Tavola, D. Bono, G. Torri, and J. Milic-Emili. Pulmonary and chest wall mechanics in anethetized paralyzed humans. J. Appl. Physiol. 70(6): 2602-2610, 1991. 46. Fredberg, J. J., and D. Stamenovic. On the imperfect elasticity of lung tissue. J. Appl. Physiol. 67(6): 2408-2419, 1989. 47. Guerin. C., M.-L. Coussa, N. T. Eissa, C. Corbeil, M. Chasse, J. Braidy, N. Matar, and J. Milic-Emili. Lung and chest wall mechanics in mechanically ventilated COPD patients. J. Appl. Physiol. 74(4): 1570- 1580,1993. 165 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 48. Hildebrandt. J. Pressure-volume data of cat lung interpreted by a plastoelastic, linear viscoelastic model. J. Appl. Physiol. 28(3): 365-372, 1970. 49. Kaczka, D. W., G. M. Barnas, B. Suki, and K. R. Lutchen. Assessment of Time-Domain Analyses for Estimation of Low-Frequency Respiratory Mechanical Properties and Impedance Spectra. Ann. Biomed. Eng. 23- 135-151, 1995. 50. Otis, A. B., C. B. McKerrow, and R. A. Bartlett. Mechanical Factors in Distributing of Pulmonary Ventilation. J. Appl. Physiol. 8:427-443, 1956. 51. Roussos, C. S., and P. T. Macklem. Respiratory Muscles. The New England Journal o f M edicine. 307(13):787-797, 1982. 52. Schuessler, T. F., S. B. Gottfried, and J. H. T. Bates. A model of the spontaneously breathing patient: applications to intrinsic PEEP and work of breathing. J. Appl. Physiol. 82(5): 1694-1703, 1997. 53. Similowski, T., and J. H. T. Bates. Two-compartment modeling of respiratory system mechanics at low frequencies: gas redistribution or tissue rheology? Eur. Respir. J. 4:353-358, 1991. 54. Suki, B., A.-L. Barabasi, and K. R. Lutchen. Lung tissue viscoelasticity: a mathematical framework and its molecular basis. J. Appl. Physiol. 76(6):2749-2759, 1994. 55. Younes, M., and G. Kivinen. Respiratory mechanics and breathing pattern during and following maximal exercise. J. A p p l Physiol.: Respirat. Environ. Exercise Physiol: 57(6): 1773-1782, 1984. 56. Saul. J. P., R. D. Berger, P. Albrecht, S. P. Stein, M. H. Chen, and R. J. Cohen. Transfer function analysis of the circulation: unique insights into cardiovascular regulation. Am. J. Physiol. 261 {H eart Circ. Physiol. 30): H1231-1245, 1991. 57. Van Den Aardweg, J. G., and J. M. Karemaker. Repetitive apneas induce periodic hypertension in normal subject through hypoxia. J. Appl. Physiol. 72(3): 821-827, 1992. 58. Bonsignore, M. R., O. Marrone, G. Insalaco, and G. Bonsignore. The cardiovascular effects of obstructive sleep apneas: analysis of pathogenic mechanisms. Eur. Respir. J. 7:786-805, 1994. 1 6 6 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 59. Chapman, K. R., E. N. Bruce, B. Gothe, and N. S. Chemiack. Possible mechanisms of periodic breathing during sleep. J. Appl. Physiol. 64(3): 1000-1008, 1988. 60. de Burgy Daly, M., and J. E. Angell-James. Role of carotid-body chemoreceptors and their reflex interactions in bradycardia and cardiac arrest. Lancet. 764-767,1979. 61. Fletcher, E. C., G. Bao, and C. C. Miller III. Effect of recurrent episodic hypocapnic, eucapnic, and hypercapnic hypoxia on systemic blood pressure. J. Appl. Physiol. 78(4): 1516-1521, 1995. 62. Gavriely, N., T. R. Shee, D. W. Cugell, and J. B. Grotberg. Flutter in flow-limited collapsible tubes: a mechanism for generation of wheezes. J. Appl. Physiol. 66(5):2251-2261, 1989. 63. Huang, L., and J. E. Ffowcs Williams. Neuromechanical interaction in human snoring and upper airway obstruction. J. A p p l Physiol. 8 6 (6 ): 1759-1763, 1999. 64. Katragadda. S., A. Xie, D. Puleo, J. B. Skatrud, and B. J. Morgan. Neural mechanism of the pressor response to obstructive and nonobstructive apnea. J. Appl. Physiol. 83(6):2048-2054, 1997. 65. Kato, H., A. S. Menon, and A. S. Slutsky. Mechanisms mediating the heart rate response to hypoxemia. Circulation 77(2):407-414, 1988. 6 6 . Narkiewicz, K., N. Montano, C. Cogliati, P. J. H. van de Borne, M. E. Dyken, and V. K. Somers. Altered Cardiovascular Variability in Obstructive Sleep Apnea. Circulation 98:1071-1077, 1998. 67. Naughton, M. T., and T. D. Bradley. Sleep Apnea in Congestive Heart Failure. Sleep D isorders 19:99-113, 1998. 6 8 . Odens, M. L., and C. H. Fox. Adult Sleep Apnea Syndromes. Am erican Fam ily Physician 52(3):859-866, 1995. 69. Parati, G., M. Di Rienzo, M. R. Bonsignore, G. Insalaco, O. Marrone, P. Castiglioni, G. Bonsignore, and G. Mancia. Autonomic cardiac regulation in obstructive sleep apnea syndrome: evidence from spontaneous baroreflex analysis during sleep. J. Hypertension 15(12): 1621-1626, 1997. 70. Pdszus, T., J. Mayer, T. Penzel, J. H. Peter, and P. von Wichert. Nocturnal Hemodynamics in Patients with Sleep Apnea. Eur J. Respir. Dis. 69:435-442, 1986. 167 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71. Roberts, D. Invited Editorial on “ Neuromechanical interaction in human snoring and upper airway obstruction”. J. Appl. Physiol. 8 6 (6 ): 1757- 1758, 1999. 72. Sato, F., M. Nishimura, H. Shinano, H. Saito, K. Miyamoto, and Y. Kawakami. Heart Rate During Obstructive Sleep Apnea Depends on Individual Hypoxic Chemosensitivity of the Carotid Body. Circulation 96(1):274-281, 1997. 73. Smith, C. S., K. S. Henderson, L. Xi, C.-M. Chow. P. R. Eastwood, and J. A. Dempsey. Neural-mechanical coupling of breathing in REM sleep. J. Appl. Physiol. 83(6): 1923-1932, 1997. 74. Somers, V., and F. M. Abboud. Chemoreflexes-Responses, Interactions and Implications for Sleep Apnea. Sleep 16:S30-S34, 1993. 75. Somers, V., A. L. Mark, D. C. Zavala, and F. M. Abboud. Influence of ventilation and hypocapnia on sympathetic nerve responses to hypoxia in normal humans. J. Appl. Physiol. 67(5): 2095-2100, 1989. 76. Stoohs, R., and C. Guilleminault. Cardiovascular changes associated with obstructive sleep apnea syndrome. J. Appl. Physiol. 72(2):583-589, 1992. 77. Wilson, C. R., S. Manchanda, D. Crabtree, J. B. Skatrud, and J. A. Dempsey. An induced blood pressure rise does not alter upper aireay resistance in sleeping humans. J. Appl. Physiol. 84(1): 269-276, 1998, 78. Zwillich, C., T. Devlin, D. White, N. Douglas, J. Weil, and R. Martin. Bardycardia during Sleep Apnea-Characteristics and Mechanism. J. Clin. Invest. 69:1286-1292, 1982. 79. Zwillich, C. W. Obstructive Sleep Anpoea Causes Transient and Sustained Systemic Hypertension. IJCP, 53(4):301 -305, 1999. 80. Donald, D. E., and A. J. Edis. Comparison of Arotic and Carotid Baroreflexes in the Dog. J. Physiol. 215:521-538, 1971. 81. Katona, P. G., J. W. Poitras, G. O. Barnett, and B. S. Terry. Cardiac vagal efferent activity and heart period in the carotid sinus reflex. Am. J. Physiol. 218(4): 1030-1037, 1970. 82. Potts, J. T., T. Hatanaka, and A. A. Shoukas. Effect of arterial compliance on carotid sinus baroreceptor reflex control of the circulation. Am. J. Physol. 270 {H eart Circ. Physiol. 39): H988-H1000, 1996. 168 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83. Shoukas, A. A., and M. C. Brunner. Epinephrine and the Carotid Sinus Baroreceptor Reflex. Circ. Res. 47(2):249-257, 1980. 84. Chapleau, M. W., and F. M. Abboud. Contrasting Effects of Static and Pulsatile Pressure on Carotid Baroreceptor Activity in Dogs. Cir. Res. 61(5):648-658, 1987. 85. Eckberg, D. L. Nonlinearities of the Human Carotid Baroreceptor- Cardiac Reflex. Cir. Res. 47(2): 208-216, 1980. 8 6 . Franz, G. N. Nonlinear Rate Sensitivity of The Carotid Sinus Reflex as a Consequence of Static and Dynamic Nonlinearities in Baroreceptor Behavior. Ann. N. V Acad. Sci. 156(2):811-824, 1969. 87. Kent, B. B., J. W. Drane, B. Blumenstein, and J. W. Manning. A Mathematical Model to Assess Changes in the Baroreceptor Reflex. Cardiology 57:295-310, 1972. 8 8 . Kubota, T., H. Chishaki, T. Yoshida, K. Sunagawa, A. Takeshita, and Y. Nose. How to encode arterial pressure into carotid sinus nerve to invoke natural baroreflex. Am. J. Physiol. 263 (H eart Circ. Physiol. 32): H307- H313, 1992. 89. Melcher, A. Carotid baroreflex heart rate control during the active and the assited breathing cycle in man. Acta. Physiol. Scand. 108:165-171, 1980. 90. Parati, G., A. Frattola, S. Omboni, G. Mancia, and M. Di Rienzo. Analysis of heart rate and blood pressure variability in the assessment of autonomic regulation in arterial hypertension. Clinical Science. 91 Suppl: 129-132, 1996. 91. Piepoli, M., P. Sleight, S. Leuzzi, F. Valle, G. Spadacini, C. Passino, J. Johnston, and L. Bemadi. Origin of Respiratory Sinus Arrhythmia in Conscious Humans - An Important Role for Arterial Carotid Baroreceptors. Ciculation 95(7): 1813-1821, 1997. 92. Sleight, P. The importance of the autonomic nervous system in health and disease. Aust. N ZJ. M ed. 27:467-473, 1997. 93. Taher, M. F., A. B. P. Cecchini, M. A. Allen, S. R. Gobran, R. C. Gorman, B. L. Guthrie, K. A. Lingenfelter, S. Y. Rabbany, P. M. Rolchigo, J. Melbin, and A. Noordergraaf. Braoreceptor responses derived from a fundamental concept. Ann. Biomed. Eng. 16:429-443, 1988. 169 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94. Thompson, C. A., D. L. Tatro, D. A. Ludwig, and V. A. Convertino. Baroreflex responses to acute changes in blood volume in humans. Am. J. Physiol. 259 (Regulatory Integrative Comp. Physiol. 28): R792-R798, 1990. 95. Van De Borne, P., P. Biston, M. Paiva, H. Nguyen, P. Linkowski, and J-P. Degaute. Cardiorespiratory transfer during sleep: a study in healthy young men. Am. J. Physiol. 269:H952-H958, 1995. 96. Burgess, H. J., J. Trinder, Y. Kim, and D. Luke. Sleep and circadian influences on cardiac autonomic nervous system activity. Am. J. Physiol. 273:H1761-H1768, 1997. 97. Parati, G., M. Di Rienzo, M. R. Bonsignore, G. Insalaco, O. Marrone, P. Castiglioni, G. Bonsignore, and G. Mancia. Autonomic cardiac regulation in obstructive sleep apnea syndrome: evidence from spontaneous baroreflex analysis during sleep. J. Hyper. 15:1621-1626, 1997. 98. Parati, G., M. Di Rienzo, G. Bertinieri, G. Pomidossi, R. Casadei, A. Groppelli, A. Pedotti, A. Zanchetti, and G. Mancia. Evaluation of the Baroreceptor-Heart Rate Reflex by 24-Hour Intra-arterial Blood Pressure Monitoring in Humans. Hypertension. 12(2):214-222, 1988. 99. Pickering, G. W., P. Sleight, and H. S. Smyth. The reflex regulation of arterial pressure during sleep in man. J. Physiol. 191:46p-48p, 1967. 100. Vaile, J. C., T. J. Stallard, M. Al-Ani, P. J. Jordan, J. N. Townend, and W. A. Littler. Sleep and blood pressure: spontaneous baroreflex sensitivity in dippers and non-dippers. J. Hyper. 14:1427-1432, 1996. 101. Berger, R. D., J. P. Saul, and R. J. Cohen. Transfer function analysis of autonomic regulation I. Canine atrial rate response. Am. J. Physiol. 256 (H eart Circ. Physiol. 25): H142-H152, 1989. 102. Brown, J. H., Parasympathetic neuroeffector mechanism in the heart - Introductory remarks. Fed. Proc. 43(11):2597, 1984. 103. Berntson, G. G., J. T. Bigger. Jr., D. L. Eckberg, P. Grossman, P. G. Kaufmann, M. Malik, H. N. Nagaraja, S. W. Porges, J. P. Saul, P. H. Stone, and M. W. Van Der Molen. Heart rate variability: Origins, methods, and interpretive caveats. Psychophysiology. 34:623-648, 1997. 104. Floras, J. S. Clinical Aspects of Sympathetic Activation and Parasympathetic Withdrawal in Heart Failure. JACC. 22(4):72A-84A, 1993. 170 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105. Levy, M. N. Cardiac sympathetic-parasympathetic interactions. Fed. Proc. 43(1l):2598-2602, 1984. 106. Malliani, A., M. Pagani, F. Lombardi, and S. Cerutti. Cardiovascular Neural Regulation Explored in the Frequency Domain. Circulation. 84(2):482-492, 1991. 107. Malliani, A. The Pattern of Sympathovagal Balance Explored in the Frequency Domain. News Physiol. Sci. 14:111-117, 1999. 108. Moser, M., M. Lehofer, A. Sedminek, M. Lux, H.-G. Zapotoczky, T. Kenner, and A. Noordergraaf. Fleart Rate Variability as a Prognostic Tool in Cardiology - A Contribution to the Problem From a Theoretical Point of View. Circulation. 90(2): 1078-1082, 1994. 109. Quan, K. J., M. D. Carlson, and M. D. Thames. Mechanisms of Heart Rate and Arterial Blood Pressure Control: Implications for the Pathophysiology of Neurocardiogenic Syncope. Pace. 20:764-774, 1997. 110. Saul, J. P., R. D. Berger, M. H. Chen, and R. J. Cohen. Transfer function analysis of autonomic regulation II. Respiratory sinus arrhythmia. Am. J. Physiol. 256 (H eart Circ. Physiol. 25): H152-H161, 1989. 111. Magosso, E., and M. Ursino. A mathematical model of CO2 effect on cardiovascular regulation. Am. J. Physiol. Heart Circ. Physiol. 281:H2036-H2052, 2001. 112. Kitney, R. I., and S. R. Seydnejad. Investigation of HRV by Model Analysis. Frontiers of Blood Pressure and Heart Rate Analysis, chapter 9, Eds M. Di Rienzo et al., IOS Press, 1997. 113. TenVoorde, B. J., Th. J. C. Faes, T. W. J. Janssen, G. J. Scheffer, and O. Rompelman. Respiratory Modulation of Blood Pressure and Heart Rate Studied with a Computer Model of Baroreflex Control. Comuter Analysis of Cardiovascular Signals, chapter 9, Eds M. Di Rienzo, IOS Press, 1995. 114. Baseili, G., S. Cerutti, F. badilini, L. Biancardi, A. Porta, M. Pagani, F. Lombardi, O. Rimoldi, R. Furian, and A. Malliani. Model for the assessment of heart period and arterial pressure variability interactions and of respiration influences. Med. & Biol. Eng. & Comput. 32:143-152, 1994. 115. Beyar, R., and Y. Goldstein. Model studies of the effects of the thoracic pressure on the circulation. Ann. Biomed. Eng. 15:373-383, 1987. 171 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116. Beyar, R., S. Sideman, and U. Dinnar. Cardiac assist by intrathoracic and abdominal pressure variations: a mathematical study. Med. & Biol. Eng. & Comput. 22:507-515, 1984. 117. Goldstein, Y., R. Beyar, and S. Sideman. Influence of pleural pressure variations on cardiovascular system dynamics: a model study. Med. & Biol. Eng. & Comput. 26:251-259, 1988. 118. Olsen, C. O., G. S. Tyson, G. W. Maier, J. W. Davis, and J. S. Rankin. Diminished stroke volume during inspiration: a reverse thoracic pump. Circulation 72(3):668-679, 1985. 119. Peters, J., C. Fraser, R. S. Stuart, W. Baumgartner, and J. L. Robotham. Negative intrathoracic pressure decreases independently left ventricular filling and emptying. Am. J. Physiol. 257 (Heart Circ. Physiol. 26): H120-131, 1989. 120. Robotham, J. L., D. Cherry, W. Mitzner, J. L. Rabson, W. Lixfeld, and B. Bromberger-Bamea. A re-evaluation of the hemodynamic consequences of intermittent positive pressure ventilation. C ritical Care M edicine. 11(10):783-793, 1983. 121. Peters, J., M. K. Kindred, and J. L. Robotham. Transient analysis of cardiopulmonary interactions I. Diastolic events. J. Appl. Physiol. 64(4): 1506-1517, 1988. 122. Peters, J., M. K. Kindred, and J. L. Robotham. Transient analysis of cardiopulmonary interactions II. Systolic events. J. Appl. Physiol. 64(4): 1518-1526, 1988. 123. Robotham, J. L., J. Rabson, S. Permutt, and B. Aromberger-Bamea. Left ventricular hemodynamics during respiration. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 47(6): 1295-1303, 1979. 124. Robotham, J. L., W. Lixfeld, L. Holland, D. MacGregor, A. C. Bryan, and J. Rabson. Effects of respiration on cardiac performance. J. Appl. P hysiol.: Respirat. Environ. Exercise Physiol. 44(5): 703-709, 1978. 125. Shabetai, R., N. O. Fowler, and M. Gueron. The effects of respiration on aortic pressure and flow. Am. Heart. J. 65(4):525-533, 1963. 126. Summer, W. R., S. Permutt, K. Sagawa, A. A. Shoukas, and B. Bromberger-Barnea. Effects of Spontaneous Respiration on Canine Left Ventricular Function. Circ. Res. 45: 719-728, 1979. 172 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127. Grodins, F. S., J. Buell, and A. J. Bart. Mathematical analysis and digital simulation of the respiratory control system. J. Appl. Physiol. 22(2): 260- 276, 1967. 128. White, D. P., J. V. Weil, and c. W. Zwillich. Metabolic rate and breathing during sleep. J. Appl. Physiol. 59(2):384-391, 1985. 129. Lange, R. L., J. D. Horgan, J. T. Botticelli, T. Tsagrais, R. P. Carlisle, and H. Kuida. Pulmonary to arterial circulatory transfer function: importance in respiratory control. J. Appl. Physiol. 21(4): 1281-1291, 1966. 130. Spencer, J. L., E. Firouztale, and R. B. Mellins. Computational expressions for blood oxygen and carbon dioxide concnetraions. Ann. of Biomed. Eng. 7:59-55, 1979. 131. Lambertsen, C. J. Chemical control of respiration at rest. Medical Physiology. St. Louis: C.V. Mosby Co. 1774-1827, 1980. 132. Read, D. J. C., and J. Leigh. Blood-brain tissue PCO2 relationships and ventilation during rebreathing. J. Appl. Physiol. 23:53-70, 1967. 133. Thoresen, M., and L. Walloe. Changes in cerebral blood flow in humans during hyperventilation and CO2 breathing (Abstract). J. Physiol. Lond. 298: 53P, 1980. 134. Lambertsen, C. J. Medical Physiology. St. Louis: C. V. Mosby Co. 1749- 1773, 1980. 135. Berthon-Jones, M, and C. E. Sullivan. Ventilatory and Arousal Responses to Hypoxia in Sleeping Humans. Am. Rev. Respir. Dis. 125:632-639, 1982. 136. Corfield, D. R., C. A. Roberts, M. J. D. Griffiths, and L. Adams. Sleep- related changes in the human “neuromuscular” ventilatory response to hypoxia. Res. Physio. 117:109-120, 1999. 137. Douglas, N. J., D. P. White, J. V. Weil, C. K. Pickett, R. J. Martin, D. W. Hudgel, and C. W. Zwillich. Hypoxic Ventilatory Response Decreases During Sleep in Norman Men. Am. Rev. Respir. Dis. 125:286-289, 1982. 138. Gleeson, K., C. W. Zwillich, and D. P. White. Chemosensitivity and the ventilatory response to airflow obstruction during sleep. J. Appl. Physiol. 67(4): 1630-1637, 1989. 173 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139. Modarreszadeh, M., E. N. Bruce, H. Hamilton, and D. W. Hudgel. Ventilatory stability to CO2 disturbances in wakefulness and quiet sleep. 1. Appl. Physiol. 79(4): 1071 -1081, 1995. 140. Parisi, R. A., N. H. Edelman, and T. V. Santiago. Central Respiratory Carbon Dixoide Chemosensitivity Does Not Decrease during Sleep. Am. Rev. Respir. Dis. 145:832-836, 1992. 141. Shea, S. A. Life withouth ventilatory chemosensitivity. Resp. Physiol. 110:199-210, 1997. 142. Khoo, M. C. K. A model-based evaluation of the single-breath CO2 ventilatory response test. J. A p p l Physiol. 68(l):393-399, 1990. 143. Khoo, M. C. K., A. Gottschalk, and A. I. Pack. Sleep-induced periodic breathing and apnea: a theoretical study. J. Appl. Physiol. 70(5): 2014- 2024, 1991. 144. Dunai, J. M. Wilkinson, and J. Trinder. Interaction of chemical and state effects on ventilation during sleep onset. J. Appl. Physiol. 81(5):2235- 2243, 1996. 145. Eldridge, F. L. Relationship between respiratory nerve and muscle activity and muscle force output. J. Appl. Physiol. 39(4):567-574, 1975. 146. Milic-Emili, J., and W. A. Zin. Relationship between neuromuscular respiratory drive and ventilatory output. Handbook of Physiology. Washington D.C.: American Physiology Society. 3(l):631-646, 1987. 147. Read, D. J. C., S. Freedman, and E. R. Kafer. Pressure developed by loaded inspiratory muscles in conscious and anesthetized man. J. Appl. Physiol. 37(2):2G7-218, 1974. 148. Gallagher, C. G., and M. Younes. Effect of pressure assist on ventilation and respiratory mechanics in heavy exercise. J. Appl. Physiol. 66(4): 1824-1837, 1989. 149. Kaczka, D. W., E. P. Ingenito, and K. R. Lutchen. Technique to Determine Inspiratory Impedance during Mechanical Ventilation: Implications for Flow Limited Patients. Ann. Biomed. Eng. 27:340-355, 1999. 150. Mead, J., and E. Agostoni. Dynamics of breathing. Handbook of Physiology. Washington D. C.:American Physiology Society. 3(1):411- 426, 1964. 174 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 151. Riddle, W., and M. Younes. A model for the relation between respiratory neural and mechanical outputs. II. Methods. J. Appl. Physiol.: Respirat Environ. Exercise Physiol. 51(4):979-989, 1981. 152. Rossi. A., S. B. Gottfried, L. Zocchi, B. D. Higgs, S. Lennox, P. M. A. Calverley, P. Begin, A. Grassino, and J. Milic-Emili. Measurement of Static Compliance of the Total Respiratory System in Patients with Acute Respiratory Failure during Mechanical Ventilation. Am. Rev. Respir. Dis. 131:62-677, 1985. 153. Pengelly, L. D., A. M. Alderson, and J. Milic-Emili. Mechanics of the disphragm. J. Appl. Physiol. 30(6): 797-805, 1971. 154. Younes, M., and W. Riddle. A model for the relation between respiratory neural and mechanical outputs. I. Theory. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 51(4):963-978, 1981. 155. Younes, M., W. Riddle, and J. Polacheck. A model for the relation between respiratory neural and mechanical outputs. III. Validation. J. Appl. Physiol.:R espirat Environ. Exercise Physiol. 51 (4):990-1001, 1981 156. Van Den Aardweg, J. G., R. P. Van Steenwijk, and J. M. Karemaker. A chemoreflex model of relation between blood pressure and heart rate in sleep apnea syndrome. Am. J. Physiol. 268 (H eart Circ. Physiol. 37): H2145-H2156, 1995. 157. Bruce, E. N. Chemoreflex and vagal afferent mechanisms enhance breath to breath variability of breathing. Res. Physiol. 110:237-244,1997. 158. St. Croix, C. M., D. A. Cunningham, and D. H. Paterson. Nature of the interaction between central and peripheral chemoreceptor drives in human subjects. Can. J. Physiol. Pharm acol. 74:640-646, 1996. 159. Hayward, L. F., A. K. Johnson, and R. B. Felder. Arterial chemoreflex in conscious normotensive and hypertensive adult rats. Am. J. Physiol. 276 (Heart Circ. Physiol. 45): H 1215-H1222, 1999. 160. Henry, R. A. I.-L. Lu, L. A. beightol, and D. L. Eckberg. Interactions between CO2 chemoreflexes and arterial baroreflexes. Am. J. Physiol. 274 (H eart Circ. Physiol. 43): H2177-H2187, 1998. 161. Narkiewicz, K., Ph. J. H. van de Borne, N. Montano, M. E. Dyken, B. G. Phillips, and V. K. Somers. Contribution of Tonic Chemoreflex Activation to Sympathetic Activity and Blood Pressure in Patients with Obstructive Sleep Apnea. Circulation. 97:943-945, 1998. 175 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 162. Narkiewicz, K., P. J. H. van de Bome, C. A. Pesek, M. E. Dyken, N. Montano, and V. K. Somers. Selective Potentiation of Peripheral Chemoreflex Sensitivity in Obstructive Sleep Apnea. Circulation. 99:1183-1189, 1999. 163. Ren, X., and P. A. Robbins. Ventilatory responses to hypercapnia and hypoxia after 6 h passive hyperventilation in humans. J. Physiol. 514(3):885-894, 1999. 164. Somers, V., and F. M. Abboud. 3. Cardiovascular Aspects of Sleep Apnea - (a) Hypertension and Sleep Apnea - Chemoreflexes-Responses, Interactions and Implications for Sleep Apnea. Sleep. 16:S30-S34, 1993. 165. Somers, V. K., A. L. Mark, D. C. Zavala, and F. M. Abboud. Contrasting effects of hypoxia and hypercapnia on ventilation and sympathetic activity in humans. J. Appl. Physiol. 67(5): 2101-2106, 1989. 166. Somers, V. K., A. L. Mark, and F. M. Abboud. Interaction of Baroreceptor and Chemoreceptor Reflex Control of Sympathetic Nerve Activity in Normal Humans. J. Clin. Invest. 87:1953-1957, 1991. 167. Bernadi, L., F. Keller, M. Sanders, P. S. Reddy, B. Griffith, F. Meno, and M. R. Pinsky. Respiratory sinus arrhythmia in the denervated human heart. J. Appl. Physiol. 67(4): 1447-1455, 1989. 168. Taha, B. H., P. M. Simon, J. A. Dempsey, J. B. Skatrud, and C. Iber. Respiratory sinus arrhythmia in humans: an obligatory role for vagal feedback from the lungs. J. Appl. Physiol. 78(2): 638-645, 1995. 169. Widdicombe, J. G. Respiratory reflexes. Handbood of Physiology. Washington D. C.: American Physiological Society. 3(1 ):585-630, 1964. 170. St. Croix, C. M., M. Satoh, B. J. Morgan, J. B. Skatrud, and J. A. Dempsey. Role of Respiratory Motor Output in Within-Breath Modulation of Muscle Sympathetic Nerve Activity in Humans, (in printing) 171. Eckberg. D., C. Nerhed, and B. G. Wallin. Respiratory Modulation of Muscle Sympathetic and Vagal Cardiac Outflow in Man. J. Physiol. 365:181-196, 1985. 172. Leevers, A. M., P. M. Simon, L. Xi, and J. A. Dempsey. Apnoea following normocapnic mechanical ventilation in awake mammals: a demonstration of control system inertia. J. Physiol. 472:749-768, 1993. 176 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 173. Seals, D. R., O. Suwamo, M. J. Joyner, C. Iber, J. G. Copeland, and J. A. Dempsey. Respiratory Modulation of Muscle Sympathetic Nerve Activity in Intact and Lung Denervated Humans. Cir. Res. 72:440-454, 1993. 174. Simon, P. M., J. A. Dempsey, D. M. Landry, and J. B. Skatrud. Effect of Sleep on Respiratory Muscle Activity during Mechanical Ventilation. Am. Rev. Respir. Dis. 147:32-37,1993. 175. Beme, R. M., and M. N. Levy. Physiology. St. Louis: C. V. Mosby Co, 1983. 176. Schmidt, R. F., and G. Thews. Human Physiology. Berlin: Springer- Verlag, 1983. 177. Orem. J., and C. D. Barnes. Physiology in Sleep. New York: Academic Press, 1980. 178. Achermann, P., and A. A. Borbely. Simulation of Human Sleep: Ultradian Dynamics of Electroencephalographic Slow-Wave Activity. J. of Biol. Rhym. 5(2): 141 -157, 1990. 179. Borbely, A. A. A two process model of sleep regulation. Human neurobiol 1:195-204, 1982. 180. Borbely, A. A., and P. Achermann. Sleep Homeostasis and Models of Sleep Regulation. Principles and Practice of Sleep Medicine, chapter 9, 3rd edition. Eds. M.H. Kogger, et al. Philadelphia, 2000. 181. Berry, R. B., and K. Gleeson. Respiratory Arousal From Sleep: Mechanisms and Significance. Sleep 20(8):654-675, 1997. 182. Berry, R. B., M. A. Asyali, M. I. Mcnellis, and M. C. K. Khoo. Within- night variation in respiratory effort preceding apnea termination and EEG delta power in sleep apnea. J. Appl. Physiol. 85(4): 1434-1441, 1998. 183. Khoo, M. C. K., S. S. W. Koh, J. J. W. Shin, P. R. Westbrook, and R. B. Berry. Ventilatory dynamics during transient arousal from NREM sleep: implications for respiratory control stability. J. Appl. Physiol. 80(5): 1475-1484, 1996. 184. Khoo, M. C. K., J. J. W. Shin, M. H. Asyali, T-S Kim, and R. B. Berry. Ventilatory dynamics of transient arousal in patients with obstructive sleep apnea. Resp. Physiol. 112:291-303, 1998. 177 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 185. Morgan, B. J., T. Denahan, and T. J. Ebert. Neurocirculatory consequences of negative intrathroacic pressure vs. asphyxia during voluntary apnea. J. Appl. Physiol. 74(6):2969-2975, 1993. 186. Eckberg, D. L, and P. Sleight. Valsalva’s Manoeuvre. Human Baroreflexes in Health and Disease. Oxford: Calrdendon Press. 61-76, 1992 187. Weiss, J. W., S. H. Launois, and A. Anand. The Acute Hemodynamic Response to Upper Airway Obstruction During Sleep. Sleep Apnea- Implications in Cardiovascular and Cerebrovascular Disease, chapter 9. Eds. T. D. Bradley et al. New York, 2000. 188. Guilleminault, C., and A. Robinson. Central Apnea. Otolaryngologic Clinics o f North Am erica, 31 (6): 1049-1065, 1998. 189. Guilleminault, C., and M. A. Quera-Salva, G. Nino-Murcia, and M. Partinen. Central Sleep Apnea and Partial Obstruction of the Upper Airway. Ann. Neurol. 21:465-469, 1987. 190. Khoo, M. C. K., R. E. Kronauer, K. P. Strohl, and A. S. Slutsky. Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 53(3):644-659, 1982. 191. Naughton, M. T. Pathophysiology and treatment of Cheyne-Stokes respiration. Thorax 53:514-518, 1998. 192. Javaheri, S. Heart Failure and Sleep Disordered Breathing: Central Sleep Apnea-Hypopnea Syndrome in Heart Failure: Prevalence, Impact, and Treatment. Sleep 19(10):S229-S231, 1996. 193. Staniforth, A. D., W. J. M. Kinnear, R. Starling, D. J. Hetmanski, and A. J. Cowley. Effect of oxygen on sleep quality, cognitive function and sympathetic activity in patients with chronic heart failure and Cheyne- Stokes respiration. European H eart Journal 19:922-928, 1998. 194. Tobin, M. J., and J. V. Snyder. Cheyne-Stokes respiration revisited: Controversies and implications. Cri. Care Med. 12(10):882-887, 1984. 195. Wilcox, I., S. G. McNamara, T. Wessendorf, G. N. Willson, A. J. Piper, and C. E. Sullivan. Prognosis and sleep disordered breathing in heart failure. Thorax 53 Suppl(3): S25-S28, 1998. 178 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bibilography: Achermann, P., and A. A. Borbely. Simulation of Human Sleep: Ultradian Dynamics of Electroencephalographic Slow-Wave Activity. J. of Biol. Rhym. 5(2): 141-157, 1990. Arts, T., R. S. Reneman, and P. C. Veenstra. Ann. Biomed. Eng, 7: 299-318, 1979. Attinger, E. O., and A. Anne. Simulation of the cardiovascular system. Ann.NY Acad. Sci. 128(3):810-829, 1966. Avolio, A. P. Multi-branched model of the human arterial system. Med. Biol. Eng. Comput. 18: 709-718, 1980. Axen, K., and S. S. Haas. Range of first-breath ventilatory responses to added mechanical loads in naive men. J. Appl. Physiol.: Respirat: Environ. Exercise Physiol. 46(4): 743-751, 1979. Bai, J., H. Lu, J. Zhang, and X. Zhou. Simulation Study of the Interaction between Respiration and the Cardiovasculr System. M ethod o f Info in M ed. 261-263, 1997. Ballard, R. D. The Sleep Apnea Syndrome: Obstructive and Mixed Apneas. Cardiorespiratory Disorders during Sleep. New York: Futura Publishing. 109-140, 1990. Baseili, G., S. Cerutti, F. badilini, L. Biancardi, A. Porta, M. Pagani, F. Lombardi, O. Rimoldi, R. Furian, and A. Malliani. Model for the assessment of heart period and arterial pressure variability interactions and of respiration influences. Med. & Biol. Eng. & Comput. 32:143-152, 1994. Bates, J. H. T., K. A. Brown, and T. Kochi. Respiratory mechanics in the normal dog determined by expiratory flow interruption. J. Appl. Physiol. 67(6): 2276- 2285, 1989. Berger, A. J., R. A. Mitchell, and J. W. Severinghaus. Regulation of Respiration. The New England Journal o f M edicine. 297:92-97, 1977. Berger, R. D., J. P. Saul, and R. J. Cohen. Transfer function analysis of autonomic regulation I. Canine atrial rate response. Am. J. Physiol. 256 (H eart Circ. Physiol. 25):H142-H152, 1989. Bemadi, L., F. Keller, M. Sanders, P. S. Reddy, B. Griffith, F. Meno, and M. R. Pinsky. Respiratory sinus arrhythmia in the denervated human heart. J. Appl. Physiol. 67(4): 1447-1455, 1989. 179 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Berne, R. M., and M. N. Levy. Physiology. St. Louis: C. V. Mosby Co, 1983. Bemtson, G. G., J. T. Bigger. Jr., D. L. Eckberg, P. Grossman, P. G. Kaufmann, M. Malik, H. N. Nagaraja, S. W, Porges, J. P. Saul, P. H. Stone, and M. W. Van Der Molen. Heart rate variability: Origins, methods, and interpretive caveats. Psychophysiology. 34:623-648, 1997. Berry, R. B., and K. Gleeson. Respiratory Arousal From Sleep: Mechanisms and Significance. Sleep 20(8):654-675, 1997. Berry, R. B., M. A. Asyali, M. I. Mcnellis, and M. C. K. Khoo. Within-night variation in respiratory effort preceding apnea termination and EEG delta power in sleep apnea. J. Appl. Physiol. 85(4): 1434-1441, 1998. Berthon-Jones, M, and C. E. Sullivan. Ventilatory and Arousal Responses to Hypoxia in Sleeping Humans. Am. Rev. Respir. Dis. 125:632-639, 1982. Beyar, R., and Y. Goldstein. Model studies of the effects of the thoracic pressure on the circulation. Ann. Biomed. Eng. 15:373-383, 1987. Beyar, R., S. Sideman, and U. Dinnar. Cardiac assist by intrathoracic and abdominal pressure variations: a mathematical study. Med. & Biol. Eng. & Comput. 22:507-515, 1984. Beyar, R., Y. Kishon, S. Sideman, and U. Dinnar. Computer studies of systemic and regional blood flow mechanisms during cardiopulmonary resuscitation. Med. Biol. Eng. Comput. 22:449-506, 1984 Bonsignore, M. R., O. Marrone, G. Insalaco, and G. Bonsignore. The cardiovascular effects of obstructive sleep apneas: analysis of pathogenic mechanisms. Eur. Respir. J. 7:786-805, 1994. Borbely, A. A. A two process model of sleep regulation. Human neurobiol 1:195- 204, 1982. Borbely, A. A., and P. Achermann. Sleep Homeostasis and Models of Sleep Regulation. Principles and Practice of Sleep Medicine, chapter 9, 3rd edition. Eds. M.H. Kogger, et al. Philadelphia, 2000. Boyers, D. G., J. G. Cuthbertson, and J. A. Luetscher. Simulation of the human cardiovascular system: a model with normal responses to change of posture, blood loss, transfustion, and autonomic blockade. Simulation 18: 197-205, 1972. Braakman, R., P.Sipkeman, and N. Westerhof. A dynamic nonlinear lumped parameter model for skeletal muscle circulation. Ann. Biomed. Eng. 17: 593-616, 1989. 180 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Brown, J. H., Parasympathetic neuroeffector mechanism in the heart - Introductory remarks. Fed. Proc. 43(11):2597, 1984. Bruce, E. N. Chemoreflex and vagal afferent mechanisms enhance breath to breath variability of breathing. Res. Physiol. 110:237-244,1997. Burgess, H. J., J. Trinder, Y. Kim, and D. Luke. Sleep and circadian influences on cardiac autonomic nervous system activity. Am. J. Physiol. 273 :H1761-HI 768, 1997. Campbell, K., M. Zeglen, T. Kagehiro, and H. Rigas. A pulsatile cardiovascular model for teaching heart-blood vessel interaction. Physiologist 25: 155-162, 1982. Cavalcanti, S., and E. Bleardinelli. Modeling of Cardiovascular Variability Using a Differential Delay Equation. IEEE Trans. Biomed. Eng. 43:982-989, 1996. Chapleau, M. W., and F. M. Abboud. Contrasting Effects of Static and Pulsatile Pressure on Carotid Baroreceptor Activity in Dogs. Cir. Res. 61(5):648-658, 1987. Chapman, K. R., E. N. Bruce, B. Gothe, and N. S. Chemiack. Possible mechanisms of periodic breathing during sleep. J. Appl. Physiol. 64(3):1000-1008, 1988. Coleman, T. Mathematical Analysis of Cardiovascular Function. IEEE Trans. Biom ed Eng. 32:289-294, 1985. Corfield, D. R., C. A. Roberts, M. J. D. Griffiths, and L. Adams. Sleep-related changes in the human “neuromuscular” ventilatory response to hypoxia. Res. Physio. 117:109-120, 1999. D ’Angelo, E., F. M. Robatto, E. Calderini, M. Tavola, D. Bono, G. Tom , and J. Milic-Emili. Pulmonary and chest wall mechanics in anethetized paralyzed humans. J. Appl. Physiol. 70(6): 2602-2610, 1991. Dagan, J. Pulsatile mechanical and mathematical model of the cardiovascular system. Med. Biol. Eng. Comput. 20: 601-607, 1982. de Burgy Daly, M., and J. E. Angell-James. Role of carotid-body chemoreceptors and their reflex interactions in bradycardia and cardiac arrest. Lancet. 764- 767,1979. DeBoer, R. W., J.M. Karemaker, and J. Strackee. Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am. J. Physiol. 253 (Heart Circ. Physiol. 22): H680-H689, 1987. 181 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Donald, D. E., and A. J. Edis. Comparison of Arotic and Carotid Baroreflexes in the Dog. J. Physiol. 215:521-538, 1971. Douglas, N. J., D. P. White, J. V. Weil, C. K. Pickett, R. J. Martin, D. W. Hudgel, and C. W. Zwillich. Hypoxic Ventilatory Response Decreases During Sleep in Norman Men. Am. Rev. Respir. Dis. 125:286-289, 1982. Dunai, J. M. Wilkinson, and J. Trinder. Interaction of chemical and state effects on ventilation during sleep onset. J. Appl. Physiol. 81(5):2235-2243, 1996. Eckberg, D. L, and P. Sleight. Valsalva’s Manoeuvre. Human Baroreflexes in Health and Disease. Oxford: Calrdendon Press. 61-76, 1992 Eckberg, D. L. Nonlinearities of the Human Carotid Baroreceptor-Cardiac Reflex. Cir. Res. 47(2): 208-216, 1980. Eckberg. D., C. Nerhed, and B. G. Wallin. Respiratory Modulation of Muscle Sympathetic and Vagal Cardiac Outflow in Man. J. Physiol. 365:181-196, 1985. Eldridge, F. L. Relationship between respiratory nerve and muscle activity and muscle force output. J. Appl. Physiol. 39(4):567-574, 1975. Fairbanks, D. N. F., S. Fujita, T. Ikematsu, and F. B. Simmons. Snoring and Obstructive Sleep Apnea. New York: Raven Press, 1987. Fletcher, E. C., G. Bao, and C. C. Miller III. Effect of recurrent episodic hypocapnic, eucapnic, and hypercapnic hypoxia on systemic blood pressure. J. Appl. Physiol. 78(4): 1516-1521, 1995. Floras, J. S. Clinical Aspects of Sympathetic Activation and Parasympathetic Withdrawal in Heart Failure. JACC. 22(4):72A-84A, 1993, Franz, G. N. Nonlinear Rate Sensitivity of The Carotid Sinus Reflex as a Consequence of Static and Dynamic Nonlinearities in Baroreceptor Behavior. Ann. N. Y. Acad. Sci. 156(2):811-824, 1969. Fredberg, J. J., and D. Stamenovic. On the imperfect elasticity of lung tissue. J. Appl. Physiol. 67(6): 2408-2419, 1989. Gallagher, C. G., and M. Younes. Effect of pressure assist on ventilation and respiratory mechanics in heavy exercise. J. Appl. Physiol. 66(4): 1824-1837, 1989. Gavriely, N., T. R. Shee, D. W. Cugell, and J. B. Grotberg. Flutter in flow-limited collapsible tubes: a mechanism for generation of wheezes. J. Appl. Physiol. 66(5):2251-2261, 1989. 182 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Gleeson, K., C. W. Zwillich, and D. P. White. Chemosensitivity and the ventilatory response to airflow obstruction during sleep. J. Appl. Physiol. 67(4): 1630-1637, 1989. Goldstein, Y., R. Beyar, and S. Sideman. Influence of pleural pressure variations on cardiovascular system dynamics: a model study. Med. & Biol. Eng. & Comput. 26:251-259, 1988. Grodins, F. S. Integrative cardiovascular physiology: a mathematical synthesis of cardiac and blood vessel hemodynamics. Q. Rev. Biol. 34:93-116, 1959. Grodins, F. S., J. Buell, and A. J. Bart. Mathematical analysis and digital simulation of the respiratory control system. J. Appl. Physiol. 22(2): 260-276, 1967. Guerin. C., M.-L. Coussa, N. T. Eissa, C. Corbeil, M. Chasse, J. Braidy, N. Matar, and J. Milic-Emili. Lung and chest wall mechanics in mechanically ventilated COPD patients. J. Appl. Physiol. 74(4): 1570-1580, 1993. Guilleminault C., and M. Partinen. Obstructive Sleep Apnea Syndrome: Clinical Research and Treatment. New York: Raven Press, 1990. Guilleminault, C., and A. Robinson. Central Apnea. O tolaiyngologic Clinics o f North Am erica. 31 (6): 1049-1065, 1998. Guilleminault, C., and M. A. Quera-Salva, G. Nino-Murcia, and M. Partinen. Central Sleep Apnea and Partial Obstruction of the Upper Airway. Ann. Neurol. 21:465-469, 1987. Hammer, P., D. Litvack, and J. P. Saul. Interpreting Open- and Closed-loop Transfer Relations Between Cardiorespiratory Parameters: Lessons Learned from a Computer Model of Beat-to-Beat Cardiovascular Regulation. M ethods o f Information in M edicine. 36(4-5):237-240, 1997. Hardy, H. H., and R. E. Collins, and R. E. Calvert. A digital computer model of the human circulatory system. Med. Biol. Eng. Comput. 20: 550-564, 1982. Hayward, L. F., A. K. Johnson, and R. B. Felder. Arterial chemoreflex in conscious normotensive and hypertensive adult rats. Am. J. Physiol. 276 {Heart Circ. Physiol. 45): H 1215-H1222, 1999. Henry, R. A. I.-L. Lu, L. A. beightol, and D. L. Eckberg. Interactions between CO2 chemoreflexes and arterial baroreflexes. Am. J. Physiol. 274 {H eart Circ. Physiol. 43): H2177-H2187, 1998. 183 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hildebrandt. J. Pressure-volume data of cat lung interpreted by a plastoelastic, linear viscoelastic model. J. Appl. Physiol. 28(3): 365-372, 1970. Huang, L., and J. E. Ffowcs Williams. Neuromechanical interaction in human snoring and upper airway obstruction. J. Appl. Physiol. 86(6): 1759-1763, 1999. Jager, G. N., N. Westerhof, and A. Noordergraaaf. Oscillatory flow impedance in electrical analog of arterial system: represenation of sleeve effect and non- Newtonian properties of blood. Circ. Res. 16:121-133, 1965. Javaheri, S. Heart Failure and Sleep Disordered Breathing: Central Sleep Apnea- Hypopnea Syndrome in Heart Failure: Prevalence, Impact, and Treatment. Sleep 19(10):S229-S231, 1996. Kaczka, D. W., E. P. Ingenito, and K. R. Lutchen. Technique to Determine Inspiratory Impedance during Mechanical Ventilation: Implications for Flow Limited Patients. Ann. Biomed. Eng. 27:340-355, 1999. Kaczka, D. W., G. M. Barnas, B. Suki, and K. R. Lutchen. Assessment of Time- Domain Analyses for Estimation of Low-Frequency Respiratory Mechanical Properties and Impedance Spectra. Ann. Biomed. Eng. 23-135-151, 1995. Kato, H., A. S. Menon, and A. S. Slutsky. Mechanisms mediating the heart rate response to hypoxemia. Circulation 77(2):407-414, 1988. Katona, P. G., J. W. Poitras, G. O. Barnett, and B. S. Terry. Cardiac vagal efferent activity and heart period in the carotid sinus reflex. Am. J. Physiol. 218(4): 1030- 1037, 1970. Katragadda. S., A. Xie, D. Puleo, J. B. Skatrud, and B. J. Morgan. Neural mechanism of the pressor response to obstructive and nonobstructive apnea. J. Appl. Physiol. 83(6):2048-2054, 1997. Kent, B. B., J. W. Drane, B. Blumenstein, and J. W. Manning. A Mathematical Model to Assess Changes in the Baroreceptor Reflex. Cardiology 57:295-310, 1972. Khoo, M. C. K. A model-based evaluation of the single-breath CO2 ventilatory response test. J. Appl. Physiol. 68(l):393-399, 1990. Khoo, M. C. K., A. Gottschalk, and A. I. Pack. Sleep-induced periodic breathing and apnea: a theoretical study. J. Appl. Physiol. 70(5): 2014-2024, 1991. Khoo, M. C. K„ J. J. W. Shin, M. H. Asyali, T-S Kim, and R. B. Berry. Ventilatory dynamics of transient arousal in patients with obstructive sleep apnea. Resp. Physiol. 112:291-303, 1998. 184 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Khoo, M. C. K., R. E. Kronauer, K. P. Strohl, and A. S. Slutsky. Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 53(3):644-659, 1982. Khoo, M. C. K„ S. S. W. Koh, J. J. W. Shin, P. R. Westbrook, and R. B. Berry. Ventilatory dynamics during transient arousal from NREM sleep: implications for respiratory control stability. J. Appl. Physiol. 80(5): 1475-1484, 1996. Kitney, R. I., and S. R. Seydnejad. Investigation of HRV by Model Analysis. Frontier o f B lood Pressure and heart Rate Analysis. 67-88, 1997. Kitney, R. I., and S. R. Seydnejad. Investigation of HRV by Model Analysis. Frontiers of Blood Pressure and Heart Rate Analysis, chapter 9, Eds M. Di Rienzo et al., IOS Press, 1997. Kubota, T., H. Chishaki, T. Yoshida, K. Sunagawa, A. Takeshita, and Y. Nose. How to encode arterial pressure into carotid sinus nerve to invoke natural baroreflex. Am. J. Physiol. 263 (Heart Circ. Physiol. 32): H307-H313, 1992. LaCourse, J. R., G. Mohankrishnan, and K. Sivaprasad. Simulations of arterial pressure pulses using a transmission model. ,/. Biomech. 19:771-780, 1986. Lambertsen, C. J. Chemical control of respiration at rest. Medical Physiology. St. Louis: C.V. Mosby Co. 1774-1827, 1980. Lambertsen, C. J. Medical Physiology. St. Louis: C. V. Mosby Co. 1749-1773, 1980. Lange, R. L., J. D. Horgan, J. T. Botticelli, T. Tsagrais, R. P. Carlisle, and H. Kuida. Pulmonary to arterial circulatory transfer function: importance in respiratory control. J. Appl. Physiol. 21(4): 1281-1291, 1966. Leevers, A. M., P. M. Simon, L. Xi, and J. A. Dempsey. Apnoea following normocapnic mechanical ventilation in awake mammals: a demonstration of control system inertia. J. Physiol. 472:749-768, 1993. Levy, M. N. Cardiac sympathetic-parasympathetic interactions. Fed. Proc. 43(11):2598-2602, 1984. Madwed, J. B., P. Albrecht, R. G. Mark, and R. J. Cohen. Low-frequency oscillations in arterial pressure and heart rate: a simple computer model. Am. J. Physiolo. 256 (H eart Circ. Physiol. 25): H1573-H1579, 1989. Magosso, E., and M. Ursino. A mathematical model of CO2 effect on cardiovascular regulation. Am. J. Physiol. Heart Circ. Physiol. 28L.H2036-H2052, 2001 . 185 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Malliani, A. The Pattern of Sympathovagal Balance Explored in the Frequency Domain. News Physiol. Sci. 14:111-117, 1999. Malliani, A., M. Pagani, F. Lombardi, and S. Cerutti. Cardiovascular Neural Regulation Explored in the Frequency Domain. Circulation. 84(2):482-492, 1991. Mcllroy, M. B., and R. C. Targett. A model of the arterial bed showing ventricular-systemic coupling. Am. J. Physiolog. 254(H eart Circ. Physiol. 23):H609-H616, 1988. Mead, J., and E. Agostoni. Dynamics of breathing. Flandbook of Physiology. Washington D. C.:American Physiology Society. 3(1):411-426, 1964. Melcher, A. Carotid baroreflex heart rate control during the active and the assited breathing cycle in man. Acta. Physiol. Scand. 108:165-171, 1980. Milic-Emili, J., and W. A. Zin. Relationship between neuromuscular respiratory drive and ventilatory output. Flandbook of Physiology. Washington D.C.: American Physiology Society. 3(1):631-646, 1987. Modarreszadeh, M., E. N. Bruce, H. Flamilton, and D. W. Hudgel. Ventilatory stability to CO2 disturbances in wakefulness and quiet sleep. J. Appl. Physiol. 79(4): 1071-1081, 1995. Morgan, B. J., T. Denahan, and T. J. Ebert. Neurocirculatory consequences of negative intrathroacic pressure vs. asphyxia during voluntary apnea. J. Appl. Physiol. 74(6):2969-2975, 1993. Moser, M., M. Lehofer, A. Sedminek, M. Lux, El.-G. Zapotoczky, T. Kenner, and A. Noordergraaf. Heart Rate Variability as a Prognostic Tool in Cardiology - A Contribution to the Problem From a Theoretical Point of View. Circulation. 90(2): 1078-1082, 1994. Mount, L. E. The ventilation flow-resistance and compliance of rat lungs. J. Physiol. 127:157-167, 1955. Narkiewicz, K., N. Montano, C. Cogliati, P. J. H. van de Borne, M. E. Dyken, and V. K. Somers. Altered Cardiovascular Variability in Obstructive Sleep Apnea. Circulation 98:1071-1077, 1998. Narkiewicz, K., P. J. H. van de Borne, C. A. Pesek, M. E. Dyken, N. Montano, and V. K. Somers. Selective Potentiation of Peripheral Chemoreflex Sensitivity in Obstructive Sleep Apnea. Circulation. 99:1183-1189, 1999. 186 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Narkiewicz, K., Ph. J. H. van de Borne, N. Montano, M. E. Dyken, B. G. Phillips, and V. K. Somers. Contribution of Tonic Chemoreflex Activation to Sympathetic Activity and Blood Pressure in Patients with Obstructive Sleep Apnea. Circulation. 97:943-945, 1998. Naughton, M. T. Pathophysiology and treatment of Cheyne-Stokes respiration. Thorax 53:514-518, 1998. Naughton, M. T., and T. D. Bradley. Sleep Apnea in Congestive Heart Failure. Sleep D isorders 19:99-113, 1998. Noordergraaf, A. Hemodynamics. Biological Engineering. New York’ .McGraw- Hill. 391-545, 1969. Odens, M. L., and C. H. Fox. Adult Sleep Apnea Syndromes. American Family Physician 52(3):859-866, 1995. Olsen, C. O., G. S. Tyson, G. W. Maier, J. W. Davis, and J. S. Rankin. Diminished stroke volume during inspiration: a reverse thoracic pump. Circulation 72(3):668- 679, 1985. Orem. J., and C. D. Barnes. Physiology in Sleep. New York: Academic Press, 1980. Otis, A. B., C. B. McKerrow, and R. A. Bartlett. Mechanical Factors in Distributing of Pulmonary Ventilation. J. Appl. Physiol. 8:427-443, 1956. Parati, G., A. Frattola, S. Omboni, G. Mancia, and M. Di Rienzo. Analysis of heart rate and blood pressure variability in the assessment of autonomic regulation in arterial hypertension. Clinical Science. 91 Suppl: 129-132, 1996. Parati, G., M. Di Rienzo, G. Bertinieri, G. Pomidossi, R. Casadei, A. Groppelli, A. Pedotti, A. Zanchetti, and G. Mancia. Evaluation of the Baroreceptor-Heart Rate Reflex by 24-Hour Intra-arterial Blood Pressure Monitoring in Humans. Hypertension. 12(2):214-222, 1988. Parati, G., M. Di Rienzo, M. R. Bonsignore, G. Insalaco, O. Marrone, P. Castiglioni, G. Bonsignore, and G. Mancia. Autonomic cardiac regulation in obstructive sleep apnea syndrome: evidence from spontaneous baroreflex analysis during sleep. J. H ypertension 15(12): 1621 -1626, 1997. Parati, G., M. Di Rienzo, M. R. Bonsignore, G. Insalaco, O. Marrone, P. Castiglioni, G. Bonsignore, and G. Mancia. Autonomic cardiac regulation in obstructive sleep apnea syndrome: evidence from spontaneous baroreflex analysis during sleep. J. Hyper. 15:1621-1626, 1997. 187 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Parisi, R. A., N. H. Edelman, and T. V. Santiago. Central Respiratory Carbon Dixoide Chemosensitivity Does Not Decrease during Sleep. Am. Rev. Respir. Dis. 145:832-836, 1992. Pascualy, R. A., and S. W. Soest. Snoring and Sleep Apnea: personal and family guide to diagnosis and treatment. 2n d ed. New York: Demos Vermande, 1996. Pdszus, T., J. Mayer, T. Penzel, J. H. Peter, and P. von Wichert. Nocturnal Hemodynamics in Patients with Sleep Apnea. Eur J. Respir. Dis. 69:435-442, 1986. Pengelly, L. D., A. M. Alderson, and J. Milic-Emili. Mechanics of the disphragm. J. Appl. P h ysio l 30(6): 797-805, 1971. Peters, J., C. Fraser, R. S. Stuart, W. Baumgartner, and J. L. Robotham. Negative intrathoracic pressure decreases independently left ventricular filling and emptying. Am. J. P h ysiol 257 (Heart Circ. Physiol. 26): H120-131, 1989. Peters, J., M. K. Kindred, and J. L. Robotham. Transient analysis of cardiopulmonary interactions I. Diastolic events. J. Appl. Physiol. 64(4): 1506- 1517, 1988. Peters, J., M. K. Kindred, and J. L. Robotham. Transient analysis of cardiopulmonary interactions II. Systolic events. J. Appl. Physiol. 64(4): 1518- 1526,1988. Pickering, G. W., P. Sleight, and H. S. Smyth. The reflex regulation of arterial pressure during sleep in man. J. Physiol. 191:46p-48p, 1967. Pickering, W. D., P. N. Nikiforuk, and J. E. Merriman. Analogue computer model of the human cardiovascular control system. Med. Biol. Eng. 7:401-410, 1969. Piepoli, M., P. Sleight, S. Leuzzi, F. Valle, G. Spadacini, C. Passino, J. Johnston, and L. Bemadi. Origin of Respiratory Sinus Arrhythmia in Conscious Humans - An Important Role for Arterial Carotid Baroreceptors. Ciculation 95(7): 1813- 1821, 1997. Potts, J. T., T. Hatanaka, and A. A. Shoukas. Effect of arterial compliance on carotid sinus baroreceptor reflex control of the circulation. Am. J. Physol. 270 {H eart Circ. P h ysiol 39): H988-H1000, 1996. Quan, K. J., M. D. Carlson, and M. D. Thames. Mechanisms of Heart Rate and Arterial Blood Pressure Control: Implications for the Pathophysiology of Neurocardiogenic Syncope. Pace. 20:764-774, 1997. 188 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Read, D. J. C., and J. Leigh. Blood-brain tissue PCO2 relationships and ventilation during rebreathing. J. Appl. Physiol. 23:53-70, 1967. Read, D. J. C., S. Freedman, and E. R. Kafer. Pressure developed by loaded inspiratory muscles in conscious and anesthetized man. J. Appl. Physiol. 37(2):207-218, 1974. Ren, X., and P. A. Robbins. Ventilatory responses to hypercapnia and hypoxia after 6 h passive hyperventilation in humans. J. Physiol. 514(3):885-894, 1999. Riddle, W., and M. Younes. A model for the relation between respiratory neural and mechanical outputs. II. Methods. J. Appl. Physiol.: R espirat Environ. Exercise Physiol. 51(4):979-989, 1981. Roberts, D. Invited Editorial on “ Neuromechanical interaction in human snoring and upper airway obstruction”. J. Appl. Physiol. 86(6): 1757-1758, 1999. Robotham, J. L., D. Cherry, W. Mitzner, J. L. Rabson, W. Lixfeld, and B. Bromberger-Barnea. A re-evaluation of the hemodynamic consequences of intermittent positive pressure ventilation. Critical Care M edicine. 11 (10):783-793, 1983. Robotham, J. L., J. Rabson, S. Permutt, and B. Aromberger-Barnea. Left ventricular hemodynamics during respiration. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 47(6): 1295-1303, 1979. Robotham, J. L., W. Lixfeld, L. Holland, D. MacGregor, A. C. Bryan, and J. Rabson. Effects of respiration on cardiac performance. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 44(5): 703-709, 1978. Rossi. A., S. B. Gottfried, L. Zocchi, B. D. Higgs, S. Lennox, P. M. A. Calverley, P. Begin, A. Grassino, and J. Milic-Emili. Measurement of Static Compliance of the Total Respiratory System in Patients with Acute Respiratory Failure during Mechanical Ventilation. Am. Rev. Respir. Dis. 131:62-677, 1985. Roussos, C. S., and P. T. Macklem. Respiratory Muscles. The N ew England Journal o f M edicine. 307(13):787-797, 1982. Sato, F., M. Nishimura, H. Shinano, H. Saito, K. Miyamoto, and Y. Kawakami. Heart Rate During Obstructive Sleep Apnea Depends on Individual Hypoxic Chemosensitivity of the Carotid Body. Circulation 96(1 ):274-281, 1997. Saul, J. P., R. D. Berger, M. H. Chen, and R. J. Cohen. Transfer function analysis of autonomic regulation II. Respiratory sinus arrhythmia. Am. J. Physiol. 256 {Heart Circ. Physiol. 25): H152-H161, 1989. 189 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Saul. J. P., R. D. Berger, P. Albrecht, S. P. Stein, M. H. Chen, and R. J. Cohen. Transfer function analysis of the circulation: unique insights into cardiovascular regulation. Am. J Physiol. 261 {Heart Circ. Physiol. 30): H1231-1245, 1991. Schmidt, R. F., and G. Thews. Human Physiology. Berlin: Springer-Verlag, 1983. Schuessler, T. F., S. B. Gottfried, and J. H. T. Bates. A model of the spontaneously breathing patient: applications to intrinsic PEEP and work of breathing. J. Appl. Physiol. 82(5): 1694-1703, 1997. Seals, D. R., O. Suwarno, M. J. Joyner, C. Iber, J. G. Copeland, and J. A. Dempsey. Respiratory Modulation of Muscle Sympathetic Nerve Activity in Intact and Lung Denervated Humans. Cir. Res. 72:440-454, 1993. Seydnejad, S. R., and R. I. Kitney. Analysis of HRV and BPV by a Nonlinear Closed Loop Model. M ethodology and Clinical Applications o f B lood Pressure and H eart Rate Analysis. 49-71, 1999. Shabetai, R., N. O. Fowler, and M. Gueron. The effects of respiration on aortic pressure and flow. Am. Heart. J. 65(4):525-533, 1963. Sharp, J. T., F. N. Johnson, N. B. Goldberg, and P. V. Lith. Hysteresis and stress adaptation in the human respiratory system. J. Appl. Physiol. 23:487-497, 1967. Shea, S. A. Life withouth ventilatory chemosensitivity. Resp. Physiol. 110:199- 210, 1997. Shoukas, A. A., and M. C. Brunner. Epinephrine and the Carotid Sinus Baroreceptor Reflex. Circ. Res. 47(2):249-257, 1980. Similowski, T., and J. H. T. Bates. Two-compartment modeling of respiratory system mechanics at low frequencies: gas redistribution or tissue rheology? Eur. Respir. J. 4:353-358, 1991. Simon, P. M., J. A. Dempsey, D. M. Landry, and J. B. Skatrud. Effect of Sleep on Respiratory Muscle Activity during Mechanical Ventilation. Am. Rev. Respir. Dis. 147:32-37,1993. Sleight, P. The importance of the autonomic nervous system in health and disease. Aust. NZJ. M ed. 27:467-473, 1997. Smith, C. S., K. S. Henderson, L. Xi, C.-M. Chow. P. R. Eastwood, and J. A. Dempsey. Neural-mechanical coupling of breathing in REM sleep. J. Appl. Physiol. 83(6): 1923-1932, 1997. 190 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Snyder, M. F., V. C. Rideout, and R. J. Hillestad. Computer modeling of the human systemic arterial tree. J. Biomech. 1:341-353, 1968. Somers, V. K., A. L. Mark, and F. M. Abboud. Interaction of Baroreceptor and Chemoreceptor Reflex Control of Sympathetic Nerve Activity in Normal Flumans. J. Clin. Invest. 87:1953-1957, 1991. Somers, V. K., A. L. Mark, D. C. Zavala, and F. M. Abboud. Contrasting effects of hypoxia and hypercapnia on ventilation and sympathetic activity in humans. J. Appl. Physiol. 67(5): 2101-2106, 1989. Somers, V., A. L. Mark, D. C. Zavala, and F. M. Abboud. Influence of ventilation and hypocapnia on sympathetic nerve responses to hypoxia in normal humans. J. Appl. Physiol. 67(5): 2095-2100, 1989. Somers, V., and F. M. Abboud. 3. Cardiovascular Aspects of Sleep Apnea - (a) Hypertension and Sleep Apnea - Chemoreflexes-Responses, Interactions and Implications for Sleep Apnea. Sleep. 16:S30-S34, 1993. Somers, V., and F. M. Abboud. Chemoreflexes-Responses, Interactions and Implications for Sleep Apnea. Sleep 16:S30-S34, 1993. Spencer, J. L., E. Firouztale, and R. B. Mellins. Computational expressions for blood oxygen and carbon dioxide concnetraions. Ann. of Biomed. Eng. 7:59-55, 1979. St. Croix, C. M., D. A. Cunningham, and D. H. Paterson. Nature of the interaction between central and peripheral chemoreceptor drives in human subjects. Can. J. Physiol. Pharm acol. 74:640-646, 1996. St. Croix, C. M., M. Satoh, B. J. Morgan, J. B. Skatrud, and J. A. Dempsey. Role of Respiratory Motor Output in Within-Breath Modulation of Muscle Sympathetic Nerve Activity in Humans, (in printing) Staniforth, A. D., W. J. M. Kinnear, R. Starling, D. J. Hetmanski, and A. J. Cowley. Effect of oxygen on sleep quality, cognitive function and sympathetic activity in patients with chronic heart failure and Cheyne-Stokes respiration. European H eart Journal 19:922-928, 1998. Stoohs, R., and C. Guilleminault. Cardiovascular changes associated with obstructive sleep apnea syndrome. J. Appl. Physiol. 72(2):583-589, 1992. Strohl, K. P. Obstructive Sleep Apnea Syndrome. Sleep Disorders: Diagnosis and Treatment. New Jersey: Humana Press. 117-135, 1998. 191 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sud, V. K., and G. S. Sekhon. Analysis of blood flow through a model of the human arterial system under periodic body acceleration. J. Biomech. 19: 929-941, 1986. Suki, B., A.-L. Barabasi, and K. R. Lutchen. Lung tissue viscoelasticity: a mathematical framework and its molecular basis. J. Appl. Physiol. 76(6):2749- 2759, 1994. Summer, W. R., S. Permutt, K. Sagawa, A. A. Shoukas, and B. Bromberger- Bamea. Effects of Spontaneous Respiration on Canine Left Ventricular Function. Circ. Res. 45: 719-728, 1979. Taha, B. H., P. M. Simon, J. A. Dempsey, J. B. Skatrud, and C. Iber. Respiratory sinus arrhythmia in humans: an obligatory role for vagal feedback from the lungs. J. Appl. Physiol. 78(2): 638-645, 1995. Taher, M. F., A. B. P. Cecchini, M. A. Allen, S. R. Gobran, R. C. Gorman, B. L. Guthrie, K. A. Lingenfelter, S. Y. Rabbany, P. M. Rolchigo, J. Melbin, and A. Noordergraaf. Braoreceptor responses derived from a fundamental concept. Ann. Biomed. Eng. 16:429-443, 1988. TenVoorde, B. J., Th. J. C. Faes, T. W. J. Janssen, G. J. Scheffer, and 0. Rompelman. Respiratory Modulation of Blood Pressure and Heart Rate Studied with a Computer Model of Baroreflex Control. Comuter Analysis of Cardiovascular Signals, chapter 9, Eds M. Di Rienzo, IOS Press, 1995. Thawley, S. E. The Medical Clinics of North America, Symposium on Sleep Apnea Disorders. Philadelphia: W. B. Saunders, 69(6), p .1123-1152, 1985 Thompson, C. A., D. L. Tatro, D. A. Ludwig, and V. A. Convertino. Baroreflex responses to acute changes in blood volume in humans. Am. J. Physiol. 259 {Regulatory Integrative Comp. Physiol. 28): R792-R798, 1990. Thoresen, M., and L. Walloe. Changes in cerebral blood flow in humans during hyperventilation and CO2 breathing (Abstract). J. Physiol. Lond. 298: 53P, 1980. Tobin, M. J., and J. V. Snyder. Cheyne-Stokes respiration revisited: Controversies and implications. Cri. Care M ed. 12(10):882-887, 1984. Toslca, K., M. Eriksen, and L. Walloe. Short-term control of cardiovascular function: estimation of control parameters in healthy humans. Am. J. Physiol. 270 {H eart Circ. Physiol. 39): H651-H660, 1996. Ursino, M. Interaction between carotid barorgulation and the pulsating heart: a mathematical model. Am. J. Physiol. 275 {H eart Circ. Physiol. 44) :H1733-H1747, 1998. 192 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ursino, M., M. Antonucci, and E. Belardinelli. Role of active changes in venous capacity by the carotid baroreflex: analysis with a mathematical model. Am. J. Physiol. 267 ( H eart Circ. Physiol. 36): H2531-H2546, 1994. Vaile, J. C., T. J. Stallard, M. Al-Ani, P. J. Jordan, J. N. Townend, and W. A. Littler. Sleep and blood pressure: spontaneous baroreflex sensitivity in dippers and non-dippers. J. Hyper. 14:1427-1432, 1996. Van De Borne, P., P. Biston, M. Paiva, H. Nguyen, P. Linkowski, and J-P. Degaute. Cardiorespiratory transfer during sleep: a study in healthy young men. Am. J. Physiol. 269:H952-H958, 1995. Van Den Aardweg, J. G., and J. M. Karemaker. Repetitive apneas induce periodic hypertension in normal subject through hypoxia. J. Appl. Physiol. 72(3): 821-827, 1992. Van Den Aardweg, J. G., R. P. Van Steenwijk, and J. M. Karemaker. A chemoreflex model of relation between blood pressure and heart rate in sleep apnea syndrome. Am. J. Physiol. 268 {H eart Circ. Physiol. 37): H2145-H2156, 1995. Vetter, R, P. Celka, J. M. Vesin, G. Thonet, E. Pruvot, M. Fromer, U. Scherrer, and L. Bemardi. Ann. Biomed. Eng. 26:293-307, 1998. Wang, J., B. Tie, W. Welkowitz, J. Kostis, and J. Semmlow. Incremental network analogue model of the coronary artery. Med. Biol. Eng. Comput. 27:416-422, 1989. Warner, H. R., and A. Cox. A mathematical model of heart rate control by sympathetic and vagus information. J. Appl. Physiol. 17:349-355, 1962. Weiss, J. W., S. H. Launois, and A. Anand. The Acute Flemodynamic Response to Upper Airway Obstruction During Sleep. Sleep Apnea-Implications in Cardiovascular and Cerebrovascular Disease, chapter 9. Eds. T. D. Bradley et al. New York, 2000. White, D. P., J. V. Weil, and c. W. Zwillich. Metabolic rate and breathing during sleep. J. Appl. Physiol. 59(2):384-391, 1985. Whittam, A. M., R. H. Clayton, S. W. Lord, J. M. McComb, and A. Murray. Computer Modelling of Heart Rate and Blood Pressure. Comp in Cardio. 25:149- 152, 1998. Widdicombe, J. G. Respiratory reflexes. Handbood of Physiology. Washington D. C.: American Physiological Society. 3(1 ):585-630, 1964. 193 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Wilcox, L, S. G. McNamara, T. Wessendorf, G. N. Willson, A. J. Piper, and C. E. Sullivan. Prognosis and sleep disordered breathing in heart failure. Thorax 53 Suppl(3): S25-S28, 1998. Wilson, C. R., S. Manchanda, D. Crabtree, J. B. Skatrud, and J. A. Dempsey. An induced blood pressure rise does not alter upper aireay resistance in sleeping humans. J. Appl. Physiol. 84(1): 269-276, 1998. Younes, M., and G. Kivinen. Respiratory mechanics and breathing pattern during and following maximal exercise. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol: 57(6): 1773-1782, 1984. Younes, M., and W. Riddle. A model for the relation between respiratory neural and mechanical outputs. I. Theory. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 51(4):963-978, 1981. Younes, M., W. Riddle, and J. Polacheck. A model for the relation between respiratory neural and mechanical outputs. III. Validation. J. Appl. Physiol.:Respirat Environ. Exercise Physiol. 51(4):990-1001, 1981 Zagzoule, M., and J.-P. Marc-Vergnes. A global mathematical model of the cerebral circulation in man. J. Biomech. 19:1015-1022, 1986. Zwillich, C. W. Obstructive Sleep Anpoea Causes Transient and Sustained Systemic Hypertension. IJCP, 53(4):301-305, 1999. Zwillich, C., T. Devlin, D. White, N. Douglas, J. Weil, and R. Martin. Bardycardia during Sleep Apnea-Characteristics and Mechanism. J. Clin. Invest. 69:1286-1292, 1982. 194 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

A model of upper airway dynamics in obstructive sleep apnea syndrome

PDF

Effects of prenatal cocaine exposure in quantitative sleep measures in infants

PDF

A model of cardiorespiratory autoregulation in obstructive sleep apnea

PDF

Head injury biomechanics: Quantification of head injury measures in rear-end motor vehicle collisions

PDF

Development of ceramic-to-metal package for BION microstimulator

PDF

Comparisons of deconvolution algorithms in pharmacokinetic analysis

PDF

Cellular kinetic models of the antiviral agent (R)-9-(2-phosphonylmethoxypropyl)adenine (PMPA)

PDF

English phoneme and word recognition by nonnative English speakers as a function of spectral resolution and English experience

PDF

Cardiorespiratory variability in normal and sleep disordered breathing states: a comprehensive model

PDF

Assessment of minimal model applicability to longitudinal studies

PDF

Hyperspectral optical imaging for detection, diagnosis and staging of cancer

PDF

Integrative modeling of autonomic and metabolic interactions in sleep-disordered breathing

PDF

A physiologic model of granulopoiesis

PDF

Contact pressures in the distal radioulnar joint as a function of radial malunion

PDF

Dynamics of the newly formed neuromuscular synapse

PDF

Characteristics and properties of modified gelatin cross-linked with saline for tissue engineering applications

PDF

A preliminary investigation to determine the effects of a crosslinking reagent on the fatigue resistance of the posterior annulus of the intervertebral disc

PDF

A user interface for the ADAPT II pharmacokinetic/pharmacodynamic systems analysis software under Windows 2000

PDF

The effects of the vitreous state on the ocular pharmacokinetics following intravitreal drug delivery: an evaluation with quantitative magnetic resonance imaging

PDF

Bayesian estimation using Markov chain Monte Carlo methods in pharmacokinetic system analysis

Asset Metadata

Creator Fan, Hsing-Hua (author)

Core Title Cardiorespiratory interactions in sleep apnea: A comprehensive model

School Graduate School

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag biology, animal physiology,engineering, biomedical,health sciences, pathology,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Khoo, Michael C.K. (committee chair), D'Argenio, David (committee member), O'Leary, Daniel (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-538922

Unique identifier UC11339267

Identifier 3094335.pdf (filename),usctheses-c16-538922 (legacy record id)

Legacy Identifier 3094335.pdf

Dmrecord 538922

Document Type Dissertation

Rights Fan, Hsing-Hua

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA