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

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

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HEAD INJURY BIOMECHANICS: QUANTIFICATION OF HEAD INJURY MEASURES IN REAR-END MOTOR VEHICLE COLLISIONS By Jai Singh A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (Biomedical Engineering) December 1998 © 1998 Jai Singh R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UMI Number: 13 94778 UMI Microform 1394778 Copyright 1999, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. This thesis, written by J a l J j n g h _____________________________________________ under the - guidance of his/her Faculty Committee and approved by all its members, has been presented to and accepted by the School of Engineering in partial fulfillm ent o f the re quirements for the degree o f E as± £c_zi£.-S r.iejace-a.n— Ba.omed.ica.L-Eag4» e s F 4 ng------- D a te October 12, 1998 Faculty Committee /[ !\A sC iJ ^J 3 u X cA cick^ o Chai r man R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table of Contents I. Introduction - Rationale For STUDY.................................................................................................. I IL ANATOMY.....................................................................................................................................................7 HI. GENERAL BRAIN INJURY BIOMECHANICS......................................................................................14 FRACTURES OF THE SKULL.......................................................................................................... 16 EPIDURAL HEMATOMA...................................................................................................................17 CONTUSION.........................................................................................................................................17 SUBDURAL HEMATOMA.................................................................................................................18 IV. HUMAN SUBJECT TESTING - UPPER LIMITS.................................................................................20 V. CONCUSSIVE BRAIN INJURY.............................................................................................................28 VI. BRAIN INJURY CRITERION................................................................................................................ 36 WAYNE STATE TOLERANCE CURVE......................................................................................... 39 GADD SEVERITY INDEX.................................................................................................................41 HEAD INJURY CRITERION..............................................................................................................46 VIBRATIONAL MODELING.............................................................................................................49 ROTATIONAL INJURY CRITERIA................................................................................................. 54 GAMBIT................................................................................................................................................57 VII. THE MOTOR VEHICLE CONTEXT.....................................................................................................6 1 BUMPER SYSTEMS............................................................................................................................64 VEHICLE INTERIOR......................................................................................................................... 7 1 OCCUPANT KINEMATICS...............................................................................................................76 Vni. TEST PROCEDURES AND EQUIPMENT.......................................................................................... 82 ii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. D C . TEST MATRIX.......................................................................................................................................... 84 TEST SERIES T96218...........................................................................................................................84 TEST SERIES T96219...........................................................................................................................85 TEST SERIES T96220...........................................................................................................................86 TEST SERIES T96224...........................................................................................................................87 X. RESULTS....................................................................................................................................................88 STRUCK VEHICLE STATIC CENTER OF GRAVITY ACCELERATION................................. 89 HEAD STATIC CENTER OF GRAVITY LINEAR ACCELERATION.........................................91 HEAD STATIC CENTER OF GRAVITY ANGULAR ACCELERATION................................... 93 XI. DISCUSSION - LINEAR MEASURES................................................................................................... 96 DYNAMIC RESPONSE INDEX - LINEAR................................................................................. 102 Xn. DISCUSSION-ANGULAR MEASURES.......................................................................................... 106 X n. CONCLUSION.........................................................................................................................................109 XIII. APPENDIX A...........................................................................................................................................110 XIV. REFERENCES.........................................................................................................................................120 iii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List o f Figures Figure 1 Brain injury biomechanics......................................................................................................................3 Figure 2 Relevant acceleration schem a................................................................................................................ 5 Figure 3 General acceleration v. time plot............................................................................................................6 Figure 4 Lateral [parasagittal] view o f the brain..................................................................................................8 Figure 5 Medial surface of the brain.....................................................................................................................8 Figure 6 Midsaggital view of the brain ................................................................................................................ 9 Figure 7 Lateral view o f skull............................................................................................................................ 11 Figure 8 Cerebrospinal fluid flow pathway........................................................................................................ 13 Figure 9 Pathomechanical neural injury schema................................................................................................ 15 Figure 10 Mechanics of linear skull fracture...................................................................................................... 16 Figure 11 SAE J211 sign convention................................................................................................................. 21 Figure 12 +GX Tolerance as measured by plateau load vs. duration................................................................. 21 Figure 13 +GX Tolerance as measured by average acceleration vs. duration................................................... 22 Figure 14 +GX tolerance for preconditioned pilots............................................................................................ 22 Figure 15 +GX survivable abrupt impact.............................................................................................................25 Figure 16 Voluntary tolerance to peak +GX acceleration...................................................................................26 Figure 17 Voluntary tolerancing for +GX acceleration......................................................................................26 Figure 18 The Wayne State Tolerance Curve.................................................................................................... 40 Figure 19 Summary of NASA testing in context of Severity Index.................................................................44 Figure 20 Summary of impact data for utilization in HIC................................................................................ 48 Figure 21 Schematic o f a 1 degree o f freedom system...................................................................................... 50 Figure 22 Physical parameters for the Mean Strain Criterion.......................................................................... 54 Figure 23 Tolerance for concussive brain injury for unrestrained whiplash................................................... 55 Figure 24 Modified JARI concussion tolerance curve......................................................................................56 Figure 25 DAI Thresholds for various strains....................................................................................................56 Figure 26 Probability of various AIS level injuries as a function of maximum GAMBIT value.................. 57 Figure 27 Schematic for co-linear rear-end motor vehicle accident.................................................................62 Figure 28 Front bumper of a 1992 Ford F Super Duty Cab.............................................................................. 65 Figure 29 Type I Isolator Assembly................................................................................................................... 66 Figure 30 Type II Isolator Assembly.................................................................................................................. 67 Figure 3 1 Type in Isolator Assembly................................................................................................................ 67 Figure 32 Foam core bumper system from a minivan....................................................................................... 68 Figure 33 Honeycomb bumper of a 1996 Saturn SLI Sedan........................................................................... 69 Figure 34 Unirail structural components............................................................................................................70 Figure 35 Rail and crossmember equipped frame..............................................................................................70 Figure 36 Adjustable head restraint Figure 37 Integrated head restraint................................................74 Figure 38 IIHS geometrical parameters, ATD, and qualification scale............................................................75 Figure 39 Occupant and vehicle response [White & Punjabi, Figure 4-45].................................................... 77 Figure 40 Exemplar vehicle and head +GX response......................................................................................... 78 Figure 41HMF vs. Struck vehicle Delta-V.........................................................................................................79 Figure 42 Head CG & Vehicle CG Gx................................................................................................................ 79 Figure 43 Instrumentation schema......................................................................................................................83 Figure 44 Peak vehicle +GX acceleration vs. duration....................................................................................... 98 Figure 45 Average +GX acceleration magnitude vs. duration..........................................................................100 Figure 46 JARI Tolerance curve depicting the area o f interest.....................................................................101 Figure 47 Comparative peak bi-directional head response..............................................................................102 Figure 48 Linear DRI vs. Struck Vehicle Delta-V...........................................................................................103 iv R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 49 Angular velocity v. angular acceleration..........................................................................................106 Figure 50 Angular DRI vs. struck vehicle Delta-V..........................................................................................107 Figure 51 Reference frames of importance.................................................................................................... 110 Figure 52 Rotational transformation o f coordinate systems.......................................................................... 11" R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Tables Table 1 Short review of important aeromedical testing......................................................................................24 Table 2 Glasgow Coma Scale.............................................................................................................................. 28 Table 3 Abbreviated Injury Scale........................................................................................................................29 Table 4 Abbreviated Injury Scale Applied to Concussive Brain Injury........................................................... 29 Table 5 Selected SAE J211 Recommendations..................................................................................................82 Table 6 Test matrix for series T96218.................................................................................................................84 Table 7 Test matrix for series T96219.................................................................................................................85 Table 8 Test matrix for series T96220.................................................................................................................86 Table 9 Test matrix for series T96224............................................................................................................... 87 Table 10 Test T96218 vehicle acceleration........................................................................................................90 Table 11 Test T96219 vehicle acceleration........................................................................................................90 Table 12 Test T96220 vehicle acceleration........................................................................................................90 Table 13 Test T96224 vehicle acceleration........................................................................................................9 1 Table 14 Test T96218 head static center of gravity linear acceleration...........................................................92 Table 15 Test T96219 head .static center of gravity linear acceleration...........................................................92 Table 16 Test T96220 head static center o f gravity linear acceleration...........................................................92 Table 17 Test T96224 head static center o f gravity linear acceleration...........................................................93 Table 18 Test T96218 head static center of gravity angular acceleration and velocity...................................93 Table 19 Test T96219 head static center o f gravity angular acceleration and velocity...................................94 Table 20 Test T96220 head static center of gravity angular acceleration and velocity...................................94 Table 21 Test T96224 head static center o f gravity angular acceleration and velocity...................................95 Table 22 Summary of tolerance indices............................................................................................................. 96 vi R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. I. Introduction — Rationale for Study The current automotive context provides for the development o f a plethora o f intriguing pathoanatomical phenomena. With the steady increase in the utilization and reliance on the motor vehicle for transport, the number o f such interactions has and will continue to increase. Therefore, the need for careful study for purposes of determining general human tolerance and for injury mitigation is one that is clearly evident. This study was conducted for the purpose o f quantifying the potential of concussive brain injury utilizing current tolerance data and automotive injury criterion. Subjects used were restrained, occupants o f motor vehicles subjected to low velocity impact from the rear. Traumatic brain injury, including concussive brain injury, is one o f the leading causes o f mortality and morbidity in the United States [Peterson, 1994]. Kraus [1986] estimated the annual incidence o f head and brain injury, on a population basis, to be 200 out of every 100,000 while Peterson [1994] and Kraus, et al. [1994] cited gross annual figures o f incidence as being 2 million and 1.8 million, respectively. The incidence of mild injury, as a percentage o f all head injury cases, was reported as being 80% [Kraus, 1986; Peterson, 1994; Kraus, et al., 1994]. Recurrent sequelae was reported in approximately 50% o f the mild brain injury population [Evans, 1994], Motor vehicle accidents were indicated to be the primary cause of traumatic brain injury [Peterson, 1994; Kraus, et al., 1994], Kraus, et al., further indicated that 64% o f the population incurring traumatic brain injury in the motor vehicle context were vehicle occupants (versus pedestrians or motorcyclists). While a significant literature base exists in the context of both injury potential and mechanisms during severe motor vehicle accidents, the current state of knowledge, at least in terms of potential for minor collisions, is not equally concurrent. The definition of a low speed or low velocity impact is one that varies in different publications in the accident reconstruction and trauma biomechanics literature. Welcher and Szabo [1996] provided an R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. extensive review of the common definitions utilized. A number of these were deemed to be inappropriate in the discussion of the current subject manner. The working definition will be one advanced by McConnell [1993] and Szabo et al. [1994], both of whom indicated that a low speed collision was one in which the a velocity change of the struck vehicle was 8 miles per hour or less. Interest in paihoanatomic occupant response in the automotive setting has been of interest to researchers for over 40 years. The initial history of traumatic neuropathology in a mechanized setting, however, can be traced to aviation fighter pilot injury mitigation. The First World War and concomitant rise in the use of aircraft resulted in a causal increase in the number of non-penetrating traumatic neurological injuries. This in turn resulted in an increase in the interest in the identification o f clinical treatment and ergonomic design factors for the mitigation o f these injuries. Modifications and design improvements in aircraft occupant compartment and restraint system design have and continue to play a role in the development o f similar systems for the mitigation of injury in the automotive setting. Identification of critical issues in the automotive setting have led to the development and utilization of laminated windshields, occupant restraint systems composed of both lap belts and shoulder harnesses, supplemental restraint systems, and head restraints. It should be noted that these are but a few o f the historically significant ergonomic design additions that have been introduced. Definition o f Injury Injury, in the biomechanical context occurs as a result of the application of forces to biological tissue, which result in the development of tissue stress and strain tensors that approximate or exceed the mechanical load capability of that given tissue. Structural damage to loaded tissues is evidenced by disruption and in extreme cases, gross structural failure. Biological tissues, in vivo, often contain R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. specialized membrane separated fluid phase chemically reactive materials. Structural disruption of the containment membrane results in the release of intracellular fluids that in turn cause structural weakening o f surrounding healthy tissue due to biochemical interaction. In the specific context o f traumatic neuropathology, the mechanical input involves an interaction between impact and inertial phenomena, both of which result in acceleration o f neural, neurovascular, osseous, and integumentous structures. Each tissue type, based on material composition, has a characteristic value or set of values o f stress and strain at which different failure modes are evidenced. A historical examination o f the study of traumatic neuropathology or traumatic brain injury reveals a complex interaction between the fields o f biomechanical engineering and the clinical neurological sciences. The aforementioned is most easily relayed in graphic form as shown in Figure I. Biomechanical Medical Testing with Cadavers Testing with Animat Subjects Testing ot Ijdated Tissue Samples Creation ot Uiobddic Anthropomorphic Subjects T n t’ T T « P c B r a i n I n j u r y Contcxt Spcciiic Human Subject Testing M a thematic alM odS s [Geometric, M aterial, FE] ic Criterion far H um an SubjectTesting Clinical Presercation ot Patients Presenting Relevant Symptomatology Figure 1 Brain injury biomechanics 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 1 can be used to support an argument that no single definition of brain injury tolerance is exclusive o f all cases o f traumatic neuropathology. In fact, the definition is most often based on the context of the specific loading condition or neuropathology being studied. The definition can range from the maximum force loading endured by a human test subject prior to the development of pain symptomatology, causing the subject to indicate the desire to cease the test to maximum loading experienced by automobile accident and free-fall subjects prior to the development of injuries that are temporarily disabling, life threatening, or potentially life-ending. Also, a given tolerance threshold may be based on a single data point or may represent a mathematical percentile value for the development of certain modalities of injuries based on combinations o f various input parameters. Initial utilization of human cadaveric subjects resulted In data pertaining to gross structural injuries such as skull fracture, penetrative trauma of neural structures, and hematoma formation. Injuries of this type, as discussed later, can be classified as structural injuries in the sense that the neuropathology observed has an easily definable structural origin. Simultaneous development o f clinical non-radiographic diagnostic tools and biomechanical testing involving human and animal surrogates, resulted in the characterization o f a grouping o f injuries such as cerebral coma and concussion that had post exposure functional limitations without apparent structural damage. Examination o f input acceleration in the classification schema o f inertial versus acceleration loading is, however, useful in that each input form has distinguishing head resultant acceleration characteristics, which in turn result in different and at times distinct forms o f traumatic neuropathology. Generally, acceleration pulses of a body subject to an impact have a shorter duration, higher magnitude, and greater rate o f onset in comparison to acceleration pulses due to inertial loading. Gurdjian, et al. [1954], noted very early, in the historical sense, that higher magnitude accelerations pulses required less time to result in the same injury that was developed with lower magnitude acceleration pulses acting over a longer duration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Input acceleration can be introduced through a line of application that can vary in all six degrees [x, y, z, 0, ( ( > , i[/] of spatial freedom. This in conjunction with differential geometric structuring o f the head region, differential material distribution, and specialized process localization in the brain results in differential tolerance and consequence to applied head acceleration. For example, application o f similar acceleration pulses to the frontal region versus the temporal region will result in differing neuropathology. The following figure depicts the schema of the relevant acceleration quantities in the context o f an input output system. Discussions of each system will follow in the appropriate section. Internal inttractitm ot various ncruanatomiral~ structures resulting in differing acceleration values o f differing segments O utput acceleration pulse for desired structure Instrum entation system utilized Inp u t acceleration pulse ▼ M easured output acceleration pulse for desired structure Figure 2 Relevant acceleration schema A translational or rotational acceleration pulse depicts the change in acceleration as over time. Based on the neuropathology being studied, different aspects of the pulse gain greater importance in establishing a correlation to injury. The important aspects of any given pulse are the acceleration duration, the maximum acceleration, the time for which a certain value o f acceleration is noted, and the time rate of change of acceleration Q'erk). The same definitions can be applied to rotational acceleration pulses. The following diagram depicts the aforementioned terminology [modified Figure o f Fraser, 1961]. 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. PcakG Dwell time Plateau c 3 6 X 1 Total duration of impact Duration o f plateau G Decay time Rise time Time [msec] Figure 3 General acceleration v. time plot It should be noted that the acceleration versus time profile depicted in Figure 3 is only for demonstrative purposes and does not accurately depict the head acceleration response for an occupant in the subject contextual setting. Acceleration magnitude has classically been defined as a “non-dimensional” quantity based on the number of multiples of the acceleration of gravity. For example, an acceleration magnitude o f IG is the equivalent of an acceleration magnitude of 9.8 m/sec2 or 32.2 ft/sec2 . An acceleration magnitude of 2G is equivalent to an acceleration magnitude of 19.6 m/sec2 or 64.4 ft/sec2 , and so forth. Rotational acceleration is measured in units of radians/seconds2. 6 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. n. Anatomy The relevant anatomy in the subject context focuses on the soft tissue structures o f the central nervous system connoted as the encephalon, its surrounding osseous structures, its constituent membranous structures, and vascular structures. The study of the pathomechanical and therefore anatomical aspects of the non-encephalic central nervous system structures and the structures of the peripheral nervous system is beyond the scope of this discussion. The adult brain is an approximate 1400 gram structure composed of the cerebrum, brainstem, and cerebellum. The cerebrum is composed o f two lateral hemispheric structures that are together referred to as the telencephalon. The hemispheric surfaces are convoluted, forming fissure-like sulci between the projecting gyri. The hemispheres are connected and communicate via the corpus collosum. The hemispheres are divided into five lobes, each containing morphological regions, that when lessioned, result in the loss or diminishment of functionality localized at the lesion site. The frontal lobe is demarcated by the central sulcus, laterally, extending to the frontal pole anteriorly. Inferior demarcation is via the lateral sulcus. The frontal lobe contains regions specializing in primary and secondary motor control. The parietal lobe lies posterior to the central sulcus, extending posteriorly to the occipital lobe. Parietooccipital separation occurs via a median sulci bearing the same name. The parietal lobe lies superior to the temporal lobe. The parietal lobe contains the primary cerebral sensory cortex and the primary cerebral somatosensory cortex. The temporal lobe extends from the temporal lobe to the occipital lobe, as mentioned above. The temporal lobe contains the primary auditory area of the cerebral cortex. The occipital lobe lies in a position, as defined above, and contains the primary cerebral visual cortex. The limbic lobe is an internal structure, encircling the corpus collosum, and primarily contains structures associated with the hippocampus. Figure 4 [modified Figure 1.4 of Fix] is a parasagittal view of the brain depicting the relative position of the four external lobes. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Central sulcus Frontal lobe ^ Parietal lobe Temporal pole Paricto-occipital sulcus Occipital pole Cerebellum Medulla Figure 4 Lateral [parasagittal] view of the brain Figure 5 [modified Figure 1.5 of Fix] is a median or midsagittal view o f the human brain, depicting the frontal, parietal, and occipital lobes. Note the central and parietooccipital sulci and the genu of the corpus collousm. Central sulcus Parietal lobe ____ I Frontal lobe Parieto-occipital sulcus Occipital jjm jLg lobe Temporal lobe Corpus callosum [genu] Hippocampal sulcus Figure 5 Medial surface o f the brain 8 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The diencephalon lies between the telencephalic and mid-brain structures, and primarily contains thalamic and endocrine based structures. The mesencephalon or the mid-brain lies between the diencephalon and the pons, which itself lies caudal to the aforementioned structure. The medulla is rostrally limited by the pons and caudally limited by the spinal cord. The pontomedullary junction is defined by the foramen magnum, the pyramidal or motor decussation, and the existence of the first cervical ventral nerve roots. The cerebellum is posterior to the brainstem and inferior to the occipital and temporal lobes. Attachment to the brainstem occurs via the three cerebellar peduncles. Figure 6 depicts the important mid-sagittal structures including the spinomedullary junction [modified figure 1.6 of Fix]. Brain material, as with other biological material, is non-linear, anisotropic, and inhomogeneous. Central nervous system organization is based on morphological grouping of white and gray matter, with the former consisting solely of the myelinated axonal processes of the cell bodies of the latter. Ultrasonic testing of fresh lamb brain tissue by Lin, et al. [1997] resulted in an estimation of bulk moduli of the white and gray matter to be 2.41 GPa and 228 GPa, respectively. The respective densities of the white and gray matter [genu and rostrum J Corpus callosum [splcniumj Third ventricle Fourth ventricle Midbrain Cerebellum Medulla Interventricular Corpus callosum Corpus callosum foramen [body] Spino-mcdullary junction Figure 6 Midsaggital view o f the brain 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. were taken as being 1.043 g/cm3 and 1.039 g/cm3 with the assumption o f minimal shear modulus in comparison to bulk modulus [Holboum, 1943]. The higher bulk modulus of the white matter was attributed to the fibrous nature of the sheath components [also by Arbogast, et al, 1997]. Anisotropy was noted with the bulk modulus of the mixed tissue in the supero-inferior axis being greater than in the other principle anatomic axes. Arbogast, et al, characterized the instantaneous elastic shear moduli of porcine brain stem specimens as 681 Pa for gray matter and 1036 Pa for white matter. Comparison with bulk moduli values reported by Lin, et ?.I [1997], as indicated above, validate the assumption o f the relative variance, by orders o f magnitude, in brain shear and bulk moduli. The important biomechanical manifestation of this will be discussed in a later section. The osseous structure covering the encephalon is formed by 8 cranial bones. Those that cover and protect the superior aspect form the cranial vault, while those that provide protection for the inferior aspect form the cranial base or basilar aspect. The cranial bones of interest are the frontal bone, the parietal bone [2], the occipital bone [2], the sphenoid bone, and the ethmoid bone. The bones of the cranial vault are interconnected through a system of non-mobile synarthrotic joints termed sutures. The sutures are named based on anatomical position. The following figure depicts the aforementioned osseous structures [modified figure 6-1 ofNorkin & Levangie], 10 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Parietal External auditory meatus Squamus part o f temporal Coronal suture Lambdoid suture \ / Frontal Maxilla O cciput Body of mandible Figure 7 Lateral view of skull The brain is invested by three distinct layers of connective tissue, which are together referred to as the meningis. The pia mater is a delicate highly vascularized membrane that covers the surface o f the brain, including the various gyri and sulci. Adjacent to the cerebral hemispheres of the brain, the pia mater provides the vascular support to the hemispheric gray matter. Adjacent to the pontomedullary junction, vascular support is provided to the cerebral gray matter, subsequent to passage through the intervening white matter. The pia is connected to the overlying meningeal layer, the arachnoid, via a trabecular system. The arachnoid is a thin layer of nonvascular tissue. The arachnoid houses the arachnoid villi, which direct the flow of cerebrospinal fluid in a unidirectional manner from the subarachnoid space into the venous circulation. The outermost meningeal layer is termed the dura. The dura is a thick fibrous membrane composed of two separate layers. The endosteal layer of the dura approximates the internal cranial surface, forming the internal periosteum. The meningeal layer of the dura, composed of epithelial cells, forms the falx cerebri, the tentorium cerebelli, and the falx cerebelli. The falx cerebri lies in the longitudinal cerebral fissure, separating the two cerebral hemispheres and forming the superior and inferior sagittal sinuses 11 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. between its two layers. The tentorium cerebelli separates the temporal and occipital lobes o f the cerebrum from the cerebellum and infratentorial brainstem. The falx cerebelli separates the lateral cerebellar lobes. The potential cranial space defined by the separation between the periosteal and meningeal layers of the dura is termed the epidural space. The meningeal arteries and veins are contained within this space. The potential space between the dura and the arachnoid is termed the subdural space. The space contains the physical pathways for the superior cerebral veins, which pass to the superior sagittal sinus for purposes of drainage into the venous pool. This space between the arachnoid and pia is termed the subarachnoid space. The space, in the adult human, extends caudally to the level of the lumbar cistern, which is located at approximately S2. The subarachnoid space contains cerebrospinal fluid. Cerebrospinal fluid is a filtrate of blood secreted by various choroid plexi, which are composed o f capillary beds in conjunction with ependymal cells, lying within the ventricular system o f the nervous system. Cerebrospinal fluid functions as a mechanical damper, preventing contusive damage to neural tissue. It also exhibits endocrine, nutritional, and immunological roles. The ventricular system itself is composed o f fluid filled cavities located within the brain. The lateral ventricles lie within the region o f the cerebral hemispheres, communicating with the third ventricle by means of the interventricular foramen of Monro. The third ventricle passes cerebrospinal fluid into the fourth ventricle by means o f the cerebral aqueduct. Fluid is passed in to the cistema magna, which is a segment of the subarachnoid space, via the bilateral foramen of Luschka and the single median foramen of Magandie. Passage through the arachnoid villi into the superior sagittal sinus returns the cerebrospinal fluid into the venous pool for recirculation. Cerebrospinal fluid is moved through the central nervous system without any active pump mechanism, per se. The total volume of fluid that is typically contained at any given time is approximately 140 mL. On a daily basis, 500 mL of cerebrospinal fluid is produced by the ventricular choroid plexi. The continual R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. production of fluid forces the existent fluid through the appropriate passages, directed by unidirectional flow apertures, into the venous circulation. The following figure [modified Figure 2.3 o f Fix] depicts the relevant structures in the cerebrospinal fluid pathway. The arrows depict the direction o f fluid flow. Superior sagittal sinus Great cerebra sYcin o f Galen v.»] Third ventricle Cerebral aquaduct Fourth ventricle W 7 ^Cistema [7 magna 4 Subarachnoid |i space — Subdural space I — Epidural space Pia mater — J Arachnoid - Dura mater — Central canal -Conus mcdullaris Filum Tcrminalc Lumbar cistern Figure 8 Cerebrospinal fluid flow pathway 13 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. III. General Brain Injury Biomechanics The potential for traumatically induced neuropathology is, generally a function of the magnitude o f the developed head acceleration, the onset rate of head acceleration, and the interaction between the point of load application and the resultant direction of head acceleration. In general then Type & Severity of Injury = / {magnitude, onsetrate, direction) [I] As stated in the introduction, contact and inertial loading of the head result in injury by the development of structural loads that are greater than the tissue tolerance values, for a given region. It is also noted that each type o f loading had typical characteristic acceleration magnitudes and onset rates. This same idea can be presented in a slightly different manner by describing the way in which the impact energy is managed [Gennarelli & Thibault, 1989]: Energy = E n e r g y ^ , = £ E v e n t s + £ E v e n ts ^ [2] Where; co n ta ct E n e r g y j t e p a t c ^ l K n ^ Jis^posed^kultvnlum ccnhngc rfu n p a tctljtrtx n ta vep ra p a g a tia n 1 Y E vents.^, - E n e r g y + E n e r g y [4] Intrinsic to the energy management discussion is the time course over which the event occurs. The development of clinical symptomatology predominantly follows the pattern depicted in Figure 9, but once again it should be noted that the etiological relationship is solely based on the level o f loading characteristically developed by inertial and impact loading. 14 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Focal Injuries Intracerebral Hematoma Vault Sc Basilar Fractures ' ’ I Coup Contusion I Epidural Hematoma] l3£G6ncussura3fel | Coma Remote Injuries Impact Loading Inertial Loading Stress Wave Injuries Contra-coup Contusion Subdural Hematoma Input loading condition Linear Sc Depressed Skull Fracture Translational Skull Deformation Skull Volume Change j Stress Wave Propagation Figure 9 Pathomechanical neural injury schema Fracture refers to osseous dissociation, which may result in comminuted or well defined bone fragments. The osseous fracture debris are either displaced or non-displaced (in relation to the pre-fracture site). Areas relating to the cranial vault reference the osseous skull superior to the encephalon while those referencing the basilar area refer to the osseous skull inferior to the encephalon. A hematoma refers to a localized mass o f extravasated blood that is wholly confined within an organ, tissue, or space. Hemorrhage refers to the escape o f blood through the walls of vascular tissue. Contusion refers to the collection of blood, under an unbroken skin layer. Epidural hematoma refers to the collection of blood between the meningeal dura and the periosteal dural layer. Subdural hematoma refers to the collection of blood between the meningeal dura and the arachnoid layer. Subarachnoid hematoma refers to the collection o f blood between the arachnoid membrane and the pia mater. An intracerebral hematoma is based on the collection of blood within the cerebrum. 15 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Contusion to the tissue underlying an impacted area is referred to as a coup contusion, while that o f the opposite pole is referred to as a contracoup contusion. Intermediate coup contusions are based on a specific type of expressed neuropathology, which will be discussed in a later section. Fractures o f the skull Linear fractures o f the skull arise solely due to impact phenomenon, which result in failure of the skull due to localized bending, failure, and subsequent crack propagation. A model based on differential compression and tension tolerances was proposed by Gennarelli (1989), which is summarized in the following diagram: Compression of Outer Table Tension of Inner Table Bone is weaker in Tension Local Skull Inbending Fracture Initiation at the Inner Table Impact to the Skull Fracture length & direction = f [skull thickness at impact site] Fracture Propagation along Path of Least Resistance Figure 10 Mechanics of linear skull fracture The model is valid in cases where the thickness o f the impacted area is such that local bending effects are significant. In cases where the impacted area o f the skull is thick enough to prevent the local effects of depression, tensile loading is developed of the outer table, distant from the site of impact. Tensile failure at a site distant to the impact site in conjunction with inner table compression proximal to the impact site is the mechanism proposed for development of remote vault fractures and basilar fractures. It should once again be noted, as a matter of review, that the osteal aspect of the skull consists of two layers of compact bone with an intervening cancellous or diploe layer. The superficial and deep layers o f compact bone are named the outer and inner table, respectively. 16 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Depressed skull fracture represents a form o f contact phenomena based on concurrent compressive failure o f the softer cancellous bone core with shear failure of the cortical shell. SAE J885 [1993] indicates that a contact area of approximately 2 in2 (13 cm2 ) represents the boundary between distributed and concentrated loading. Contact areas smaller than approximately % in2 (5 cm2 ) result in local skull perforation, with the perforation site being equal in size to the impacting object. Differing results were obtained, however, in tests conducted by Hodgson et al. (1970) in which cylindrical impactors of contact area o f 0.31 in2 were dropped against the frontal bone of cadaver subjects. Resulting fracture patterns included linear as well as localized elliptical fracture patterns. Similar testing conducted with impactors of 3.1 in2 contact areas resulted solely in the development of linear fractures. Epidural Hematoma Laceration of the superior sagittal vein, superior sagittal sinus, or middle meningeal artery have all been linked to the development o f epidural hematoma. The injury can occur via laceration or by, as according to Gennarelli (1989) through significant skull depression. Contusion Coup contusions arise at the impact site due to direct trauma or due to pressure gradient formation across neural tissue, with injury occurring subsequent to resumption o f pre-impact positioning. Impact results in trauma due to the development of compressive tissue stress of the impacted tissue. Cycling of the tissue through a pressure gradient could result in failure as the tissue is compressed, failure due to tensile loading as the tissue returns to its preimpact position, or cavitation if the local pressure is low enough to result in localized water content phase change at physiological temperature. 17 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The brain, as a fluid mass, moves relative to the skull under both conditions of impact and inertial loading. Contrecoup contusion occurs secondary to the inertia of the brain in conjunction with tissue attachments opposite to the site o f impact or opposite to the direction of movement. Motion of the skull due to impact is antecedent to motion of the brain. The brain remains at rest relative to the skull, which result in tensile failure of neural tissue on the counterpole, with respect to the point of impact. Gauer [1950] noted that the time rate of change o f acceleration played a special role in the development of contrecoup contusion injuries. Intermediate coup contusion injuries are based on the development of vascular ruptures distant from the meningeal attachment between the skull and encephalon. Gennarelli [1989] postulated an injury mechanism based on approximation of neurovascular structures against internal stiffer structures such as the falx cerebri, the tentorium cerebelli, and/or the falx cerebelli. Cortical contusion and associated intracerebral hematoma have been indicated to occur as a result o f both impact as well as inertial loading. Injury could possibly occur as a result of the rupture of deep cerebral vasculature secondary to contusion of the surrounding neural tissue. Subdural hematoma Rupture of the superior cerebral veins, also referred to as the bridging veins, results in extravasatea blood clotting in the region between the dura and the arachnoid. The superior cerebral veins drain into the superior sagittal sinus. Association with concomitant cortical contusion or laceration results in the terminological determination of complex subdural hematoma. Testing of isolated tissue samples by Lowenhielm (1974) indicated that mechanical response of the human bridging vein is strain-rate dependent. A factor of 3 increase in the strain rate resulted in a gross reduction in the specimen elongation at failure. Haut and Lee, as referenced by Thibault (1990), indicated that elongation at failure of human bridging 18 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. veins is independent o f the rate at which the loading in applied. Thibault (1990) indicated that use of the injury criterion proposed by either o f the aforementioned groups did not correctly account for the in-vivo case secondary to the lack of use o f perfused specimens. 19 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. IV. Human SubjectTesting — Upper Limits The upper tolerance limits o f human subject testing, in which acceleration loading levels can be correlated with the development of subjective complaints as well as gross injury, have been utilized for all primary axes o f loading [Snyder, 1961]. A review of the human tolerance testing literature, as included in the Bioastronautics Data Book [NASA, 1971] and in German Aviation Medicine in World War II [1954] reveal a differential classification of abrupt versus sustained acceleration loading based on duration of application [NASA, 1971] and on mechanical response o f the human circulatory and respiratory system [Ruff, 1950]. An application duration o f less than or equal to 0.2 seconds for the impact conditions is suggested, with an application of greater than 0.2 seconds for sustained acceleration. The designation was proposed by Stapp in 1961 in the context of aeronautical testing. Ruff [1950] provided a division between impact and sustained acceleration application based on the lack or presence, respectively, of circulatory and respiratory system damage secondary to hydrostatic injury mechanisms, which in turn require significant time duration applications for development. Due to the ethical, financial, and time considerations, a majority o f the studies cited are based on testing involving humans as well as non-human subjects. Where possible, with concomitant maintenance o f test integrity, the human and non-human subject tests have been separated. Due to the nature of the application in which a majority o f the studies were conducted, a physiological axis system was chosen that unfortunately differs from that which was presented in SAE J211 recommended practice. The data as presented in this discourse utilizes the latter convention, such that conformity with current standards is maintained. The following figure depicts the axis labeling for the system suggested by SAE J211. 20 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 11 SAE J211 sign convention The primary axial tolerance of interest is the +GX direction, or “eye-balls in” loading in terms o f the vernacular. Acceleration in the +x direction results in anterior displacement of the bones that form the orbit with respect to the orb, which secondary to inertia, remains at rest. This results in an apparent posterior movement of the eyeballs “in [to]” the socket. Figure 12 [modified Figure of Fraser] represents the plateau load as a function of plateau load duration for maximum voluntary tolerance in the +GX direction for human volunteers utilizing restraint harnesses, couches, or anti-G suits, depending on the series from the data was taken [Fraser, 1966]. Each method of occupant restraint will provide for a different occupant response to the same vehicle acceleration profile. G limitation -G, Transverse acceleration (+G,) G limitation -G, G limitation -G, Time [sec| Figure 12 +GX Tolerance as measured by plateau load vs. duration. 21 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The following figure represents the average acceleration loading incurred by subjects as a function of duration of loading [Chambers, 1963]. The ability to withstand a given +GX average acceleration load and a given duration of application is considered safe or unsafe based on the positioning with respect to the depicted tolerance line. TTTT .01 J32. .05 .1 .2 .5 1 0 2 0 S.0 10 20 S O Time [mln| Figure 13 +GX Tolerance as measured by average acceleration vs. duration Finally, Figure 14 depicts the tolerance of highly motivated pilots who were appropriately restrained and conditioned to the effects of acceleration loading [Fraser, 1961]. The acceleration values depicted represent average values or dwell values. s a e e < 600 400 200 300 0 too Endurance tim e [sec| Figure 14 +GX tolerance for preconditioned pilots 22 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The following table represents a short review o f significant individual and multiple test series in which +GX acceleration tolerance values were obtained. A more complete review is presented subsequently. Snyder [1961] who originally reviewed the material presented below noted that test subjects were commonly if not solely young healthy male subjects that were tested under conditions of rigid restraint with voluntary termination of exposure prior to levels corresponding with irreversible injury. Source: Peak acceleration [G]: Duration [sec]: Jolt [G/sec]: Comment: Henschke [1945] 28.8 0.01 Maximum tolerance without symptoms o f cerebral concussion was 34_ 3 G. Belt and harness utilized, head unsupported Stapp 11.5 — 31.5 0.165-0.405 489-1065 There subjects, twelve tests on a 2000 ft rocket track. Defined a safe exposure limit for human tolerance to deceleration as being 30G for a duration o f 0.11 seconds. Stapp [1949] 45 0.09 500 No test subject shock Stapp [1949] 45 023 413 Run 215, Delayed Effects Spatz [1950] 30 0.10 Rearward seated deceleration Swing apparatus. No restraint. Lap belL Headaches o f varying duration Lombard [1951] 36 [approximated] Impacts to the occipital region of Human volunteers without subjective or objective signs o f concussive brain injury. Accelerometers mounted in the impactor. Average acceleration o f 18 G. Stapp [1951] Stapp [1951] Stapp [1955] 50 0.25 500 10 - 35 0.15 - 0.42 500-1200 1 0 -3 5 0 .15-0.42 500-1200 Adjustable upper torso Two tests on a 2000 ft rocket Track. Observed signs of decreased blood pressure, pallor, increased pulse rate Two tests on a 2000 ft rocket Track. Observed signs o f decreased blood pressure, pallor, increased pulse rate. Beeding [1957] 26.8-28.6 0.067 - 0.077 6432 — 940.5 Acceleration values specifically 23 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. measured at the head. Subjects developed mild discomfort, skin abrasions, headaches, chest pain, brief disorientation, cervical and lumbar pain, and decreased blood pressure. Stapp [1958] 135 60 035 5000 5000 Persistent Injury Transient Injury Stapp [1968] 38 0.16 1300 Test subject shock USAF [1969] 45 25 0.10 0.20 Double harness with 3” shoulder straps, seat belt with thigh straps, chest belt Beeding & Moselv [1960] 85 0.04 3800 Fifty tests with young male Subjects that utilized shoulder harnesses, lap belts, and inverted v-straps. Acceleration values measured at the chest. Snyder [1961] 15 400-800 Increased deep tendon reflex Snyder [1961] 20 400-800 Stunning o f subjects for 10-15 Seconds, euphoria, hand tremor, decreased coordination, talkativeness, increased muscle tone, and gross involuntary morions o f the head, trunk, and upper extremities. Snyder [1961] 25 400-800 Absence o f deep tendon reflexes For several seconds followed by hyperactivity for approximately I minute. Snyder [1961] >25 1000 Abnormal EEG patterns for Several minutes post-impact. Table 1 Short review of important aeromedical testing Testing in which chimpanzee subjects were utilized [Sonntag, 1958] and analysis o f free fall data indicates a survival limit for +GX direction acceleration of less than 237 G with 0.35 seconds duration and 11,250 G/sec onset rate. Figure 17 is often produced and referred to in discussions of +GX tolerances. Acceleration dwell levels of up to 0.01 seconds reveal a linear decrease in tolerable dwell acceleration values for increases in dwell time. Snyder indicated that is in a system governed by a low frequency response, such as the human system in the context of impact, impact durations exceeding 0.01 seconds do not result in an increase in the human response to a given input. Long duration impacts, however, allow for 24 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. significant development o f hydraulic effects, thereby further reducing tolerance values than that just predicted by extrapolation of the region o f dwell accelerations of less than 0.0 L seconds. W 4 t l 30 2 0 to S 4 3 1 ■ 001 .002.003 .005 O U K A IIU N OF- U N IF O R M A C C E L E R A T IO N I k I « G , KTKF5T -T O -a ACX} Figure 15 +GX survivable abrupt impact As stated in the discussion subsequent to the presentation o f Figure 15, utilization of the “Eiband” tolerance curve in the subject context is misleading due to the differences in acceleration pulse waveform. Another misapplication o f the above is based on the lack of observance title of the axis, which indicates that vehicle [motor vehicle or sled] dwell acceleration was measured and not the acceleration of any segment o f the occupant. The following tolerance curve is based on a collection of data representing predicted acceleration loading in transverse falls [duration of less than 0.03 seconds], short track impact facility testing [duration of between 0.03 and 0.10 seconds], high speed sled runs [duration o f between 0.1 to 1.0 seconds], and centrifuge testing [durations of between 2 and 1000 seconds]. 25 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. • __ a _____ _ _ _ __ _ . _ _ _ ____ _ _ _ _ _ _ - _ ____ _ _ ____ — E — — - = — - -■ — — - - ------- — - - — A N S Y E R S E 1 . P A L L S I jO A M A C E l r z o H E i s I □ □ e _ H □ - _ _ _ _ _ ___ - _ _ /O L U H T A R T a J K £ T R A H S V E R S 6 Tl< 5 1 — - - — - - — nh □ • A C C E L c R A i r«i d□ ' J _ _ _ _ S A F E z o t I E . — ■ ! — 7 7 , 7 t m 1h 1 5 2 2 — H : — □ = T — — = =— 1 — - - — - - ■ — r i I k U . tz l i U f . J X u - u .01 .02.03.05 .1 2 J i I 2 3 3 10 20 30 50 100 200300300 1000 Duration [sec| Figure 16 Voluntary tolerance to peak +GX acceleration Figure 17 depicts human tolerance in terms of vehicle acceleration and duration o f peak acceleration. The voluntary tolerance line for +GX is based on two data points. The two data points above the tolerance line were obtained by Stapp. The first data point was for a 50 G peak run, with duration of 0.25 seconds, and an acceleration onset rate of 600 G/sec. The second date point was for a 40 G peak run, with duration of 0.15 seconds, and an acceleration onset rate of 1500 G/sec. 70 60 s U S O s o '■ = 40 ra & > S 30 u c j £ +Gx 600 g/ ISC + G *i 1 00 - i s / > H iN XK.C 0 H ^ M C Q NCUS D R R H A f s « ] _ L/W*_I & -fG x 100 • 0 g /s » c bareL y c RECO VER : o » E D ts It :tou s. A , 5 D A YS 20 10 0 ..01 .02 .03 .O S .1 .2 -3 5 1.0 2 3 5 Duration of peak acceleration [sec] 1 0 Figure 17 Voluntary tolerancing for +GX acceleration Examination o f Table 1 reveals tolerance values that appear to be contradictory. For example, the testing o f Snyder [1961] resulted in the indication acceleration applications of 20 G with onset rates o f between 26 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 400 and 800 G/sec resulted in the development of objective symptomatology. This is in apparent contradiction to the “safe” threshold established by Stapp [1951, 1955] of 30 G with an onset rate of between 489 and 1065 G/sec and a duration o f 0.11 seconds. It is difficult to make direct comparisons between testing by individual researchers and also between different studies between the same researcher secondary to the variation in the test vehicle utilized, the occupant restraint system utilized, and the location at which the acceleration values, onset rates, and durations were measured. It is also important to note that a majority o f the studies cited in Table I excluding the study by Lombard [1951] and maybe certain others were conducted to study the effects of deceleration on the human subjects [-Gx or eyeballs out]. There is a certain degree o f similarity between human tolerance to +GX and -G x acceleration [in general] but full “isotropicity” is not present. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. V. Concussive Brain Injury Concussion is defined clinically as: “A clinical syndrome characterized by immediate transient impairment of neural function such as alteration of consciousness, disturbances of vision, equilibrium, etc. due to mechanical forces. [Committee of the Congress of Neurological Surgeons]” The utilization of subjective terminology delineating the time course of impairment is not consistent and, in the clinical setting, is often arbitrary. Numerical valuations defining “transient” impairment vary from a few minutes for the most minor forms o f diffuse injury to six hours for comatose delineation. The level of trauma to the brain as measured by levels of consciousness is determined per clinical examination and subsequent numerical rating to the performance of a battery of tests. The Glasgow Coma Scale, as the latter is named, is given in the following table. Glasgow Coma Scale Eye Opening Task Spontaneous To Sound To pain No Response E4 3 2 I Motor Response Task Obey M6 Localizes 5 Withdrawal 4 Abnormal Flexion 3 Extension 2 No Response 1 Verbal Response Oriented V5 Confused 4 Inappropriate 3 Incomprehensible 2 No Response 1 EMV Score 3-15 Table 2 Glasgow Coma Scale Subjects presenting with Glasgow Coma Scale scores o f between 13 and 15 are indicated to have sustained minor or mild brain injury'. Ommaya [1988] applied the general Abbreviated Injury Scale [AIS] to concussive injuries. The general AIS code is presented in Table 3 with the specific application given in Table 4. 28 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Code Category L Minor 2 Moderate 3 Serious 4 Severe 5 Critical [Survival Uncertain] 6 Maximum [Virtually Unsurvivable] Table 3 Abbreviated Injury Scale AIS Level Concussion Grade Clinical Description Pathologic Description 1 I Confusion without amnesia Not Known — Variable 2 II Amnesia without coma [Type A & B — Slow & Rapid Onset] 3 III Coma with duration < 6 hours [Classical Cerebral Concussion] 4 IV Coma with duration 6-24 hours [Severe Head Injury] Increasing structural pathology 5 __________ V_________________ Coma with duration > 24 hours [Severe Head Injury]___________ Increasing structural pathology Table 4 Abbreviated Injury Scale Applied to Concussive Brain Injury Cerebral concussion is believed to occur, on the macroscopic level, as a result o f differential displacement of the brain with respect to the surrounding osseous skull. The conditions resulting in concussion can be created through direct head acceleration and by impact. In the latter, it should be noted that the impact in and of itself, does not cause the neuropathology, but does result in the condition in which relative brain to skull acceleration can occur. Historically, both prismatic and rotational acceleration have been listed as being inclusively causal o f the phenomenon of concussive brain injury. Most studies at first utilized canine and feline subjects followed by use of sub-human primates. Concussion thresholds were scaled from animal test data as support for varying concussion mechanism hypotheses. Also, testing of isolated tissue samples, human cadavers, and animal cadavers were conducted for correlation with the live animal tests. Due to the ethical implications, fewer tests involving human subjects under controlled conditions have been conducted. The relative contribution o f both prismatic and rotational acceleration in the context of cerebral concussion potential has been examined by a number of research groups. Holboum [1943], in his landmark paper, 29 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. indicated that translational acceleration was not sufficient enough to generate the stress-strain state required for the development o f diffuse and focal lesions. This has clearly been refuted in testing utilizing subhuman primate subjects. Presented, as discussed before, was a discussion which the relatively large bulk modulus o f brain tissue, in comparison to the relatively low shear modulus, was provided as a basis. Short duration acceleration loading resulted in an injury potential that was proportional with the resultant head velocity while long duration acceleration loading resulted in an injury potential that was proportional with the resultant head acceleration. Otnmaya [1970] indicated a similar relationship in discussion of angular motion and resultant injury potential. Gurdjian and Webster [1943] and Gurdjian and Lissner [1944] impacted the heads o f lightly anesthetized canine subjects with hammers, impactors, and falling weights. Pathologic changes in blood pressure, respiration, and reflexes were utilized to localize the sight o f injury to the medullary centers [including the reticular formation] o f the brain. Nuclei of the reticular formation o f the brain are responsible for regulation o f cardiac, respiratory, and sleep-wake function. Spatz [1950] indicated that, in as early as 1921, Breslauer-Schuck had shown both structurally determinable and structurally non-visible, i.e. “traceless disorders,” cerebral concussion to be localized to the brain stem. Epidural impact by air pulses of known magnitude and duration through a skull opening of lightly anesthetized canine subjects by Gurdjian, et al. [1954], elucidated the presence of chromatolysis in reticular formation cells. The latter pathology is defined as the destruction o f nucleic chromatin. Gurdjian, Webster and Lissner [1955], using a definition o f cerebral concussion consisting of an acute, post-traumatic state associated with unconsciousness, pallor, and shock, indicated that neural tissue damage could occur via compression against adjacent structures, tensile failure, and due to shear loading from pressure gradient formation. Impacts to free and restrained heads o f lightly anesthetized canine subjects by Gurdjian, et al. [1965], resulted in the development of chromatolysis in the brain stem. Due to the findings of damage in both cases, the role of cervical spine in the context o f medullary injury was listed as being minimal. Impact testing to the occipital region w'as 30 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. conducted by Hodgson, et al. [1969]. Concussion was determined as per the development o f post-impact temporary unconsciousness, temporary depression o f pupillary and comeal reflexes, transient loss of righting reflex, depression of gag and bite reflex, diminished response to noxious and pain stimuli, apnea, bradycardia, or bradyapnea. Once again, predominant areas o f chromatolysis were found in the brain stem without concomitant cervical cord damage. The proposed mechanism of injury was o f brain stem shear secondary to pressure gradient formation. The lack o f concomitant or exclusive cortical damage was utilized to indicate the minimal contribution, in comparison to prismatic acceleration, or rotational acceleration. It should be noted that the above described testing usually resulted in the subjects sustaining other forms of gross traumatic neuropathology such as skull fracture and meningeal hematoma formation. Ommaya, et al. [1970], created a tolerance curve for concussive brain injury based on data obtained from inertial loading o f sub-human primates. Injury causation was apportioned as being 50% to inertial effects, with a proportional relationship to rotational acceleration and an inverse relationship to translational acceleration. The remaining potential was due to contact effects. The distributive apportionment for the latter increased if the head was restrained and not free to move following the impact. Restrained subjects were placed in a mobile chair that was impacted at its base. Cervical spine range of motion was not limited by the presence of a head restraint. Results were scaled utilizing the methodology discussed previously. Details of the tolerance curve that was developed from this testing will be discussed in a later section. Hirsch and Ommaya [1970] conducted testing to examine the effects of limiting cervical range o f motion in sub-human primate subjects. Subjects were restrained in the manner described above, with the addition that certain individuals o f the test group were tested with a cervical collar in place. Head restraints were not utilized. Concussive brain injury resulted in at least half of the uncollared subjects while it developed in only 12% of collared subjects. The proximal cause for the difference was indicated to be the reduction of head rotational acceleration secondary to reduced cervical range o f motion in the collared subjects. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Unterhamscheidt [1971] conducted impact tests in which the unrestrained heads o f feline subjects were allowed to move in primarily prismatic post-impact motion. Sub-human primate head impacts with primarily rotational post-impact motion were also conducted. Traumatic pathology of the prismatically translated subjects was based on pressure gradient formation while that o f the rotationally translated subjects was based on relative brain rotation with respect to the skull. Gennarelli at al. [1972] performed comparative testing of 25 squirrel monkeys in which approximately half o f the cadre were subjected to head center of gravity prismatic acceleration while the remaining subjects were subjected to rotational acceleration of equivalent head center of gravity tangential acceleration magnitude. Head fixation and path determination was accomplished via a helmet that was rigidly attached to the HAD-II apparatus. Cerebral concussion development was monitored through use of somatic evoked potentials. Rotational accelerations o f 1.08 * 105 to 3.17 * 105 rad/sec2 resulted in cerebral concussion in all subjects while prismatic acceleration testing did not result in cerebral concussion in any tested subject. Gross cerebral neurovascular damage in addition to cerebral concussion was noted in all subjects, and therefore determination o f potential mediator sights for cerebral concussion can not be accurately determined. As an item of interest, however, gross lesions were elucidated at intracerebral discontinuities, but not at the brain stem. Ono, et al. [1980], conducted impact testing on 63 subjects of various sub-human primate derivation. A graded concussion criterion, similar to that of Ommaya, was utilized. A modified HYGE sled with a compressed air driven impactor was utilized. Impactor application occurred in a plane parallel to the Frankfort plane. Tests were conducted with subjects restrained in a manner in which post-impact trajectory was primarily translational, rotational, or was unrestrained. A softer impactor was utilized for the latter test configuration. Concussive brain injury was indicated, with a more profound grading, in all subjects in whom the post-impact motion was primarily prismatic. The tolerance threshold for concussive brain injury obtained from this testing will be discussed later. 32 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Thibault and Gennarelli [1985] utilized a HYGE shock tester that was modified such that the prismatic motion of the system was converted into angular motion via a kinematic linkage to develop a criterion for angular acceleration injury tolerance. Utilizing baboon subjects, programmable reproduction o f acute subdural hematoma, cerebral concussion, and difiiise axonal injury was noted. The results o f the latter in conjunction with isolated giant squid axon and physical model testing, were utilized to provide a cerebral concussion threshold o f 5,000 rad/sec2 at angular velocities of 75 rad/sec. Elson and Ward [1994], however, caution against relating cerebral concussion solely to rotational effects due to the difficulty in the decoupling of prismatic and rotational motion in the experimental setting secondary to the structure o f the head neck complex. Initial movement is usually prismatic, with predominating rotational acceleration during the later aspects of the motion as cervical stiffness increases due to the combined muscular activation of the posterior extensors and anterior flexors. Ommaya [1988] stated that the proximal injury vector in the case of rotational acceleration is the development o f surface shear strains that descend in a centripetal manner towards deeper structures. Clinical correlation was based on the sequential loss o f memory [amnesia] followed by a loss of sensorimotor function. The latter did not occur without the former, but documented cases of the former occurring without the latter were discussed. Memory loss was stated to indicate less severe concussive trauma as indicated by progression o f the strain to cortical and proximal subcortical structures of the frontal and occipital lobes, while medullary involvement was indicative of more severe cases of concussive trauma secondary to the deep positioning within the cranial structure. Centripetal strain progression was noted to be enhanced in areas o f structural and material discontinuity. On the microscopic scale, tensile and shear loading of the axonal tissue as a result of the acceleration of the brain result in transient membrane dysfunction. Loading of the brain, with respect to the skull, in shear 33 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. results in tensile loading on myelin sheaths o f the involved axons, which in turns results in tensile separation, in the case of profound diffuse axonal injury, from the Nodes o f Ranvier. The diffuse axonal injury mechanism for cerebral concussion has been visualized as a focal lesion in the corpus collosum, a focal lesion in the rostral brain stem, and widespread diffuse lesion o f the cerebrum as manifested by axonal retraction bulbs [Rowland, 1990]. The aforementioned structures, anatomically, are positioned in areas that exhibit geometric restriction, such as in the case of the brainstem as it courses caudally through the foramen magnum. Utilization of isolated tissue models has shown a high correlation between the development o f shear strain and rotational acceleration. Hodgson and Thomas [1979] conducted impact tests of mounted fresh stumptail monkey midsaggital hemisections, extending to the vertebral C7 level, under conditions o f prismatic, fixed rotation, and free rotation. Maximum values of shear strain, due to traction of the spinal cord, were found in the brainstem periphery for fixed rotational loading. Shear strains were negligible for the prismatic acceleration case. Uniaxial tensile loading of giant squid axons by Thibault and Gennarelli [1985] indicated that strains o f 5 to 10% with strain rates in excess of 50 sec'1 resulted in membrane depolarization with concomitant decrease in excitability. Recovery of resting membrane potential occurred over the course o f a number of minutes. Uniaxial elongation at 25 to 50% at comparable strain rates resulted in rupture. In cases o f minor diffuse axonal injury, tensile loading of axons results in membrane compromise. The resulting extravasation of sequestered solutes such as Ca2 + and other highly reactive substances results in tissue damage. LaPlaca and Thibault [1997] noted that removal of extracellular Ca2 + in the buffer solution of neurons undergoing deformation resulted in a reduced damage response for similar loading conditions in contrast to the case where the Ca2 + was allowed to remain in the buffer. LaPlaca and Thibault [1997] devised a novel device that allowed for tolerance testing of individual and grouped multipolar neurons to fluid shear stress with varying rates of onset. Neurons were cultured on the inferior plate of a parallel plate R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. viscometer, with the superior plate separated by a fluid layer o f known thickness. Shear stress applied by differential rotation of the superior plate with respect to the fixed inferior plate for various shear stresses and onset rates was tested. Cytosolic Ca2 1 - and extracellular lactate dehydrogenase concentrations were monitored. High shear stress loading resulted in varying neuronal uniaxial strains ranging from 0.01 to 0.53. Cytosolic Ca2 + and extracellular lactate dehydrogenase values were increased in high strain rate (> I sec'1 ) loading in comparison to quasistatic (< I sec'1 ) loading, clearly suggesting a significant viscoelastic character to the response. The importance of the latter was also noted by Thibault [1993], Meaney & Bain [1997], and Arbogast, et al. [1997]. Groups of closely associated neurons, for the same input shear stress and onset rate, exhibited a lower average uniaxial strain in comparison individual neurons. The latter could be attributed to the interdigitation between the processes o f the multipolar neurons, resulting in a lower exposed surface area per neuron, and thereby minimizing the developed strain. Concomitant measurement o f both [Ca2 + ] and strain allowed for the conclusion of variability in both for similar input shear stress, indicating neuron strain as the initial factor In the damage response. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. V I.' Brain Injury Criterion As will be shown in the following discussion, a number of brain and head injury criterion have been proposed based on testing utilizing varied numbers and types o f test subjects. Utilization o f animal, and especially sub-human primates, has resulted in the development of scaling methods based on similitude principles. Kikuchi et al. [1982] employed a scaling methodology based on a set o f assumptions to scale sub-human primate test data to corresponding levels in the human. They assumed similar geometrical shapes, relative structural dimensional similarity, and similar material properties. The following items o f terminology were defined: a = head acceleration t = head acceleration duration v - impact speed I = average skull radius h = average skull thickness The following three non-dimensional parameters were defined: 1 v -t a-h 7 T , — — 7t2 — 7t3 — , [5] h h v~ The ratio between the average radius and the average thickness of the human head was defined as 1/h, with the average head weight indicated to be 1.35 kg. The following law was proposed by Holboum [1943] for the purpose of scaling sub-human primate acceleration response data to the corresponding response that would be observed in humans. The angular 36 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. acceleration that would be experienced by a human, a h, based on that experienced by a sub-human primate, a „ can be defined as: Where Me and Mh define the brain mass for the test subject and the human, respectively. Assuming that the relationship between mass, density and volume hold, and that mass is proportional to the cube o f the length of the brain, then the above equation can be written in the following form: Where the term X represents the ratio of the characteristic length of the human brain to the animal brain. The scaling procedure, referred to as the equal stress-equal velocity scaling procedure, scales translational acceleration by 1 A., scales time by X, and scales angular acceleration by l/A .2. Limitations of this method of scaling include that only brains o f equivalent geometrical structure can be scaled, and that the time dependence in terms of the plastic effects o f impact reaction is not represented. Thibault and Gennarelli [1985] used the following scaling methodology: M 2/3 m J [8] Where 37 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 9 p = the measured angular acceleration o f the primate subject 0 m = the scaled angular acceleration for a human m o M p = mass o f the primate brain M m = mass o f the human brain The following equation was used by Ono et al. [1980] for the creation o f the tolerance lines for human tolerance values based on sub-human testing: 0 D = — [9] c o Where 0 D — angular velocity resulting in damage 0 D = angular acceleration resulting in damage c o = natural frequency of rotation o f the brain in rad/sec Based on the use of a single degree of freedom spring-mass system, it was indicated that differing long and short duration acceleration responses occur at between 1/3 to 1/4 the period o f the natural frequency o f the system. For the subject study, only short duration acceleration pulses were applied. The experimental values for angular acceleration were compared, for each species, to those obtained from the following scaling equation: Where M = the mass of the brain in grams C = constant derived from experimental data (gram*radians/sec2 ) 38 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A measured natural frequency of rotation for the rhesus monkey was 5-10 Hz. Based on the experience with one human subject, the corresponding natural frequency of the human brain was indicated to be 4-5 Hz. The use of an angular velocity threshold of 300 to 350 rad/sec and the use o f the aforementioned rotational natural frequency of the rhesus monkey brain resulted in the corresponding angular acceleration values from between 10,000 to 20,000 rad/sec2 for the tolerance threshold for the rhesus monkey. The constant C was calculated to be 2.16 x 10s rad*gmA (2/3)/sec2 . Based on the analysis of the direct versus the indirect contact data for the rhesus monkey, it was indicated that a 50% increase in the magnitude of head rotation was required for the development of cerebral concussion in cases of indirect impact. Wayne State Tolerance Curve The first documented development of a criterion for traumatic brain injury as a function of force loading by either direct impact or by inertial loading was initiated by the Ford Motor Company in 1954 in cooperation with Wayne State University. The purpose of this initial study was to determine the relationship between acceleration and the time required for fracture production in skulls o f four embalmed cadavers. The data from the latter in conjunction with additional isolated cadaver head drop testing was used to produce the portion o f the curve for impact durations up to 6 msec. Additional cadaver impact testing involving frontal impacts with laminated and tempered automobile safety glass was utilized for extension of the tolerance curve for impact durations of up to 12 msec. The Society of Automotive Engineers [1993] reported that testing conducted by Gurdjian, et al., in which pressure pulses applied to the dura with concomitant parietal and temporal region pressure measurement was utilized for impact durations of up to 10 msec. The latter may have formed a segment of the cadaver testing that was conducted to determine the tolerance for impact durations extending from 6 to 10 msec. Acceleration values were measured by accelerometers placed on the occiput for frontal cadaver impacts. 39 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Extension o f the tolerance curve for acceleration application durations of greater than 12 msec was conducted by Eiband and Stapp in which human volunteers were placed on rocket sleds that were rapidly decelerated from a constant velocity. The loading vector was inertial secondary to the differential movement between the free head and the restrained upper thorax. From the latter, an average acceleration asymptote o f 42 G was indicated for acceleration pulses o f greater than 12 msec, in duration. Additional work by Patrick, et al. [1965] indicated, based on documented cases o f volunteers surviving frontal impacts of magnitude greater than 45 G, that an asymptote of 80 G was more reasonable for long duration loading. The following figure is the Wayne State Tolerance Curve [Figure 73 o f Sances, 1986], which depicts the rate of average antero-posterior acceleration, measured at the external occipital protuberance, plotted as a function o f the time duration o f application. 5 0 0 olSOLATEO HEADS 1 • INTACT CADAVER HEAOS .♦VERTEX IMPACTS-!----- 4 0 0 o £ 3 0 0 " 200 < L > o < 100 100 Time (ms) Figure 18 The Wayne State Tolerance Curve All combinations o f average acceleration and acceleration durations occurring above the tolerance line suggest that reversible concussion without residual pathology can occur. Clinical correlation by Sances [1986] and work by Gurdijian [1961] are provided as a foundation for the relationship of human linear skull fracture as a predictor for concussive brain injury. 40 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A number o f authors including Versace [1971], however, have indicated that the Wayne State Tolerance Curve is flawed as a functional predictor for concussive brain injury. The majority of the complaints are based on the paucity of the data points used for the creation of the curve and for the subjects utilized in the creation of the curve. Fan [1971] even indicated that a majority of the subjects in tests that were utilized for the creation of the Wayne State Tolerance Curve did not exhibit skull fracture. The significance of the latter is based on, as stated above, the high degree of correlation predicted between occurrence o f skull fracture and the potential for concussive brain injury. With the former not being established in test specimens utilized for the creation of the tolerance curve, the ability for the prediction of the latter becomes difficult at best. Another complaint is based on the usable definition of average acceleration. Versace [1971] indicated that the definition of average acceleration as defined by Patrick et al. was one of being greater than half of the peak acceleration value. It was further indicated that the acceleration pulse waveforms used in the creation o f the Wayne State Tolerance Curve were o f the triangular or sinusoidal type. Also, it was recommended by Patrick et al. that the existence o f very sharp spikes in the acceleration profile be ignored. The use o f the Wayne State Tolerance Curve for providing graded levels o f injury for differing average acceleration magnitudes and time profiles was discouraged. Gadd Severity Index Gadd [1966] suggested the use of an injury criterion based on a time-dependant acceleration function. It was observed that as the time duration of exposure to an impact increased, the tolerable magnitude of impact acceleration decreased exponentially. An injury criterion based on integration of an exponentially weighted head acceleration function [based on the Wayne State Tolerance Curve] was provided. A weighting factor, on the acceleration term, o f 2.5 was utilized based on a straight-line approximation of the Wayne State Tolerance Curve, as plotted on Iog-log paper, for application durations of between 1.0 and 50 msec. An asymptote towards a fixed value o f acceleration magnitude was indicated as being existent for 41 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. acceleration waveforms o f similar shape. The criterion then, proposed by Gadd for injury potential for frontal impacts was termed the severity index [SI] and was defined as follows: Where a = acceleration response function n = weighting factor, usually 2.5 msec t = duration pulse length A Severity Index calculation of 1,000 entailed “a danger to life but not death.” In specific, a SI value of 1,000 was the threshold for the occurrence o f serious head injury in frontal impacts between a structure and a cadaver, anthropomorphic test dummy, or a 15 pound headform. Gadd also suggested a SI value o f 1,500 as being the limit prior to injury for non-contact or distributed force loading conditions. This value was based on acceleration values o f approximately 45 G as underwent by Stapp. No resulting clinical brain dysfunction or head trauma was noted, but the occurrence of retinal hemorrhages were indicated. A Severity Index value of 1000 was the median value for the number of occupants who survived and the number who did not, based on data provided by the FAA for laboratory simulations of field accident cases, some o f which, resulted in fatality. The Severity Index applied to prior sub-human primate and human volunteer testing. Gadd [1971] utilizing the I//’ inertial scaling factor for data obtained by Sonntag [1968] utilizing chimpanzee subjects, indicated that the equivalent human head acceleration plateau would correspond to approximately 100 G. Using a ramped acceleration function, the resultant SI value was 2000 for humans. In the discussion of United States Air Force rocket sled testing, Gadd mentioned that the provided whole- body acceleration values did not take into consideration the relative movement o f the head with respect to a [II] 42 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. restrained torso and the fall and rise for the acceleration versus time profiles, and the subsequent amplification o f the observed head acceleration due to the former factors. Human volunteers were required to assume chin to chest positioning to minimize injury. This resulted in resultant acceleration composed of components in both the anteroposterior and superoinferior directions. Discussion of Stapp’s experimental run number 110, resulted in a total exposure time of 150 msec, with a peak head acceleration, measured by a uniaxial anteroposterior accelerometer, o f 48 G for a period of approximately 75 msec. Integration of the acceleration-time profile resulted in an SI value of 550. Assuming a 45° angulation o f the linear accelerometer, estimated peak acceleration levels in the antero-posterior plane can be shown to be 68 G. This results in a SI value of 1200. For run number 215, assuming a 45° angulation of the accelerometer, resulted in a linear acceleration of 64 G. The SI value for this level of peak acceleration was given as 1500. In the discussion of Daisy Track Series testing, Gadd reported that the sled acceleration profiles contained average acceleration onsets of 1040 G/sec with plateau acceleration levels of 34 G. It is interesting to note that the heads of the volunteers were not restrained. Based on calculations from survivors of extreme free falls, survivability can be expected with plateau head accelerations reaching 100 to 200 G with an acceleration duration of between 10 to 40 msec. The following diagram depicts head injury tolerance as a function of plateau head acceleration level and acceleration duration [Figure 7.2 of Sances, 1986]. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chimponzecs Seated to tem on, Sonnfog Human Codover Fre« Ball Skull Fractures, U u n tr 200 . 150 c/j . t : io o Chimpanzees,— I — J----- Vvying Restraint.Stapp E tb a n d ------ NASA injured humans 20 Eibond NASA •uranjiffed- NASA 1966 Fraser -Gz- 400 1000 1 0 40 4 1 0 0 1 0 , 0 0 0 Time [msec] Figure 19 Summary of NASA testing in context of Severity Index Validation testing by Hodgson and Thomas was conducted through frontal fracture studies in 15 cadaveric skulls and in monkeys. It was stated that a “good” degree of correlation was obtained between the Gadd Severity Index and concussion in monkeys. It was stated by Hodgson that the use of a “theoretical stopping distance vs. velocity kinematics chart” be employed in conjunction with the use of the Gadd Severity Index. Hodgson further recommended the use of the Gadd Severity Index in the design of football helmets. A value o f 1,500 was recommended as the severity index limit. In comparison of head injury related fatalities, before and after the inclusion of this design parameter, which occurred in 1971, fatalities were reduced by 50%. The National Highway Traffic Safety Association (NHTSA) indicated in October 1971, that a SI o f less than 1,000 was an acceptable head injury criterion. Recently, based on the use of tri-axial accelerometers, 44 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. instead o f the uniaxial ones used previously, a SI of 1,500 has been deemed as an acceptable limit for head injury criterion. For passenger vehicles manufactured before August 3 L , 1976, a SI value of 1,000 is used. Versace [1971], however, was critical o f the use of the Severity Index for determination o f human head injury tolerance because o f the method o f derivation, the way in which the Severity Index was fit to the tolerance limit data, and the way in which the acceleration magnitude of a given pulse was applied. When plotted as a log-Iog curve, the Wayne State Tolerance Curve approximates a straight line with an intercept of the average acceleration axis of log (15.85 G), resulting in a slope of -0.4. After manipulating the resultant linear equation, the resultant equation formulation arises: 1000 = T- A 2"5 15.85 = A -T04 where. T = Duration of the acceleration pulse A = Average acceleration The above equation was indicated to be a pure linear curve fit to the observed data and in no way provided a means for grading injury severity. A poignant complaint was that if the above equation was an effective method o f injury severity scaling, then the second form of the Severity Index, with the acceleration term being unity, would mean that the value o f the exponent o f the acceleration term was not important. Also, the equation represented above could be modeled in any number of equivalent terms, by changing the exponents o f the acceleration and time components and by varying the numerical equality that defines the tolerance line. 45 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The tolerance to acceleration for the region between 30 to 100 msec, revealed an inaccurate fit between the Severity Index tolerance line in comparison with the observed data for the Wayne State Tolerance Curve and the curve proposed by Eiband. The use o f differing exponents and differing constant values for differing durations of acceleration was proposed by Versace as being a more accurate way o f modeling the data presented in the WSTC and the Eiband curve. It was further indicated that the use of differing acceleration waveforms of the same shape and effective acceleration magnitude could result in differing values o f calculated Severity Index, and result in discrepancies with the WSTC in excess o f 50%. Both Sances [1986] and Versace [1971] indicated that the Severity Index, based on input waveform, could deviate from the WSTC by as much as 54%. Another problem with the use of the Severity Index occurs in the attempted determination of injury tolerance for waveforms of low average acceleration values and large time durations. For example an acceleration pulse o f duration of 1000 seconds and average acceleration magnitude of 1 G would result in a calculated SI value of 1000. For this reason, a possible limit for the duration of applicable acceleration durations might be needed. Head Injury Criterion John Versace, in 1971, proposed an empirical head injury tolerance criterion that, however, still had a basis in the Wayne State Tolerance Curve. The resultant criterion was termed the Head Injury Criterion (HIC) and had the following formulation: ( i V 2 2 5 HIC = ( « .- « .) • U J Ja(t)'d t lI 46 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Where a = the acceleration curve ti and t2 are any two points on the acceleration curve that maximize the equation HIC < 1000 (value used for injury threshold) The HIC can be expressed in terms o f the specific kinetic energy and the acceleration over the time interval (ti-ti). The resulting formulation is: Prasad, et al. [1985] indicated that the basis for the HIC formulation was a set o f six data points from the Wayne State Tolerance Curve, which represent the tolerance levels for head acceleration for impact durations ranging from 1 to 6 msec. The principal difference between the WSTC and the HIC, as indicated by Sances [1986] is that HIC is an integration over the pulse, while the WSTC is based on average acceleration. It was indicated by Hodgson that head impacts not containing a critical HIC interval of less than 15 msec should be considered safe as far as cerebral concussion is concerned. Acceleration profiles that are represented by a step input or a square wave function result in an identical HIC and SI rating. A half-sine wave acceleration profile results in a maximum HIC that is 9.4 percent lower than the resultant maximum SI value. A triangular pulse waveform results in a maximum HIC value which is 13.8 percent lower than the corresponding SI value. The Federal Motor Vehicle Safety Standard (FMVSS) indicates that the resultant acceleration at the center of the head of a crash test dummy should be of a magnitude such that the HIC does not exceed a value of 1,000 for any time interval (fi, t2 ) in which the head of the anthropomorphic test subject is in contact with a part of the vehicle other than the seat belt system. The latter value of HIC for a given acceleration pulse has been indicated to be the threshold for the occurrence of cerebral concussions. Studies examining the r [14] 47 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. biomechanical validity of increasing the HIC value to 1,500 have been undertaken by Nahum and Smith [1976], Got, et al. [1978], Tam'ere, et al. [1982], and Prasad, et al. [1985]. The results o f the aforementioned studies were discussed by Prasad, et al. [1985]. Twenty-nine cases o f induced skull fracture were found in 54 cadaver head impact tests. HIC values ranged from 175 to 3400 with associated durations of 0.9 to 10.1 msec. The lowest HIC value associated with cadaveric skull fracture was 450 and die highest HIC value not associated with skull fracture was 2351. Fracture types ranged from basilar fractures to comminuted skull fractures. Based on the data o f Got, et al [1978], it was indicated that a threshold for skull fracture, based on HIC, was not established. The following figure [Figure 1 o f Prasad et al., 1985] demonstrates a plot o f the average acceleration as a function of the HIC duration for cadaveric skull fracture. Uniform bands o f HIC values are also plotted. • H odfltaa “ Pr»ctar« O H0tfgaofi ~ WindalWtfd tartan *•«-»*•€«*• ■ APft - fractu r* Q AP* - N * ft-tra« tw « u C t« O i v a HIC I f OQ iaso 1QQ0 7 f 0 100 HIC duration [msec] Figure 20 Summary o f impact data for utilization in HIC v With increasing HIC levels, one notices an increase in the incidence of post impact cadaveric skull fracture. Between the HIC ranges of 1000 and 1500, nine o f fifteen cadavers sustained skull fracture. Ten out of seventeen cadavers sustained brain injury as indicated through the visualization of extrvasated ink, for HIC 48 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. values within the range of 1000 and 1500. Based on limiting the maximum HIC duration to 15 msec, as a result o f mathematical inconsistencies (the same as with the SI) that arise from the HIC formulation for long duration impacts, the longest HIC duration associated with either skull fracture or brain injury was 13.7 msec, with the majority of impacts that caused either skull fracture or brain injury having HIC durations of less than 10msec. Based on the data, it was concluded that the threshold for brain damage, utilizing HIC, ranged from 516 to 2351. Based on the use o f certain statistical methods, it was concluded that for a given HIC level, both skull fracture and brain damage have an equal probability for occurring. For an impact with a corresponding HIC level of 1500, a 56 percent chance o f severe injury was noted to occur, while only a 16 percent chance o f injury was noted for a HIC value of 1000. With respect to non-impact cases a study of the field data resulted in no cases o f brain damage to occupants that were employing a 3 point restraint system and who did not have head contact with any interior frontal vehicle components [Prasad et al., 1985]. Due to the reliance of HIC on prismatic acceleration, without direct consideration o f angular acceleration, it was recommended by the Association for the Advancement of Automotive Medicine [1989] that HIC did not provide sufficient indication as to the potential for brain injury. An injury criterion utilizing inputs comprised of both angular and prismatic acceleration was suggested as a possibility for a replacement criterion. Vibrational Modeling Payne, as cited by Brinn and Staffeld [1970], suggested the use of a “Physiological Index” based on the displacement response mass-spring model subjected to an input perturbation. Characteristics for the head mass and spring stiffness were derived from whole body testing utilizing human volunteers. The following figure depicts a general one degree o f freedom system subjected to measured skull acceleration d2 y[t]/dr as 49 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. determined by a forcing function F[t]. The resultant displacement, as measured, with respect to the equilibrium position of the mass, is defined as x[tj. |— ► *© F(t) Figure 21 Schematic of a 1 degree of freedom system It is assumed that the reader has knowledge of differential equations and is familiar with the methods utilized in the derivation of the equation of motion for harmonic systems. The equation of motion for the above indicated system is given by the following: mx(t)+cx(t)+ kx(t) = f{t) [15] The following terminology has been utilized in mechanical engineering for the study o f vibrational systems, and therefore is pertinent to the subject discussion. The natural frequency co ■ i [16] The critical damping coefficient c = 2m c o = 2'Jhn [17] 50 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. The damping ratio £ = — = ^ £ - [18] 2m co The particular solution is dependent on the forcing function that is utilized- Substitution of the definitions given in [16], [17], and [18] into the characteristic equation of motion results in the following form o f the homogeneous solution: Au l=-<fm±mV<?2 - l [19] Validity of any vibrational model is dependant on the level of accuracy with which the parameters C , and c o are defined with respect to the dynamic properties o f the brain. Payne, in his model, utilized a zero value of damping, a natural frequency o f20.55 Hz., and a maximum allowable deflection of 1.857 inches. Slattenschek, as cited by Brinn and Staffeld [1970], Slattenschek, et al. [1971], and Sances [1986], proposed a model known as the Vienna Institute Index [JTI] with a natural frequency o f c o = 101 Hz as noted by Brinn and Staffeld [1970] or as f = 635 rad/sec as noted by Sances [1986] and a damping coefficient of 1, which provided for a suitable fit to the Wayne State Tolerance Curve utilizing a displacement limit of 2.35 mm. The physical parameters were provided by McElhaney, et al. [1970], in their discussion of the work of Brinn and Staffleld as the weight o f the brain being 10 lb, the damping coefficient being 33.00 Ib-sec/in and the stiffness being 10,400 lb/in. The tolerance index was given as the ratio of the measured or predicted displacement to the maximum displacement limit. The equation of motion is given as: 51 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. x + 2%cox+ 0 1 zx = F(t) [20] J = v x . ; [21] where x[t] Relative displacement of the brain with respect to the skull x(r) = Relative velocity o f the brain with respect to the skuil Xf) = Relative acceleration o f the brain with respect to the skull C O = Natural frequency o f the system $ Damping coefficient F(f) = Forcing function based on measured acceleration at the skull X o Maximum allowable displacement J Tolerance index X m Maximum displacement, x[t], generated by the model for a given F[t] Tolerance index values of less than unity were considered to be safe. Utilization of a triangular skull acceleration function provides for a deviation, at a maximum, o f 4 % from the Wayne State Tolerance Curve. Valid impact durations ranged between 2.5 and 50 msec. Brinn and Staffeld [1970] proposed a the Effective Displacement Index [EDI], which was a harmonic model similar to the JTI but allowed for variation in the damping coefficient as based on parameter observations from biomechanical testing. The parameter values chosen were, therefore, not solely based on the level o f approximation of the Wayne State Tolerance Curve. Utilizing the same form of the equation of 52 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. motion as [20], the system displacement response was compared with a maximum allowable displacement of between 3.75 to 4.5 nun. The natural frequency utilized was c o =482 rad/sec. The damping coefficient was allowed to vary, based on application, but was cited as being 0.707 by Sances [1986]. The acceptable acceleration duration was given as being between 5 and 250 msec. The Revised Brain Model [RBM] was proposed by Fan [1971] as an improvement to the Vienna Institute Index. The Revised Brain Model utilized the same system design as depicted in figure [21] and characterized by equation [20]. A damage criterion based on time duration of impact acceleration for long and short duration impacts, with respect to a 20 msec pulse duration, was utilized. Short duration impacts resulting in “local intracranial pressure” changes correlated with a velocity criterion while long duration impact resulting in cavitation or brain stem damage correlated with a displacement criterion. Utilization of a damping factor o f C , = 0.4 correlated with Wayne State Tolerance Curve tolerable angular velocity and prismatic displacement values o f 175 rad/sec and 1.25 in respectively. The former correlated with a prismatic velocity o f 135.3 in/sec. Correlation to the Wayne State Tolerance Curve for determination of critical values of displacement and velocity make the applicability o f the Revised Brain Model suspect for utilization in the determination o f concussive brain injury. The Mean Strain Criterion [MSC], consisting of a two mass model connected by a parallel spring-damper, was proposed by Stalnaker and McEIhaney. System parameters were determined from testing o f subhuman primates and human cadavers. Dimensional analysis was used to scale injurious predicted strain values from subhuman primate testing. A spring constant and damping coefficient of 8.6 kN/mm and 0.35 Nsec/mm were respectively utilized. The predicted brain strain compared with the maximum allowable strain o f 0.0061 mm/mm, which was based on taking the ratio of the model displacement with respect to the anteroposterior transverse length of 143.8 mm. The latter was given as the average distance across the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. cranium while the former was the unilateral displacement of the head. The Mean Strain Criterion was not based on the Wayne State Tolerance Curve. Figure 22 Physical parameters for the Mean Strain Criterion Ommaya [1985] indicated that for conditions in which angular loading was predominant, a rotational velocity of greater than or equal to 30 rad/sec with a concomitant acceleration of magnitude of less than 1700 rad/sec2 would correspond to an Abbreviated Injury Scale level 2 injury. Impacts with peak angular velocities of magnitude of less than 20 rad/sec and angular accelerations o f less than 4500 rad/sec2 corresponded to Abbreviated Injury Scale 0 or L injuries. Rotational Injury Criteria Figure 23 [modified Figure of Ommaya, 1970] depicts the tolerance bands for concussive brain injury in humans based on scaled data from 2 sub-human primate species, as presented by Ommaya [1970], plotted in terms of tolerable angular acceleration versus tolerable angular velocity development for a given time duration of loading application. 54 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. JPrxm «r«MC / / r / / S * Rotational acceleration [rjtd/!lKA2] Figure 23 Tolerance for concussive brain injury for unrestrained whiplash Once again it should be noted that longer duration loading results in a potential for injury that more closely correlates with the resultant head angular velocity while shorter duration loading results in a potential for injury that more closely correlates with resultant head angular acceleration. Ono, et al. [1980] as discussed previously provided a concussive brain injury criterion based in the form o f a tolerance curve. The latter was plotted as the average acceleration versus the duration o f acceleration loading. Data was scaled from occipital impact testing involving subhuman primates. The resulting tolerance curve has been termed the Japanese Automotive Research Institute [JARI] tolerance curve. 55 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 700 600 Threshold of C o o ciB sio n tn h u m a n 200 100 Duration [msec] Figure 24 Modified JARI concussion tolerance curve Gennarelli and Thibault [1989], based on the results of subhuman primate testing, provided a tolerance threshold for the threshold strain values for the spectrum o f diffuse brain injury based on peak rotational acceleration and velocity measured during the course of loading application. A uniaxial strain o f 0.05 was given as the low level for the occurrence of concussive brain injury, while a uniaxial strain value o f 0.20 was given as the lower tolerance level for the occurrence of severe diffuse axonal injury. 5 0 0 0 0 HIC =1000 " % > 3 0 0 0 0 1 " 2 0.21 O . IS 0 .0 5 , 5 0 0 3 0 0 200 100 Peak Rotational velocity [rad/sec] Figure 25 DAI Thresholds for various strains 56 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. GAMBIT Newman [1986] proposed the Generalized Model for Brain Injury Threshold (GAMBIT) which was based on both linear and angular components o f acceleration. The GAMBIT model can be thought o f as the equivalent, in the context o f decomposing acceleration components, o f the normal and shear stresses for a generalized loading condition. When used in conjunction with a probability curve, the GAMBIT equation predicts the possibility o f sustaining various levels of injury in accordance with the AIS. Figure 26 shows the GAMBIT curve. No Injury 0.8 m m n O.G C3 j o o 0.4 - C u 0.2 0 * ■ Unsurvivable/ Unbearable Injury 0.25 O.S 0.75 1 I-25 1.5 Maximum GAMBIT value t .75 Figure 26 Probability of various AIS level injuries as a function of maximum GAMBIT value The resulting equation for the GAMBIT curve is the following: G(t) = a(t)> J U c J y * [ 22] Where a(t) a(t) n, m, s the instantaneous value of translational head acceleration the instantaneous value of rotational head acceleration empirical constants selected to fit the given data 57 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The use of n=m=s=l provides a linear weighting function for the translational and rotational components of head acceleration, while n=m=s=2 provides for an elliptical fitting function. The final form o f the GAMBIT equation is derived by assigning critical values for translational and rotational accelerations, over which unacceptable levels o f injuries would be seen. Also, based on observations through validation testing, which will be described in the following section, it was determined that the maximum values for both translational and rotational head acceleration occur at approximately the same time, resulting in the following simplification of the model: a(t) -» a mand cc(t) -» ccra [23] The value used for the critical level of translational acceleration, as a limit for injury, was deemed to be 250 G, which when drawn intersecting the translational acceleration axis on an translational acceleration versus rotational acceleration plot, forms a region, assuming a rotational axis intercept o f 10,000 rad/sec2 , in which injuries to cadavers are not found. Also, according to Newman, the current data used for validation and boundary determination of the GAMBIT curve exists primarily for cases of high translation/low rotation and high rotation/low translation. Based on the data present, the use of an elliptical fitting function is no more appropriate than the use of a linear fitting function. Therefore, the resulting revised GAMBIT becomes G =— <1 [24] 250 10,000 58 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Newman cited three test series that were used for validation of the GAMBIT model. The first set involved the use o f 9 cadavers and was conducted by Nushoitz [1984]. Two specimens in specific were discussed. In both cases, reperfused cadavers were impacted in the frontal region using padded impactors. One o f the test subjects sustained subarachnoid hematoma in the right frontal lobe and subarachnoid hemorrhage in the parietal area. The other subject suffered no discernible injuries. The cadaveric subject sustaining injury had a locus in the translational acceleration range of 140G’s - 190G’s, and had rotational accelerations that were of higher magnitudes than that of the non-injured subject. The HIC values o f the injured and uninjured subjects v/ere 1063 and 1073 respectively. Thirty subhuman primates (rhesus monkeys) were tested by Gennarelli et al. in which they were subjected to angular acceleration pulses in the sagittal plane. Head motion was controlled such that the tangential acceleration was proportional to the angular acceleration throughout the fixed radius. Based on this, the maximum rotational and translational accelerations were indicated to have occurred at the same instant in time. Newman, based on the trends observed for the subject tests, indicated that the injury level increased with increasing head rotational acceleration for a fixed level of tangential acceleration. Newman indicated that, based on data showing differing levels of tolerance for human head accelerations, based on varying the anatomical contact point, a six-degree of freedom (one for each direction of principal angular and translational direction) model with critical values of acceleration for each of the degrees of freedom could be established. The equivalent translational and rotational acceleration terms, which are based on orthogonal critical values for each of the principal directions, would be substituted into the original equation: equiv [25] 59 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Another possible improvement discussed by Newman was the possible inclusion of time dependence o f the allowable average acceleration, such as that shown by the Wayne State Tolerance Curve (WSTC). The resultant, for GAMBIT, would be the production o f a 3 dimensional plot, the surface o f which would define the injury tolerance limits for a given level of angular acceleration, translational acceleration, and time. Ommaya et al. conducted a series of tests in which sub-human primates were impacted or underwent cervical hyperflexion-extension based injuries for the purpose of determining a threshold for the onset of cerebral concussion. Based on previous work, it was indicated that relative rotation between the head and cervical spine was necessary for the production o f brain injury in the absence o f skull fracture. 60 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. VII. The Motor Vehicle Context Aligned, colinear rear-end motor vehicle bumper to bumper collisions can be viewed as a biphasic sequential event train. The first event phase is constituted by the vehicle to vehicle collision. The vehicle speed change between the pre-impact and post-impact condition, or AV, o f the struck vehicle is one of the primary determinates of injury potential for the vehicle occupant. Factors such as the relative vehicle masses and relative vehicle stiffness, and restitution characteristics in conjunction with the relative closing speed of the striking vehicle can be utilized to determine the struck vehicle change in velocity. Vehicle stiffness responses are determined by parameters such as bumper system performance and make-up and the crush performance o f underlying structures such as the rear and front inner structures. The vehicle-to- vehicle aspect o f the collision provides for the initial conditions for the occupant loading. The latter can be modeled as a second collision, one that is between the occupant and the internal aspects o f the struck vehicle. The factors affecting the latter, including both geometric as well as engineering aspects of the vehicle interior will be discussed in depth in the following sections. The mechanics o f rear-end motor vehicle accidents involving colinear, bumper to bumper impacts have been examined by a number o f authors [Maclnnis Engineering Associates, Szabo et al., 1994, Bailey et al., 1995, Szabo & Welcher, 1996]. In that the primary thrust of this thesis is not the detailed discussion of the motor vehicle accident reconstruction aspect of vehicle to vehicle collisions, the reader is asked to refer to Szabo & Welcher [1997], A short summary of the pertinent formulations, in final form, is presented here. Terminology, as described below, will be utilized throughout. The subscript o f [1] will refer to the striking or bullet vehicle while the subscript of [2] will refer to parameters related to the struck or target vehicle. mt = vehicle mass [kg or slugs] w; = vehicle weight [N or lb] 61 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. g = acceleration due to gravity [m/sec2 or ft/sec2 ] V ; = vehicle pre-impact velocity [m/sec or ft/sec] v;’ = vehicle post-impact velocity [m/sec or ft/sec] f = drag factor [dimensionless] At = time duration of the collision event [sec] e = vehicle to vehicle restitution [dimensionless] Av; = vehicle change in velocity [m/sec or ft/sec] vc = closing velocity [m/sec or ft/sec] = vt — v2 vs = separation velocity [m/sec or ft/sec] = v2’ — V[’ The following diagram depicts the general vehicle orientation during the pre-impact phase: m i 1 1 1 1 1 1 - > + X Vehicle 1 [bullet vehicle] Vehicle 2 [target vehicle] Figure 27 Schematic for co-Iinear rear-end motor vehicle accident The equations governing the kinematics of the collision o f the type indicated in Figure 27 are given by conservation o f momentum, conservation of energy, and the coefficient o f restitution. Conservation of linear momentum in the +X direction results in the following formulation: m, -v, + m 2 -v2 = m, -v' +m , - v' [27] Conservation o f energy results in a formulation in which the initial kinetic energy o f the system is converted into post-impact vehicle kinetic energy, energy utilized in the causation of permanent vehicle crush, and energy dissipated as a result o f braking of the striking vehicle during the course o f the collision pulse. Obviously, if the striking vehicle is not being braked during the course of the collision, then the latter term is reduced to zero. Braking by the operator o f the struck vehicle is minimized during the collision phase as a result of occupant kinematic considerations. jm ,(v,)2+ i m 2( v J = im ,^ v l j + I m 2^v2) + X F « ‘At + Z Eo [28] 62 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The term SF^At refers to the impulse applied as a result of braking, with Fe^ being defined as the product of the drag factor f, the acceleration due to gravity g, and the mass of the striking vehicle, mi- In other words, the externally applied force is equivalent to the product of the drag factor and normal force on the tires of the vehicle. The energy dissipated as a result of permanent vehicle crush depends on the bumper systems present on the vehicles. The coefficient of restitution is a measure of the relative elasticity [or plasticity] o f the collision and is defined as the ratio of the separation velocity to the closing velocity. [29] Rearranging [27], [28], and [29] results in the following formulation for the respective vehicle speed change in terms of the above indicated physical parameters and the closing speed. w, -(l+ e)-v c + g - ^ F ca - At Av, [30] K + w 2) w, •(l + e)-vc - g - £ F H 1I-At Av, = ------------? -------------- [jI] (w, -t-w,J For a typical aligned rear-end motor vehicle accident the collision duration varies from between 100 to 150 msec, depending on the bumper characteristics o f the involved vehicles. In the experimental setting, factors such as the weights of vehicles, the acceleration due to gravity, and drag factors are usually known or can be accurately estimated prior to the conduction of any given collision test. The relative closing speed of the vehicles can be measured using a time trap consisting o f two electrical tape switches [connected to a differential timer] placed a known distance apart. Vehicle center of gravity 63 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. accelerations are measured through the use o f a tri-axial accelerometer array. Integration o f the resultant acceleration versus time trace provides the vehicle velocity as a function o f time, with the explicit indication that the area contained under the acceieration-time curve is a direct measure o f the vehicle center o f gravity speed change. Separation speeds, collision event durations, restitution, and vehicle displacements can be determined through analysis o f the acceleration data. Use o f standard video and high speed cameras in conjunction with the proper photogrametric methodologies can provide a complimentary method o f validation of the aforementioned measured and derived quantities. The vehicle to vehicle impact aspect o f aligned rear-end bumper to bumper motor vehicle collisions involves the interaction between the front bumper system and subjacent structures of the striking vehicle and the rear bumper system and subjacent structures of the struck vehicle. With the implicit assumption that the subject context involves bumper to bumper contact without an underride or an override collision and with the primary focus being occupant kinematics and loading of the struck vehicle operators cephalic region, a detailed discussion of the mechanics of the vehicle to vehicle collision event need not be discussed in detail. A brief discussion o f the relevant aspects o f vehicle structural design, however, will be presented. Bumper Systems The function of motor vehicle bumper systems, as defined by Federal Regulation Part 581, is solely for the minimization of damage to the front and rear of the involved vehicle in low speed motor vehicle collisions. Mitigation of motor vehicle occupant injuries, in the context o f Federal Regulation Part 581, is not discussed as a factor that must explicitly be taken into account for the vehicle to perform in an acceptable manner. Any benefits or deleterious effects due solely to bumper system design, without consideration of the remaining segments o f the vehicle, can then be considered to have occurred as being secondary. 64 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The simplest bumper system consists of a face bar mounted to the frame horns or the front subframe through a set of mounting brackets. The response of the latter form of bumper system is variable in terms o f structural response. Steel face bars mounted to the vehicle frame through robust mounts provide for a stiff bumper response and therefore provide for a decrease in observed deformation of the impacted region, but may also decrease the collision duration, and for a given vehicle speed change provide for an increased acceleration response o f the vehicle and the occupants of the vehicle. Chrome face bars or step bumpers mounted through low yield mounting brackets, such as those typically found on pick-up trucks, sport utility vehicles, and mini-vans provide a less stiff structural response at low speeds and deform under low impact loads. The following is an example of a simple face bar bumper mounted to the frame horns via a set o f brackets. Figure 28 Front bumper of a 1992 Ford F Super Duty Cab All isolator equipped bumper systems dissipate impact energy through the forced motion of fluid through an annulus or median orifice [Macinnis Engineering Associates]. An isolator is consistent o f a piston and housing cylinder assembly attached to the bumper face bar at one extremity and attached to the vehicle frame or front substructure at the other extremity. Siegmund, et al., [1995] described three types o f isolators commonly found on passenger motor vehicles. A Type I isolator is comprised, in addition to the piston tube and housing assembly, of a variably tapered diameter metering pin, an annulus, and a floating 65 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. piston. Compression of the bumper face bar results in hydraulic fluid motion through the annulus which in turn causes the floating piston to compress the gas in the piston tube assembly. Continued compression results in increasing resistance due to a decreasing annular diameter due to passage through it of segments o f the metering pin of increased diameter. At the cessation of the loading on the face bar, the compressed gas expands and the piston returns to its pre-compressed state. The following schematic [Figure 1 of Siegmund et al., 1995] depicts a typical Type I piston type isolator: Figure 29 Type I Isolator Assembly Type II isolators are similar to Type I but do not contain a metering pin. Compression of the face bar results in forced fluid flow through a constant diameter median orifice. The following figure depicts a schematic [Figure 3 of Siegmund et al., 1995] o f a Type II isolator. HYDRAULIC FLUID FILLED CYLINDER TUBE ASSEM BLY G A S FILLED PISTO N TUBE ASSEMBLY SEALING 3ALL—7 FLOATING PISTON /ANNULUS STOP' RING PISTON TUBE PISTON SEAL CYLINDER' TUBE B U M PER - B RA C K ET FRAME B RA C K ET FRAME — ‘ TUBE BRACKET Region of increased Constant diameter Region o f constant diameter Region o f increasing diameter 66 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. CYLINDER TUBE STOP RING FLOATING PISTON ,r-O R IF IC E PISTO N TUBE FLUID FILLED CAVITY BUM PER MOUNT GAS FILLED CAVITY Figure 30 Type II Isolator Assembly Type III isolators lack the gas filled piston tube and instead contain an extrudable material that passes through a variable numbered plunger orifice plate into a sealed chamber. The mechanism o f return for this type of isolator has not been published. The following schematic [Figure 4 of Siegmund et al., 1995] depicts a Type m isolator. PLUNGER ORIFICE PLATE FLOATING PISTON CYLINDER TUBE PLUNGER PIN ^ CAVITY FILLED IMTH UNKNOWN MATERIAL SEAL 4- HOLES 8 HOLES -B U M PER MOUNT Figure 31 Type ffl Isolator Assembly Stroking of the piston into the housing assembly usually results in the development o f striations around the stroked region o f the piston due to scraping of pain or due to scraping o f metal. Initiation o f piston stroke requires a colinearly aligned acceleration of approximately 1.2G [Siegmund et al., 1995]. A vehicle speed change of a given magnitude results in the development of scrape marks of a given length. Testing [Macinnis Engineering Associates, King et al., 1993; Bailey et al., 1995; Siegmund et al., 1995] has 67 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. delineated the stroke length versus AV relationship for a number o f vehicles in addition to empirical relationships for vehicles grouped under the same make. Foam core bumper systems consist of a plastic bumper cover with a subjacent foam layer overlying a subjacent rigid bumper reinforcement bar, which is usually mounted to the frame. During the course o f a collision impulse the foam core is compressed with a return to the its preimpact position following the cessation o f the applied load. Due to the compressibility of the foam core, two situations in the context o f vehicle crush damage become reasonably probable. The first is that permanent vehicle structural damage may initiate prior to permanent foam core deformation [King, 1993]. The second is that the maximum dynamic crush usually exceeds the permanent residual crush. Under certain impact conditions the latter may result in compression of, for example, a front bumper system to the point that involvement and resultant buckling of the hood panel is evidenced. Following the collision impulse, the bumper system, barring any residual plastic deformation, returns to its preimpact position. The material utilized in the foam generally consists of polyurethane or polystyrene. The following figure depicts a foam core equipped bumper system. Figure 32 Foam core bumper system from a minivan 68 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Honeycomb energy absorber equipped bumper systems consist o f plastic honeycomb whose walls are parallel to the longitudinal vehicle axes placed between an outer bumper cover and an inner bumper reinforcement bar. Honeycomb energy absorbers are similar to foam cores in that for low and moderate speed collisions, little to no permanent damage occurs to them while damage to surrounding or subjacent structures is a more likely probability. Honeycomb energy absorbers, however, provide for a stiffer structural response in high speed collisions with the ridges o f the honeycomb possibly lacerating the plastic bumper cover under the application of a compressive load. The following figure depicts a honeycomb energy absorber. Figure 33 Honeycomb bumper o f a 1996 Saturn SL1 Sedan The major body structure of motor vehicles is usually either of the unibody type or involves frame rails with numerous transversely aligned crossmembers. Seven separate components form the primary load bearing structure for unibody type frames. These are the radiator support, the front unirails, the rear unirails, the stmt tower / apron assembly, the stmt type wheelhouse assembly, the rocker panel assembly 69 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. including the center pillar, and the suspension crossmember. The following diagram depicts an exploded view of the aforementioned structures {Mitchell, 1998]. WHEELHOUSE ASSEMBLY \ STRUT TYPE STRUT TOWER/ APRON ASSEMBLY SUSPENSION CROSSMEMBER REAR UNIRAIL CENTER PILLAR FRONT UNIRAILS RADIATOR SUPPORT ROCKER PANEL ASSEMBLY HINGE PILLAR Figure 34 Unirail structural components The following figure depicts the main components of a frame rail equipped vehicle [Mitchell, 1998]. Frame rail Frame crossmember Figure 35 Rail and crossmember equipped frame A majority of motor vehicles, in the low speed regime, do not show appreciable frame damage or damage of other structural components. The latter may not be true for sport utility vehicles, pick up trucks, and minivans in that they are not required to and usually do not meet the same level o f damage prevention in low-speed collisions as do motor vehicles covered under the aforementioned bumper standard. Due to the 70 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. minimal level o f frame and other structural component involvement in the subject context, a further discussion will not be presented at this time. Pick-ups, sport utility vehicle, and minivans are not immune to frame involvement in low-speed collision secondary to the lack o f collision energy management by the bumper systems. Vehicle Interior The internal aspects of the motor vehicle in conjunction with the driver’s segment o f the occupant compartment provide for, given a vehicle center o f gravity speed change, the direction and magnitude of loading that is imposed on the driver. The typical seating position of an operator o f a motor vehicle operator involved in an aligned rear-end impact provides a set of limitations on the direction of both occupant post-impact motion and the direction o f loading. A majority o f such collisions occur with the struck vehicle being stopped and the operator o f the same being unaware o f the impending collision. Furthermore, a normal driving posture is defined as being seated upright, having both hands on the steering wheel, foot on the brake, and with the gaze directed forward. Occupant restraint is usually via a 3-point lap belt and shoulder harness restraint system. A head restraint of some form is also usually present, with the statement being more applicable for later model year vehicles. With the above described set o f initial conditions, it is an implicit assumption based on observational fact that any preimpact cervical or lumbar rotation or lateral flexion is minimized. With a further assumption of an aligned co-linear impact, the collision impulse is directed through the center o f gravity of the struck vehicle resulting in forward translation. In relation to the operator of the struck vehicle, this results in a primarily sagittal plane movement. With the above-indicated caveats in mind, internal vehicle structures such as the A-pillar, the B-pillar, the headliner, the steering column, or the front dash [with the latter two, the assumption o f no seat back failure is implicit] do not directly contact the occupant. Salient geometrical and design aspects o f the occupant 71 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. restraint system, the seatback, and the head restraint will be discussed as applicable in regards to occupant kinematics in the following section. Primary occupant restraint in motor vehicle accident is through the use of either a 2-point restraint consisting o f a lap belt or a 3-point [Type 2 as defined under SAE J140a] restraint consisting of a lap belt and integrated shoulder harness. The United States Government Federal Motor Vehicle Safety Standard mandates the placement of 3-point occupant restraint systems in the front outboard seats of all current passenger cars. Given the time duration that the latter has been in effect and based on the experience o f this author in examination o f real-world motor vehicle accidents, the majority o f the focus o f this section will be on 3-point restraint systems. SAE Jl40a defines the seat belt assembly as an occupant injury mitigating device composed o f any strap, webbing, or similar device consisting of all buckles, fasteners, and hardware. The typical constituents include the actual belts, the latch plate, the buckle, the retractors, and various adjusters. Attachment hardware consists o f the assemblies for attachment o f the lap or pelvic portion of the restraint system, which is anchored to the floor of the vehicle, and the shoulder or upper torso portion of the restraint system, which is anchored to the B-pillar of the vehicle. The latter, however, is not the case for automatic passive restraint systems. Proper 3-point restraint system positioning is with the shoulder harness located anteriorly over the thoracic wall and with the pelvic restraint located over the anterior inferior iliac spine. Motor vehicle occupants, without the use of restraint systems, are relatively uncoupled to the interior of the vehicle. In a rear-end motor vehicle collision, assuming rigid body motion, the vehicle is accelerated from its pre-impact velocity to its final post-impact velocity during the contact duration, which involves both the loading and the unloading phase o f bumper engagement. The operator o f the struck vehicle, due to inertia, remains at rest with respect to the vehicle. As the vehicle continues to displace with respect to the occupant, various segments of the occupant anatomy contact and differentially compress the seat back. The elastic potential energy stored in the seatback due to compression eventually overcomes the static resistance that is provided by the inertia of the segments of the occupant that are in contact with the 72 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. aforementioned segments of the seatback. As the seatback unloads and returns to its pre-compressed state it applies a force to the occupant resulting in forward occupant motion with respect to the interior of the vehicle. In the absence of an occupant restraint system and given a certain pre-impact positioning of the occupant with respect to anterior structures of the vehicle interior such as the steering column and front dash, the probability of contact with these structures is greatly increased. Occupant restraint systems then function to prevent differential movement, and therefore probability of contact, between the occupant and the internal aspects o f the vehicle [King & Yang, 1995], Also, as a general explicit design feature, a majority o f motor vehicles for a given vehicle center o f gravity speed change provide for a significantly lower peak deceleration than would, for example, the cephalic region of an occupant undergoing the same center o f gravity speed change. Coupling with the motor vehicle also causes the occupant to experience roughly the same deceleration as is experienced by the vehicle center o f gravity [King & Yang, 1995; Carpenter, 1998]. In the collision regime that is of interest, local loading under the restrained areas does not in and o f itself provide for a significant potential for injury. Head restraints have been required, since January 1, 1969, as per the Federal Motor Vehicle Safety Standard Number [FMVSS] 202 to be present in the front outboard seating positions of all passenger cars. The requirements were extended to light trucks and vans weighing under 10,000 pounds as of September I, 1991. FMVSS 202 requires head restraints, at a minimum, to be 27.5 inches above the seating reference point at their highest position, not deflect more than four inches under a 120 pound load or not allow the angle of the head with respect to the torso of a 95th percentile anthropomorphic test subject to exceed 45° under an 8G acceleration. The primary function of head restraints has been to reduce to extent of cervical extension undergone by an occupant of a motor vehicle that is impacted in the rear [NHTSA, 1996; Viano & Gargan, 1996; HHS, 1997]. By positioning a material body to impede the rearward progress of the head during a rear end motor vehicle collision, the extent of cervical extension required for rigid body motion is reduced. The comparison is to the case where the head and cervical spine are free to move to their full extent with respect to each other and with the latter, about the upper thoracic spine. Invariably, the contact between the head and the head restraint, resultant compression of the head restraint, and subsequent 73 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. unloading of the head restraint results in the generation of head center of gravity acceleration. In fact, it can be stated that the contact with the head restraint provides for the primary acceleration on the head during the course collisions of the subject context. Head restraints are either adjustable or integrated in design. Adjustable head restraints are normally positioned with two frame extensions that are slotted at various increments along their length. The extensions slide into their respective housings located in the superior aspect o f the seat. Certain head restraints are also adjustable in the fore and aft direction based on either a superior frame or inferior frame mounted swivel apparatus. Integrated head restraints are constituted by direct seatback extension and are usually molded for headform fit. The latter is not a requirement, per se, for definitional purposes. A review of data obtained from IIHS was conducted by Viano & Gargan [1995] resulting in the determination that o f 1915 separate observations, 65% o f trucks and 59% of vans were equipped with integrated head restraints while 14.5% o f larger passenger vehicles and station wagons were equipped with integrated head restraints. The following figures depict an adjustable head restraint and an integrated head restraint. Both figures were obtained from the April 12, 1997, IIHS Status Report. Figure 36 Adjustable head restraint Figure 37 Integrated head restraint 74 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Head restraint efficacy, in terms of reduction of cervical extension, can be examined in terms o f head restraint geometrical parameters [NHTSA, 1995; IIHS, 1995; Viano & Gargan, 1995, Svensson et al., 1996; HHS, 1997] and in terms of engineering design parameters [NHTSA, 1995; Viano & Gargan, 1995; Svensson et al., 1996; Welcher, 1998]. The Insurance Institute for Highway Safety in both 1995 and in 1997 classified adjustable head restraints based solely on the geometrical considerations of backset between the posteriormost aspect o f the headform of a 50th percentile male anthropomorphic test device and the anteriormost aspect o f the head restraint and by the vertical offset between the superiormost segments of the headform of a 50th percentile male anthropomorphic test device and the superiormost segment o f the head restraint. These parameters were utilized based on determination of their relevance to determination o f injury potential for cervical extension by numerous authors [Severy, 1968; Kahane, l982;Nygren, 1985; Svensson et al., 1993; Ono & Kanno, 1993, Svensson et al., 1995; Szabo & Welcher, 1996]. The test specification and procedures for transduction of the measured quantities into qualitative measures are discussed at length in HHS, 1995, NHTSA, 1996, and IIHS, 1997. For demonstrative purposes only, a geometrical representation of the latter is indicated in Figure 38. The following figure, obtained from the April 12, 1997, IIHS Status Report depicts a schematic of the geometrical offset parameters measured and also depicts the actual test device utilized in the conduction of the measurements. Figure 38 IIHS geometrical parameters, ATD, and qualification scale 75 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In the context of engineering design parameters, one o f the most important purposes o f minimizing differential occupant motion between different segments and therefore reducing the potential for certain forms of injury is the relative stiffness of the seatback or the recliner in comparison to the stiffness o f the head restraint. Foret-Bruno et al. [1993] indicated that the trend was for increased recliner stiffness in seats of motor vehicles produced after 1976. With increasing recliner stiffness, for a given vehicle AV in a rear end motor vehicle collision, the probability o f seatback failure by means o f breakage under occupant loading is reduced. In the latter case, the presence o f a head restraint was found to decrease the potential for cervical injury. Svensson et al, 1995, in using Hybrid in anthropomorphic test subjects fitted with the Rear Impact Dummy neck [RID neck] undergoing square pulse accelerations while seated on modified motor vehicle seats affixed to sleds, noted that a sole increase in recliner frame stiffness resulted in slight increases in the maximum head to torso displacement. Increased stiffness of the lower seat back cushion in conjunction with an increased depth of the upper seat back cushion resulted in reduction of the head to torso displacement. Nilson et al [1994] as cited in NHTSA [1996] examined the effects of recliner stiffness on occupant kinematics through a MADYMO model o f an anthropomorphic test subject equipped with a RID neck. For an approximate 20 mph impact the conclusion was made that increased recliner stiffness resulted in “a probable increase in occupant protection as measured by head/torso angle, Cl neck movement and head acceleration.” Occupant Kinematics The kinematics of an occupant, seated in the aforementioned manner, involved in collisions of the subject type have been reviewed by a number of authors [Severy et al, 1955; Szabo & Welcher, 1992; McConnell et al, 1993; West et al, 1993; McConnell et al, 1995; Szabo & Welcher, 1996; Nielsen et al, 1997], The work o f Severy et al, 1955, represents the pioneering study into occupant kinematics through the use o f instrumented human subjects exposed to rear-end, bumper to bumper, aligned motor vehicle collisions. The applicability of the results obtained by Severy, however, to modem day motor vehicle collisions are 76 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. limited due to changes in vehicle structural and internal design and due to questionable instrumentation. For example the rate at which the vehicle and occupant acceleration data was sampled allowed for the realistic probability o f aliasing problems. Also utilization o f uniaxial accelerometers for occupant acceleration measurement resulted in incomplete and, at times, incorrect measurement secondary to out of plane motion o f the accelerometer. In general, three triaxial accelerometer blocks or a combination of a triaxial and biaxial accelerometer blocks in conjunction with a rigid body assumption and certain head anthropometric dimensions is required for the determination of head center of gravity acceleration. Vehicle center of gravity acceleration can be measured by means of a single triaxial accelerometer block placed at the approximate vehicle center of gravity. For the majority o f late model year vehicles, a computer program such as Expert Autostats [4N6XPR.T Systems, 1998] can provide the approximate longitudinal and lateral location of the vehicle center o f gravity. Figure 39 depicts a summary of the head and vehicle response as plotted versus collision duration as determined by Severy, et al [1955] and as presented by White and Punjabi [1990]. Examination of Figure 39 reveals approximately 6 samples per 100 msec or a sampling rate of approximately 60 Hz. A sampling rate of 60 Hz as explained below, is extremely low and does not meet current accepted SAE guidelines. HEAD o» z o < c uJ tu SHOULDER o o < VEHICVE c o £ 3 0 0 200 100 TIME. MILUSECONOS Figure 39 Occupant and vehicle response [White & Punjabi, Figure 4-45] 77 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A comparison of the peak head Gx acceleration magnitude and the peak vehicle Gx acceleration magnitude has resulted in the indication of a head multiplication factor in which the former is defined as being equal to two times the latter. Indiscriminate use of a head multiplication factor of two for all motor vehicle collisions is patently false and an incorrect application of the work of Severy [1955]. Figure 40 is an acceleration versus time plot from on the test cases in which it can be seen that the peak head acceleration response is equal in magnitude to the peak vehicle acceleration response. This is more representative of the current research date that the prior work of Severy, et al. & r£?T V c tr a lc - 3 n d h c a d Gx c o m b i n e d '; ;; _ J-' -i: ^ -.'I.. L ' . . : * ^ - i - . Vehicle *Gx acceleration H ead ♦Gx acceleration Figure 40 Exemplar vehicle and head +GX response Figure 41 depicts the head multiplication factor as a function of struck vehicle Delta-V. There is no apparent trend in this figure. In passing, the average head multiplication factor for the subject series was 1.39. 78 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 0 2 4 6 8 Struck vehicle Delta-V [mph] Figure 41HMF vs. Struck vehicle Delta-V for all tests in the subject study McConnell et al [1993, 1995], based on a kinematic study of occupant motion due to rear end motor vehicle impact, described five stages o f occupant motion. The studies, especially the 1995 study, provide for one o f the most complete studies on occupant kinematics that is available in the general literature. Struck vehicle Delta-V ranged from 3.6 to 6.8 miles per hour. The following figure depicts the vehicle center of gravity and the head center o f gravity, x-direction, acceleration as a function of time. H eat^yerudeC G (Cxj Phase 11 Phase 2 Phase 3jPhase 4 Phase 5 Figure 42 Head CG & Vehicle CG Gx Phase 1 comprised the first 0 to 100 msec of the collision duration. Examination of Figure 42 reveals that the majority of the vehicle acceleration is over before significant occupant head acceleration is noted. The 79 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. peak vehicle acceleration occurs at approximately 50 msec with the vehicle reaching its post-impact velocity at between 100 to 110 msec following the initiation o f the collision event. There was no detectable occupant motion for at least 50 to 60 msec o f the collision. During the same time, the struck vehicle, the seat, and the base of the seatback were moved forward from 2.5 to 3 inches and the seatback deflected rearward from 3 to 5 degrees. The latter was determined from analysis of high-speed film footage. Forward movement of the rearward sloped seatback resulted in the appearance o f the occupant’s thigh elevating with respect to the seat, but tracking of the pelvis and hip with respect to ground revealed the occupant segments to remain at rest while the seat moved out from underneath the occupant. With the latter being the case, it was noted that the lumbar region contacted and compressed the seatback at a higher level than if the occupant had just moved horizontally rearward. Compression of the seatback by the lumbar region and the pelvic region resulted in deflection of the entire seatback rearward from the stationary torso. From 60 to 80 msec o f the collision duration the vehicle and seatback anterior displacement was noted to be 4 inches with a rearward seatback deflection of 6 to 7 degrees. The upper torso, as a result of anterior traction by the pelvic region and the intersection of the lower portion o f the trunk on the rearward sloped seatback, appeared to be laid back on the anteriorly displacing and posteriorly deflecting seatback. A 2 to 3 inch ramping of the region from the shoulders to T1 on the seatback was noted. Continued interaction between the middle back and the anteriorly displacing seatback resulted in straightening o f the thoracic kyphotic curve, which in turn increased the ramping o f the upper torso with respect to the seatback. There was no head motion observed during the first 80 msec following the initiation o f the collision event. The base o f the cervical spine, however, was anteriorly displaced as a result o f traction by T l. At a time of 100 msec following the initiation of the collision event the base o f the cervical spine and Tl had displaced anteriorly by another 0.4 to 0.8 inches. Additionally, the upper aspect o f the cervical spine had initiated its anterior translatory motion at a time of 100 msec following the initiation of the collision event. Phase 2, defined as the principal acceleration phase, is from 100 to 200 msec following the initiation o f the collision event. During the first 10 to 20 msec of Phase 2, the recliner obtained its maximum rearward 80 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. deflection of 10° to 14°. The head acceleration noted during this phase appeared to be primarily rotational with an axis about the head-neck complex center of gravity. Between 10 to 70 msec into Phase 2, the head had rotated 10 to 15 degrees with subsequent anterior translation as a result of tractive loading by the anteriorly displacing superior cervical spine. During the last 20 msec o f Phase 2, the maximum head rotation and neck extension o f between 18° to 51° was noted. For all struck vehicle Delta-V’s of greater than 5 m iles per hour, the contact with the head restraint was with the lower occipital scalp, resulting in the head restraint being driven in a downward manner on the adjustable mounts. Phase 3, defined as the head overspeed/torso recovery phase, is from 200 to 300 msec following initiation of the collision event. The seatback had returned to its pre-impact position with the torso reaching a velocity that was slightly greater than that o f the vehicle center of gravity. The head had reached a greater velocity than the torso early in Phase 3, with a measured deceleration of 1.5 to 2.5 G, which was attributed to the action of the cervical musculature. Phase 4, defined as the head deceleration/torso rest phase, was from 300 to 400 msec following the initiation of the collision event. In this phase the head continued anteriorly at a greater rate than the upper torso, but did so in a manner such that the eyes were level as a result of the action o f the cervical musculature. The torso and the lower body had achieved their post-impact rest positions. Phase 5, defined as the restitution phase, was from 400 to 600 msec following the initiation o f the collision event. In this phase the head had almost achieved the vehicle AV and was moving into its pre-impact position. 81 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. v m . Test Procedures and Equipment Data acquisition was conducted by members of Biomechanical Research and Testing under various rear- end impact conditions. Salient features such as vehicle make, vehicle model, vehicle year, frame structure, bumper structure, head restraint type and position, etc will be discussed as necessary during the course o f the presentation. In order to minimize physiologic variation between occupants only tests conducted with the same occupant will be presented for consideration. Linear acceleration, angular acceleration, and vehicle speed change was sampled and processed according to the Society of Automotive Engineers (SAE) J211 recommended practice for instrumented impact testing [SAE, 1996; Szabo & Welcher, 1996]. The following table represents selected recommendations. Sampling Rate 10,000 Hz Presample Filter SAE Class 1000 Vehicle Acceleration Filter SAE Class 60 [Class 180 for AV calculation] Head Linear Acceleration Filter SAE Class 1000 Head Angular Acceleration Filter SAE Class 1000 Table 5 Selected SAE J211 Recommendations Power spectral density (PSD) analysis of typical head accelerations in the subject context was discussed by Szabo and Welcher [1996]. A majority o f the signal power was noted to be below approximately 75 Hz. The latter is not unexpected given that J211 was created as a guideline for testing involving anthropomorphic test subjects in high severity collisions where the acceleration response of the subject would exhibit signal power at higher frequencies as a result o f impacts between the components of the “stiff’ test subject and “stiff’ interior segments of the vehicle such as the roof rail or header panel. SAE further recommends a minimal sampling rate of 8 times the highest signal frequency component for purposes of minimizing aliasing. Szabo and Welcher [1996] recommended a sampling rate of 1000 Hz for sampling of data in the subject setting. 82 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Vehicle center of gravity acceleration was measured via a triaxial block o f E C Sensor 3031-050 (50G) accelerometers. Occupant head acceleration was measured using three triaxial blocks o f IC Sensor 3031-50 (50G) accelerometers attached to a lightweight headband. The headband was tightly affixed in a circumferential manner to the occupants’ head in a manner that approximated a rigid body condition. One triaxial block was located in the sagittal plane above the forehead while the other two were located above the respective external auditory meati. All three triaxial blocks were positioned parallel to the Frankfort Plane [contains the head static center o f gravity]. Raw acceleration data was prefiltered through a SAE Class 100 low pass filter and stored on an onboard data acquisition system. The prefiltered acceleration data was subsequently transferred to a secondary system where the data is filtered as indicated above. The head static center o f gravity acceleration was calculated utilizing the algorithm presented by Alem and Holstein [1977] as discussed in Appendix A. Three anthropometric dimensions are utilized by the program for the calculation o f the head static center of gravity acceleration; the circumferential distance between the triaxial blocks placed above the external auditory meati, the superior displacement between the external auditory meati and the respective triaxial block, and the superior displacement between the forehead triaxial block and the inferior aspect o f the orbit. Validation testing of the algorithm was conducted by Szabo and Welcher [1996] via a Hybrid E H anthropomorphic test subject for which actual static head center of gravity accelerations were measurable. The following figure provides a schematic o f the instrumentation setup. Transfer onto 2" system following test Prefiltered data Filtered data ready for additional analysts Prefilter through a low pass SAE Class 100 filter Storage on onboard data acquisition system . Test setup file containing appropriate anthropometric measures and signal filters Head peripheral triaxial block accelerations [3] Vehicle static center o f gravity triaxial acceleration Additional triaxial block accelerations for cervical, lumbar, etc. that are utilized as needed Figure 43 Instrumentation schema 83 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. IX. Testing M atrix The following section describes the attributes of the instrumented volunteer vehicle-to-vehicle collision tests that were utilized in the acquisition of the relevant head acceleration data. As stated before, all tests utilized in the subject setting were conducted with a single volunteer for the purpose o f minimizing physiologic variation. The occupant was a 36 year old Caucasian male with an approximate height of 68 inches. Test Series T962I8 The following series consisted of 5 vehicle to vehicle impacts in which the target vehicle was a 1989 Hyundai Excel and the bullet vehicle was a 1988 Ford Festiva. The Hyundai weighed approximately 2127 pounds with the Ford weighing approximately 1713 pounds. The rear bumper system of the Hyundai consisted o f a foam core impact absorber and a subjacent reinforcement bar mounted to the vehicle rear body. The front bumper system of the Ford consisted of a face bar with a suprajacent right and left support cover. Both vehicles were equipped with unibody frame construction. The driver’s seat of the Hyundai was equipped with an adjustable head restraint that was positioned such that its superior aspect was approximately flush with the external occipital protuberance o f the occupant. The driver’s seat was equipped with a standard 3-point restraint system. Test reference Bullet vehicle Target vehicle Closing speed [mph] Bullet post-impact velocity [mph] Target AV [mph] Restitution T96218-01 1988 Ford Festiva 1989 Hyundai Excel 4.46 0 3 7 23 5 0.44 T96218-02 19S8 Fond Festiva 1989 Hyundai Excel 6 S 5 1.62 4.68 0.44 T962I8-03 1988 Ford Festiva 1989 Hyundai Excel 7.04 1.51 4.84 0.47 T96218-04 1988 Ford Festiva 1989 Hyundai Excel 7.14 1.15 5.08 0.55 T96218-05 1988 Ford Festiva 1989 Hyundai Excel 8.17 1.70 5.56 0.47 Table 6 Test matrix for series T96218 84 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The first two tests of the series were conducted with the occupant o f the struck vehicle unbelted, unaware o f the impending collision, and utilizing normal braking. The third test of the series was conducted with the occupant unbelted, unaware of the impending collision, and with no utilization o f the vehicle brakes. Utilization o f the service brakes, as indicated above, typically does not provide sufficient increase in the struck vehicle inertial load secondary to the initial rearward motion of the occupant with respect to the struck vehicle and the resultant removal o f the foot from the brake pedal. The fourth test was conducted with the occupant unbelted, aware of the impact, and with utilization of the vehicle emergency brake. The final test was conducted with the occupant unbelted, unaware of the impending collision, and with utilization o f normal braking. Test series T96219 The following consisted o f 3 vehicle to vehicle impacts in which the target vehicle was a 1987 Pontiac Grand AM and the bullet vehicle was a 1984 Oldsmobile Cutlass Supreme Brougham. The Pontiac weighed approximately 2565 pounds with the Oldsmobile weighing approximately 3200 pounds. The rear bumper o f the Pontiac was equipped with piston-type energy absorbers. The front bumper of the Oldsmobile consisted of an impact bar mounted to the vehicle frame via piston type energy absorbers. The Pontiac was constructed utilizing a unibody frame approach while the Oldsmobile was constructed of frame rails with cross beam supports. The driver’s seat of the Pontiac was equipped with an adjustable head restraint. The driver’s seat o f the Pontiac was equipped with a standard 3-point occupant restraint system. The following table lists the salient aspects of the test matrix: Test reference Bullet vehicle Target vehicle Closing speed [mph] Bullet post-impact velocity [mph] Target AV [mph] Restitution T96219-01 1984 Oldsmobile 1987 Pontiac Grand AM 2.50 0 3 0 1.70 0.32 T962I9-02 1984 Oldsmobile 1987 Pontiac Gmnd AM 6.70 2 3 0 4.80 0.34 T96219-03 1984 Oldsmobile 1987 Pontiac Grand AM 6.40 2.60 4 J 0 0 J 0 Table 7 Test matrix for series T96219 85 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. AH three of the tests indicated in Table 4 were conducted with the occupant restrained and in a normal seating position. In all cases the occupant was as unaware as reasonably probable o f the impending collision prior to its occurrence. Test series T96220 The following consisted o f seven vehicle to vehicle impacts in which the target vehicle was a 1989 Nissan Stanza and the bullet vehicle was a 1984 Pontiac 6000. Both o f the aforementioned vehicles weighed 3300 pounds. The rear bumper of the Nissan consisted of an impact bar mounted to energy absorbing pistons. The front bumper o f the Pontiac consisted o f an impact bar mounted to energy absorbing pistons. Both vehicles were constructed utilizing a unibody frame approach. The driver’s seat o f the Nissan was equipped with an adjustable head restraint. The driver’s seat of the Nissan was equipped with a standard 3- point occupant restraint system. The following table lists the salient aspects of the test matrix: Test reference Bullet vehicle Target vehicle Closing speed [mph] Bullet post-impact velocity [mph] Target AV [mph] Restitution T96220-01 1984 Pontiac 6000 1989 Nissan Stanza 1.19 0.36 0.91 0.48 T96220-Q2 1984 Pontiac 6000 1989 Nissan Stanza 1.28 0 2 5 0.79 039 T96220-Q3 1984 Pontiac 6000 1989 Nissan Stanza 4.58 1.53 3.38 038 T96220-04 1984 Pontiac 6000 1989 Nissan Stanza 3.69 0.92 2.28 035 T96220-05 1984 Pontiac 6000 1989 Nissan Stanza 4.97 1.50 356 057 T96220-06 1984 Pontiac 6000 1989 Nissan Stanza 7.97 2.52 5.67 038 T96220-Q7 1984 Pontiac 6000 1989 Nissan Stanza 8.09 2.07 535 0.41 Table 8 Test matrix for series T96220 All seven of the tests indicated in Table 8 were conducted with the occupant restrained and in a normal seating position. In all cases the occupant was as unaware as reasonably probable o f the impending collision prior to its occurrence. All o f the seven tests were conducted under various braking conditions on the part of the occupant o f the target vehicle. 86 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Test series T96224 The following consisted o f 4 vehicle to vehicle impacts in which the target vehicle was a 1993 Ford Taurus 4-door sedan and the bullet vehicle was a 1994 Pontiac Grand AM SE 4-door sedan. The Ford weighed approximately 3146 pounds with the Pontiac weighing approximately 2816 pounds. The rear bumper o f the Ford consisted o f a face bar mounted to the vehicle via a set of piston type energy absorbing isolators. The front bumper o f the Pontiac consisted of a face bar with a subjacent honeycomb energy absorber. Both vehicles were constructed utilizing a unibody frame approach. The driver’s seat of the Ford was equipped with an adjustable head restraint. The driver’s seat of the Ford was equipped with a standard 3-point occupant restraint system. The following table lists the salient aspects of the test matrix: Test reference Bullet vehicle Target vehicle Closing speed (mph] Bullet post-impact velocity [mph] Target AV [mph] Restitution T96224-01 1994 Pontiac Grand AM 1993 Ford Taurus 5 TO 0.90 3.8 096 T96224-02 1994 Pontiac Grand AM 1993 Ford Taurus 9.00 2.70 5.60 0 J2 T96224-03 1994 Pontiac Grand AM 1993 Ford Taurus 5.40 NA 3.60 NA T96224-04 1994 Pontiac Grand AM 1993 Ford Taurus 10.60 NA 690 NA Table 9 Test matrix for series T96224 All four of the tests indicated in Table 9 were conducted with the occupant restrained and in a normal seating position. In all cases the occupant was as unaware as reasonably probable o f the impending collision prior to its occurrence. All four of the tests were conducted under normal braking conditions on the part of the occupant o f the target vehicle. 8 7 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. X. Results In analyzing the data procured in the aforementioned human volunteer tests a determination was needed in terms of applicability o f the criterion that were presented in the earlier aspects o f this discussion. The injury tolerance curve as predicted by the Wayne State Tolerance Curve [WSTC] and the injury criterion of the Severity Index [SI] were both deemed as precursors of the Head Injury Criterion [HIC] and for that reason were not explicitly determined. Even with the calculation of the latter a question o f necessity and of applicability was raised secondary to the lack of accounting of angular head acceleration in the HIC algorithm and due to the fact that no specific quantitative tolerance value was found for the subject application. A HIC o f 1000 has specific relevance for head injury potential in high speed frontal collisions as conducted by the National Highway Traffic and Safety Administration [NHTSA] during the course of the 30 mile per hour frontal FMVSS-208 tests and the 35 mile per hour frontal NCAP tests or during the Insurance Institute for Highway Safety [HHS] 40 mile per hour offset frontal tests. For the aforementioned reasons it was determined that the use of HIC for the subject study was counterindicated. Use o f injury criterion based on the single degree o f freedom vibrational models such as the mean strain criterion was not considered for the purposes of this discussion secondary to the lack of accounting of angular acceleration and due to the lack o f utility in the field. The angular acceleration based criterion of Ommaya and the JARI tolerance curve in addition to the combined GAMBIT curve were utilized. The tolerance curve as presented by Gennarelli and Thibault [1989] as denoted in Figure 25 was not used secondary to a peculiarity that was noted in tolerance curve. For all of the uniaxial strain isolines it was noted that for certain values of peak angular velocity [for example 50 rad/sec] one could pass from a region of low angular acceleration where DAI was not predicted to an intermediate value of angular acceleration where DAI was predicted to an even higher value of angular acceleration were DAI was once again not predicted. As stated above a single occupant was utilized in all of the tests that comprised this study. The latter, therefore, should be seen as the nominal test case. The a priori assumption, which was validated secondary to the lack of any physiologic symptomatology in the test subject, was that the anatomic variation due to 88 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. involvement in any given test was minimal. Descriptive statistical analysis was not utilized in the subject study. Each test series was, when initially conducted, done so independently o f the other tests in terms of fulfillment o f an overall comprehensive strategy or plan. The latter resulted in significant interseries variation in terms of deterministically significant quantities such as recliner to head restraint stiffness, bumper system design, etc. Struck vehicle static center o f gravity acceleration The following tables present the salient observed and calculated values for the struck vehicle acceleration. The end point on the acceleration duration measurement for the vehicle was measured at the point on the acceleration time trace at which the magnitude of the Gx acceleration vector was approximately of zero magnitude. Acceleration onset time, by definition based on linking the initiation o f the data collection with the application of the impact force to the rear of the vehicle via the electric tape swish, was taken to be at 0 seconds. Peak -x-direction acceleration magnitudes in comparison to the respective +x-direction vehicle center of gravity varied from 5.8% to 50.7%. Vehicle center of gravity peak +y-direction accelerations varied from 7.2% to 14.3% of the magnitudes of the respective peak +x direction vehicle center of gravity peak accelerations. The magnitudes of the -y-direction vehicle center of gravity accelerations were similar to those of the respective +y-direction vehicle center o f gravity accelerations. Vehicle center of gravity peak +z direction accelerations varied from 17.6% to 64.1% of the magnitudes of the respective peak +x direction vehicle center of gravity peak accelerations. Once again, the magnitudes of the -z-direction vehicle center of gravity accelerations were similar to the +z-direction vehicle center of gravity accelerations. Vehicle +x-direction center of gravity accelerations ranged from 0.40 to 7.83 G. 89 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Test reference Target AV [mph] P e a k v eh icle G x a c c e le r a tio n [ G / Peak vehicle acceleration magnitude [G] Time o f peak G, acceleration [msec] Acceleration duration [msec] T96218-01 2.95 221 2.21 595 118 T96218-02 4.68 4 2 0 4.68 435 108 T96218-03 4.84 4 2 0 4 2 2 695 99 T962I8-04 5.08 3.87 352 475 108 T962I8-05 556 4.76 5.44 42 5 95 Table 10 TestT962I8 vehicle acceleration Test reference Target AV [mphl P e a k v e h ic le G r a c c e le r a tio n [ G / Peak vehicle acceleration magnitude [G] Time o f peakGx acceleration [msec] Acceleration duration [msec] T962I9-01 1.70 054 3.09 305 156 T96219-02 4.80 252 3.05 345 127 T96219-03 450 328 329 305 148 Table 11 TestT96219 vehicle acceleration Test reference Target AV [mph] P e a k v e h ic le G x a c c e le r a tio n ( G f Peak vehicle acceleration magnitude [G] Time o f peak G. acceleration [msec] Acceleration duration [msec] T96220-01 051 050 051 575 148 T96220-02 0.79 0.40 0.40 355 150 T96220-03 328 1.76 1.75 385 169 T96220-04 228 1.15 1.18 395 173 T96220-05 326 1.73 5.44 53.9 168 T96220-06 5.67 3.19 32 2 695 151 T96220-07 525 323 3.47 735 137 Table 12 Test T96220 vehicle acceleration R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Test reference Target AV [mph] P e a k v e h ic le G t a c c e le r a tio n [ G [ Peak vehicle acceleration magnitude [GI Time of peak G x acceleration [msec] Acceleration duration [msec] T96224-0I 3.8 234 2.25 513 156 T96224-02 5.60 4.12 4 3 0 563 118 T96224-03 3.60 333 3 3 2 673 138 T96224-04 6.90 7.83 7.85 373 109 Table 13 Test T96224 vehicle acceleration Head static center o f gravity linear acceleration The following tables present the salient observed and determined struck vehicle occupant static head center of gravity linear acceleration values. The acceleration duration indicated was for +GX acceleration. Head acceleration onset was taken at a time when the magnitude o f the x-direction acceleration was at 2% of the peak acceleration. Head contact was taken as continuing to the point in time when the head acceleration time trace indicated a zero head acceleration. Head center of gravity peak -x-direction acceleration magnitudes varied from 31.8% to 120.5% of the respective peak +x-direction head acceleration magnitudes. In all but two of the nineteen cases the -x-direction head acceleration was less than 71% of the respective +x-direction head acceleration. Head center o f gravity +y-direction acceleration magnitudes varies from 9.7% to 51.0% in comparison with the respective +x-direction acceleration magnitudes. The negative y-direction acceleration magnitudes were similar in magnitude as the +y-direction acceleration values. Given the test protocol, it was not expected that the lateral head center of gravity acceleration would be of significant magnitude. It was surprising to note, especially in conjunction with the apparent lack of discussion in the literature, of the magnitude of the head center of gravity +z-direction acceleration response. Respectively, in comparison to the +x-direction head center of gravity acceleration magnitudes, the +z-direction responses varied from 89.7% to 202.3%. In all but one of the 19 tests, the +z-direction acceleration magnitudes exceeded the respective +x-direction magnitudes. The head center of gravity peak -z-direction acceleration response magnitude varied from 26.1% to 101.7% o f the respective peak +x- 91 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. direction acceleration response. In all except for two of the nineteen tests the aforementioned response was significantly less than unity in comparison to the respective peak +x-direction response. Test reference Target AV [mph] P e a k h e a d G x a c ce le ra tio n [O J Peak head Q t acceleration [G] Peak head acceleration magnitude [G] Time o f peak Gx acceleration [msec] Acceleration duration [msec] T96218-OI 2.95 2J7 2.66 3.50 196.6 200 T96218-02 4.68 4.88 7.72 8.54 174.7 203 T96218-03 4.84 6.24 82)7 10.69 177.6 187 T96218-04 5.08 4.25 7.73 8.15 132.7 154 T96218-05 5.56 6.77 11.88 13.78 171.7 174 Table 14 Test T96218 head static center o f gravity linear acceleration Test reference Target AV [mph] P e a k h e a d Gx a ccele ra tio n [ G [ Peak head Gx acceleration [G] Peak head acceleration magnitude [G] Time of peak Gx acceleration [msec] Acceleration duration [msec] T96219-01 1.70 1.62 036 1.12 142.7 212 T962I9-02 4.80 3.91 791 8.05 142.7 209 T96219-03 4.50 3.09 5.45 6.21 130.7 •no Table 15 Test T96219 head static center o f gravity linear acceleration Test reference Target AV [mph] P e a k h e a d Gx accele ra tio n [ G / Peak head G, accelerauon [G] Peak head acceleration magnitude [G] Time of peak Gx acceleration [msec] Acceleration duration [msec] T96220-01 091 0.99 0.69 1.05 183.6 187 T96220-02 0.79 039 035 039 203.6 243 T96220-03 338 237 2.71 3.69 187.6 193 T96220-04 238 1.13 132 1.75 184.6 210 T96220-05 336 239 3.76 4.44 188.6 189 T96220-06 5.67 738 11.16 13.4 174.7 170 T96220-07 535 6.00 8.79 10.6 183.6 187 Table 16 Test T96220 head static center o f gravity linear acceleration 92 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Test reference Target AV [mph] P e a k h e a d G t a c c e le r a tio n [ G / Peak head G, acceleration [G] Peak head acceleration magnitude [G] Time of peak G, acceleration [msec] Acceleration duration [msec] T96224-01 3.8 3.64 4.06 600 190.6 196 T96224-02 5.60 703 11.40 1300 170.7 175 196224-03 3.60 3.44 4.75 5.70 196.6 187 T96224-04 6.90 7.56 150 13.1 165.7 241 Table 17 Test T96224 head static center of gravity linear acceleration Head static center o f gravity angular acceleration The following table presents the salient observed and determined struck vehicle occupant, static, head center o f gravity angular acceleration and velocity values. The nomenclature is based on the axis about which the head rotation is occurring [i.e. a y denotes head angular acceleration about the y axis]. Instantaneous angular velocity values are given for the times at which the peak angular accelerations occurred. The head center of gravity angular acceleration response was more normative in the sense that, expect for one of the nineteen tests, the head angular acceleration about the -y axis predominated the system response. Test reference Target AV [mph] Peak angular tzx acceleration [rad/sec2] P e a k a n g u la r a , a c ce le ra tio n fr a d ls e c 2/ Peak angular a , acceleration [rad/sec2 ] Angular to, velocity [rad/sec] A n g u la r o \ velo city [ r a d /s e c j Angular to* velocity [rad/sec] T96218-01 2.95 65.4 [197.6 msec] -188.0 [186.6 msec] 68.9 [192.6msec] -97.1 [174.7msec] -0093 0023 -1.488 -1.421 T96218-02 4.68 1310 [177.6 msec] -506.7 [178.6 msec] 138.0 [216.6msec] -242.6 [148.7msec] 0073 -1.891 0.067 -2.094 T96218-03 4.84 278.6 [170.6 msec] -628.7 [168.7 msec] 2050 [161.6 msec] -286.4 [142.7 msec] -1.44 3.02 -3.04 -205 T96218-04 5.08 106.8 [135.7 msec] -276.8 [146.7 msec] 90.7 [162.7 msec] -117.7 [88.8 msec] 0075 -1.00 -106 -103 T962I8-05 506 467.7 [178.6 msec] -753.1 [164.7 msec] 463.8 1165.7 msec] -293.8 [148.7 msec] 0.733 400 -2.45 -303 Table 18 Test T96218 head static center of gravity angular acceleration and velocity 93 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Test reference Target AV [mph] Peak angular a , acceleration [rad/sec2] P e a k a n g u la r a , a c c e le r a tio n [ r a d is e tr j Peak angular a c acceleration [rad/sec2] Angular velocity [rad/sec] A n g u la r to , v e lo c ity [ r a d /s e c f Angular coz velocity [rad/sec] T96219-01 1.70 37.6 [209.6 msec] -36.0 [206.6 msec] 255 [2495msec] -31.2 [130.7msec] 0594 41.895 0.140 4)521 T96219-02 4.80 110.5 [212.6 msec] -428.8 [192.6 msec] 111.4 [212.6msec] -221.7 [191.6msec] 41.061 -1.121 -1502 -1560 T962I9-03 4.50 110.7 [103.8 msec] -273.8 [197.6 msec] 37.7 [271.4 msec] -101.8 [138.7 msec] 0.023 -0.153 41.426 0.021 Table 19 Test T96219 head static center o f gravity angular acceleration and velocity Test reference Target AV [mph] Peak angular ctx acceleration [rad/sec2] P e a k a n g u la r a , a c c e le r a tio n [ra d /s e c ? / Peak angular a t acceleration [rad/sec2] Angular (ux velocity [rad/sec] A n g u la r to, v e lo c ity ( r a d 's v c j Angular to* velocity [rad/sec] T96220-01 0.91 12.1 [176.6 msec] -365 [203.6 msec] 8.72 [187.6 msec] -135 [131.7 msec] -0524 4)543 4) .615 -0.402 T96220-02 0.79 0.996 [200.6 msec] -135 [210.6 msecl 553 [3335msec] -135 [446.1msec] 41.891 0.662 -1511 -1.410 T96220413 358 27.4 [158.7 msec] -131.8 [194.6 msec] 30.8 [178.6 msec] -565 [196.6 msec] 4)578 -0.019 -0.616 -0.682 T96220414 258 115 [173.7 msec] -17 [215.6 msec] 127 [143.7 msec] -2054 [183.6 msecl -0538 0558 -0.074 -0566 T96220435 356 4058 [166.7 msec] -1905 [195.6 msec] 20.8 [136.7 msec] -80.7 [161.7 msec] 41.179 4)518 0.489 -0.074 T96220416 5.67 645 [153.7 msec] -189.1 [162.7 msec] 90.7 [2645 msec] -84.0 [193.6 msec] -1.08 654 4)516 -0.824 T96220417 555 2125 [279.4 msec] -1845 [192.6 msec] 312.6 [2715 msec] -182.0 [290.4 msec] 4)536 -3.81 .010 0561 Table 20 Test T96220 head static center of gravity angular acceleration and velocity R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Test reference Target AV [m p h I Peak angular c * x acceleration [rad/sec2 ] P e a k a n g u la r cC y a c c e le ra tio n [ r a d f s e c j Peak angular a* acceleration [rad/sec2 ] Angular Ox velocity [rad/sec] A n g u la r tu, v elo city [raclisec/ Angular o)z velocity [rad/sec] T96224-01 3.8 86.5 [168.7 msec| -192.8 [200.6 msec] 56.1 [220.6 msec] -40.7 [298.4 msec] 0.116 -0204 0.117 028 T96224-02 5.60 204.9 [173.7 msec) -657.7 [173.7 msec[ 238.7 [162.7msec] -1315 [I40.7msecl 154 0.172 -156 -1.41 T96224-03 3.60 545 [212.6 msecl -2125 [187.6 msec] 64.7 [198.6 msec] -605 [178.6 msec] -0236 3.47 159 4.90 T96224-04 6.90 1225 [168.7 msec] -9365 [168.7 msec] 377.7[154.7 msec] -111.7 [185.6 msec] -0.186 3.00 -1.44 -0.052 Table 21 Test T96224 head static center of gravity angular acceleration and velocity R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. XI. Discussion — L inear m easures Examination o f the existing linear acceleration tolerance curves provides for a number of different methods of quantifying human head tolerance to linear acceleration. However, differences are present in the group o f tolerancing indices that make cross-index correlation and comparisons a difficult if not an grossly improbable task. The following table summarizes the relevant criterion that were reviewed in the prior sections. Unless stated otherwise, the acceleration parameters are given in terms of the load experienced by the occupant. Reference Figure Number Variables Considered Tolerance Value Fraser[1966] 12 Plateau load vs. Duration Approximately 25 G Chambers [1961] 13 Average acceleration vs. Duration 31- 33 G „g for 0.001 to 0.002 min duration Fraser [1961] 14 Plateau load vs. Duration Approximately 16 G Eiband [1959] 15 Vehicle plateau load vs. Duration 55-60 G for 0.01 to 0.02 sec duration Webb[1963] 16 Peak acceleration vs. Duration 40-100 G for .01 to .012 sec duration Webb [1964] 17 Peak vehicle acceleration vs. Duration 48-66 G for 0.001 to 0.03 sec duration Table 22 Summary of tolerance indices Distillation and interpretation of the collected data was conduced by a comparative analysis with the preexistent tolerance and injury prediction indicators. Assumption o f a trapezoidal acceleration function was made by Fraser [1966], Chambers [1961], Fraser [1961], and Eiband [1963]. Comparing a trapezoidal acceleration function with the occupant Gx linear head acceleration responses in the subject case [see Appendix A] revealed a marked difference in profile shape. The question that must then be asked is which parameter does the dwell acceleration correlate to in the subject tests — the average acceleration or the peak acceleration. For the subject analysis, where applicable, it was assumed a priori that the dwell acceleration values correlated with the peak acceleration values of the subject tests. Also, the full time course during which the head was undergoing acceleration in the +GX direction was utilized as the equivalent of the plateau duration. The employment of the latter represents the worst case scenario. If the dwell 96 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. accelerations correlated with the average accelerations then the predicted peak accelerations would be twice the value as denoted per Table 22. If a more stringent limit was utilized for the duration o f application, then for a lower duration one would expect a higher tolerable acceleration level. For each o f the injury measures utilized it was determined that the loading imposed on the occupants as a result o f the subject testing did not, to a reasonable degree o f engineering certainty, indicate any potential for the occurrence of concussive head injury. Another factor that needs to be taken in consideration is the acceleration onset rate [jolt]. Examination of the acceleration profiles in the testing for this research reveals a peak acceleration onset rate of 600 G/sec. The majority of tests in which conditions of medical shock were documented occurred when the acceleration onset rate was at least 1300 G/sec coupled with high peak accelerations and high durations. Table 1 reveals acceleration onset rates o f 413 to 5000 G/sec. The relatively low acceleration onset rate of the subject series of testing coupled with the relatively low peak acceleration values once again provides for the lack of potential for concussive head injury. The tolerance curve presented by Fraser [1966] as depicted in Figure 12 was not extensively examined for two reasons. The first is that the paucity of data that was utilized for the creation of the tolerance curve. The second factor is that the minimum time duration of 1.0 sec as depicted on the axis of Figure 12 was an order o f magnitude greater than the time durations that were observed in the subject case. Extrapolation to time duration values o f 0.01 seconds would have been difficult secondary to the lack o f explainable rationale for the extrapolation methodology. In other words, Figure 12 depicts a plateau tolerance of approximately 25 G for plateau durations from 1.0 to 2.0 seconds. One would expect, based on examination of the other tolerance measures as well as volumetric and hydrostatic considerations, that the tolerable plateau load would increase for decreasing load duration. Figure 12, however, does not provide a mechanism by which the latter could be extrapolated. Regardless, a plateau load o f 25 G far exceeded the peak occupant head +GX loads that were experienced in the subject tests. 97 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Examination o f the +GX tolerance values as based on examination of peak vehicle/sled acceleration versus the duration o f application o f the peak acceleration was presented in Figure 17. The following figure depicts the subject data plotted on the backdrop of Figure 17. The area of interest, depicting the average vehicle Gx acceleration, is shaded. ch c JO C 5 U _ c > a c j u 03 O £ 70 60 6 00 V » c 6 0 * +Gx, 1 0 0 tfsmc ► ; j IN 0 C K .C ) HEMC CNCUS. 3RRHAC s « ] _ I A l* \_1 ■ 40 >5] — JO & ff too • 0 g /* * c b a r e Ly c ; RECOVER :at ED It :io u s, 4 iO f t * 5 DAYS ..V W Z Lo- i f I ■ > « 1 1.0 2 3 S 10 Duration o f peak acceleration [sec] Figure 44 Peak vehicle +GX acceleration vs. duration The data from the subject group of tests falls well below the accepted range of human tolerance values to +GX acceleration in cases where the tolerance values, as presented by the above indicated figures, is applicable. Extrapolation of the voluntary tolerance limit for +GX peak acceleration durations from 0.001 to 0.03 seconds is presented in Figure 44. One would not expect, nor does a reasonable explanation exist based on current understanding o f human response to trauma, for the extrapolation of the tolerance curve to be other than that as depicted above. It is well excepted that as the peak applied +GX acceleration magnitude is increased that the tolerable or survivable time span for duration of the same is decreased. Also, it has not been shown in the literature that a linear extrapolation is necessarily incorrect. In the subject case the peak vehicle +GX acceleration magnitudes are well within an order o f magnitude less than what would be required for concomitance with the voluntary tolerance levels. For the subject analysis the time span was determined by finding the local rise and drop time to 90% of the peak +GX vehicle center of gravity acceleration. A tolerance range of 98%, as used in determining the duration of head contact as 98 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. indicated in the previous section, would have resulted in the prediction o f a lower potential for approach of the voluntary tolerance level than shown here. Use o f the aforementioned as a tolerance predictor, however, has a number o f limitations. It is an inherent assumption in the formulation of the +GX tolerance curve as depicted in Figures 17 and 44 that the occupant is tightly coupled with the vehicle/sled. In the historical development o f the tolerance curve depicted in Figures 17 and 44 one has to note the aeronautical context. The majority o f the tests were conducted with the occupant tightly coupled to the vehicle/sled by means of a 5-point restraint system, which was the operating condition for actual aeronautic and astronautic operations. In the subject motor vehicle case the use o f a 3-point restraint system allows for a lowered degree of occupant coupling to the vehicle and may result in a higher magnitude of occupant head acceleration in the direction of loading. Examination of Figure 16 reveals the lower limit for voluntary transverse impacts of duration of between 100 to 200 msec to be approximately 25 and 20 G [peak] respectively. Examination of the subject data reveals that there was not a single test in which the peak +GX acceleration reached the 20 to 25 G range. It is once again restated that the 20 to 25 G region represents the lower aspect of the voluntary tolerance region and does not represent a predicted injury threshold. Figure 13 depicts the average +GX occupant acceleration and the duration for which the latter is applied. Figure 45 depicts the subject data plotted as an overlay to Figure 13. 99 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 100 .01 .02 .05 2.0 Time [min| Figure 45 Average +GX acceleration magnitude vs. duration The gray shaded region in Figure 45 depicts the data from the nineteen tests that comprised the subject endeavor. The time duration of acceleration, as depicted on the axis, was expanded to include contact durations of interest. ft should be noted that the measured values lie well below the expected tolerance threshold o f between 35 to 40 average +GX head acceleration that is predicted for the application durations of interest. The final tolerance curve to be utilized in the discussion of preexistent linear +GX acceleration tolerance curves is the Japanese Automotive Research Institute curve as depicted in Figure 24. In utilization o f the aforementioned a minor adjustment had to be made to the data used secondary to the duration of acceleration loading in the subject context being an order greater in magnitude than the range depicted on the axis o f the original tolerance curve. For the subject presentation the duration of the peak head center of gravity +GX acceleration with the aforementioned 90% tolerance bands will be utilized instead. The valuations presented on the abscissa will constitute both the average accelerations and the peak accelerations, with the latter being the worst case scenario. 100 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 700 Q « S O T Duratiop (msec] [ _ AeaofirtErest 0 20 40 60 Duration (msecl Figure 46 JARI Tolerance curve depicting the area of interest In examining Figure 46 it is evident that even in the case in which the peak acceleration values of the head center of gravity are utilized that the threshold for concussion is not reached as per the JARI tolerance curve. An approximate one order of magnitude difference is present between the measured acceleration values and those values for which initiation of concussive brain injury was predicted. It must be stated that in the same manner in which the Head Injury Criterion [HIC] was found to be unsuited for determination of concussion based on sole reliance on linear acceleration that the JARI tolerance curve may also not be suitable for evaluation of concussive injury potential. In fact, the latter argument can be made for any tolerance curve for the prediction of concussive brain injury that is based solely on linear acceleration criteria. 101 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Dynamic response index - linear As stated before, it was slightly surprising to notice the large linear head center of gravity +GZ response. As a graphical reminder o f the latter the comparative peak +GX and +GZ responses are depicted as functions o f struck vehicle Delta-V in Figure 47. ♦ Peak head G x response ! ■ Peak head G z response j 0 2 4 6 8 Struck vehicle Delta-V [mph] Figure 47 Comparative peak bi-directional head response In order to take the latter into account, the omnidirectional head translational response referred to as the Linear Dynamic Response Index [DRI], will be utilized. The term “Dynamic Response Index” should not be confused with the aeronautical term of the same name, in which the unidirectional head and spine deflection and system natural frequency are utilized [Brinkley, et al., 1971; Chiou, et al., 1993]. The following is the mathematical definition for the Linear Dynamic Response Index: DRI = [(a J 2 +(aJ 2 +(a J 2?5 t32] 102 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The following figure represents the Linear DRI plotted as a function of struck vehicle Delta-V. 18 0 1 2 3 4 5 6 7 8 Struck Vehicle Delta-V [mph] Figure 48 Linear DRI vs. Struck Vehicle Delta-V As expected a linear increase is noted in the calculated Linear DRI with increases in struck vehicle Delta- V. It is of interest to note that the linear DRI is similar to the orthopedic foraminal compression test in which the extended cervical spine is compressed. Linear regression with forced fitting through the origin using the EXCEL “LINEST” function and fitting without the origin as a segment o f the data set results in Equations 33 and 34. Forced fitting of the regression function through the origin provides for the more reasonable solution since a negative DRI in of itself is not possible based on the definition and a positive linear DRI without a measurable struck vehicle Delta-V is also unreasonable due to violation of the causality relationship. D R I linear ~ 2.69 * [A V s,ruclachicle ] P3] DRIr m c a r = 2.77 ■ [ A F ; „ ,,J - 3 .6 4 [34] 103 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The dynamic response index, as a prediction of injury, is only valid when the peak head linear center of gravity +GX and +GZ accelerations occur within the same temporal vicinity. In the case where a temporal shift is present between the respective peak directional magnitudes, for example, utilization of +GX and +GZ tolerance values must be conducted separately. In all but one of the subject 19 tests, there was sufficient overlap between the areas represented under the acceleration-time traces o f the +GX and +GZ head, linear, center of gravity acceleration responses to provide a useful predictive tool. This is grossly evident by means of visual inspection o f the figures represented in Appendix B. The elucidation of the magnitudes and temporal placement of the +GZ acceleration magnitudes does not in any manner provide credence or validity to an argument indicating that the potential for concussive brain injury, to a reasonable degree of engineering certainty, is present in a low speed rear-end motor vehicle accidents in which the struck vehicle occupant is seated in a normal manner. The observational discovery of the +GZ acceleration profiles does not affect the causal relationship between the system input and the system output, with the latter being the lack of significant potential for concussive brain injury under the context of consideration. Use o f the DRIiinear serves as an indicator of injury potential in the same manner as the previously described injury measures. However, beyond these measures the DRii;n c a r does provide for the incorporation of the salient aspects o f the complete linear acceleration profile. Injury measures and predictors that are based solely on a +GX criterion remain wholly applicable in the situations in which the predominant component o f the acceleration vector is the +GX . Even in cases in which a comparable +GZ acceleration component exists, the use o f the criterion based solely on +GX acceleration magnitudes continues to provide an indicator for injury potential. It is obvious that even though the +GZ values were not reported by a number o f previous authors during the course o f research and testing one can reasonably assume, based on the subject sample, that a large component o f +GZ acceleration was present. If one assumes a similar relative valuation of the peak directional acceleration magnitudes and if one assumes a similar time of occurrence of the peaks then it can be reasonably argued that the +GX acceleration magnitude in and of itself predicts, albeit incompletely, that the potential for concussive does not exist. 104 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The use o f the DRIIin c a r as a reasonable predictor for concussive injury will require future work. The most obvious o f which is a determination o f the minimum values o f the D RI|,-n < a r at which the potential for injury, to a reasonable degree o f engineering certainty, is present. This would involve an analysis o f data for which concussive injury was determined to be present and for which an injury measure based on +GX acceleration values was noted. The intrinsic assumption in the latter is that the +GZ acceleration time history was also recorded. The latter may be a valid assumption for current day testing, but one only has to review the data presented by Severy to realize that the assumption may not be valid for older test protocols. Also, due to the nature as well as the age of a number o f the older published injury tolerances found in the aeromedical context, it may prove to be difficult to obtain access to the original publications in which the complete data sets may have been reported. 105 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. XII. Discussion — Angular measures The angular injury tolerance curve presented by Ommaya, et al. was depicted in Figure 23. Examination of the curve as presented in Figure 49 reveals that the subject data does not appear, even with the most severe tests, on the origin o f the tolerance curve of an angular acceleration value of 1,000 rad/sec2 with an angular velocity value of 10 rad/sec. The subsequent figure depicts a plot o f measured head center of gravity - a y angular velocity versus -a y acceleration. Rotational acceleration [rad/secA 2] Rotational acceleration [rad/sec * 2] Figure 49 Angular velocity v. angular acceleration 106 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The GAMBIT curve, as presented above, normalized the head injury potential using a probability scale based on Abbreviated Injury Scale [AIS] valuations. Both the head angular acceleration and the head linear acceleration components were considered. Once again, due to the relatively minor magnitude o f the quantified maximum Gambit values, all of which indicated substantially less then even an AIS I level injury, it was deemed that an attempt to plot the data points on the actual curve would result in a skewed depiction o f the actual results. A maximum GAMBIT value of 0.169 was calculated for test 4 of series T96224. The calculation o f an angular Dynamic Response Index [DRI] was not as crucial as was the quantification for the linear acceleration case secondary to the predominance of the -y-direction angular response in comparison to the angular response about the x and z axes. For the sake of completeness, however, the angular DRI was calculated with the results presented in the following figure as a function of the struck vehicle Delta-V. 1200.00_________.__ Si 1000.00 800.00 o 600.00 a, c * os • | 400.00 c e £ a b 2 0 0 .0 0 . 0.00 ♦ ♦ 3 4 5 Struck Vehicle D elta-V [m phl Figure 50 Angular DRI vs. struck vehicle Delta-V The relationship between the angular DRI and the struck vehicle Delta-V does not provide for as linear a relationship as did the linear DRI. It appears as if a plateau is present for struck vehicle speed changes from less than one mile per hour up to approximately three miles per hour where the head angular DRI is quantified as being approximately 100 rad/sec2 . Increasing struck vehicle speed changes o f three miles per hour and greater result in a linearly increasing angular DRI. The latter may be due to a number of factors including lack of significant head to head restraint contact during the lower struck vehicle Delta-V events 107 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. or due to the increased transnational component of the head-neck complex secondary to the rotational inertia of the head. 108 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. XIII. Conclusion Nineteen human volunteer vehicle to vehicle low speed rear-end motor vehicle collisions were conducted with the stated purpose o f measuring and quantifying appropriate head injury measures, in each test case the quantified linear, angular, and combined concussive brain injury criteria indicated, to a reasonable degree o f engineering certainty, no likelihood o f injury. This in turn was consistent with the lack o f any symptomatology on the part o f the test subject in any of the tests o f the test series. The linear dynamic response index was defined as the magnitude of the triaxial head center o f gravity linear acceleration response. In all but one case, significant area overlap was noted between the +GX and +GZ acceleration-time responses. In all but one o f the tests, the peak +GZ response magnitude was greater than the +GX response magnitude. The two facts in conjunction indicate the equivalent of a foraminal compression type maneuver with the cervical spine in extension and a superoinferior force applied to the vertex and/or the occipital region. Further study needs to be conducted on the effects of this loading condition for the quantification of+GZ human acceleration response for both the head and the head-cervical spine complex. The angular dynamic response index, as defined, was not as significant in the sense that the -Oy head angular acceleration response dominated in comparison to the rotational acceleration about the other two axes. The subject study should be viewed as in introductory or exploratory study into head acceleration response in the context o f Iow-speed rear-end motor vehicle collisions. The relationship between effects of recliner to head restraint stiffness, head restraint type, and a host of other factors that were discussed in the vehicle context section need to be isolated in a classic design of experiments [DOEjmanner such that the effects of each independent variable can be quantified. The nominal case needs to be expanded through additional directed testing and by using the existing human volunteer tolerance database such that a contiguous comprehensive database is established for all ranges of reasonable human anthropometric variations. 109 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. X m . Appendix A — Measurement of Head Acceleration The measurement of motion properties of a rigid body in three dimensional space requires the determination o f six parameters, which are the three center of gravity linear accelerations and three center of gravity angular accelerations. A number of methods for the determination of these quantities have been described in the literature. The methods differ in how peripheral acceleration values are determined secondary to the number o f uniaxial accelerometers used and the manner in which they are clustered. Alem and Holstein described a method for measuring the three-dimensional motion characteristics of the head by using data from a nine uniaxial accelerometer set-up. The data obtained is then manipulated using least squares fitting in order to minimize the measured error. The accelerometers are arranged in a triaxial cluster, with the individual uniaxial accelerometers placed such that each block provides the orthogonal components of acceleration at the block center. The position vector of each block center is predetermined with respect the center of gravity o f the head, which is coincidental with the origin o f the anatomical reference frame. This information is used to construct the coordinate transformation matrix that relates the instrument reference frame to the anatomical reference fra m e; The following diagram denotes the instrument, anatomical, and inertial reference frames. K Anatomical Reference Fram e Inertial Reference Frame I Figure 51 Reference frames of importance 110 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The coordinates o f the anatomical reference frame (i, j, k) can be used to describe the position vectors of the triaxial block centers with respect to the head center o f gravity denoted by Q0. /> l = .Pl,-i + /JlJ.-j-t-P lJC -k P2 - P2r -i + P lj -1+P2,. -k [35] P3 = P3, A + P3J ■j-hP3K k The acceleration vectors of the triaxial centers expressed in the anatomical reference frame are given by the following equation set. Al — Alj 'i + Alj * j + Al £ -k A 2 = A 2 , - i + A 2 j -j + A 2 K -k [36] A3 = A3r i + A3J -j + A3/.-k The acceleration vectors given in [36] can also be determined using rigid body dynamics, based on the translational acceleration, angular acceleration, and angular velocity of the rigid body. A\ = A + axP l + axcoxPl A2 = A + ax.P2 + ct)xa)xP2 [37] A3 = A+axP3+coxa)xP3 Where: A = Translational acceleration of the rigid body a = Angular acceleration of the rigid body c o = Angular velocity o f the rigid body The unknowns of the system, using the formulation of rigid body dynamics provided in [38] are the three dimensional terms o f the rigid body translational acceleration, angular acceleration, and angular velocity. Written in terms of the anatomical reference frame, the components are: 1 1 1 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A - A , - i + Aj •j-i-AK -k a = a , -i+ a , -j+a*. -k a) =6), -i+co,-j+a)K -k [38] It can be observed that there a total of 9 unknown quantities, but it should also be noted that the angular velocity can also be determined from integration of the angular acceleration. Least Squares Solution The position and acceleration quantities given in [35] and [37] can be written in column vector form: > 1 / > 2 , ' ~ P 3/ P l = Ph F2 = P2, P3 = P3, P h P 'l. P3* ’A l,' ~ A2, " ' A3/ Al = Al, A2 = A2, A3 = A3, -Al*. 1 V C S 1 1 U > * L . The angular acceleration and angular velocity vectors can be written in a similar manner ’a , ’ a = C O = CO, -a * - Computation of cross products involving the position and angular velocity quantities denoted in [38] is facilitated by determination o f the skew symmetric matrices o f those column vectors. The skew-symmetric matrix o f a vector quantity T is given by following relationship: 112 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. ~T,' ' 0 i ---- i T = Tj [P]= T* 0 -T , r TJ --- 1 o A skew symmetric matrix is one that is defined as being the negative of its transpose. The cross product of two vector quantities is equivalent to the skew symmetric matrix of the first times the column vector of the second. The quantities of [39] can then be rewritten, in the general form, as 0 C O J ‘ ' 0 Pk Ps ' = 0 -CO, and [P] = P, 0 - p, C O , 0 r p> p, 0 Calculating the cross products o f the column vectors from [39] results in the following equation set: M -[p i]- [«]+[«]■([<»]• {pi} ) - =0 [a]-[P 2]-[o\+ [co]-([co]-{P 2})-{A 2} = 0 [40] [A]-[P 3]-[a]+H-([ffl]-{P3})-{^3} = 0 The equation set presented in [40] can be described using the following matrix notation: [4x« - [PL • [4x. + [ V L =0 [4 1 ] Where: a " H - ( H - [ p i] ) - lA r a {P},,3=- [P2] M,xi = ■ [a>\<lco\[P2])-[A2} u [P3l >]-([a,].[P3D-[^3l R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. Equation [41] then is a set of nine scalar equations in 6 unknowns. The redundancy can be eliminated with the realization that the actual measurement process results in the presence of experimental error, and therefore the left side of the aforementioned equation is not exactly equal to zero, but is instead equal to a small error matrix: [ 4 * . - [ 4 , 3 - [ < 4 * « + H w = ( 4 ,. [ 4 2 ] Assuming a unity variance among the different error quantities, the overall error can be minimized by sequentially taking the square of the errors, taking the partial derivatives o f the squared errors with respect to the unknown quantities, and then setting that quantity equal to zero. Therefore, 0 [43] d m 4 4 T ' 0 t441 Least squares solution — angular acceleration Equation [44] can be expanded by means of the chain rule: Solving for the partial derivative of the transpose o f the error column vector with respect to the angular acceleration, by substitution of [42] as the error term results in: 114 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Equation [46] can now be substituted into [45] resulting in: [47] Expansion o f [47] results in: -Mr -M+Mr -M=o [48] Least squares solution — translational acceleration For simplification purposes, it was assumed that the reference point Q0 was located at the centroid o f Qt, Q2, and Q3. This assumption was deemed valid for the subject application based on the manner in which the instrumentation was attached to the test subjects. The head center of gravity acceleration can be approximated as: Equation [48] can be simplified by removal o f the first term. Solving for the angular acceleration results in the following: , ^ {Al}+{A2}+{A3} [49] 115 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. w - S > r ■■[/•]■' f c r - H [50] The above is a system o f three simultaneous differential equations in which the unknowns are the three angular velocity terms and their respective derivatives, the angular acceleration terms. All of the other values are either known or determined by direct measurement. The solution to the above system is obtained through numerical integration. Angular motion In order to specify the orientation of the inertial reference frame o f the rigid body, the determination of the Euler angles as functions of time needs to made. The Euler angles define the transformation matrix that describes the rotation o f the anatomical reference frame with respect to the laboratory reference frame. [i,j\k] = [H]-[l,J,K] [51] The set of Euler angles, defining the transformation matrix, must be structured such that consecutive rotations occur about different axes. The first rotation is one o f v p r degrees about the original K axis. The second rotation is one of 0 degrees about the new J axis. The final rotation is one of < ( ) degrees about the new I axis. 116 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. First Rotation K Second Rotation Third Rotation J ► I Jk. Figure 52 Rotational transformation of coordinate systems The transformation matrices for each sequential rotation are given in the following manner: C O S Iff — sin ^ 0 o' COS# 0 sin# O ' T 0 0 O ' sin ty COS^ 0 0 0 I 0 0 0 COS0 -s in ^ 0 Rot- = Ror,, = 0 0 1 0 y .o -sin # 0 COS# 0 0 sin^ COS0 0 0 0 0 1 0 0 0 l_ _o 0 0 I Each o f the above 4x4 matrices can be interpreted in the following manner: Rotation Translation fu s *Ul_ Perspective ScaleFactor The transformation matrix H for the subject case is obtained through matrix multiplication in sequential order. Utilizing only the rotational aspect of the matrix: H = Rott)r - Roty l 7 • R ot,, = -s in # 0 I cos#-sin (p cos < f > 0 cos#-cos0 — sin# 0 [52] 117 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The angular velocity vector in the inertial reference frame can be written in terms of the contributions from each o f the anatomical angular velocity components: — sin# 0 f ~ = cos8 -sin cos^ 0 - to * 0)K cos#-cos0 — sin# 0 .®>. The unknowns in the above equation are the three Euler angles, as denoted by their trigonometric quantities, and their rates of change a> [, Q )j, and c d k l - Rearranging the above equation and solving for the unknowns results in the following. 1 ► = ------------------ cos# 0 sin$> cos^l 0 cos^ — sin?J 1 sin#-sin^ sin#-cos^ ’to,' •• 03 j [54] Numerical integration of the above equation results in the three Euler angles and their rates of change. Translational Motion The following section discusses the methodology for the determination of the translational acceleration, velocity, and position vectors of an arbitrary point on the rigid body with respect to the inertial reference frame. An arbitrary body point on the rigid body, with respect to the anatomical reference frame, has a position vector that is given as: P B = P B l ' i + P B t ' \ + P B K ' ^ [ 5 5 ] 118 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Knowing the rigid body angular acceleration, angular velocity, and the translational acceleration of the rigid body center of gravity, then the absolute acceleration of the arbitrary point can be given, in the anatomical reference frame, according to equation [56] as: Ab = A + a x P B+ o } kcoxPb [56] Expansion o f the acceleration vector, in the most general terms, along the anatomical reference frame, and then writing it in terms of the components along the inertial reference Same, results in the following relationship: .r y [57] The transformation matrix [H] is the same that was described earlier in this section. It should be noted that only the rotational segment o f the transformation matrix is being used here. 119 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. XIV. Reference List Arbogast, Kristy B, Michael T Prange, David F Meaney, and Susan S Margulies. “Properties o f Cerebral Gray and White Matter Undergoing Large Deformation.” 7th Injury Prevention Through Biomechanics Symposium. 1997. Alem, NM, and GL Holstein. “Measurement of 3-D Motion.” Bailey, Mark N, Bing C Wong, and Jonathan M Lawrence. “Data and Methods for Estimating the Severity of Minor Impacts.” SAE Publication 950352. Society of Automotive Engineers. New York. 1995. Brinkley, JW and JT Shaffer. “Dynamic Simulation Techniques for the Design o f Escape Systems: Current Applications and Future Air Force Requirements.” Symposium on Biodynamic Models and their Applications. WPAFB, OH: Armstrong Medical Research Laboratory, 1971; AMRL-TR-71-29. Brinn, J and SE Staffeld. “Evaluation of Impact Test Accelerations: A Damage index for the Head and Torso.” SAE Publication 700902. Society of Automotive Engineers. Warrendale, PA. 1970. Carpenter, Nicholas J. Personal communications. 1998. Chiou, Wen-Yaw, Bang-Lee Ho, and Dean L Kellogg. “Hazard Potential o f Ejection with Canopy Fragmentation.” Aviation. Space, and Environmental Medicine. 1993; 64:9-13. Clarke, Thomas D, C Dee Gragg, James F Sprouffske, Edwin M Trout, Roger M Zimmerman, and William H Muzzy. “Human Head Linear and Angular Accelerations During Impact.” SAE Publication 710857. Society o f Automotive Engineers. New York. 1971. Evans, Randolph W. “The Postconcussion Syndrome: 130 Years of Controversy.” Seminars in Neurology. 14(1), pp. 3 2 — 39, March 1994. Fan, William RS “Internal Head Injury Assessment.” SAE Publication 710870. Society o f Automotive Engineers. New York. 1971. Foret-Bruno, JY, F Dauvilliers, C Tarriere, and P Mack. “Influence o f the Seat and Head Rest Stiffness on the Risk o f Cervical Injuries in Rear Impact.” 13th International Technical Conference on Experimental Safety Vehicles. Fraser, T Morris. “Sustained Linear Acceleration.” Bioastronautics Data Book. NASA: Washington. 1973. Fraser, T Morris. “Rotary Acceleration.” Bioastronautics Data Book. NASA: Washington, 1973. 120 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Gadd, Charles W. “Use o f a Weighted-impulse Criterion for Estimating Injury Hazard.” SAJE Publication 660793. Society of Automotive Engineers. New York. 1966. Gadd, Charles W. Tolerable Severity Index in Whole-Head. Nonmenchanical Trauma. 15th Stapp Conference Workshop. November 17, 1971 Gennarelli, Thomas A. Head Injury Biomechanics: A Review Gennarelli, Thomas A, LE Thibault, and AK Ommaya. “Pathophysiologic Responses to Rotational and Translational Accelerations of the Head.” SAE Publication 720970. Society of Automotive Engineers. New York. 1972. Gennarelli, Thomas A, Lawrence E Thibault, Hume Adams, David I Graham,. Carson J Thompson, and Robert P Marcincin. ‘Diffuse Axonal Injury and Traumatic Coma in the Primate. Annals o f Neurology. Volume 12 (6). December, 1992. Gennarelli, Thomas A, Lawrence E Thibault, G Tomei, R Wiser, D Graham, and J Adams. “Directional Dependence of ^Vxonal Brain Injury due to Centroidal and Non-Centroidal Acceleration. SAE Publication 8672197. Society of Automotive Engineers. New York. 1986. Gennarelli, Thomas A and Lawrence E Thibault. “Clinical Rationale for a Head Injury Angular Acceleration Criterion.” Head Injury Mechanisms: The Need for an Angular Injury Criterion. Association for the Advancement of Automotive Medicine. Des Plaines, IL, 1989. Goldsmith, Wemer. “Meaningful Concepts of Head Injury Criteria. Head Injury Mechanisms: The Need for an Angular Injury Criterion. Association for the Advancement of Automotive Medicine. Des Plaines, IL, 1989. Got, C, A Patel, A Fayon, C Tarriere, and G Walfisch. “Results of Experimental Head Impacts on Cadavers: The Various Data Obtained and Their Relations to Some Measured Physical Parameters.” SAE Publication 780887. Society of Automotive Engineers. New York. 1978. Gray, Henry. Gray’s Anatomy. Ed. T. Pickering Pick and Robert Howden. Philadelphia: Running Press, 1974. Gurdjian, ES, and JE Webster. “Experimental Head Injury with Special Reference to the Mechanical Factors in Acute Trauma.” Surgery. Gynecology and Obstetrics. Volume 76, 1943. Gurdjian, ES, and HR Lissner. “Mechanism o f Head Injury as Studied by the Cathode Ray Oscilloscope, Preliminary Report.” Journal of Neurosurgery. Volume 1, 1944, pp. 393-399. 121 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Gurdjian, ES, HE Lissner, JE Webster, FR Latimer, and BF Haddad. “Studies on Experimental Concussion.” Neurology. Volume 4, 1954, pp. 674-681. Gurdjian, ES, JE Webster, and HE Lissner. “Observations on the Mechanism of Brain Concussion, Contusion, and Laceration.” Surgery. Gynecology and Obstetrics. Volume 101, 1955. Gurdjian, ES and HR Lissner. “Concussion — Mechanism and Pathology.” 7th Stapp Car Crash Conference. Charles C Thomas. Springfield, Illinois, 1965. Gurdjian, ES, and HR Lissner. “The Position and Motions of the Head at Impact.” 8th Stapp Car Crash and Field Demonstration Conference. Wayne State University Press. Detroit, 1966. Haut, Roger C, Charles W Gadd, and Richard G Madeira. “Nonlinear Viscoelastic Model for Head Impact Injury Hazard.” SAE Publication 720963. Society o f Automotive Engineers. New York. 1972. Hirsch, Arthur E, and Ayub Ommaya. “Protection from Brain Injury: The Relative Significance of Translational and Rotational Motions of the Head After Impact” SAE Publication 700899. Society of Automotive Engineers. New York. 1970. Hodgson, VR, LM Thomas, ES Gurdijian, OU Fernando, SW Greenberg, and J. Chason. “Advances in Understanding Experimental Concussion Mechanisms.” SAE Publication 690796. Society of Automotive Engineers. New York. 1969. Hodgson, VR, Jule Brinn, LM Thomas, and S W Greenberg. “Fracture Behavior of the Skull Frontal Bone Against Cylindrical Surfaces. SAE Publication 700909. Society o f Automotive Engineers. New York. 1970. Hodgson, VR and LM Thomas. “Comparison of Head Acceleration Injury Indices in Cadaver Skull Fracture.” SAE Publication 710854. Society of Automotive Engineers. New York. 1971. Hodgson, VR, and LM Thomas. “Effect of Long-Duration Impact on Head.” SAE Publication 720956. Society of Automotive Engineers. New York. 1972. Hodgson, VR, and LM Thomas. “Concussion Levels Determined by HPR Windshield Impacts.” SAE Publication 730970. Society of Automotive Engineers. Warrendale, PA. 1973. Holboum, AHS. “Mechanics of Head Injuries.” The Lancet. October 9, 1943, pp. 438 — 441. Howard, Richard P, John Bomar, and Cleve Bare. “Vehicle Restitution Response in Low Velocity Collisions.” SAE Publication 931842. Society of Automotive Engineers. New York. 1993. 122 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Insurance Institute for Highway Safety. “Status Report.” April 12, 1997. Kahane, Charles. “An Evaluation o f Head Restraints: Federal Motor Vehicle Safety Standard 202.” National Highway Traffic Safety Administration. February 1982. NTIS Publication: PB89-158380. Kikuchi, Atsumi, Koshiro Ono, and Norio Nakamura. “Human Head Tolerance to Lateral Impact Deduced from Experimental Head Injuries Using Primates.” SAE Publication 826035. Society o f Automotive Engineers. New York. 1982. King, David J, Gunter P Siegmund, and Mark N Bailey. “Automotive Bumper Behavior in Low-Speed Impacts.” SAE Publication 930211. Society of Automotive Engineers. New York. 1993. King, Albert I and King H Yang. “Research in Biomechanics o f Occupant Protection.” The Journal o f Trauma: Injury. Infection, and Critical Care. 38(4), 1995. Kraus, Jess F. “Epidemiological Aspects of Brain and Spinal Cord Injuries.” Mechanisms o f Head and Spine Trauma. Ed. Anthony Sances, Daniel J. Thomas, Charming L. Ewing, Sanford J. Larson, and Friedrich Unterhamscheidt. Goshen, NY: Aloray Publisher. 1986. Kraus, Jess F, David L McArthur, and Terry A Silberman. “Epidemiology of Mild Brain Injury.” Seminars in Neurology. 14 (I), pp. 1-7, March 1994. LaPIaca, Michelle C and Lawrence E Thibault. “An In Vitro Traumatic Model to Examine the Response o f Neurons to a Hydrodynamically-Induced Deformation. Annals of Biomedical Engineering. 25, pp. 665- 677, 1997 LaPIaca, Michelle C, Kenneth A Barbee, Brett R Blackman, and Lawrence E Thibault. “An In Vitro Injury Model for Investigating Mechanisms of Traumatic Neural Injury.” 6th Injury Prevention Through Biomechanics Symposium. 1996. Lighthall, JW, JW Melvin, and K Ueno. “Toward a Biomechanical Criterion for Functional Brain Injury.” SAE Publication 896074. Society of Automotive Engineers. New York. 1989. Lin, Shan-Cheun, Sheu-Jane Shieh, and Michelle J Grimm. “Ultrasonic Measurements o f Brain Tissue Properties.” 7th Injury Prevention Through Biomechanics Symposium. 1997. Lombard, Charles F, Smith W Ames, Herman P Roth, and Sheldon Rosenfeld. “Voluntary Tolerance o f the Human to Impact Accelerations o f the Head.” The Journal of Aviation Medicine. 22(2), pp. 109-116. 1951. 123 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Maclnnis Engineering Associates. Passenger Car Bumpers. Maclnnis Engineering Associates; Richmond, BC, Canada. McConnell, Whitman E, Richard P Howard, Herbert M Guzman, John B Bomar, James H Raddin, James V Benedict, Harry L Smith, and Charles P Hatsell. “Analysis o f Human Test Subject Kinematic Responses to Low Velocity Rear End Impacts.” SAE Publication 930889. Society of Automotive Engineers. New York. 1993. McConnell, Whitman E, Richard P Howard, Jon Van Poppel, Robin Krause, Herbert M Guzman, John B Bomar, James H Raddin, James V Benedict, and Charles P Hatsell. “Human Head and Neck Kinematics After Low Velocity Rear-End Impacts- Understanding Whiplash.” SAE Publication 952724. Society of Automotive Engineers. New York. 1995. McElhaney, James, Richard Stalnaker, and Verne Roberts. Discussion o f SAE 700902. SAE publication # 700902. Society o f Automotive Engineers. New York. 1970. Meaney, David F and Allison C Bain. ‘Relationship Between Structural Modeling and Hyperelastic Material Behavior: Application to CNS White Matter.” 7th Injury Prevention Through Biomechanics Symposium. 1997. Mitchell Collision Estimating Guide. Domestic Volume. Volume 98/1. Nahum, AM, and RW Smith. “An Experimental Model for Closed Head Impact Injury.” Proceedings of the 20th Stapp Car Crash Conference. Society of Automotive Engineers. Warrendale, Pa., 1977. Netter, Frank H Atlas of Human Anatomy. Summit, New Jersey: Ciba-Geigy Corporation, 1995. Newman, James A. “A Generalized Acceleration Model for Brain Injury Threshold (Gambit).” International IRCOBI Conference on the Biomechanics of Impacts, pp. 121-131, 1986. Newman, James A, Suzanne Tylko, and Ted Miller. “Toward a Comprehensive Biomechanical Injury Cost Model.” 36th Annual Proceedings of the American Association for the Advancement o f Automotive Medicine, pp. 271-287, 1992. Nielsen, GP, JP Gough, DM Little, DH West, and VT Baker. “Human Subject Responses to Repeated Low Speed Impacts Using Utility Vehicles.” SAE Publication 970394. Society o f Automotive Engineers. New York. 1997. NHTSA. “Head Restraints - Identification of Issues Relevant to Regulation, Design and Effectiveness.” November 4, 1996. 124 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Nusholtz, Guy S, John W Melvin, and Nabih M Alem. “Head Impact Response Comparisons o f Human Surrogates.” SAE Publication 791020. Society of Automotive Engineers. New York. 1979. Nusholtz, Guy S, Paula Lux, Patricia Kaiker, and Miles A Janicki. “Head Impact Response - Skull Deformation and Angular Accelerations.” SAE Publication 841657. Society o f Automotive Engineers. New York. 1984. Nusholtz, Guy S, Patricia S Kaiker, and Richard J Lehman. “Critical Limitations on Significant Factors in Head Injury Research.” SAE Publication 861890. Society of Automotive Engineers. New York. 1986. Nygren, A, and TH Gustafsson. “Effects of Different Types of Headrests in Rear-end Collisions.” 10th International Technical Conference on Experimental Safety of Vehicles. March 1985, pp. 85-90. Ommaya, AK, P Yamell, AE Hirsch, and EH Harris. “Scaling of Experimental Data on Cerebral Concussion in Sub-Human Primates to Concussion Threshold for Man. SAE Publication 670906. Society of Automotive Engineers. New York. 1967. Ommaya, AK, FJ Fisch, RM Mahone, P Corrao, and F Letcher. “Comparative Tolerances for Cerebral Concussion by Head Impact and Whiplash Injury in Primates.” SAE Publication 700401. Society of Automotive Engineers. New York. 1970. Ommaya, AK. “Biomechanics of Head Injury: Experimental Aspects.” The Biomechanics of Trauma. [Nahum and Melvin Eds.] pp. 245-269. 1985. Ommaya, AK. “Mechanisms and Preventive Management of Head Injuries: A Paradigm for Injury Control.” 32n d Annual Proceedings of the Association for the Advancement o f Automotive Medicine. 1988. Ono, Koshiro, Atsumi Kikuchi, Marumi Nakamura, Hajime Kobayashi, and Norio Nakamura. “Human Head Tolerance to Sagittal Impact - Reliable Estimation Deduced from Experimental Head Injury Using Subhuman Primates and Human Cadaver Skulls.” Ono, Koshiro and Munekazu Kanno. “Influences of the Physical Parameters on the Risk of Neck Injuries in Low Impact Speed Rear-end Collisions.” Padgaonkar, AJ, KW Krieger, AI King. “Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers.” Transactions of the ASME. 42(3), Series E, pp. 552-556. 1975. Patrick, LM, HR Lissner, and ES Gurdjian. “Survival by Head Design.” Proceedings of the Seventh Stapp Car Crash Conference. Charles C. Thomas, Springfield, IL, 1965. 125 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Peterson, Patti L. “Clinical Aspects of Traumatic Brain Injury.” Head and Neck Injury. Ed. Robert Levine. SAE Publication P-276. Society of Automotive Engineers, Warrendale, Pa., 1994. Porta, David J. “Introduction to Head and Neck Anatomy.” Head and Neck Injury. Ed. Robert Levine. SAE Publication P-276. Society of Automotive Engineers, Warrendale, Pa., 1994. Prasad, Priya, and Harold J Mertz. “The Position of the United States Delegation to the ISO Working Group 6 on the Use o f HIC in the Automotive Environment.” SAE Publication 851246. Society of Automotive Engineers. New York. 1985 Princemaille, Y, X Trosseille, P Mack, C Tarriere, F Breton, and B Renault. “Some New Data Related to Human Tolerance Obtained from Volunteer Boxers.” SAE Publication 892435. Society of Automotive Engineers. New York. 1989. Rowland, Lewis P and Daniel Sciarra. “Head Injury.” Chapter 54 in Merritt’s Textbook of Neurology. Ed. Lewis P. Rowland. “Human Tolerance to Impact Conditions as Related to Motor Vehicle Design - SAE J885.” SAE Vehicle Occupant Restraint Systems and Components Standards Manual. SAEHS-13. Warrendale, PA., 1993. Sances, Anthony Jr., Daniel J Thomas, Charming L Ewing., Sanford J Larson., And Friedrich Unterhamscheidt. Mechanisms of Head and Spine Trauma. Goshen, NY: Aloray Publisher. Severy DM, JH Mathewson, and CO Bechtol. “Controlled Automobile Rear-End Collisions, an Investigation of Related Engineering and Medical Phenomena.” Canadian Medical Services Journal. November, 1955. pp. 727-759. Slattenschek, A, W Tauffkirchen, and G Benedikter. “The Quantification of Internal Head Injury by Means of Phantom Head and the Impact Assessment Methods.” SAE Publication 710879. Society of Automotive Engineers. New York. 1971. Snyder, Richard G. “Impact.” Bioastronautics Data Book. NASA: Washington, 1973. Sonntag, RW, WA Newsom, SD Leverett, and VE Kirkland “Use of Contoured Restraint Systems in Exposure o f Large Primates to — 150 gx Impact.” SAE Publication 680778. Society of Automotive Engineers. New York. 1968. Spatz, Hugo. “Brain Injuries in Aviation.” German Aviation Medicine in World War II. Department of the Air Force. 1950. 126 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Stalnakar, RL, JW Melvin, GS Nusholtz, NM Alem, and J Benson. “Head Impact Response.” SAE Publication 770921. Society o f Automotive Engineers. New York. 1977. Stapp, John P. “Review of Air Force Research on Biodynamics o f Collision Injury.” SAE Publication 660805. Society o f Automotive Engineers. New York. 1966. Stedman’s Medical Dictionary. Baltimore: Williams & Wilkins, 1995. Svensson, Mats Y, P Lovsund, Y Haland, and S Larsson. “The Influence o f Seat-Back and Head-Restraint Properties o f the Head-Neck During Rear-Impact.” 1993 International IRCOBI Conference on the Biomechanics o f Impact. 1993. pp. 395-406. Svensson, Mats Y, Per Lovsund, Yngve Haland, and Stefan Larsson. “The Influence o f Seat-Back and Head-Restraint Properties of the Head-neck Motion During Rear-Impact.” Accident Analysis and Prevention. 28 (2), pp. 221-227, 1996. 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Society of Automotive Engineers. New York. 1971. Viano, David C. “Biomechanics o f Head Injury - Toward a Theory Linking Head Dynamic Motion, Brain Tissue Deformation, and Neural Trauma.” SAE Publication 881708. Society of Automotive Engineers. New York. 1988. Viano, David C and Martin F Gargan. “Headrest Position During Normal Driving: Implication to Neck Injury Risk in Rear Crashes.” Accident Analysis and Prevention. 28 (6), pp. 665-674, 1996. Votaw, Charles L. “Morphoiogy o f the Nervous System as Related to Trauma.” SAE Publication 700195. Society of Automotive Engineers. 1970. Ward, Carley, Marian Chan, and Alan Nahum. “Intracranial Pressure - A Brain Injury Criterion.” SAE Publication 881304. Society of Automotive Engineers. New York. 1988. West, DH, JP Gough, and GTK Harper. “Low Speed Rear-end Collision Testing Using Human Subjects.” Accident Reconstruction Journal. May/June, 1993, pp. 22-26. Welcher, Judson B, and Thomas J Szabo. “Introduction to Low Speed Impacts.” Texas A&M Low Speed Course Notes. Texas A&M Extension. 1996. White, Augustus, and Manohar Punjabi. Clinical Biomechanics of the Spine. Lippincott-Raven, Philadelphia, 1990. 128 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. IMAGE EVALUATION TEST TARGET (Q A -3 ) ✓ / ✓ / / < « ^ *v * > ° * CP- I-?, / , 1 . 0 l.l I S H I M I S I S iii i s I S IL 8 m u i IS u. S m H i m 1.8 1 .2 5 1 .4 1 . 6 150mm A P P L I E D _ = = IM/1GE . In c _=r= 1653 East Main Street - = ~ - Rochester, NY 14609 USA J= E rj = Phone: 716/482-0300 -= = ^ -= Fax; 716/288-5989 O 1993. Applied Image. Inc.. All Rights R eserved R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.

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Asset Metadata

Creator Singh, Jai Prakash (author)

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

School Graduate School

Degree Master of Science

Degree Program Biomedical Engineering

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

Tag engineering, biomedical,health sciences, rehabilitation and therapy,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Khoo, Michael C.K. (committee chair), [illegible] (committee member), D'Argenio, David (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-27870

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Legacy Identifier 1394778.pdf

Dmrecord 27870

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Rights Singh, Jai Prakash

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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...

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