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A nonlinear pharmacokinetic model used in calibrating a transdermal alcohol transport concentration biosensor data analysis software

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A nonlinear pharmacokinetic model used in calibrating a transdermal alcohol transport concentration biosensor data analysis software

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Content A NONLINEAR PHARMACOKINETIC MODEL USED IN CALIBRATING A TRANSDERMAL ALCOHOL TRANSPORT CONCENTRATION BIOSENSOR DATA ANALYSIS SOFTWARE Copyright 2014 by ZHENGDAI A Thesis Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of Requirements for the Degree MASTER OF SCIENCE (APPLIED MATHEMATICS) August 2014 Zheng Dai Table of Contents Abstract Introduction Transdermal alcohol transport model A Nonlinear Pharmacokinetic Model Numerical Results ofPharmacokinetic Model with Optimal Parameters Numerical Results ofPharmacokinetic Model with Population parameters Reference Appendix I Appendix II Appendixiii 4 8 II 18 22 23 27 30 Abstract In Rosen's earlier work [I] [ 4], blood (BAC) or breath (BrA C) alcohol concentration was estimated from biosensor measurements of transdermal alcohol concentration (TAC) by forward distributed parameter models, which need to be calibrated by alcohol challenge data. The alcohol challenge data was collected from a TAC biosensor and a breath analyzer after giving patient who was wearing with a TAC biosensor a measured dose of alcohol and blowing into a breath analyzer. This process is required for each patient before the device was used to estimate BrAC from field TAC In this research, we used a pharmacokinetic metabolic absorption/elimination model and drinking diary to estimate the BrAC or BAC, and then we used the estimated BrAC or BAC and TAC data of first episode as the alcohol challenge data to calibrate forward distributed parameter model for transdermal transport of ethanol. The pharmacokinetic model can be determined by solving a nonlinear least squares problem using adjoint based gradient computation. We compared the parameters of the forward model obtained using BrAC from alcohol challenges with that obtained using estimated BrAC from our pharmacokinetic model and drinking diary. We assessed the efficacy of our calibration approach by comparing the performances of forward models with two groups of parameters generated by original calibration approach and our approach. Finally, we calibrated the transdennal alcohol transport model using the pharmacokinetic model with both population parameters and per-patient parameters and computed peak BrAC, time of peak BrAC and area under the BrAC curve in two cases. I. Introduction When alcohol is consumed, it enters the bloodstream and most of it is broken down by chemical reactions in the liver, the rest of it leaves body in variety of sways such as respiration, urination and perspiration. Blood alcohol concentration (BAC) is most commonly used as a metric of alcohol intoxication. It is usually expressed as the mass of alcohol per volume of blood. For example, a BAC of 0.10 means that there are 0.10 g of alcohol for every decilitre of blood. Breath alcohol concentration (BrAC) is a measure of the amount of alcohol in breath, and can be measured with a breathalyzer. Since blood alcohol concentration (BAC) data is hard to collect and the output of breathalyzer is an estimation of BAC, we use the estimated BAC from breathalyzer instead of getting it directly from the blood. Transdermal alcohol concentration (TAC) is a measure of the amount of alcohol at the surface of skin. Approximately 1% of the alcohol consumed by humans is excreted through skin in the form of perspiration [2]. Several kinds oftransdermal alcohol sensors (I AS) have been invented to measure TAC, including the WrisTAS1M (Giner, Inc., Newton, MA) and SCRAM 0 (Alcohol Monitoring Systems, Inc., Denver, CO) [2] [3]. Since it is difficult to convert TAC data into more meaningful BAC or BrAC data, these sensors are used mostly as abstinence monitors. However, these sensors could allow for the monitoring of BAC or BrAC over weeks interpreted appropriately. When these devices measure TAC, an oxidation reduction reaction happens producing an electrical current, the strength at which provides a measure of the number of ethanol moledules. Although the devices are bench calibrated when produced, studies have shown that TAC data collected by TAS are highly dependent on subjects and sensors. In earlier work [1] [ 4], Rosen created mathematical models and software, that converts TAC data into BrAC (or BAC depending on which is used in the calibration). That approach was to build a forward 1 mathematical model that converts BrAC or BAC into TAC after calibrating the parameters using data collected from a particular subject and sensor in a clinic or laboratory. The model can be inverted by deconvolution to obtain estimated BAC or BrAC from TAC data collected by TAS. All the process can be viewed as a blind deconvolution. In other words, there are two steps to obtain the estimate of BAC or BrAC from TAC First, BAC or BrAC data are collected from a clinic or laboratory and used to determine two or three parameters of a parabolic diffusion equation and its inversion. Second, input TAC data from field drinking episodes to the inversion of model and then estimates of BrAC are obtained. Three statistics are produced that are of interest to alcohol researchers and clinicians. They are peak BrAC, time of peak BrAC and area under the BrAC curve. Collecting the challenge data needed for Step one is burden for both patients and researchers; a patient equipped up an TAS sensor is given a measured dose of alcohol then needs to blow into a breathalyzer over a period of several hours. In this paper our goal is to lessen the burden by simplifying this process. We have developed a pharmacokinetic model for the absorption and elimination of ethanol, permitting us to estimate BrAC or BAC data from a drinking diary. The estimated BrAC or BAC data combined with TAC data can then be used to calibrate the forward model. In the simplified process, all a patient needs to do to collect the challenge data is wear theTAS sensor and create a drinking diary for the first episode. The drinking diary is record of the number of standard drinks consumed during the episode and the time at which the last drink is finished. A standard drink is an alcoholic beverage containing 0.56 fl. oz. or 14 grams of pure ethanol, as defined by the Natimal Institute of Alcohol Abuse and Alcoholism (NIAAA). An outline of the paper is as follows. In Section II, we describe the transdermal alcohol transport 2 model (also called the forward model), the blind deconvolution problem, the method calibrating of the model identifying the convolution filter, and the calibrated deconvolution model used to estimate BrAC or BAC from TAC data. In Section III, we describe our nonlinear pharmacokinetic based model whose input is the number of standard drinks and output is BAC or BrAC In Section IV, we show numerical results that fit the nonlinear pharmacokinetic model to data. We also compare the calibration of the forward model using on the one hand our linear pharrnacokinetic model with per-patient parameters and the alcohol challenge data m the other hand. In Section V, we compare both the kernel function and the peak BrAC, time of peak BrAC and the BrAC curve from forward model using our linear pharmacokinetic model with population parameters and the alcohol challenge data. 3 II. Transdermal alcohol transport model and the deconvolution The Transdermal alcohol transport model is based on the assumptim that ethanol molecules diffuse through the interstitial fluid of the epidermal layers of the skin. This assumption leads to a system of equations with unknown parameters that describes the rate at which ethanol molecules diffuse through the layers of the skin, enters and leaves the skin. Let <p(t,x) be the concentration of ethanol molecules in the interstitial fluid at timet and at depth x, u(t) the input BrAC or BAC, y(t) the TAC measured by the TAS sensor, q 1 andq 2 two unknown parameters dependent on the subject and TAS sensor. The model in one dimensim is given below (see [ 4] for more details) a~ a 2 ~ a,(t,x) = q 1 ax' (t,x) 0 <X< 1,t > 0 (2.1) q 1 a~ (t, 0)- <p(t, 0) = 0 ax t > 0 (2.2) q 1 a~ (t, 1) + <p(t, 1) = q 2 u(t) ax t > 0 (2.3) <p(O,x) = 0 0 <x < 1 (2.4) y(t) = <p(t,O) t > 0 (2.5) To obtain the output y(t) which is convolved by Jl(t) with a convolution kernel or filter k(·) = k( q, · ), where q = (q,q,)' such thaty(t) = s; k(q; t- r)u(r)dr, we rewrite the model in variational form and then apply the theory of linear semigroup of operators. We define the inner product in H 1 (0,1) as (t/J 1 , t/J 2 ) = fa' t/J 1 (x )t/J 2 (x )dx (when t/J 1 (x ), t/J 2 (x) E H 1 ( 0,1)), then the equation (2.1) becomes ( ~: (t,x), t/J(x)) = q 1 (~:'; (t,x), t/J(x)) (2.6) Integrate this equation by parts and plug in the boundary conditions, then (2.6) simplifies to 4 ( :: (t, x), lj!(x)) + a( q, <p, ljJ) = q 2 u( t )lj!(1), (2.7) Where a(q 1 ,<p, lj!) = q 1 f 0 1 <p'(t,x)lj!'(x)dx + <p(t, O)lj!(O) + <p(t, 1)ljJ(1), c(ljJ) = lj!(O) according to the initial condition (2.4), and for allljJ(x)EH 1 (0,1), the equation (2.6) is true. Then the problem (2.1)-(2.5) can be written in weak form as follows (rp,lj!)+a(q; <p,lj!) = b(q; lj!)u, lj!(x)EH 1 (0,1) 'Pit=O = 0 E H 1 , y = c(<p) (2.8) (2.9) where ( · , · ) is the extension of the inner product in H to the duality space between H 1 and H 1 ', function a(q; ·, ·) : H 1 x H 1 --> R, b(q; ·) : H 1 --> R and c( ·) : H 1 --> R. For q E Q, defines a linear bounded operator A(q) E L(H 1 ,H 1 ')by (A(q)ljJ 1 , lj! 2 ) = -a(q; lj!, lj! 2 ), the linear operators B(q): R --> H 1 ' by (B(q)v, lj!) = b(q; ljJ )v = q 2 ljJ(1)v,and C: V --> R by Clj! = lj!(O). The system of equations (2.1)-(2.5) in strmg form can be written as rp(t) = A(q)<p(t) + B(q)u(t), t > 0, <p(O) = 0 ,y(t) = C<p(t), t > 0. (2.10) (2.11) It has been shown in [ 4] that { eA(q)t: t ~ 0} is an analytic semigroup on H 1 ' , then we can obtain that y(t) = C J; eA(q)(t-s) B(q)u(s )ds, which means k(q; t) = C eA(q)t B(q), t > 0 for q = (q, q 2 ) Since all we have in challenge alcohol data are values of y and u at discrete time, we sampling timeT > 0 which is given and set 'Pi = <p(ir, ·) ,y, = y(ir) and u, = u(ir), i = 0,1,2, ... Then we can write down the iterated equations according to (2.1 0)-(2.11 ), 'Pi+ 1 = A(q)<p, + fi(q)u, Yi = C<pi, i = 0,1,2, ... , <flo = 0 E H 1 (2.12) (2.13) In this case, A(q) = eA(q)T E L(H, H 1 ), B(q) = J; eA(q)s B(q)ds E L(R, H 1 ). Consequently, we have 5 B(q) = (A(q) -l)A(q)- 1 B(q) (2.14) A(q)- 1 B(q) = b(q) (2.15) (2.16) It follows that (2.17) And let k;(q) = CA(q)'- 1 (A(q)- I)b(q), i = 1,2, ... , (2.18) then we have (2.19) Since the first step is to calibrate the forward model, which means estimating the parameters q 1 and q 2 mnnerically, the approximation should be approached in finite dimensions. For N = 1,2,3 ... , let {<PJ}7= 0 be the finite basis of space H 1 (0,1), HN = span{<PJ}7=o c H 1 and PN:H--> HN denote the orthogonal projection from H onto HN based on inner product Also we can easily define AN(q) E L(HN,HN) to be the linear operator in finite dimension andAN(q) = (Pt A(q)- 1 )- 1 , where Pt is the orthogonal projection of H 1 onto HN with respect (·;)a= a(q; ·, ·). Then we set (2.20) where iJn(q) is the vector which represents b(q) E HN The estimating discrete time convolution kernel is (2.21) Assume fij is the BrAC or BAC data used to calibrate and Yj is the TAC data, then the problem is to look 6 for the parameters qN• = (qf', qf(') which minimize (2.22) The optimization problem has been solved in paper [1] [ 4], they used an iterative constrained gradient to solve it After solving this problem, we obtain the estimates of the two parameters q 1 and q 2 , which means the model has been calibrated. However, the estimated parameters are highly dependent on the subject and m which episode is chosen. Then the TAC data of all episodes collected by TAS can be deconvolved with the estimated parameters to the BrAC or BAC data. Also in order to make sure the estimate for BrAC or BAC is both physically and mathematically reasonable, all the TAC and BrAC or BAC data should be positive. Besides the two parameters q 1 and q 2 , Rosen gives the other two nonnegative regularization parameters r 1 and r 2 which are used in case of over-fit, so that the fit is more natural. 7 III. A Nonlinear Pharmacokinetic Model for Alcohol Absorption, Metabolism and Elimination When alcohol drink is consumed, ethanol enters the blood stream through the stomach and intestines. The human body is composed of 70% water in which ethanol is highly miscible, so ethanol diffuses throughout the body through the bloodstream. The majority of the ethanol is metabolized in the liver with the help of a family of enzymes called alcohol dehydrogenase (ADH). A small amount of the ethanol is exported out of body through perspiration and urination. At lower ethanol concentrations, this metabolized reaction involves first-order kinetics. However, it becomes zero-order kinetics at higher concentrations and it shows thatADH cannot catalyze the reaction effectively. Many models [5] have been created to describe the zero-order kinetics. There are already in use to determine when drivers of motor vehicles are over the legal intoxication limit. These models are only used for high BAC or BrAC levels. The parameters in these models are determined using stratified population data (by gender, weight, and total body water). In this section, we create a model to describe all levels of BAC concentration for calibrating our forward model. In order to show both zero-order and first-order kinetics, our model combines a linear term with a 11ichaelis-Menten term. Based on the assumption that there is no ethanol in the blood at the beginning, our model becomes . ( ) ( ) Ku(t) u t = av t - --(-)' t > 0 M+u t (3.1) with initial condition u(O) = 0, where u(t) is the blood alcohol concentration (BAC) or Breathe alcohol concentration (BrA C), v(t) is the rate at which the subject is ingesting alcohol at timet, the parameter a is the normalized rate at which the human body absorbs ethanol into the bloodstream, the parameter K is the maximum rate of elimination achieved when the blood alcohol concentration is at a high level and the parameter M is the substrate concentration when the elimination rate is K/2. Using Euler's method to 8 estimate the derivative by an explicit forward difference approximation, we get (3.2) We estimate the parameter K, M, and a using the drinking dairy and BrAC or BAC data of multiple subjects. The data take the form of { v,,j, il,,J j = 0,1,2, ... , N,, i = 1,2, ... , L, where N, is the number of standard drinks ingested, and L is the number of subjects. We determine the three parameters K, M, and a by solving the least squares optimization problem below, In equation (3.3), u,,j(K, M, a) denotes the BrAC data or BAC data generated by our model for subject i at time j with parameters K, Manda. We solve this optimization problem by gradient projection method with constraining gradient to keep all parameters positive; otherwise they are not physically reasonable. First, notice that VJ(K,M,a) = Ir=, V];(K,M,a) (3.4) where ]JK,M,a) = F(u(K,M,a)) (3.5) ~ ~ [ ]T Rewriting equation (3.2) in matrix form as G(K, M, a, u) = 0' where i1 = u, 0• u," ... u, N 'we have ' ' ' [ VJJK,M,a) = vF(i1(K,M,a))(ai1;a(K,M,a)) (3.6) (ac;ail) * ail;a(K,M,a) = -acja(K,M,a) (3.7) Assume that:Z is the solution to the linear equation ( ~ ~)T ~ ~ c~ )T ac;au z =\IF u(K,M,a) (3.8) Then we have 9 V];(K,M,a) = -zT acja(K,M,a) (3.9) The vector Z satisfies a backward linear recurrence, namely (3.10) fork= N,,N,- 1, ... ,1,0 andzN, = 2( uN,- ilN,). The gradientV],(K, M, a) can be computed exactly by computing uandz first based on (3.2) and (3.10), then plug in them into (3.9) to get (3.11) 10 IV. Numerical Results ofPharmacokinetic Model with Optimal parameters Luczak, associate professor of Psychology in University of Southern California, reported a project in which 32 Asian American subjects participated, they wore a TAS sensor for more than two weeks and the sensor recorded the TAC data point every 5 minutes. In their ftrst drinking episode wearing the device, subjects were given a measured dose of alcohol and then blew into a breath analyzer at specified time intervals, so we obtained their drinking diary, BrAC data and TAC data for the ftrst episode. This is used for calibrating our transdermal alcohol transport model. After they left laboratory, they were asked to record Br AC data for at least one episode in the field, for the purpose of testing the forward model. Figure 1 shows the complete BrAC and TAC data of subject 1. Field Data for Patient: 1001 I + 4 o f± + .t: + * .j\: + :)t: + + 500 1000 Data Point Figure 1: complete BrAC and TAC data of + TAC Data BrAC Data t + * + + * + + + -lj: + + + 15 -§ 0 ro 0.06 ~ We used the drinking diary and BrAC data collected in the ftrst episode to fit our nonlinear pharmacokinetic model. The values of the parameters are shown in Table 1 along with their means and 11 standard deviations. parameters K M Alpha 1 3.5829 8.5688 2 0143 2 3.3178 8.7132 2.1499 3 3.5524 6.8269 3.1420 4 3.3003 8.2195 2.2687 5 3.9509 8.2674 2.2192 6 0.9918 1.6227 2.2419 7 3.2279 7.1546 1.6757 8 3.4180 7.3989 2.7200 9 2.1250 4 0917 3.2375 10 3.7599 8.2531 1.5492 11 0.0156 0.0001 2.3660 12 2.5181 4.3686 2.6325 13 2.4000 3.9248 2.5878 14 3.1927 6.9198 1.6445 15 2.1171 5.3596 3.1079 16 2.8873 5.9554 2.7311 17 20345 3.9630 2.5207 18 2.8850 6.5806 0.9393 19 3.3592 8.8232 1.9720 20 3.3515 6.5704 1.9933 21 3 0266 5.4526 2.8500 22 2.9889 7 0888 1.9755 23 0.0195 0.0029 2.2943 24 2.8400 60674 2.2916 25 2.9789 5.3638 3.2564 26 3.3721 6.5408 1.9258 27 3.1678 5.8769 2.3261 28 3.2802 6.9206 1.4956 29 3.5842 9.7405 2.1727 30 3.2160 70660 1.3965 31 1.4864 4.4484 3 0319 32 0.0113 00000 1.9128 fl 2.6862 5.8172 2.2701 (J 1.0849 2.5676 0.5680 Table 1: optimal parameters for 32 episodes 12 To check how well these models fit, we used our nonlinear pharmacokinetic model with those optimal parameters showed in Table 1 to simulate each BrAC data of the episodes. Then we get 32 figures which shows how the model fit challenge BrAC data of the 32 subjects with drinking diary. (Here we only shows the first four figures (Figure 2-5), others are in the Appendix I ) ooo~--~--~~---~--;=~ s"""' ==;=;<''""• "' ""'c ?1 BrAC Data ~r--7-~~-~~ - .~ -~~~ -7 ,~ -~ .~~~ Time(lr.o) Figure 2 !'i:irnoMrl!f'!Rr~ BrACD I'Itll. ~r-~-7-~-~~ .~~HH~~~~~ Time(t'n) Figure 4 \ 0.05 \ '10 . > \', '~ "" v~ ·~ 0.02 om I v --- SinliAatedBrAC BrAC Data ·------:- --~ ~~-7-7-~-~~ .~~~~~~~~ 0.0 2 O.Ql ' o Time (ln) Figure 3 I Sil'l"'Ua te.:J BrAC ~c~ ---:-----:c--" ·~t"-&fH'oJ~'t-- ; ....... ~_,.,~.ii! ,, . Time(IY~i Figure 5 After usmg our nonlinear pharmacokinetic model, we obtained the estimated BrAC data from 13 drinking diary and then we used both estimated BrAC and challenge BrAC data to calibrate our transdermal alcohol transport model. Table 2 shows the values of parameters in the forward model (2.1 )-(2. 5), r 1 and r 2 are two nonnegative regularization parameters which are used in case of over-fit. The optimal parameters in the first four columns of Table 2 were calibrated by challenge BrAC data, and the parameters calibrated by estimated BrAC from our model are in the second four columns of Table 2. (Note that only 24 subjects recorded their BrAC data by breath analyzer of at least one episode except the first one, so there are 24 essential data that can be used in our forward model.). q, q, r, r, q, q, r, r, 1 0.459271 1.103439 010 011 0.483496 l.lll503 010 011 2 2.561709 1.88501 010 011 1.448102 2 025268 010 011 4 0.197979 0.390341 0.15 071 0.213004 0.387216 0.27 1.39 5 0.766391 0.896977 011 010 0.786506 0.903854 011 010 6 1506515 2.616839 011 0.20 1215502 2.746907 0.14 0.23 7 0.255184 1.452187 0.64 4 01 0.238655 1.618922 0.32 3.28 8 706170.2 1. 726884 010 011 706170.2 1. 726884 010 011 9 0.564904 1.301934 011 010 0.512024 1.345851 011 010 10 1335660 1.553146 0.15 0.48 3.345625 1. 72625 010 011 11 365546.3 2.149143 0.26 1.99 712730.8 2.300272 0.47 4.61 12 7 064411 1.848172 010 010 4.763438 1.888537 010 010 13 0.484036 0. 708431 0.15 071 0.460216 0.742418 0.27 1.39 14 0.322196 2 093454 0.27 1.39 0.327035 2.196162 0.32 3.28 15 1.58482 2 093244 0.15 071 1.230278 2.23782 010 011 17 0.232788 1.407264 010 011 0.226569 1.485391 010 011 18 1.017016 1.35461 0.21 0.90 0.680578 1.55777 010 011 19 0.121222 4.198857 010 011 0.136576 4.112522 010 011 21 0.933204 1.061556 010 011 0.878307 1.098905 010 011 23 0.392992 0.706089 010 011 0.394828 0.705152 010 011 24 0.901711 0. 808835 010 010 0.721883 0.877389 010 010 26 0.416809 0.967738 011 0.20 0.399057 1.04457 0.27 1.39 27 0.369395 1.088844 0.02 0.25 0.377526 1.137521 011 0.25 29 1336411 2.425216 010 011 1336411 2.425216 010 011 32 1007920 0.673555 010 011 892138.3 0.676637 010 011 14 t In the transdermal alcohol transport model, we have y(t) = f 0 k(q; t- r)u(r)dr, so we can compare the differences of two kernel function k (q; t) coming from two groups of parameters. Figure 6-9 shows the two kernel functions of subject 1, 2, 4 and 5 obtaining from challenge BrAC and estimated Br AC in one coordinate system. (The other 20 figures are shown in Appendix II ) . ~ 0_3 . 1 025 ~ 0.2 ~ 0.15 1 0.1 0.05 .. Kernel fu'dion celbrated by chelenge BrAC ~ Kemelfu'1ctlon e1lt>rflted byes:imlted BrAC 10 Figure 6: Kernel function for subject 1 0 12,-------~----------~----~--~----- 1 ! Kemel1\nctlon celibnlted by ehelenge BfAC - Kemet h.nction Cl!l~brated by e'SIImated BrAC 01 0.08 0.08 0.04 0.02 ' Timet Figure 8: Kernel function for subject 4 15~-----------,~~~==~~~~~ I --Kernel fiSICllon calibrated by c:Nfenoe BtAC II . (}- Kernel flft:lion calibnled by Mlimaled BrAC . 0 7 0.6 10 " Figure 7 Kernel function for subject 2 K«<''f:lfli'IC IIOI'I C:I!IIDbret.ed by ch&llertQe Bt AC - Kemell~tron cr~librMed by esltm eoted BrAC Timet Figure 9: Kernel function for subject 5 From Figure 5 to Figure 9, we can see that the two groups of kernel function are pretty close, which means it is possible that we can use our nonlinear pharmacokinetic model with drinking diary instead of challenge BrAC. Then we use the BrAC and TAC data from one other filed episode (not the first one) to 15 test the two calibration approches. Similarly we only show the results of first four subjects below, others are presented in Appendix III. Figure 10-13 exhibit the test results with two groups of parameters, the picture on the left presents the results using parameters calibrated by challenge Br AC data and the picture on the right shows the test results of forward model with parameters calibrated by estimated Br AC by the same TAC and BrAC data. (Note that the only differences between two pictures are the black lines which stands for the estimated field BrAC) 0 035 003 02 Estimated BrAC With F~k:j BrAC Dat!l: PID 1001 RK 1 Dal'~ 03-Ma)'-2014 332 - 334 Tifl'lC (I\ou'$J + Field BrA C Data •~··• Es\imated Field BrAC + Scaled Fiek:l T AC Data E~imaled BrAC 11.~th l'iekl BrAC Data: PID 1001 Rec 1 Date 03-May-20 14 '' 0 .1S- o .te• 'ij" i ] 0.14: . : # • ~0 12 i 1 0_1 : ~ 0 .00 i ~ \ 0 .00 : 0 .0< -~ f : "' 0.02 \ + I '" 326 '"' 330 332 334 Tl'lle(hO U'S) - FieldBrACDela ••••• Estlmated Fleld BrA.C Scale<ll'ieldTAC D<I.ta 331 f 338 "' Figure 10: Test results offorwardmodel for subject 1 with two groups ofparameters E~im01led BrAC'III'ittl Field BrA.c Data: PID 1002 R:ec1 Dale O :l-May.-2014 t Field BrAC Da h ~ • •••• E5limliled Field BrAC + Scaled Field TACD&tb. 0.0~ - ,1 Time thouB) Figure 11: Test results of forward model for subject 2 with two groups of parameters 16 1:0-;!.imal!'!d BrACwitl Field BrAC Oala: PI() 1004 Rec 1 Date Q3..May-2014 t FieldBrACDala ~ ••••• El.1imilled Field BrAC + Sc81ed Fl~ TAC D&~ 0.01 _._ o.ooe ~ l\ ~ ......... f \ ~ 0006 \ f \ .... 1,~ \ .:/ v \ I\ 0 002 " \ I I t ... . .. . . . . . , ....... \t il I I f \ +l+fHff+ ~~ - ~ + : + +HHI\ftH 0 I~ M I I I :'-~ I I II 1 I I I \~.,-,.~tf"lM""""Hl:N II U I I I 1 \ . ._,. • ~ w u ~ • 00 Time (~} O.ot E~olimllled SrA. C with Field BrAC D<lbl: PID 100-4-Rec 1 Dille OJ·Mily-2014 Time~hcoln- t + FieldBrACData •••••EstimaledField BrAC + Scaltd Fi-eld TAC ~IB ,, .... : \ I •.,. .. ·. ! \ i + ..... " ..,:' . ' Figure 12: Test results of forward model for subject 4 with two groups of parameters B1:irns1edBrACwitl'l Field BrAC Dr.t11.: PID 1005 Ree 1 Dste D Hrte.y-201 4 Estimated BrAG willl Meld Sr.A.C ~a: PID 1005 Rec 1 Dale 03-~ay-2(114 •••••E~olimilledfield BrAC - Sc 11.led Field T.A.C Dola 0.03:.- - Fle-ld BrACDali'll ••••• E~imiJied Field BrAC - Scaled Field T AC ~e 0.03 o. o:. I 0.025 t ~ 0.02 ~ ~ 0.015 ~ i 0.02"5 t ~ 0 .02 ] i 0.015 - • 0.01 001 - 0.005 0 .005 - ! 320 325 330 335 A--- ~10 315 "" Timll (l"loln) Figure 13: Test results of forward model for subject 5 with two groups of parameters Table 2 shows us that the parameters of transdermal alcohol transport model using challenge BrAC and estimated BrAC data are relatively close. Figure 6-9 exhibits that the kernel functions coming from these two groups of parameters are very similar to each other. In Figure 10-13, we see that the estimated BrAC from the forward model ts similar using both calibration approaches. Hence, the challenge BrAC data can be replaced by estimated BrAC data generated by our nonlinear pharmacokinetic model with accurate drinking diary, without influencing much of the performance of transdermal alcohol transport model. 17 V. Numerical Results ofPharmacokinetic Model with Population parameter In the previous sections we have showed that our nonlinear pharrnacokinetic model with suitable parameters can be used to replace the challenge alcohol data. However, we used the per-patient optimal parameters for each subject in that section. To obtain three parameters we still have to collect the challenge BrAC data. In this section we used the challenge BrAC data and drinking diary of 18 of 24 subjects to estimate parameters values that can be used as the whole population. We then uses challenge BrAC and drinking diary of the other 6 subjects to test how well the population parameters works. The 18 subjects were picked randomly from the 24 subjects, they are subject I, 5, 6, 7, 8, 9, 10, II, 12, 13, 17, 18, 21, 23, 26, 27, 29, 32, and the 6 subjects left are 2, 4, 14, 15, 19, and 24. To obtain the parameters we fit all the 18 episodes together. The population parameters we obtained are shown below, K M Alpha Population parameters 3.30378 6.648514 2.20789 The figure below show the three kernel functions for each of the remaining subjects using the three different calibration approach (challenge BrAC data, estimated BrAC from the pharmacokinetic model with optimal parameter, and estimated BrAC from the pharmacokinetic model with population parameter). 18 Timt t Figure 14: Kemel function for subject 2 Tinw t Figure 16: Kemel function for subject 14 09 ·0.10;----!---,_--:---~.---:-----;:----:------:! Ttmel Figure 18: Kemel function for subject 19 0 . 12 0.1 f\' I cai bratedbychalel"l',leBrAC ---.::o- caibratedbyestimated BrAC'fl1thoptimalparl!lmeters - cei bretedby estlmatedBrAC'fl1thpopi.A!Itionparemeten r~ f \\ · ~ ' Ttrrt~: l Figure 15: Kemel function for subject 4 25 ---calb'Med""melenoeBrAC -v-etltlnlt'dby •sittnetedBrAC~optti'T'd lp.ar•rnefer$ t calbrated by est~ed BrAC ....ttl~J'(JJJ'.Jatloo p&< lmelers ' Tl~l 10 12 16 Figure 17: Kemel function for subject 15 0 5 7\ 0.1~ 0 1 0.~ · calbratedbycJ\aler9eBrAC (• catbrated cy H(imal:ed BrAC """h opltf'NI paramt\IR t calbrated by esttnated BrAC with p¢pt.Mtion p.arilme(ers \ · '- 2 ~----~ .~--~ 10~--~ 1~ ,----~-- ,. Tune t Figure 19: Kemel function for subject 24 19 For all calibration methods, we then used the transdermal alcohol transport software to compute peak BrAC, time of peak BrAC and area under the BrAC curve. Table 3 shows the statistics obtained for each of 6 test subjects along with the same statistics from the raw BrAC data. All the statistics are from other field episode (not the first one) which used as a test. (Note that Statistics I are from raw BrAC data, Statistics II are computed by software calibrated by challenge BrAC data, and Statistics III are computed by software calibrated by our pharmacokinetic model with population parameters. P stands for peak BrAC, T stands for time of peak BrAC, and A stands for area under the BrAC curve.) Statistics I Statistics II Statistics III p T A p T A p T A Subject 2 0.016289 274.5833 0.010814 0.030859 274.0833 0.016005 0.034599 274.0833 0.010803 Subject 4 0.0098707 33.3333 0.010798 0.0074923 39 0.020739 0.0059692 39.1667 0.017426 Subject 14 0.018494 158.75 0.023566 0.011659 160.3333 0.0090496 0.010641 160.3333 0.011472 Subject 15 0.036029 253.3333 0.10262 0.027198 253.3333 0.087523 0.016988 253.3333 0.051249 Subject 19 0.016106 85.3333 0.013694 0.098856 81 0 0.094996 81 0 Subject 24 0.062411 129.0833 0.051587 0.055214 120 0.080681 0.054814 120 0.072046 Table 3: Statistics computed by software in different calibration approach In Table 3, we see that P, T, A of Statistics III and Statistics II are not so close to that of Statistics I because of the difficulty of deconvolution from TAC to BrAC or BAC, and the differences between Statistics II and Statistics III are very small as we expected. In order to see how close they are, we computed the errors of Statistics II and Statistics III with respect to Statistics I in Table 4. 20 Statistics II Statistics III Error ofP Error ofT Error of A Error ofP Error ofT Error of A Subject 2 0.015 0.500 0.005 0.018 0.500 0.000 Subject 4 0.002 5.667 0.010 0.004 5.833 0.007 Subject 14 0.007 1.583 0.015 0.008 1.583 0.012 Subject 15 0.009 0.000 0.015 0.019 0.000 0.051 Subject 19 0.083 4.333 0.014 0.079 4.333 0.014 Subject 24 0.007 9.083 0.029 0.008 9.083 0.020 Table 4: Error of Statistics II and III with respect to Statistics I In Table 4, the error of Statistics II and III with respect to Statistics I are very close, some statistics of Statistics III are even better than that of Statistics II. Hence, we can conclude that it is possible to use our pharmacokinetic model with population parameter in calibrating transdermal alcohol transport model instead of the BrAC challenge data. This will lessen the burden on researchers and patients. After using the pharmacokinetic model calibrated population parameters, patients are only required to record their drinking diary for the first episode when wearing theTAS device. The software will then deconvolve the TAC data to BrAC or BAC data. 21 Reference [I] Rosen,!. G., Luczak, S.E. and Weiss, J, (2014). Blind deconvolution for distributed parameter systems with unbounded input and output and determining blood alcohol concentratim from transdermal biosensor data, AppL Math and Camp, 231 pp. 357-376. [2] Swift, R M (2003). Direct measurement of alcohol and its metabolites. Addiction, 98S, pp. 73-80. [3]Swift, R M. and Swette, L. L. (1992). Assessment of ethanol consumption with a wearable, electrmic ethanol sensor/recorder. In R Litten, and J Allen (Eds.), Measuring alcohol consumption: Psychosocial and biological methods. Totowa, NJ: Hum ana Press. [ 4] Durnell, M, Rosen, I. G., Sabat, J, Shaman, A, Tempelman, L. A, Wang, C, and Swift, R M, (2008) Deconvolving an estimate of breath measured blood alcohol concentration from biosensor collected transdermal ethanol data, AppL Math and Camp., 196, pp. 724-743. [5]Hustad, J T. P. and Carey, K. B., (2005) Using calculations to estimate blood alcohol concentratims for naturally occurring drinking episodes: A validity study, J StudAlcohol66, No. I, pp. 130- 138. 22 Appendix I Using nonlinear pharmacokinetic model to estimate challenge BrAC data with optimal parameter for each subject (from subject 5-32). ::~:aBrAC I 0 06 ~ I Smultlled Bt-ACI ":- BrACOata 0.06 1 \ IV < 0.01; J \ \ ' v \v \ 0.0<4 \ 0 0< \ \ 0.03 \ 003 \ \ c c \:c "Z 0.02 v 0.02 1 '._ c ' ,, I v '~ ' 0.01 ~ ' .___ .; '-.. · - . ...__ , ' ·- - -- -- o, 0 ., .. 7 • 9 10 · ·- 10 Tlme (m) Time (hrs) - Sin'Uated BrAC 0.06 I Sim.Died BrAC 004 c BrACOata /\ BrACData 1\ 0.1) )5 1\ 0.05 \ f '\ O.Ol \ c / \ \ 0.04 0.03 I I \ 0.02 \ ' . ; ' ) \ ' o' n '· ' ~' 0.02 I '" -......,, ,. I " 001 I I -., ~~ 0.01 ~--........_,__ O.OCO --- 0 ·. ---------~- , 0 ' ' 6 1 0 0 ' 4 Time (hM} Tlme(IYs) :~~~~::a BrAC t 0.04 I Sin'IU!IIMBrAC v " BrA COata ' \ 1 \ 0.06- '\v I \ 0.00 V , \ % \ \ i 0025 t-._0.04 - \" \ 1··1 \ ,. 0.02 \ · \ 0 0.01 5 1 \ 0 .02 I ~ '-._;. 0.01 ""· -" "· 0 . 0 1 i '~-- 0.000 ~"-. - ---- · ··------ - - ---- - ;-;. "7= , 0 . " j . · fo 0 0 7 10 0 ' T~(tr.o;) Tlme(ksj 23 10 ~ o<>< 1 : I looo \ t,: I I \ 00 1 '• 005- 1 \ 1 \ r \ 0.04- \ \ .) - -' i I \ !,., I \ '"- ! I \ ~ I ~ '· "1 o. o.j I o· 0 \ \ ~--,-. ~ -~ 6 3 Tlrne (ln) " -Sin'UatedBrAC~ ,-, BrACOati - _"- .~~ -= -- :: -· :- -:-~==~ -~ -~ -~.~~.-- '" 4 ~\IY5l rktwttnJ ,_ .. \ 001 0.005 0 0 0.07 :\ ; \ \ \, ~ o, ' 0025 0 . 02 1\ t ... i \\ - ~ I 1 I ~ ~ ' " · ~tedarAc l 1 ----:;-- BrACDe.ta ;-------- ---------- " · - . 10 ... 5 ... ,..6~-rs _ g ,m,. (.tnl - SinUe.tedBrAC ,-, Br.A.C O:n ·---------- --~" 24 003 0.02 I 0.01 J I -~ .. ~ -----~-- ~~----~--~~--~ ~~--~ .--~~~~~~~~ Tlffitl' (t· n ) 007 0J)6 I ::; 0 . 05 ! \ I 0.03 I 0.02 O .Ot I \ \ \ \ '· ' \ \ 4 Time ftrsl -Sim..Mt~BrAC BrAC Oata I ~~--~--~--~·~~ ~ -~~7 ,~~~~~~ .~ -~~~~ , . Tln"'e' (h-s ) o.orl------~------~------~----==..,.... ;:;o=:=. ,": ..,o; ,=;A"'" C BrACOat-a ooz O.G1 10 005 - ~ I' 0.1)4 1 \ \ \ \< \ Sirr'KM.tedBrAC BrACOata ~~--~--7---~--~~~ ,~ -~~ .~ -~ -~:~~ ~ -~ -~.~~~-~-~ 10- i ltne(h-il) 0.06 - 0.01 -t I •o 0 . 05 0.045 I 0.03S 'iii 0.03 ;'_ ~ 0025 l " ~ 002 0.015 001 0 .005 \ \ ·>~ ' n me !ln) .. ....____ - ---- - - - · ---------- 10 9 - 10 - Sin'Ue.tedBrAC ' BrACOata 25 "' 0 0.00 0.07 r\ n v 1 \ t '' \ " \ 0.05 I' I v \ 0 '· ,. 0.04 I Sirn~Ji!ted&Ac l o BrACData ,r 00~ '' '-h> -~~~r ;-;--.. 7 . ...,.;o TlnMiitr5) SimulatedBrAC Ti!Tllll(ln) 0.045 ', :l _ l' O.ot 5 0.01 I 0.005 1 I Sirn.Mted BrAG v BrAC D ata I ~- . --~--~--~--~~~ ,~-1~~~ .~ -~.~~~~ 1 '0 Time (ln) Time (In) SinJJated BrAC 26 Appendix II Kernel functions of20 subjects obtaining from challenge BrAC and estimated BrAC dat. 1.6 ,, 1.2 \ ~ 0.6 \ \ 0.6 • o .• 0.2 1 ----'t'-- Kernel function calibrated by chalenge BrAC I ._. Kernel function (;alibraled by estimated BrAC • Time t 10 12 16 --+-Kernel function calibrated by challenge BrAC I v K¥l'IOI fl.n:C1¢1'1 calibrated by estrn:ated BrAC . Timet '·',----~-~--~r== ,=cK=..,.=:c=,""'s= ,,., ="cc '~=.c,..,07by=.,. c=? ,.=.,.=c.,O'C"'3 ---e---Kemelllrdion calibrated by e!i.l:imll.led BrAC 0.5 0.45 ~ o . •- r \i 0.35 \\ \\ 0.3- l * o . , I 02-J \\ ·~, ' 0.15- 0.1 - 0.05 oo 0.7 '' --+-- Kemelfin:tionclllibratedbychll~ BrAC ~ Kernel f\nction ealibrttled by esdme.ted BrAC 10 12 _,. Kernel fl.flefion ct librale-r:t by challenge BrAC ---:---K~lflnttion cdbr&l:~byestirrete<:3 BrAC • '""' --+-- Kerroel function ctllibftlted by cll8Jerl9e BrAC ---e--- Kerroel fll'lction caibfated by e~lmated BrAC 10 12 16 Time t 16 " 27 " " 09 0.7 - ' ' I ' l<emetf\.ln(llonc•lltntedby~BrAC I ._,_ Kf'mt41\.ncbon Clllmilecl by Htln'olted 8rAC I J K.mei~on..alltuttdtft~BrACI _..__ Kemlllll r...nctlon c•tn ted bV Hlmated BrAC _ " Tune! KtrMII'I.n:bonctlllitnlfllbycNierlge6rAG --- Kernt!f\.nctlonctlll:nltdbyesumeledBI'AC ~·0~--~----~--~----~ .----~--~~--~--- r.,., oosJ 0 0 0.2 I : K~~oncaltlratedby~BrACI - Kemelhndlon caltnted by esm.ted Bt/loC • ,..,., to " 14 - Klllf'llll tunc:lion edbreted tlf a.lenge BrAC ~Kernel fUndlon calbrMed by estimlll:ed BtAC • r""' 10 12 " " I ' Kemdk.rdlon~eclbyc:h~SrAC I ---;-- Kemet rudion caM:nl:rd by~ BrAC 07',---~---------r=~~ .~~ =.~~mi~==. =~ =.~=~ ==~~~AC K.nel fl.n:tion ~cd by e'Wimalt:d SrAC 00 Timrt 28 . 0.35 ,.- 0.3 01 - Kerf'lf1 fl.ll'ldlonce.bated f:l(~ BrAC :.> K emej l'liiCliOn t.lllnted by e"imated BfAC • ,,,.., ' ' ' I , l(emelf\rlctlonc•llbrltedbyc:t~MenQe BrACJ ---r- Kernel JLnc:tioo c•libnltlld bye5bmlted &p.c 12 16 " , ,,, -------;== , ==;:; K ..,. :::::::;:= , ... =: , "',.=:,,.;;:,.=: .. ,. =;:;:; .,=:: .......,::==:., ;:=::.~ c - Kemel ll.ndion cliln ted by e!M:irnllte<l BrAC , ' t ~ 1 5 \ ~ 5 ! t ~ " • ~ t ~ ,. 0.5 ~ 00 10 T1 me t 0.7 0.6 0.5 0.3 02 01 ~ 02 ~ Cl.1!i 01 0.05 00 I + Kemelf\n:tjoncalbrated bycllalerlg$BrAC ~ ~Kemelfln:tioncajbrliedbye~tedBr~ 0 . 45 .,.-.,-------------------::-:-: :-;1 ~ Kemd fl.ndion c:itlibrated by chllenge BrAC 035 t • I ' • ~ , . -:--- Kernel fl.lltdon eaftn ted by estimated BtAC ' r~• to I Kemel rt.-dion cUbnle d by chatenoe BrAC I - Kernel fl.nction c8iobnltt'd by estimated BrAC • '""' 10 16 " 29 Appendixiii: Test results of 20 subjects with two groups of parameters. Picture on the left is the results using parameters calibrated by challenge BrAC data and picture on the right shows the test result of forward model with parameters calibrated by estimated Br AC by same TAC and BrAC data. (Note the only difference is the black line which stands for the estimated field BrAC). 0 01 _ 0,008 ~ "' ~ 0.006 ~ 0.002 0.01G 0,01-4 'e0.012 1 l 001 ~ ! o.ooa . -t 0 .006 • 0.002 0.08 Loo- .. ~ ~ 0.05 - .. ~ 004 - . ~ ~ 0.03 - 0.02 - 0,01- 160 Estma!ed BrAC l'.~th Field BrAC Data· PIO 1006 Re<: 1 Date 03-May-20 1 4 Ti~M(h<:us) l F;Od&ACO•" I ••••• Estimated Field BrAC - Sc!!!le-d Ari::ITAC DMa ' . E~llmated BrAC wirtl Field BrAC D~ta: PIO 1007 Rer;: 1 Date 03-Mily-2014 I I FieldBrACDilli f ••••• Es.ti!TI3ted F1eld8rAC + Scaledfiekl TA: D&ta Estimated BrAC '!'nih Field BrAC Dtta: PIO 1008 Rec 1 Date O J·M&)'-2014 l ~ il n ll :: H I : :+ ! i " IS~ "' m Time Ulou·s) + Field6rACDat! ••••• Estimated Field BrAC + Scaled Field TAC Data : ll H H rr : ~ "' 1" 190 0.09 0 ~ 0.06 t ~ 0.05 - J ~ 0,04 - ~ if 0.03 0.02 - 0 100 E!>lirretedBrAC •ith Firt! BrAC Data: PIO 1006 Rec 1 ~e03-M!y-2014 Estimated BrAC \Wh Reid BrAC Data: P IO 1007 Rec 1 Date 03-M:~~y-2014 0.02 I Fiekl BrAC Data O .QIS ••••• Estmated Field BrAC I 5ealedF1el:I TACOata Estimate(! BrAC .,.,tth Field BrAC Data: PID 1008 Rec 1 Date 03-May-2014 I . . .. i ~ II :: :: - : ~ : ~~ 165 170 175 Time(hoW's) FieldBrACData ....... Estimated Field BfAC &:01led Field TAC 0011 01 ~ H i! ~ r : ! ' 180 185 190 30 0.09 0.00 ~ il O.OO • g 0.05 - 0.025- ~ 0.02 ~ 1!. ~ 0.015- Estun &ted BfAC wilt. Fteld BfAC Data : PIO 10i)!j Rec 1 Date O~May-2<114 I Field BrAC Oat~ r ••••• Estil'nel(edF~BrAC I Scaled F""ldd TAC Oat~ Time(tlolnl Estimated 6rAC with Field BrAC Data: PIO 1010 Rec 1 Otte 03-May-2014 ' " + + ~ ~ * • m • m • • m m T~me(hol.n) 0.016 O .ot6 0.014 '· ""' 0.002 E$limated Bt"AC 'With field BrAC Dill : Plt<l1011 Ret 1 t<late 0:7May·:.!l14 1 Field8rACD<lt' •••••EstimatejjFiddBf-"C 1 So:ai+dF"IekiTACOe.ta Estimnled BrAC • ·ith Field BrAC Data· PID 1012 Ree 1 Di!tle O~May-2014- I ... FieldBrACOeta • •••• E'5timatedReld BrA.C + sealeclFieki TACD81:a 176 178 100 182 184 186 16.$ 190 Time ("hotn\ 009 OM o.oz 50 Estimaled8rACwilh F~8rAC011t": PI01009Ree 1 DateOJ..May-2014 " 0.025 '""" ~ ~ 0.08 it ~ 0.06 1 0.02 0.018 0 .014 ii 1 0 .0 1 2 t ~ OQI . ~ 0 .008 ~ ~ 0 .006 0001 I - Field BrAC Otte ••-••EstimatedField BfAC 1 ScaledFteldTACData 70 75 Estimated BfAC'floitll Het! BrAC Data: PIO 1010 Rec 1 Date 03-May.2Q14 + . ' - + Time (hou"l l t FieldBrACData ••••• E~timated Fidd BrAC Scaled FiN:I TACO.Ii Estrnltted BrAC · ft'ith Field BrAC Dlt.ta: PID 1012 Rec 1 Oete 03-M&y-2014 t 7B · 1so Tfne tholss) 31 0.\ 0_ 02 0.018 0.016 i 0.014 to.o 12 u ~ ! 00\ ~ 0.003 • 0006 0.004 Estimated BrAG 'Mth Field BrAC Data PIO 1013 Rec 1 Date OJ-,..ay-2014 - Field BrAC Data ••••• Estimated~ BrAC - SceledFieldTACData 96 .. 102 104 106 100 110 112 Time iholnl Ei!obmnted BrAC·Mth F1eld BrAC Data: PID 1014 Rec 1 Date 03-Mit'f"2014 E~tirrWed BrAG 'Mltl F".eld BfAC Data PID 1015 Rec 1 Dille 0:3-MIIy·2014 o.o.s,--~-~-----~-~--==: ,:'=:R =: ,so.;;; ._. ;;cc; o 2,.:= , = c;- O(J.I 10.015 0.01 0.005 ----· ~~m..tt:t.l l'""*-' ~AC I SCaled Reid T AC Data + " + - + + .. I #_;•..,. --;" " · .. - : f \. . :.1 "\ -t~* ' .\ . + \ .. . ++ + + ~~~ !~\ 1-l' l \ ,- - -.. + : \ -; ~~ .. ---~~~--~'{;_!__ -- t I ~:-,~-:~- ~ m rn - m = m B m a ~ Time tho..nl 0 .\ Estimated BfAC Vlith Field BrAC Data: PID 1013 Rec 1 Date 03-May-2014 + FleldBrACOata I ···-·EstimatedField BrAC + Scaled F1 e-ld TACDala 96 96 100 102 104 106 108 110 112: 114 116 0.02 Q ,Qt!;l 0-016 ~o.01• t 0.012 ~ ! 0.0\ ~ 0.008 "- 0000 0.00~ I 0 002 .. \ 50 0.035 00\ 0.005 Time iho\ni Estimated BrAC I'Ath fie-ld BrAC Oatil: PID 1014 Rec 1 O~e 03--M~y-2014 "' 242 , .. I - Field BrACD!tl:a ••••• Ed imat•d FiNd ~AC Scaled f ield TAC Data 170 175 , ., 2(8 246 250 252 2M 256 256 260 Time (tw;..nl 32 0.1 O JJ6 001 0.02 Estimated BrAC 10J th Field Br.6..C Oala: PIO 1017 Rec 1 Dat e 03-May-2014 ' Esm.ted&AC'Mth Fie«:! BrAC Oat1: PIO 1016 Flee 1 o.te 03-Msy-2014 26 26 JO 32 " :l6 " _. F1 eldBrAC Det!a ••• •• Estimated Field BrAC + Seated Fiet H AC Dat1 40 42 44 . ~"""'""'"""""' ..!'!'tlltl!'r!"~~ll!,.,.~""'" .. "'=""----.r~ ro ~ M ~ M Tme (l1iol.n) Estimated BrAC 'Mth Field BrP.C Data: PIO 1017 Fl ee 1 Date 03-Ma)'-201 4 ' 0 1 Est! mated BrAC lMU\ Fiftt &"AC Data PIO 1016 RK 1 Date OJ.May-2014 ' ' ' .,, 0.1 + Flt-ld BI...COIII •••••EstttralldFilldBrAC + Sc1led F1tilld T AC Data 1 R eid BrAC Data I •••••E.stli'I"DtedF!ft:IBrAC ~ Se61edAeldTAC.Dttl fl + :: n i! : i i i i i 0~ • • , ····-·-·-·--~--J . .. L-- -····· - .. ~ ro n M ~ oo y.,_(l'loi.n) 33 003 Estimllled Bf...CV!ith Fielll BrAC o.t1 PIO 1021 Rec 1 o.te 03-Miy-2014 + Fiek:IBtACO&ta II ··••• EttimatedFieldBrAC + SeMel Fletll AC o.te ~ ~ " ~ 45 ~ 0.07 006 Time1holn) Estimated BfA.C .,.!ilh Fielll BrAC D1t1· PIO 1023 Rec 1 Dill 03·Mey-2014 Time iholn) · = + FltkiBtA.CDela ••••• E~maled Field BrAC + Seeltclf'let:llACo.tl 003 - " 1 0.1 # ~ Estmtttd BrA<: with Flri:JBt"-C Oaca PID1D21 Rtc 1 O.teQ3.May-2014 + FIKI BrAC Dlla · ·-· • E11irreledFietl BfAC 1 Socaa.dFi&ldTACOaiJ E~~oiii'Tlaled BrAC · ;.1th FiKI &AC O&la. PIO 1024 R.c 1 O&tt 03-Me.y-2014 I Fleld&AC O.te •••••EstimaltdF14'1dBr..t.C + Sc81edfiei!ITAC O.te 34 C.45 0.4 ~ 03 ~ • g·o.2 s .. ! 0_2 0.03 0.005 0.025 - i 0.02 - 0.01 E'5tirmt~d BrAC ..Uth Field BrAC CWa: PID 102$ Rec 1 De.te (}.'}May-2014 I ! FieklBrACDal:a •••••Estime.ledFi!!ldBrAC + Scaled Fil"'d TAC Data Estimat~ BrAC \I!ith Field BrAC Dsfa· PID 1027 Re<: i Date 03 May-2014 300 302 Tirne(ho.rs) F~dBrACDateo ••••• 8 tii"'"VVted Field BrAC - St3led Fie-ld T AC Oat!! Estimat~ BrAC IIIith Field BrAC Dsf!ll: PID 1029 Re<: 1 Date 03-May-2014 2 ilo '" 290 Tirne(ho.rs) - FJ.eldBrAC Dateo ••••• E.stimfated Field BrAC - Sealed Field T AC Daleo '" - + + + + ' " 003 Q 02 0.2 0.18- o _1e· • i 0 .14- {;,0.12 - ~ ~ 0.1 ~ 0_ 08 - • 0.00 0.025 I 0.02 ~ " ~ 0.015 ~ 0.01 E:..timated BrAC10~Ih Field Br AC Data: PID 1026 Rec I D;li.e 03-May.-2014 Time(hou"S} I Fteld BrACOatl ••••·E~irn;ll.edFieldBrAC I Scalto<J FieldTN: Diilil E~im:oled 8rAC \¥~h Field BrAC D:ol3: PID 10'27 Rec 1 Dale DJ-IA:oy-2014 I Fiek:l BrACDtJI.a ••••• E~inl:lted F~kl BrAC + Scaled F~d T 1'£ Data Estimated !'I~ with Field BrAC Dat:a: 1"10 1029 Rec 1 Date 03-May-2014 l ' ' ''" B<AC Da" } •••••EstimatedFieldBrAC + Scaled Flek: TAC Data ' ' " 35 oco,--""' -""' ~ .. - "' _""_ - _" -""~"-•c_ .,.... __ .,_o_ •<m_R« --;-'- """ - <»~ "'"' ..:...;_"'_ " __ -:1 I I FleldlrACo.tJ ••••• Eitl'nll'ld Field BrN: 001 l ScaMd Fitlld TAC Dlla ... ,,. 001 0 06 ~ITtlledBrACwltlFieldQrAC 01!1 P10 t002Rec 1 o.te03-J.t~2014 ' ' I 1' ..-:l S,AC )I(a •••• •E~«<FiKi f7AC I SWedFteld TAC Da.tJ 36

Abstract (if available)

Abstract In Rosen's earlier work [1] [4], blood (BAC) or breath (BrAC) alcohol concentration was estimated from biosensor measurements of transdermal alcohol concentration (TAC) by forward distributed parameter models, which need to be calibrated by alcohol challenge data. The alcohol challenge data was collected from a TAC biosensor and a breath analyzer after giving patient who was wearing with a TAC biosensor a measured dose of alcohol and blowing into a breath analyzer. This process is required for each patient before the device was used to estimate BrAC from field TAC. In this research, we used a pharmacokinetic metabolic absorption/elimination model and drinking diary to estimate the BrAC or BAC, and then we used the estimated BrAC or BAC and TAC data of first episode as the alcohol challenge data to calibrate forward distributed parameter model for transdermal transport of ethanol. The pharmacokinetic model can be determined by solving a nonlinear least squares problem using adjoint based gradient computation. We compared the parameters of the forward model obtained using BrAC from alcohol challenges with that obtained using estimated BrAC from our pharmacokinetic model and drinking diary. We assessed the efficacy of our calibration approach by comparing the performances of forward models with two groups of parameters generated by original calibration approach and our approach. Finally, we calibrated the transdermal alcohol transport model using the pharmacokinetic model with both population parameters and per‐patient parameters and computed peak BrAC, time of peak BrAC and area under the BrAC curve in two cases.

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A fully discrete approach for estimating local volatility in a generalized Black-Scholes setting

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Inverse modeling and uncertainty quantification of nonlinear flow in porous media models

Asset Metadata

Creator Dai, Zheng (author)

Core Title A nonlinear pharmacokinetic model used in calibrating a transdermal alcohol transport concentration biosensor data analysis software

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Applied Mathematics

Publication Date 08/06/2014

Defense Date 08/06/2014

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

Tag nonlinear pharmacokinetic model,OAI-PMH Harvest,transdermal alcohol transport

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Rosen, I. Gary (committee chair), Haskell, Cymra (committee member), Lototsky, Sergey V. (committee member)

Creator Email zhengdai@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-453438

Unique identifier UC11286939

Identifier etd-DaiZheng-2774.pdf (filename),usctheses-c3-453438 (legacy record id)

Legacy Identifier etd-DaiZheng-2774-1.pdf

Dmrecord 453438

Document Type Thesis

Format application/pdf (imt)

Rights Dai, Zheng

Type texts

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

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

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA