2016, 13(5): 911-934. doi: 10.3934/mbe.2016023

Using drinking data and pharmacokinetic modeling to calibrate transport model and blind deconvolution based data analysis software for transdermal alcohol biosensors

1. 

Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, United States, United States, United States

2. 

School of Public Health, Brown University, Providence, RI 02912, United States

3. 

Department of Psychology, University of Southern California, Los Angeles, CA 90089-1061, United States

Received  September 2015 Revised  April 2016 Published  July 2016

Alcohol researchers/clinicians have two ways to collect subject /patient field data, standard-drink self-report and the breath analyzer, neither of which is passive or accurate because active subject participation is required. Transdermal alcohol sensors have been developed to measure transdermal alcohol concentration (TAC), but they are used primarily as abstinence monitors because converting TAC into more meaningful blood/breath alcohol concentration (BAC/BrAC) is difficult. In this paper, BAC/BrAC is estimated from TAC by first calibrating forward distributed parameter-based convolution models for ethanol transport from the blood through the skin using patient-collected drinking data for a single drinking episode and a nonlinear pharmacokinetic metabolic absorption/elimination model to estimate BAC. TAC and estimated BAC are then used to fit the forward convolution filter. Nonlinear least squares with adjoint-based gradient computation are used to fit both models. Calibration results are compared with those obtained using BAC/BrAC from alcohol challenges and from standard, linear, metabolic absorption, and zero order kinetics-based elimination models, by considering peak BAC, time of peak, and area under the BAC curve. Our models (with population parameters) could be included in a smart phone app that makes it convenient for the subject/patient to enter drinking data for a single episode in the field.
Citation: Zheng Dai, I.G. Rosen, Chuming Wang, Nancy Barnett, Susan E. Luczak. Using drinking data and pharmacokinetic modeling to calibrate transport model and blind deconvolution based data analysis software for transdermal alcohol biosensors. Mathematical Biosciences & Engineering, 2016, 13 (5) : 911-934. doi: 10.3934/mbe.2016023
References:
[1]

R. A. Adams, Sobolev Spaces,, Academic Press, (1975).

[2]

J. C. Anderson and M. P. Hlastala, The kinetics of transdermal ethanol exchange,, Journal of Applied Physiology, 100 (2006), 649.

[3]

H. T. Banks and K. Ito, A unified framework for approximation in inverse problems for distributed parameter systems,, Control Theory and Advanced Technology, 4 (1988), 73.

[4]

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems,, Birkhauser, (1989). doi: 10.1007/978-1-4612-3700-6.

[5]

H. T. Banks and K. Ito, Approximation in LQR problems for infinite dimensional systems with unbounded input operators,, J. Mathematical Systems, 7 (1997), 1.

[6]

D. P. Bertsekas, Nonlinear Programming (2nd ed.),, Athena Scientific, (1999).

[7]

S. P. Bradley, A. C. Hax and T. L. Magnanti, Applied Mathematical Programming,, Addison-Wesley, (1977).

[8]

K. B. Carey and J. T. P. Hustad, Are retrospectively reconstructed blood alcohol concentrations accurate?, Preliminary results from a field study,, Journal of Studies on Alcohol, 63 (2002), 762.

[9]

C.-T. Chen, Linear System Theory and Design,, Holt Rinehart and Winston, (1970).

[10]

R. F. Curtain and D. Salamon, Finite dimensional compensators and infinite dimensional systems with unbounded input operators,, SIAM J. Control and Optimization, 24 (1986), 797. doi: 10.1137/0324050.

[11]

D. M. Dougherty, N. E. Charles, A. Acheson, S. John, R. M. Furr and N. Hill-Kapturczak, Comparing the detection of transdermal and breath alcohol concentrations during periods of alcohol consumption ranging from moderate drinking to binge drinking,, Exp Clin Psychopharm, 203 (2012), 73.

[12]

M. Dumett, I. G. Rosen, J. Sabat, A. Shaman, L. A. Tempelman, C. Wang and R. M. Swift, Deconvolving an estimate of breath measured blood alcohol concentration from biosensor collected transdermal ethanol data,, Applied Mathematics and Computation, 196 (2008), 724. doi: 10.1016/j.amc.2007.07.026.

[13]

L. Edelstein-Keshet, Mathematical Models in Biology,, Society for Industrial and Applied Mathematics, (2005). doi: 10.1137/1.9780898719147.

[14]

A. R. W. Forrest, The estimation of Widmark's factor,, Journal of the Forensic Science Society, 26 (1986), 249.

[15]

J. S. Gibson and I. G. Rosen, Approximation of discrete time LQG compensators for distributed systems with boundary input and unbounded measurement,, Automatica, 24 (1988), 517. doi: 10.1016/0005-1098(88)90096-9.

[16]

A. Heck, Modeling intake and clearance of alcohol in humans,, The Electronic Journal of Mathematics and Technology, 1 (2007), 232.

[17]

N. Hill-Kapturczak, S. L. Lake, J. D. Roache, S. E. Cates, Y. Liang and D. M. Dougherty, Do variable rates of alcohol drinking alter the ability to use transdermal alcohol monitors to estimate peak, breath alcohol and total number of drinks?,, ACER, 38 (2014), 2517. doi: 10.1111/acer.12528.

[18]

N. Hill-Kapturczak, J. D. Roache, Y. Liang, T. E. Karns, S. E. Cates and D. M. Dougherty, Accounting for sex-related differences in the estimation of breath alcohol concentrations using transdermal alcohol monitoring,, Psychopharmacology , 232 (2015), 115. doi: 10.1007/s00213-014-3644-9.

[19]

N. Hill-Kapturczak, J. D. Roache, C. J. Walters, T. E. Karns, S. E. Cates and D. M. Dougherty, Validation of using transdermal alcohol concentrations to estimate breath alcohol,, ACER., ().

[20]

E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups,, American Mathematical Society, (1957).

[21]

J. T. P. Hustad and K. B. Carey, Using calculations to estimate blood alcohol concentrations for naturally occurring drinking episodes: A validity study,, Journal of Studies on Alcohol, 66 (2005), 130.

[22]

T. Kato, Perturbation Theory for Linear Operators,, Second Edition, (1976).

[23]

D. A. Labianca, The chemical basis of the breathalyzer,a critical analysis,, Journal of Chemical Education, 67 (1990), 259.

[24]

A. J. Levi and I. G. Rosen, A novel formulation of the adjoint method in the optimal design of quantum electronic devices,, Siam Journal on Control and Optimization, 48 (2010), 3191. doi: 10.1137/070708330.

[25]

M. J. Lewis, The individual and the estimation of his blood alcohol concentration from intake, with particular reference to the "hip-flask" drink,, Journal of the Forensic Science Society, 26 (1986), 19.

[26]

L. Li and T. P. Speed, Parametric deconvolution of positive spike trains,, Annals of Statistics, 28 (2000), 1279. doi: 10.1214/aos/1015957394.

[27]

J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations,, Springer-Verlag, (1971).

[28]

S. E. Luczak, I. G. Rosen and T. L. Wall, Development of a real-time repeated-measures assessment protocol to capture change over the course of a drinking episode,, Alcohol and Alcoholism, 50 (2015), 1.

[29]

S. E. Luczak, I. G. Rosen and J. Weiss, Determining blood and/or breath alcohol concentration from transdermal alcohol data, Proceedings of the 2013 American control conference,, International Federation of Automatic Control, (2013), 473.

[30]

P. R. Marques and A. S. McKnight, Field and laboratory alcohol detection with 2 types of transdermal devices,, Alcohol Clin Exp Res, 33 (2009), 703.

[31]

D. B. Matthews and W. R. Miller, Estimating blood alcohol concentration: Two computer programs and their applications in therapy and research,, Addictive Behaviors, 4 (1979), 55.

[32]

I. Najfeld and T. F. Havel, Derivatives of the matrix exponential,, Advances in Applied Mathematics, 16 (1995), 321. doi: 10.1006/aama.1995.1017.

[33]

National Highway Traffic Safety Administration, Computing a BAC Estimate,, Department of Transportation, (1994).

[34]

A. Okubo, Diffusion and Ecological Problems: Mathematical Models,, Springer-Verlag, (1980).

[35]

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer-Verlag, (1983). doi: 10.1007/978-1-4612-5561-1.

[36]

A. J. Pritchard and D. Salamon, The linear quadratic control problem for infinite dimensional systems with unbounded input and output operators,, SIAM J. Control and Optimization, 25 (1987), 121. doi: 10.1137/0325009.

[37]

I. G. Rosen, S. E. Luczak and J. Weiss, Blind deconvolution for distributed parameter systems with unbounded input and output and determining blood alcohol concentration from transdermal biosensor data,, Applied Math and Computation, 231 (2014), 357. doi: 10.1016/j.amc.2013.12.099.

[38]

I. G. Rosen, S. E. Luczak, W. Hu and M. Hankin, Discrete-time blind deconvolution for distributed parameter systems with Dirichlet boundary input and unbounded output with application to a transdermal alcohol biosensor,, Proceedings of 2013 SIAM Conference on Control and its Applications, (2013).

[39]

J. T. Sakai, S. K. Mikulich-Gilbertson, R. J. Long and T. J. Crowley, Validity of transdermal alcohol monitoring: Fixed and self-regulated dosing,, Alcohol Clin Exp Res, 30 (2006), 26.

[40]

M. Schultz, Spline Analysis,, Prentice Hall, (1973).

[41]

R. E. Showalter, Hilbert Space Methods for Partial Differential Equations,, London, (1977).

[42]

L. C. Sobell and M. C. Sobell, Alcohol time-Line follow-back: A technique for assessing self-reported alcohol consumption, In R. Z. Litten and J. P. Allens (Eds.), Measuring Alcohol Consumption,, Humana Press, (1992).

[43]

O. J. Staffans, Well-Posed Linear Systems,, Cambridge University Press, (2005). doi: 10.1017/CBO9780511543197.

[44]

R. M. Swift, Direct measurement of alcohol and its metabolites,, Addiction, 98S (2003), 78.

[45]

R. M. Swift and L. L. Swette, Assessment of ethanol consumption with a wearable, electronic ethanol sensor/recorder, In R. Litten, and J. Allen (Eds.), Measuring Alcohol Consumption: Psychosocial and biological methods,, Humana Press, (1992).

[46]

H. Tanabe, Equations of Evolution,, Pitman, (1979).

[47]

M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups,, Birkhauser, (2009). doi: 10.1007/978-3-7643-8994-9.

[48]

J. G. Wagner and J. A. Patel, Variations in absorption and elimination rates of ethyl alcohol in a single subject,, Research Communications in Chemical Pathology and Pharmacology, 4 (1972), 61.

[49]

P. E. Watson, I. D. Watson and R. D. Batt, Total body water volumes for adult males and females estimated from simple anthropometric measurements,, American Journal of Clinical Nutrition, 33 (1980), 27.

[50]

P. E. Watson, I. D. Watson and R. D. Batt, Prediction of blood alcohol concentrations in human subjects: Updating the Widmark equation,, Journal of Studies on Alcohol, 42 (1981), 547.

[51]

G. D. Webster and H. C. Gabler, Feasibility of transdermal ethanol sensing for the detection of intoxicated drivers,, Annu Proc Assoc Adv Automot Med, 51 (2007), 449.

[52]

G. D. Webster and H. C. Gabler, Modeling of transdermal transport of alcohol: effect of body mass and gender,, Biomedical Sciences Instrumentation, 44 (2007), 361.

[53]

J. Wloka, Partial Differential Equations,, Cambridge University Press, (1987). doi: 10.1017/CBO9781139171755.

show all references

References:
[1]

R. A. Adams, Sobolev Spaces,, Academic Press, (1975).

[2]

J. C. Anderson and M. P. Hlastala, The kinetics of transdermal ethanol exchange,, Journal of Applied Physiology, 100 (2006), 649.

[3]

H. T. Banks and K. Ito, A unified framework for approximation in inverse problems for distributed parameter systems,, Control Theory and Advanced Technology, 4 (1988), 73.

[4]

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems,, Birkhauser, (1989). doi: 10.1007/978-1-4612-3700-6.

[5]

H. T. Banks and K. Ito, Approximation in LQR problems for infinite dimensional systems with unbounded input operators,, J. Mathematical Systems, 7 (1997), 1.

[6]

D. P. Bertsekas, Nonlinear Programming (2nd ed.),, Athena Scientific, (1999).

[7]

S. P. Bradley, A. C. Hax and T. L. Magnanti, Applied Mathematical Programming,, Addison-Wesley, (1977).

[8]

K. B. Carey and J. T. P. Hustad, Are retrospectively reconstructed blood alcohol concentrations accurate?, Preliminary results from a field study,, Journal of Studies on Alcohol, 63 (2002), 762.

[9]

C.-T. Chen, Linear System Theory and Design,, Holt Rinehart and Winston, (1970).

[10]

R. F. Curtain and D. Salamon, Finite dimensional compensators and infinite dimensional systems with unbounded input operators,, SIAM J. Control and Optimization, 24 (1986), 797. doi: 10.1137/0324050.

[11]

D. M. Dougherty, N. E. Charles, A. Acheson, S. John, R. M. Furr and N. Hill-Kapturczak, Comparing the detection of transdermal and breath alcohol concentrations during periods of alcohol consumption ranging from moderate drinking to binge drinking,, Exp Clin Psychopharm, 203 (2012), 73.

[12]

M. Dumett, I. G. Rosen, J. Sabat, A. Shaman, L. A. Tempelman, C. Wang and R. M. Swift, Deconvolving an estimate of breath measured blood alcohol concentration from biosensor collected transdermal ethanol data,, Applied Mathematics and Computation, 196 (2008), 724. doi: 10.1016/j.amc.2007.07.026.

[13]

L. Edelstein-Keshet, Mathematical Models in Biology,, Society for Industrial and Applied Mathematics, (2005). doi: 10.1137/1.9780898719147.

[14]

A. R. W. Forrest, The estimation of Widmark's factor,, Journal of the Forensic Science Society, 26 (1986), 249.

[15]

J. S. Gibson and I. G. Rosen, Approximation of discrete time LQG compensators for distributed systems with boundary input and unbounded measurement,, Automatica, 24 (1988), 517. doi: 10.1016/0005-1098(88)90096-9.

[16]

A. Heck, Modeling intake and clearance of alcohol in humans,, The Electronic Journal of Mathematics and Technology, 1 (2007), 232.

[17]

N. Hill-Kapturczak, S. L. Lake, J. D. Roache, S. E. Cates, Y. Liang and D. M. Dougherty, Do variable rates of alcohol drinking alter the ability to use transdermal alcohol monitors to estimate peak, breath alcohol and total number of drinks?,, ACER, 38 (2014), 2517. doi: 10.1111/acer.12528.

[18]

N. Hill-Kapturczak, J. D. Roache, Y. Liang, T. E. Karns, S. E. Cates and D. M. Dougherty, Accounting for sex-related differences in the estimation of breath alcohol concentrations using transdermal alcohol monitoring,, Psychopharmacology , 232 (2015), 115. doi: 10.1007/s00213-014-3644-9.

[19]

N. Hill-Kapturczak, J. D. Roache, C. J. Walters, T. E. Karns, S. E. Cates and D. M. Dougherty, Validation of using transdermal alcohol concentrations to estimate breath alcohol,, ACER., ().

[20]

E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups,, American Mathematical Society, (1957).

[21]

J. T. P. Hustad and K. B. Carey, Using calculations to estimate blood alcohol concentrations for naturally occurring drinking episodes: A validity study,, Journal of Studies on Alcohol, 66 (2005), 130.

[22]

T. Kato, Perturbation Theory for Linear Operators,, Second Edition, (1976).

[23]

D. A. Labianca, The chemical basis of the breathalyzer,a critical analysis,, Journal of Chemical Education, 67 (1990), 259.

[24]

A. J. Levi and I. G. Rosen, A novel formulation of the adjoint method in the optimal design of quantum electronic devices,, Siam Journal on Control and Optimization, 48 (2010), 3191. doi: 10.1137/070708330.

[25]

M. J. Lewis, The individual and the estimation of his blood alcohol concentration from intake, with particular reference to the "hip-flask" drink,, Journal of the Forensic Science Society, 26 (1986), 19.

[26]

L. Li and T. P. Speed, Parametric deconvolution of positive spike trains,, Annals of Statistics, 28 (2000), 1279. doi: 10.1214/aos/1015957394.

[27]

J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations,, Springer-Verlag, (1971).

[28]

S. E. Luczak, I. G. Rosen and T. L. Wall, Development of a real-time repeated-measures assessment protocol to capture change over the course of a drinking episode,, Alcohol and Alcoholism, 50 (2015), 1.

[29]

S. E. Luczak, I. G. Rosen and J. Weiss, Determining blood and/or breath alcohol concentration from transdermal alcohol data, Proceedings of the 2013 American control conference,, International Federation of Automatic Control, (2013), 473.

[30]

P. R. Marques and A. S. McKnight, Field and laboratory alcohol detection with 2 types of transdermal devices,, Alcohol Clin Exp Res, 33 (2009), 703.

[31]

D. B. Matthews and W. R. Miller, Estimating blood alcohol concentration: Two computer programs and their applications in therapy and research,, Addictive Behaviors, 4 (1979), 55.

[32]

I. Najfeld and T. F. Havel, Derivatives of the matrix exponential,, Advances in Applied Mathematics, 16 (1995), 321. doi: 10.1006/aama.1995.1017.

[33]

National Highway Traffic Safety Administration, Computing a BAC Estimate,, Department of Transportation, (1994).

[34]

A. Okubo, Diffusion and Ecological Problems: Mathematical Models,, Springer-Verlag, (1980).

[35]

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer-Verlag, (1983). doi: 10.1007/978-1-4612-5561-1.

[36]

A. J. Pritchard and D. Salamon, The linear quadratic control problem for infinite dimensional systems with unbounded input and output operators,, SIAM J. Control and Optimization, 25 (1987), 121. doi: 10.1137/0325009.

[37]

I. G. Rosen, S. E. Luczak and J. Weiss, Blind deconvolution for distributed parameter systems with unbounded input and output and determining blood alcohol concentration from transdermal biosensor data,, Applied Math and Computation, 231 (2014), 357. doi: 10.1016/j.amc.2013.12.099.

[38]

I. G. Rosen, S. E. Luczak, W. Hu and M. Hankin, Discrete-time blind deconvolution for distributed parameter systems with Dirichlet boundary input and unbounded output with application to a transdermal alcohol biosensor,, Proceedings of 2013 SIAM Conference on Control and its Applications, (2013).

[39]

J. T. Sakai, S. K. Mikulich-Gilbertson, R. J. Long and T. J. Crowley, Validity of transdermal alcohol monitoring: Fixed and self-regulated dosing,, Alcohol Clin Exp Res, 30 (2006), 26.

[40]

M. Schultz, Spline Analysis,, Prentice Hall, (1973).

[41]

R. E. Showalter, Hilbert Space Methods for Partial Differential Equations,, London, (1977).

[42]

L. C. Sobell and M. C. Sobell, Alcohol time-Line follow-back: A technique for assessing self-reported alcohol consumption, In R. Z. Litten and J. P. Allens (Eds.), Measuring Alcohol Consumption,, Humana Press, (1992).

[43]

O. J. Staffans, Well-Posed Linear Systems,, Cambridge University Press, (2005). doi: 10.1017/CBO9780511543197.

[44]

R. M. Swift, Direct measurement of alcohol and its metabolites,, Addiction, 98S (2003), 78.

[45]

R. M. Swift and L. L. Swette, Assessment of ethanol consumption with a wearable, electronic ethanol sensor/recorder, In R. Litten, and J. Allen (Eds.), Measuring Alcohol Consumption: Psychosocial and biological methods,, Humana Press, (1992).

[46]

H. Tanabe, Equations of Evolution,, Pitman, (1979).

[47]

M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups,, Birkhauser, (2009). doi: 10.1007/978-3-7643-8994-9.

[48]

J. G. Wagner and J. A. Patel, Variations in absorption and elimination rates of ethyl alcohol in a single subject,, Research Communications in Chemical Pathology and Pharmacology, 4 (1972), 61.

[49]

P. E. Watson, I. D. Watson and R. D. Batt, Total body water volumes for adult males and females estimated from simple anthropometric measurements,, American Journal of Clinical Nutrition, 33 (1980), 27.

[50]

P. E. Watson, I. D. Watson and R. D. Batt, Prediction of blood alcohol concentrations in human subjects: Updating the Widmark equation,, Journal of Studies on Alcohol, 42 (1981), 547.

[51]

G. D. Webster and H. C. Gabler, Feasibility of transdermal ethanol sensing for the detection of intoxicated drivers,, Annu Proc Assoc Adv Automot Med, 51 (2007), 449.

[52]

G. D. Webster and H. C. Gabler, Modeling of transdermal transport of alcohol: effect of body mass and gender,, Biomedical Sciences Instrumentation, 44 (2007), 361.

[53]

J. Wloka, Partial Differential Equations,, Cambridge University Press, (1987). doi: 10.1017/CBO9781139171755.

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