Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach

The posterior distribution (PD) of random parameters in a distributed parameter-based population model for biosensor measured transdermal alcohol is estimated. The output of the model is transdermal alcohol concentration (TAC), which, via linear semigroup theory can be expressed as the convolution o...

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Autores principales:	Keenan Hawekotte, Susan E. Luczak, I. G. Rosen
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	bayesian estimation blood alcohol concentration breath alcohol concentration transdermal alcohol concentration distributed parameter systems linear semigroup theory galerkin methods posterior consistency deconvolution Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/711faaef91c2474cbf49676f470a61d3
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spelling	oai:doaj.org-article:711faaef91c2474cbf49676f470a61d32021-11-12T02:18:28ZDeconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach10.3934/mbe.20213351551-0018https://doaj.org/article/711faaef91c2474cbf49676f470a61d32021-08-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021335?viewType=HTMLhttps://doaj.org/toc/1551-0018The posterior distribution (PD) of random parameters in a distributed parameter-based population model for biosensor measured transdermal alcohol is estimated. The output of the model is transdermal alcohol concentration (TAC), which, via linear semigroup theory can be expressed as the convolution of blood or breath alcohol concentration (BAC or BrAC) with a filter that depends on the individual participant or subject, the biosensor hardware itself, and environmental conditions, all of which can be considered to be random under the presented framework. The distribution of the input to the model, the BAC or BrAC, is also sequentially estimated. A Bayesian approach is used to estimate the PD of the parameters conditioned on the population sample's measured BrAC and TAC. We then use the PD for the parameters together with a weak form of the forward random diffusion model to deconvolve an individual subject's BrAC conditioned on their measured TAC. Priors for the model are obtained from simultaneous temporal population observations of BrAC and TAC via deterministic or statistical methods. The requisite computations require finite dimensional approximation of the underlying state equation, which is achieved through standard finite element (i.e., Galerkin) techniques. The posteriors yield credible regions, which remove the need to calibrate the model to every individual, every sensor, and various environmental conditions. Consistency of the Bayesian estimators and convergence in distribution of the PDs computed based on the finite element model to those based on the underlying infinite dimensional model are established. Results of human subject data-based numerical studies demonstrating the efficacy of the approach are presented and discussed.Keenan HawekotteSusan E. LuczakI. G. RosenAIMS Pressarticlebayesian estimationblood alcohol concentrationbreath alcohol concentrationtransdermal alcohol concentrationdistributed parameter systemslinear semigroup theorygalerkin methodsposterior consistencydeconvolutionBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6739-6770 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	bayesian estimation blood alcohol concentration breath alcohol concentration transdermal alcohol concentration distributed parameter systems linear semigroup theory galerkin methods posterior consistency deconvolution Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	bayesian estimation blood alcohol concentration breath alcohol concentration transdermal alcohol concentration distributed parameter systems linear semigroup theory galerkin methods posterior consistency deconvolution Biotechnology TP248.13-248.65 Mathematics QA1-939 Keenan Hawekotte Susan E. Luczak I. G. Rosen Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach
description	The posterior distribution (PD) of random parameters in a distributed parameter-based population model for biosensor measured transdermal alcohol is estimated. The output of the model is transdermal alcohol concentration (TAC), which, via linear semigroup theory can be expressed as the convolution of blood or breath alcohol concentration (BAC or BrAC) with a filter that depends on the individual participant or subject, the biosensor hardware itself, and environmental conditions, all of which can be considered to be random under the presented framework. The distribution of the input to the model, the BAC or BrAC, is also sequentially estimated. A Bayesian approach is used to estimate the PD of the parameters conditioned on the population sample's measured BrAC and TAC. We then use the PD for the parameters together with a weak form of the forward random diffusion model to deconvolve an individual subject's BrAC conditioned on their measured TAC. Priors for the model are obtained from simultaneous temporal population observations of BrAC and TAC via deterministic or statistical methods. The requisite computations require finite dimensional approximation of the underlying state equation, which is achieved through standard finite element (i.e., Galerkin) techniques. The posteriors yield credible regions, which remove the need to calibrate the model to every individual, every sensor, and various environmental conditions. Consistency of the Bayesian estimators and convergence in distribution of the PDs computed based on the finite element model to those based on the underlying infinite dimensional model are established. Results of human subject data-based numerical studies demonstrating the efficacy of the approach are presented and discussed.
format	article
author	Keenan Hawekotte Susan E. Luczak I. G. Rosen
author_facet	Keenan Hawekotte Susan E. Luczak I. G. Rosen
author_sort	Keenan Hawekotte
title	Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach
title_short	Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach
title_full	Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach
title_fullStr	Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach
title_full_unstemmed	Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach
title_sort	deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a bayesian approach
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/711faaef91c2474cbf49676f470a61d3
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Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach

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