Tracking and blind deconvolution of blood alcohol concentration from transdermal alcohol biosensor data: A population model-based LQG approach in Hilbert space.

LQG control in Hilbert space, a novel approach for random abstract parabolic systems, and new transdermal alcohol biosensor technology are combined to yield tracking controllers that can be used to automate inpatient management of alcohol withdrawal syndrome and human subject intravenous alcohol infusion studies, and to blindly deconvolve blood or breath alcohol concentration from biosensor measured transdermal alcohol level. The approach taken is based on a full-body alcohol population model in the form of a random, nonlinear, hybrid system of ordinary and partial differential equations and its abstract formulation in a Gelfand triple of Bochner spaces. The efficacy of the approach is demonstrated through simulation studies based on laboratory collected drinking data.

Blood and Breath Alcohol Concentration from Transdermal Alcohol Biosensor Data: Estimation and Uncertainty Quantification via Forward and Inverse Filtering for a Covariate-Dependent, Physics-Informed, Hidden Markov Model.

Transdermal alcohol biosensors that do not require active participation of the subject and yield near continuous measurements have the potential to significantly enhance the data collection abilities of alcohol researchers and clinicians who currently rely exclusively on breathalyzers and drinking diaries. Making these devices accessible and practical requires that transdermal alcohol concentration (TAC) be accurately and consistently transformable into the well-accepted measures of intoxication, blood/breath alcohol concentration (BAC/BrAC). A novel approach to estimating BrAC from TAC based on covariate-dependent physics-informed hidden Markov models with two emissions is developed. The hidden Markov chain serves as a forward full-body alcohol model with BrAC and TAC, the two emissions, assumed to be described by a bivariate normal which depends on the hidden Markovian states and person-level and session-level covariates via built-in regression models. An innovative extension of hidden Markov modeling is developed wherein the hidden Markov model framework is regularized by a first-principles PDE model to yield a hybrid that combines prior knowledge of the physics of transdermal ethanol transport with data-based learning. Training, or inverse filtering, is effected via the Baum-Welch algorithm and 256 sets of BrAC and TAC signals and covariate measurements collected in the laboratory. Forward filtering of TAC to obtain estimated BrAC is achieved via a new physics-informed regularized Viterbi algorithm which determines the most likely path through the hidden Markov chain using TAC alone. The Markovian states are decoded and used to yield estimates of BrAC and to quantify the uncertainty in the estimates. Numerical studies are presented and discussed. Overall good agreement between BrAC data and estimates was observed with a median relative peak error of 22% and a median relative area under the curve error of 25% on the test set. We also demonstrate that the physics-informed Viterbi algorithm eliminates non-physical artifacts in the BrAC estimates.

Bayesian model selection for the Drosophila gap gene network.

BACKGROUND: The gap gene system controls the early cascade of the segmentation pathway in Drosophila melanogaster as well as other insects. Owing to its tractability and key role in embryo patterning, this system has been the focus for both computational modelers and experimentalists. The gap gene expression dynamics can be considered strictly as a one-dimensional process and modeled as a system of reaction-diffusion equations. While substantial progress has been made in modeling this phenomenon, there still remains a deficit of approaches to evaluate competing hypotheses. Most of the model development has happened in isolation and there has been little attempt to compare candidate models. RESULTS: The Bayesian framework offers a means of doing formal model evaluation. Here, we demonstrate how this framework can be used to compare different models of gene expression. We focus on the Papatsenko-Levine formalism, which exploits a fractional occupancy based approach to incorporate activation of the gap genes by the maternal genes and cross-regulation by the gap genes themselves. The Bayesian approach provides insight about relationship between system parameters. In the regulatory pathway of segmentation, the parameters for number of binding sites and binding affinity have a negative correlation. The model selection analysis supports a stronger binding affinity for Bicoid compared to other regulatory edges, as shown by a larger posterior mean. The procedure doesn't show support for activation of Kruppel by Bicoid. CONCLUSIONS: We provide an efficient solver for the general representation of the Papatsenko-Levine model. We also demonstrate the utility of Bayes factor for evaluating candidate models for spatial pattering models. In addition, by using the parallel tempering sampler, the convergence of Markov chains can be remarkably improved and robust estimates of Bayes factors obtained.

Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor.

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol concentration and the output being the transdermal alcohol concentration. Our approach is based on the idea of reformulating the underlying dynamical system in such a way that the random parameters are now treated as additional space variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation and thus well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may all be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject.

Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence.

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.

Deconvolving the input to random abstract parabolic systems: a population model-based approach to estimating blood/breath alcohol concentration from transdermal alcohol biosensor data.

The distribution of random parameters in, and the input signal to, a distributed parameter model with unbounded input and output operators for the transdermal transport of ethanol are estimated. The model takes the form of a diffusion equation with the input, which is on the boundary of the domain, being the blood or breath alcohol concentration (BAC/BrAC), and the output, also on the boundary, being the transdermal alcohol concentration (TAC). Our approach is based on the reformulation of the underlying dynamical system in such a way that the random parameters are treated as additional spatial variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating a functional diffusivity in a multi-dimensional diffusion equation. The resulting system is referred to as a population model, and well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods can be used to fit it to population data and to analyze the resulting fit. Once the forward population model has been identified or trained based on a sample from the population, the resulting distribution can then be used to deconvolve the BAC/BrAC input signal from the biosensor observed TAC output signal formulated as either a quadratic programming or linear quadratic tracking problem. In addition, our approach allows for the direct computation of corresponding credible bands without simulation. We use our technique to estimate bivariate normal distributions and deconvolve BAC/BrAC from TAC based on data from a population that consists of multiple drinking episodes from a single subject and a population consisting of single drinking episodes from multiple subjects.

THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs.

We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.

Development of a real-time repeated-measures assessment protocol to capture change over the course of a drinking episode.

AIMS: We report on the development of a real-time assessment protocol that allows researchers to assess change in BrAC, alcohol responses, behaviors, and contexts over the course of a drinking event. METHOD: We designed a web application that uses timed text messages (adjusted based on consumption pattern) containing links to our website to obtain real-time participant reports; camera and location features were also incorporated into the protocol. We used a transdermal alcohol sensor device along with software we designed to convert transdermal data into estimated BrAC. Thirty-two college students completed a laboratory session followed by a 2-week field trial. RESULTS: Results for the web application indicated we were able to create an effective tool for obtaining repeated measures real-time drinking data. Participants were willing to monitor their drinking behavior with the web application, and this did not appear to strongly affect drinking behavior during, or 6 weeks following, the field trial. Results for the transdermal device highlighted the willingness of participants to wear the device despite some discomfort, but technical difficulties resulted in limited valid data. CONCLUSION: The development of this protocol makes it possible to capture detailed assessment of change over the course of naturalistic drinking episodes.

Estimating BrAC from transdermal alcohol concentration data using the BrAC estimator software program.

BACKGROUND: Transdermal alcohol sensor (TAS) devices have the potential to allow researchers and clinicians to unobtrusively collect naturalistic drinking data for weeks at a time, but the transdermal alcohol concentration (TAC) data these devices produce do not consistently correspond with breath alcohol concentration (BrAC) data. We present and test the BrAC Estimator software, a program designed to produce individualized estimates of BrAC from TAC data by fitting mathematical models to a specific person wearing a specific TAS device. METHODS: Two TAS devices were worn simultaneously by 1 participant for 18 days. The trial began with a laboratory alcohol session to calibrate the model and was followed by a field trial with 10 drinking episodes. Model parameter estimates and fit indices were compared across drinking episodes to examine the calibration phase of the software. Software-generated estimates of peak BrAC, time of peak BrAC, and area under the BrAC curve were compared with breath analyzer data to examine the estimation phase of the software. RESULTS: In this single-subject design with breath analyzer peak BrAC scores ranging from 0.013 to 0.057, the software created consistent models for the 2 TAS devices, despite differences in raw TAC data, and was able to compensate for the attenuation of peak BrAC and latency of the time of peak BrAC that are typically observed in TAC data. CONCLUSIONS: This software program represents an important initial step for making it possible for non mathematician researchers and clinicians to obtain estimates of BrAC from TAC data in naturalistic drinking environments. Future research with more participants and greater variation in alcohol consumption levels and patterns, as well as examination of gain scheduling calibration procedures and nonlinear models of diffusion, will help to determine how precise these software models can become.

Blind Deconvolution for Distributed Parameter Systems with Unbounded Input and Output and Determining Blood Alcohol Concentration from Transdermal Biosensor Data.

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. A finite dimensional approximation and convergence theory is developed. The theory is applied to the problem of estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from biosensor-measured transdermal alcohol concentration (TAC) in the field. A distributed parameter model with boundary input and output is proposed for the transdermal transport of ethanol from the blood through the skin to the sensor. The problem of estimating BAC or BrAC from the TAC data is formulated as a blind deconvolution problem. A scheme to identify distinct drinking episodes in TAC data based on a Hodrick Prescott filter is discussed. Numerical results involving actual patient data are presented.

A population model-based linear-quadratic Gaussian compensator for the control of intravenously infused alcohol studies and withdrawal symptom prophylaxis using transdermal sensing.

An output feedback LQG compensator (combined controller and state estimator) for the regulation of intravenous-infused alcohol studies and treatment using a noninvasive transdermal alcohol biosensor is developed. The design is based on a population model involving an abstract semi-linear parabolic hybrid reaction-diffusion system involving coupled partial and ordinary differential equations with random parameters known only up to their distributions. The scheme developed is based on a weak formulation of the model equations in an appropriately constructed Gelfand triple of Bochner spaces wherein the unknown random parameters are treated as additional spatial variables. Implementation relies on a Galerkin-based approximation and convergence theory and an abstract formulation involving linear semigroups of operators. The model is fit and validated using laboratory collected human subject data and the method of moments. The results of numerical simulations of controlled intravenous alcohol infusion are presented and discussed.

Epilepsy surgery in children with drug-resistant epilepsy, a long-term follow-up.

OBJECTIVES: In this follow-up study, we wanted to present the long-term outcome (5-21 years) in terms of seizure freedom, seizure reduction, and the cognitive development in the first 47 children who underwent epilepsy surgery at the University Hospital in Lund from 1991 to 2007. MATERIALS AND METHODS: All children who underwent epilepsy surgery in the southern region of Sweden were assessed for cognitive function before surgery and at follow-up. A review of medical documents for demographic data and seizure-related characteristics was made by retrospectively examining the clinical records. RESULTS: Forty-seven children with a median age at surgery of 8 years (range 0.5-18.7 years) were included. Twenty-three children achieved seizure freedom, six demonstrated >75% improvement in seizure frequency, and none of the children experienced an increase in seizure frequency. Twenty-one children required a reoperation to achieve satisfactory seizure outcomes. Cognitive functional level was preserved, and the majority of patients, 34 (76%), followed their expected cognitive trajectory. The patients who became seizure free significantly improved their cognitive processing speed, even after long-term follow-up. CONCLUSIONS: Epilepsy surgery in children offers suitable candidates a good chance of significantly improved outcome and low rates of complications. Several children, however, required a reoperation to achieve satisfactory seizure outcomes. Cognitive level was preserved, and the majority of patients followed their expected cognitive trajectory. Cognitive improvements in processing speed appear to occur in parallel with seizure control and were even more pronounced in subjects with no anti-epilepsy drugs. These improvements persisted even after long-term follow-up.

HRPT2, encoding parafibromin, is mutated in hyperparathyroidism-jaw tumor syndrome.

We report here the identification of a gene associated with the hyperparathyroidism-jaw tumor (HPT-JT) syndrome. A single locus associated with HPT-JT (HRPT2) was previously mapped to chromosomal region 1q25-q32. We refined this region to a critical interval of 12 cM by genotyping in 26 affected kindreds. Using a positional candidate approach, we identified thirteen different heterozygous, germline, inactivating mutations in a single gene in fourteen families with HPT-JT. The proposed role of HRPT2 as a tumor suppressor was supported by mutation screening in 48 parathyroid adenomas with cystic features, which identified three somatic inactivating mutations, all located in exon 1. None of these mutations were detected in normal controls, and all were predicted to cause deficient or impaired protein function. HRPT2 is a ubiquitously expressed, evolutionarily conserved gene encoding a predicted protein of 531 amino acids, for which we propose the name parafibromin. Our findings suggest that HRPT2 is a tumor-suppressor gene, the inactivation of which is directly involved in predisposition to HPT-JT and in development of some sporadic parathyroid tumors.

Uncertainty Quantification in Estimating Blood Alcohol Concentration From Transdermal Alcohol Level With Physics-Informed Neural Networks.

We develop an approach to estimate a blood alcohol signal from a transdermal alcohol signal using physics-informed neural networks (PINNs). Specifically, we use a generative adversarial network (GAN) with a residual-augmented loss function to estimate the distribution of unknown parameters in a diffusion equation model for transdermal transport of alcohol in the human body. We design another PINN for the deconvolution of the blood alcohol signal from the transdermal alcohol signal. Based on the distribution of the unknown parameters, this network is able to estimate the blood alcohol signal and quantify the uncertainty in the form of conservative error bands. Finally, we show how a posterior latent variable can be used to sharpen these conservative error bands. We apply the techniques to an extensive dataset of drinking episodes and demonstrate the advantages and shortcomings of this approach.

Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol.

The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems was established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator was also established and the efficacy of the approach was demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic partial differential equation (PDE). Numerical studies included show that the maximum likelihood estimator is statistically consistent, demonstrated by the convergence of the estimated distribution to the "true" distribution in an example involving simulated data. The algorithm developed was then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation (LOOCV) method, we found an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode was then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95 error band surrounding the estimated output signal.

Social anxiety and alcohol consumption: The role of social context.

Research has identified social anxiety as a risk factor for the development of alcohol use disorder. However, studies have produced equivocal findings regarding the relationship between social anxiety and drinking behaviors in authentic drinking environments. This study examined how social-contextual features of real-world drinking contexts might influence the relationship between social anxiety and alcohol consumption in everyday settings. At an initial laboratory visit, heavy social drinkers (N = 48) completed the Liebowitz Social Anxiety Scale. Participants were then outfitted with a transdermal alcohol monitor individually-calibrated for each participant via laboratory alcohol-administration. Over the next seven days, participants wore this transdermal alcohol monitor and responded to random survey prompts (6x/day), during which they provided photographs of their surroundings. Participants then reported on their levels of social familiarity with individuals visible in photographs. Multilevel models indicated a significant interaction between social anxiety and social familiarity in predicting drinking, b = -0.004, p =.003 Specifically, among participants higher in social anxiety, drinking increased as social familiarity decreased b = -0.152, p <.001, whereas among those lower in social anxiety, this relationship was non-significant, b = 0.007, p =.867. Considered alongside prior research, findings suggest that the presence of strangers within a given environment may play a role in the drinking behavior of socially anxious individuals.

An Abstract Parabolic System-Based Physics-Informed Long Short-Term Memory Network for Estimating Breath Alcohol Concentration from Transdermal Alcohol Biosensor Data.

The problem of estimating breath alcohol concentration based on transdermal alcohol biosensor data is considered. Transdermal alcohol concentration provides a promising alternative to classical methods such as breathalyzers or drinking diaries. A physics-informed long Short-term memory (LSTM) network with covariates for the solution of the estimation problem is developed. The data-driven nature of an LSTM is augmented with a first principles physics-based population model for the diffusion of ethanol through the epidermal layer of the skin. The population model in an abstract parabolic framework appears as part of a regularization term in the loss function of the LSTM. While learning, the model is encouraged to both fit the data and to produce physically meaningful outputs. To deal with the high variation observed in the data, a mechanism for the uncertainty quantification of the estimates based on a recently discovered relation between Monte-Carlo dropout and Bayesian learning is used. The physics-based population model and the LSTM are trained and tested using controlled laboratory collected breath and transdermal alcohol data collected in four sessions from 40 orally dosed participants (50% female, ages 21 - 33 years, 35% BMI above 25.0) resulting in 256 usable drinking episodes partitioned into training and testing sets. Body measurement (e.g. BMI, hip to waist ratio, etc.), personal (e.g. sex, age, race, etc.), drinking behavior (e.g. frequent, rarely, etc.), and environmental (e.g. temperature, humidity, etc.) covariates were also collected from participants. The importance of various covariates in the estimation is investigated using Shapley values. It is shown that the physics-informed LSTM network can be successfully applied to drinking episodes from both the training and test set, and that the physics-based information leads to better generalization ability on new drinking episodes with the uncertainty quantification yielding credible bands that effectively capture the true signal. Compared to two machine learning models from previous studies, the proposed model reduces relative L2 error in estimated breath alcohol concentration by 58% and 72%, and relative peak error by 33% and 76%.

Disturbed vibrotactile sense in finger pulps in patients with Type 1 diabetes--correlations with glycaemic level, clinical examination and electrophysiology.

AIMS: In a cohort of men and women with Type 1 diabetes, prospectively followed for > 20 years, vibrotactile sense in fingers was investigated and related to neurophysiological tests, glycaemic level and clinical score. METHODS: Out of 58 patients, diagnosed at the age of 15-25 years and recruited 1984-1985, 32 patients (13 women, median age 52 years, range 44-75 years; 19 men, median age 52 years, range 39-69 years; median duration 33.5 years, range 21-52 years) accepted follow-up in 2006. Vibration thresholds were measured in finger pulps of index and little fingers bilaterally at seven frequencies and related to results of touch (monofilaments), tactile discrimination (two-point discrimination test), electrophysiology (median nerve function), glycaemic level (HbA(1c) levels since 1984-1985) and a clinical score. RESULTS: Vibrotactile sense was reduced in finger pulps, mainly in men, compared with an age- and gender-matched healthy control group with normal HbA(1c) . Vibration thresholds were increased, particularly at 250 and 500 Hz, in both index and little finger pulps. Touch and tactile discrimination correlated with vibration thresholds, but not with each other or with electrophysiology. HbA(1c) levels (at follow-up or mean values from five follow-ups since recruitment) did not correlate with any nerve function variables. Clinical scores correlated with vibrotactile sense, particularly at higher frequencies (> 125 Hz), but not with total Z-scores of electrophysiology. Duration of disease did not correlate with any variables. CONCLUSIONS: Examination of vibration thresholds in index and little finger pulps may be valuable to detect neuropathy, where thresholds correlate with symptoms and tests.

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 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.

Effects of stomach content on the breath alcohol concentration-transdermal alcohol concentration relationship.

INTRODUCTION: Wearable devices that obtain transdermal alcohol concentration (TAC) could become valuable research tools for monitoring alcohol consumption levels in naturalistic environments if the TAC they produce could be converted into quantitatively-meaningful estimates of breath alcohol concentration (eBrAC). Our team has developed mathematical models to produce eBrAC from TAC, but it is not yet clear how a variety of factors affect the accuracy of the models. Stomach content is one factor that is known to affect breath alcohol concentration (BrAC), but its effect on the BrAC-TAC relationship has not yet been studied. METHODS: We examine the BrAC-TAC relationship by having two investigators participate in four laboratory drinking sessions with varied stomach content conditions: (i) no meal, (ii) half and (iii) full meal before drinking, and (iv) full meal after drinking. BrAC and TAC were obtained every 10 min over the BrAC curve. RESULTS: Eating before drinking lowered BrAC and TAC levels, with greater variability in TAC across person-device pairings, but the BrAC-TAC relationship was not consistently altered by stomach content. The mathematical model calibration parameters, fit indices, and eBrAC curves and summary score outputs did not consistently vary based on stomach content, indicating that our models were able to produce eBrAC from TAC with similar accuracy despite variations in the shape and magnitude of the BrAC curves under different conditions. DISCUSSION AND CONCLUSIONS: This study represents the first examination of how stomach content affects our ability to model estimates of BrAC from TAC and indicates it is not a major factor.