Interpretable physiological forecasting in the ICU using constrained data assimilation and electronic health record data.

Objective: Prediction of physiological mechanics are important in medical practice because interventions are guided by predicted impacts of interventions. But prediction is difficult in medicine because medicine is complex and difficult to understand from data alone, and the data are sparse relative to the complexity of the generating processes. Computational methods can increase prediction accuracy, but prediction with clinical data is difficult because the data are sparse, noisy and nonstationary.

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.

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.

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.

Applying a novel population-based model approach to estimating breath alcohol concentration (BrAC) from transdermal alcohol concentration (TAC) biosensor data.

Alcohol biosensor devices have been developed to unobtrusively measure transdermal alcohol concentration (TAC), the amount of ethanol diffusing through the skin, in nearly continuous fashion in naturalistic settings. Because TAC data are affected by physiological and environmental factors that vary across individuals and drinking episodes, there is not an elementary formula to convert TAC into easily interpretable metrics such as blood and breath alcohol concentrations (BAC/BrAC). In our prior work, we addressed this conversion problem in a deterministic way by developing physics/physiological-based models to convert TAC to estimated BrAC (eBrAC), in which the model parameter values were individually determined for each person wearing a specific transdermal sensor using simultaneously collected TAC (via a biosensor) and BrAC (via a breath analyzer) during a calibration episode.

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.