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

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.

Flux-Type versus Concentration-Type Sensors in Transdermal Measurements

New transdermal biosensors measure analytes that diffuse from the bloodstream through the skin, making it important to reduce the system response time and understand measurement output. While highly customized models have been created for specific sensors, a generalized model for transdermal sensor systems is lacking. Here, a simple one-dimensional diffusion model was used to characterize the measurement system and classify biosensors as either flux types or concentration types. Results showed that flux-type sensors have significantly faster response times than concentration sensors. Furthermore, flux sensors do not measure concentration, but rather have an output measurement that is proportional to skin permeability. These findings should lead to an improved understanding of transdermal measurements and their relation to blood analyte concentration. In the realm of alcohol research, where the majority of commercially available sensors are flux types, our work advocates toward moving away from transdermal alcohol concentration as a metric, and instead suggests embracing transdermal alcohol flux as a more suitable alternative.