Blind Deconvolution for Distributed Parameter Systems with Unbounded Input and Output and Determining Blood Alcohol...

Area of Science:

• Control Theory
• Biomedical Engineering
• Mathematical Modeling

Background:

• Estimating blood alcohol content (BAC) or breath alcohol content (BrAC) non-invasively is crucial for various applications.
• Transdermal alcohol concentration (TAC) measured by biosensors offers a potential non-invasive method, but requires sophisticated data processing.
• Existing methods face challenges in accurately deconvoluting TAC signals to infer internal alcohol concentrations.

Purpose of the Study:

• To develop a blind deconvolution scheme for input-output systems described by distributed parameter systems.
• To apply this scheme to estimate blood or breath alcohol concentration (BAC/BrAC) from transdermal alcohol concentration (TAC) data.
• To establish a robust method for inferring internal alcohol levels from external biosensor measurements.

Main Methods:

• Development of an abstract functional analytic theory for linear quadratic control of infinite-dimensional systems.
• Reformulation of the blind deconvolution problem as constrained linear and nonlinear optimization problems.
• Development of a finite-dimensional approximation and convergence theory, applied to a distributed parameter model of transdermal ethanol transport.

Main Results:

• A novel blind deconvolution scheme was successfully developed and theoretically validated.
• The method was applied to estimate BAC/BrAC from TAC data, demonstrating its practical applicability.
• Numerical results using actual patient data confirmed the effectiveness of the proposed approach.

Conclusions:

• The developed blind deconvolution scheme provides a powerful tool for estimating BAC/BrAC from TAC measurements.
• The distributed parameter system model accurately represents transdermal ethanol transport.
• The methodology offers a promising advancement for non-invasive alcohol monitoring.