Model based time of death estimation in forensic medicine
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Estimating the time of death is an important building block of homicide investigations. One of the most reliable and widely accepted methods is based on corpse cooling. The purely phenomenological model dominating in court practice suffers from a lack of applicability to nonstandard situations as well as from difficulties in integrating multiple measurements. Newer mechanistic models based on computational simulating corpse cooling by solving the heat equation on CT-generated personalized anatomies promise to fill this gap and provide higher accuracy as well as more reliable uncertainty quantification. The challenge with mechanistic models is the number of not precisely known parameters, ranging from tissues' heat capacities to anatomy and thermal probe positioning. We formulate the time of death estimation problem as a Bayesian inverse problem and discuss relevance of parameters based on their sensitivity, impact of mesh resolution, anatomy, and thermal probe location as well as extended measurement schemes and design of experiment aspects. We illustrate these topics at several examples and discuss numerical topics such as finite element discretization, model reduction, and machine learning approaches.