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Keywords
Temperature-based estimation of time of death (ToD) can be per-
formed either with the help of simple phenomenological models of corpse
cooling or with detailed mechanistic (thermodynamic) heat transfer mod-
els. The latter are much more complex, but allow a higher accuracy of
ToD estimation as in principle all relevant cooling mechanisms can be
taken into account.
The potentially higher accuracy depends on the accuracy of tissue and
environmental parameters as well as on the geometric resolution. We in-
vestigate the impact of parameter variations and geometry representation
on the estimated ToD based on a highly detailed 3D corpse model, that
has been segmented and geometrically reconstructed from a computed to-
mography (CT) data set, differentiating various organs and tissue types.
From that we identify the most crucial parameters to measure or estimate,
and obtain a local uncertainty quantifcation for the ToD.
This thesis is devoted to the interdisciplinary work between mathematicians and forensic
experts: the modeling of the human body cooling process after death laying the
foundation for the estimation of the time of death. An inverse problem needs to be
solved. In this thesis the inverse problem computes the time of death given the measured
body temperature and the Forward Model that simulates the body cooling
process. The Forward Model is based on the heat equation established by Fourier.
This differential equation is numerically solved by the discretization over space by the
Finite Element Method and the discretization over time by the Implicit Euler Method.
The applications in this thesis demand a fast computation time. A model reduction is
achieved by the Proper Orthogonal Decomposition in combination with the Galerkin
Method. For reasons of simplification the computations and the measurements are
restricted to a cylindrical phantom that is made out of homogeneous polyethylene.
The estimate of the time of death is accompanied by an uncertainty. The inverse problem
is incorporated by Bayesian inference to interpret the quality of the estimate and
the effciency of the experiment. The uncertainty of the estimate of the time of death
is minimized by approaching the Optimal Design of the Experiment. An objective
function measures the certainty of the data and lays the foundation of the optimization
problem. Solving the optimization problem is successfully done by relaxing the
complex discrete NP-hard problem and applying a gradient-based method.
The results of this thesis clearly show that the design of an experiment has a great in-
uence on the outcome of the quality of the estimate. The comparison of the estimate
and its properties based on different designs and conditions reveals the effciency of
the Design of Experiment in the context of the estimation of the time of death.
Temperature based death time estimation is based either on simple phenomenological models of corpse cooling or on detailed physical heat transfer models. The latter are much more complex, but allow a higher accuracy of death time estimation as in principle all relevant cooling mechanisms can be taken into account. Here, a complete work flow for finite element based cooling simulation models is presented.
The following steps are demonstrated on CT-phantoms:
• CT-scan
• Segmentation of the CT images for thermodynamically relevant features of individual
geometries
• Conversion of the segmentation result into a Finite Element (FE) simulation model
• Computation of the model cooling curve
• Calculation of the cooling time
For the first time in FE-based cooling time estimation the steps from the CT image over segmentation to FE model generation are semi-automatically performed. The cooling time calculation results are compared to cooling measurements performed on the phantoms under controlled conditions. In this context, the method is validated using different CTphantoms. Some of the CT phantoms thermodynamic material parameters had to be experimentally determined via independent experiments. Moreover the impact of geometry and material parameter uncertainties on the estimated cooling time is investigated by a sensitivity analysis.