Determination of time-dependent skin temperature decrease rates in the case of abrupt changes of environmental temperature

Abstract

The present study deals with the development of a method for determining time-dependent temperature decrease rates and its application to postmortem surface cooling. The study concentrates on evaluating skin cooling behavior since data on skin cooling in the forensic literature are scarce. Furthermore, all heat transfer mechanisms strongly depend on the temperature gradient between body surface and environment. One of the main problems in modelling postmortem cooling processes is the dependence on the environmental temperature. All models for postmortem rectal cooling essentially presuppose a constant environmental temperature. In medico-legal practice, the temperature of the surrounding of a corpse mostly varies; therefore, an approach for extending the models to variable environmental temperatures is desirable. It consists in ‘localizing’ them to infinitesimal small intervals of time. An extended model differential equation is obtained and solved explicitly. The approach developed is applied to the single-exponential Newtonian model of surface cooling producing the following differential equation: T S ′(t)=−λ(t)(T S (t)−T E (t)) (with T S( t) the surface/skin temperature, T E( t) the environmental temperature, λ( t) the temperature decrease rate and T S′( t) the actual change of skin temperature or first-order derivative of T S). The differential equation directly provides an estimator: λ(t)=− T S ′(t) T S (t)−T E (t) for the time-dependent temperature decrease rate. The estimator is applied to two skin cooling experiments with different types of abrupt changes of environmental temperature, peak-like and step-like; the values of the time-dependent temperature decrease rate function were calculated. By reinserting them, the measured surface temperature curve could be accurately reconstructed, indicating that the extended model is well suited for describing surface cooling in the case of abrupt changes of environmental temperature.