Modelling postmortem surface cooling in continuously changing environmental temperature.

Abstract

Heat loss depends on the temperature gradient between body surface and environment. Skin cooling data in the forensic literature are scarce and models for skin cooling have not been developed. The dependence on the environmental temperature is a general problem in modelling postmortem cooling processes; most models of rectal cooling are therefore restricted to constant ambient temperatures. Since surface in contrast to core temperatures are highly sensitive to changes of ambient temperature, a model for skin cooling has to take into account such changes. The present study provides an estimator for the time-dependent function of the temperature decrease of the skin and presents a model of the cooling process. The formulae are developed on the basis of skin cooling data of the exposed skin of the forehead in a 40-year-old female (163 cm, 62.1 kg). The single exponential Newtonian model for the surface temperature T(S) valid for constant environmental temperature T(E):T(S)(t)=(T(S)(0)-T(E))e(-lambda(t))+T(E) is localized to small time intervals. By Taylor series expansions a differential equation directly providing an estimator for the temperature decrease rate lambda is derived. The solution of this differential equation represents the extended Newtonian model valid for non-constant environmental temperatures and non-constant temperature decrease rates. The extended model is tested successfully by reinserting the estimated values for the temperature decrease rate: the reconstructed and the measured skin temperature decrease curves completely overlap each other. The temperature decrease rate is a function of the difference between skin and environmental temperature and of the actual change of the skin temperature. A scatter plot of this function shows a structured cloud of points lying in one plane. The temperature decrease rate can thus be parametrized by a simple affine equation with three coefficients determined by linear regression. Inserting the affine equation in the extended Newtonian model leads to an inhomogeneous, non-linear differential equation which is solved by recursion. With knowledge of the initial temperature and the course of the environmental temperature the decrease of the skin temperature can be predicted with very good results. The model is validated with good results in 12 further experimental skin cooling curves of ten different individuals.