RESUMEN
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.
RESUMEN
The temperature-oriented death time determination is based on mathematical model curves of postmortem rectal cooling. All mathematical models require knowledge of the environmental conditions. In medico-legal practice homicide is sometimes not immediately suspected at the death scene but afterwards during external examination of the body. The environmental temperature at the death scene remains unknown or can only be roughly reconstructed. In such cases the question arises whether it is possible to estimate the time since death from rectal temperature data alone recorded over a longer time span. The present study theoretically deduces formulae which are independent of the initial and environmental temperatures and thus proves that the information needed for death time estimation is contained in the rectal temperature data. Since the environmental temperature at the death scene may differ from that during the temperature recording, an additional factor has to be used. This is that the body core is thermally well isolated from the environment and that the rectal temperature decrease after a sudden change of environmental temperature will continue for some time at a rate similar to that before the sudden change. The present study further provides a curve-fitting procedure for such scenarios. The procedure was tested in rectal cooling data of from 35 corpses using the most commonly applied model of Henssge. In all cases the time of death was exactly known. After admission to the medico-legal institute the bodies were kept at a constant environmental temperature for 12-36 h and the rectal temperatures were recorded continuously. The curve-fitting procedure led to valid estimates of the time since death in all experiments despite the unknown environmental conditions before admission to the institute. The estimation bias was investigated statistically. The 95% confidence intervals amounted to +/-4 h, which seems reasonable compared to the 95% confidence intervals of the Henssge model with known environmental temperature. The presented method may be of use for determining the time since death even in cases in which the environmental temperature and rectal temperature at the death scene have unintentionally not been recorded.