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)=-lambda(t)(T(S)(t)-T(E)(t))(with T(S)(t) the surface/skin temperature, T(E)(t) the environmental temperature, lambda(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:lambda(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.

The present paper aims at analysing the significance of the anatomical structures of the human skull base for mechanical modelling. Three different Finite-Element (FE)-models of the human neurocranium were developed. The most complex model (1242 solid cuboid elements) contains holes and spaces functionally simulating the foramina and fissures and additional element layers for the inner relief of the skull base (petrous temporal and sella). Of the less complex models, one (1256 solid cuboid elements) includes only the 3 cranial fossae, while the other (400 solid cuboid elements) represents a rotationally symmetrical ellipsoid with a hole for the foramen magnum. Two linear static loadcases, one with a transverse loading direction (pressure of 250 kg on the left temporal surface, bearing on the right temporal surface) and the other with a sagittal loading direction (pressure of 250 kg on the frontal surface, bearing on the occipital surface) were computed. The loadcase analyses show, qualitatively and quantitatively, similar equivalent von Mises stress values and distributions in the two more complex models while the elementary geometric model leads to significantly different absolute stress values and distributions. The results of the most complex model are highly compatible with experimental observations on transverse and sagittal fractures of the skull base.

With the help of the law of Stefan and Boltzmann and a model for the cooling of exposed skin derived from the data of Lyle and Cleveland [7], the radiation energy loss ER can be calculated according to the following formula:\(\)

With the help of the law of Stefan and Boltzmann and a model for the cooling of exposed skin derived from the data of Lyle and Cleveland [7], the radiation energy loss E-R can be calculated according to the following formula.E-R(t) = epsilon sigma A(R) (0)integral(t) ([(T-S(0) - T-E) e(-z't) + T-E] - T-E(4)) d t'where epsilon represents the emissivity of the skin (0.98), a the Stefan-Boltzmann constant, A(R) the radiating surface area, T-S(0) the skin temperature at death, T-E the environmental temperature and Z' = 0.1017 the gradient of the skin temperature curve.Additionally, an energy loss due to conduction and convection E-C has to be taken into account. Comparing the energy losses due to radiation, conduction and convection with the decrease E-T of the thermal energy in the body, calculated from mean heat capacity (3.45 kJ/(kg degrees K)), body mass and decrease of mean body temperature, there is a surplus of energy in the very early postmortem period, which can be explained only by an internal source of energy E-I. Alltogether the following balance equation can be formulated:E-T+ E-I = E-R + E-CSince the body temperature decreases in the early postmortem period, E-I can be estimated by: E-I(t) greater than or equal to max (E-R(t) - E-T(t), 0). The values obtained range up to 500 kJ for a medium sized (175 cm), medium weight (75 kg) body at an environmental temperature of 5 degrees C and are compatible with estimations of Lundquist [6] for supravital energy production by breakdown of glycogen.