A thermographic study of surface cooling of cadavers

Modelling postmortem surface cooling in continuously changing environmental temperature

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.

Supravital energy production in early post-mortem phase - estimate based on heat loss due to radiation and natural convection

The temperature-based determination of the time since death in the early post-mortem (pm) period plays an important role in medico-legal practice. In contrast to the common opinion according to which convection and conduction are mainly responsible for post-mortem heat loss, a considerable part of energy is emitted by thermal radiation. The present paper concentrates on the heat loss due to radiation and natural convection. Since both heat transfer mechanisms depend on the temperature gradient between skin and environment, the skin temperature was measured in corpses of different constitution (lean, medium and obese) and its decrease fitted by a single-exponential model. Heat loss due to radiation was calculated according to the non-linearized form of the law of Stefan and Boltzmann, heat loss due to natural convection according to the semi-empirical thermodynamic laws; the shape of the body in supine position was approximated to a semi-cylinder of finite length. The power due to radiation ranged between 386kJ/h (lean) and 550kJ/h (obese), that due to natural convection between 307kJ/h (lean) and 429kJ/h (obese) initially. Cumulative energy loss amounted to 2167kJ (lean) and 4239kJ (obese) by radiation and 1485kJ (lean) and 2922kJ (obese) by natural convection up to 20h pm. The energy loss due to radiation plus natural convection initially exceeded the energy loss due the decrease of the energy content of the body (mass x heat capacity x temperature decrease). This surplus can be explained only by exothermal processes in the phase of intermediary life and directly provides lower bounds for supravital energy production. Cumulative supravital energy ranges between 1139kJ up to 5h pm in the lean and 2516kJ up to 10h pm in the obese corpses. The courses of supravital energies and powers are presented as functions of time. Under standard conditions like still air (no forced convection) and insulating ground (little conductive heat transfer), the lower bounds represent estimates for total supravital energy production.

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

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.