Body mass and corrective factor: impact on temperature-based death time estimation

Model-based methods play an important role in temperature-based death time determination. The most prominent method uses Marshall and Hoare's double exponential model with Henssge's parameter determination. The formulae contain body mass as the only non-temperature parameter. Henssge's method is well established since it can be adapted to non-standard cooling situations varying the parameter body mass by multiplying it with the corrective factor. The present study investigates the influence of measurement errors of body mass m as well as of variations of the corrective factor c on the error of the Marshall and Hoare–Henssge death time estimator t _D. A formula for the relative error of t _D as a function of the relative error of m is derived. Simple approximations of order 1 and 0 nevertheless yield acceptable results validated by Monte Carlo simulations. They also provide the rule of thumb according to which the quotient of the standard deviations D(t _D) of the estimated death time and D(m) of the body mass is equal to the quotient of the estimated death time t _D and the body mass m (D(t _D)/D(m) ≈ t _D/m). Additionally, formulae and their approximations are derived to quantify the influence of Henssge's body mass corrective factor c on death time estimation. In a range of body masses between 50 and 150 kg, the relative variation of the body mass corrective factor is approximately equal to the relative variation of the death time (Δt _D = (t _D/c)Δc). This formula is applied and compared to computations and to experimental cooling data with good results.