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) a parts per thousand 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 (Delta t (D) = (t (D)/c)Delta c). This formula is applied and compared to computations and to experimental cooling data with good results.