Mathematical modeling of errors for determining time of death based on the Newton’s–Richman’s cooling law

Abstract

Abstract. A mandatory element of the development and implementation of diagnostic technologies for determining the time of death by the thermal method is the assessment of their possible errors. For equations of cadaver cooling that have a deterministic character, the estimation of errors is possible on the basis of a mathematical model of indirect measurement. In this article, a mathematical model is proposed for estimating the maximum absolute errors in determining the prescription of death on the basis of the Newtons - Richmans cooling law under conditions of constant and changing ambient temperature.
 Aim. To develop, on the basis of a mathematical model of indirect measurement, a method for estimating errors in determining the prescription of death on the basis of the Newtons - Richmans cooling law.
 Material and methods. Mathematical modeling of errors in determining the time of death in conditions of constant and changing ambient temperature is carried out on the basis of the Newtons - Richmans law. The computer program code is written in the C# programming language using the Microsoft Visual Studio 2019 application.
 Results. On the basis of the indirect measurement model, a method for estimating the maximum absolute errors in determining the time of death during cooling according to the Newtons - Richmans law under conditions of constant and changing ambient temperature is developed. The results obtained allow us to carry out an analytical determination of the errors in time the prescription of death in the early postmortem period.
 Conclusions. A mathematical model is developed for estimating the maximum absolute errors in determining the time of death on the basis of the Newtons - Richmans cooling law under conditions of constant and changing ambient temperature. The developed mathematical model is implemented in the format of the application program Warm Bodies NRN. The proposed method is advisable to use in forensic medical expert practice in determining the time of death.