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

Background: A mandatory factor in the development and implementation of diagnostic technologies for determining the time of death by the thermal method is the assessment of possible errors. For equations of cadaver cooling that have a deterministic character, error estimation is possible using a mathematical model of indirect measurement. Here, a mathematical model has been proposed for estimating the maximum absolute error in determining death on the basis of the Newton's–Richman's cooling law under conditions of constant and changing ambient temperature. Aim: Using a mathematical model of indirect measurement, this study developed a method for estimating errors in determining the prescription of death according to the Newton's–Richman's cooling law. Material and methods: Mathematical modeling of errors in determining the time of death in conditions of constant and changing ambient temperature was conducted according to the Newton's–Richman's law. The computer program code was drafted in the C# programming language using the Microsoft Visual Studio 2019 application. Results: Based on the indirect measurement model, a method for estimating the maximum absolute errors for determining the time of death during cooling according to the Newton's–Richman's law under conditions of constant and changing ambient temperature was developed. The results obtained allowed us to analytically determine errors in time the prescription of death in the early postmortem period. Conclusions: We developed a mathematical model for estimating maximum absolute errors while determining the time of death according to the Newton's–Richman's cooling law under conditions of constant and changing ambient temperature. The developed mathematical model was implemented as an application program Warm Bodies NRN. The proposed method might be used in forensic medical expert practice for determining the time of death.