Science and Innovations in MedicineScience and Innovations in Medicine2500-13882618-754XFSBEI of Higher Education SamSMU of Ministry of Health of the Russian Federation11074810.35693/2500-1388-2022-7-3-179-185Research ArticleEstimation of the postmortem interval by the method of finite element modeling of postmortem heat transfer in human headNedugovGerman V.<p>PhD, Associate professor of the Department of forensic medicine</p>nedugovh@mail.ruhttps://orcid.org/0000-0002-7380-3766Samara State Medical University04092022731791850309202203092022Copyright © 2022, Nedugov G.V.2022<p><strong>Aim</strong> to develop a two-dimensional finite element model (FEM) of postmortem heat transfer in head to determine the postmortem interval (PMI).</p>
<p><strong>Material and methods.</strong> The finite element modeling of the geometry and postmortem heat transfer in an adult's head was carried out using the ELCUT 6.5 Student application. A hemisphere with a radius of 98 mm was used as a geometric model of the cerebral part of the head, consisting of evenly distributed homogeneous layers: the scalp, the bones, the cerebrospinal fluid of the subarachnoid space and the brain. For FEM validation we used the evaluation of the cooling curves convergence obtained by FEM and by the Marshall Hoare and Newton Richman cooling laws under conditions of constant and linearly varying ambient temperature.</p>
<p><strong>Results. </strong>A scalable two-dimensional FEM for finding the postmortem temperature field of the head was developed. The model allows for accounting any changes in the ambient temperature, combined heat exchange conditions and the dependence of thermophysical parameters of biological tissues on the ambient temperature. The FEM check-out under standard cooling conditions showed the maximum convergence of the results of finding the postmortem temperature field with the results of valid phenomenological mathematical models when only convective heat exchange with a heat transfer coefficient equal to 6 W/(м<sup>2</sup>К) was set on the outer edge. The developed FEM is characterized by the stability of the results of determining the prescription of death coming to deviations of the initial temperature field of the calculated region from its physiological level.</p>
<p><strong>Conclusion.</strong> It is advisable to use the proposed FEM in the forensic medical expert practice when determining the prescription of death coming.</p>corpse coolingpostmortem intervalmathematical modelingfinite element methodохлаждение трупадавность наступления смертиматематическое моделированиеметод конечных элементов[Potente S, Henneicke L, Schmidt P. Prism - A novel approach to dead body cooling and its parameters. Forensic Sci Int. 2021;325:110870. doi: 10.1016/j.forsciint.2021.110870][Laplace K, Baccino E, Peyron PA. Estimation of the time since death based on body cooling: a comparative study of four temperature-based methods. Int J Legal Med. 2021;135(6):2479-87. doi: 10.1007/s00414-021-02635-7][Nedugov GV. Mathematical modeling of the corpse cooling. Kazan, 2021. (In Russ.). [Недугов Г.В. Математическое моделирование охлаждения трупа. Казань, 2021]. ISBN 978-5-00118-790-5][Smart JL. Estimation of time of death with a fourier series unsteady-state heat transfer model. J Forensic Sci. 2010;55(6):1481-7. doi: 10.1111/j.1556-4029.2010.01467.x][Igari Y, Hosokai Y, Funayama M. Rectal temperature-based death time estimation in infants. Leg Med (Tokyo). 2016;19:35-42. doi: 10.1016/j.legalmed.2016.02.002][Mall G, Eisenmenger W. Estimation of time since death by heat-flow Finite-Element model. Part I: method, model, calibration and validation. Leg Med (Tokyo). 2005;7(1):1-14. doi: 10.1016/j.legalmed.2004.06.006][Mall G, Eisenmenger W. Estimation of time since death by heat-flow Finite-Element model part II: application to non-standard cooling conditions and preliminary results in practical casework. Leg Med (Tokyo). 2005;7(2):69-80. doi: 10.1016/j.legalmed.2004.06.007][Wilk LS, Hoveling RJM, Edelman GJ, et al. Reconstructing the time since death using noninvasive thermometry and numerical analysis. Sci Adv. 2020;6(22):eaba4243. doi: 10.1126/sciadv.aba4243][Weiser M, Erdmann B, Schenkl S, et al. Uncertainty in temperature-based determination of time of death. Heat Mass Transfer. 2018;54:2815-26. doi: 10.1007/s00231-018-2324-4][Smart JL. Use of postmortem temperature decay response surface plots of heat transport in the human eye to predict time of death. J Forensic Sci. 2014;59(2):390-8. doi: 10.1111/1556-4029.12333][Nelson DA, Nunneley SA. Brain temperature and limits on transcranial cooling in humans: quantitative modeling results. Eur J Appl Physiol Occup Physiol. 1998;78(4):353-9. doi: 10.1007/s004210050431][Zhu L, Diao C. Theoretical simulation of temperature distribution in the brain during mild hypothermia treatment for brain injury. Med Biol Eng Comput. 2001;39(6):681-7. doi: 10.1007/BF02345442][Schenkl S, Muggenthaler H, Hubig M, et al. Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis. Int J Legal Med. 2017;131(3):699-712. doi: 10.1007/s00414-016-1523-0][Muggenthaler H, Hubig M, Schenkl S, Mall G. Influence of hypo- and hyperthermia on death time estimation - A simulation study. Leg Med (Tokyo). 2017;28:10-14. doi: 10.1016/j.legalmed.2017.06.005][Mall G, Hubig M, Beier G, et al. Supravital energy production in early post-mortem phase - estimate based on heat loss due to radiation and natural convection. Leg Med (Tokyo). 2002;4(2):71-8. doi: 10.1016/ s1344-6223(02)00005-6][Mall G, Hubig M, Beier G, Eisenmenger W. Energy loss due to radiation in postmortem cooling. Part A: quantitative estimation of radiation using the Stefan-Boltzmann law. Int J Legal Med. 1998;111(6):299-304. doi: 10.1007/ s004140050175]