The Discrete Model for the System of the Myocardium and Coronary Vessels

Vitaliy B. Maksymenko, Valentina A. Danilova, Vladyslav V. Shlykov


Background. The numerical heat transfer model for a system of myocardium coronary vessels is considered.

Objective. The goal is to develop a discrete model for the physical system of myocardium and coronary vessels that would make it possible to explore the process of hypo- and hyperthermia with cardiopulmonary bypass.

Methods. To solve the differential equation of heat conduction in the MSC Sinda thermal system the network method (TNM – Thermal Network Method) is used, in which system of heat equations is presented in the form of cellular-centered nodes and resistances between the nodes using the finite difference method. In constructing the model of myocardial in the MSC Sinda system the thermal contact between three-dimensional bodies is implemented – the myocardium, coronary arteries, a liquid cooling of heart.

Results. Implementation of the model of heat exchange in the MSC Sinda system for infarction cooling process gives on the final process step in establishing the heat balance the temperature difference at the boundary between the myocardium and coronary vessels not more than 0,5 °C. However, in the areas of the myocardium that are removed from the coronary vessels the temperature difference exceeds 1,0 °C. The use of additional cooling for hearts allows for the cooling of myocardium with using of ice surface, that provides the unevenness reduction of the heart temperature during its cooling with cardiopulmonary bypass. This result allows exploring the dynamics of the process of hypo- and hyperthermia with cardiopulmonary bypass.

Conclusions. The discrete 3D-model of heat transfer in the layer structure of the myocardium and coronary vessels allows us to investigate the process of hypo- and hyperthermia with cardiopulmonary bypass. The simulation results also make it possible to perform the analysis of the temperature distribution on the surface of the myocardium provided free convection of heat between the layers. 


Thermogram; Myocardium; Temperature distribution; Vascular pathology

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J.H. Lienhard IV and J.H. Lienhard V, A Heat Transfer Textbook. Cambridge, UK: Phlogiston Press, 2016.

J.R. Howell et al., Thermal Radiation Heat Transfer. New York: CRC Press, Taylor & Francis Group, 2011.

P. Moin, Fundementals of Engineering Numerical Analysis. New York: Cambridge University Press, 2010.

A.K Oppenheim, “Radiation analysis by the network method”, Trans. ASME, pp. 54, 1954.

Astrium, SINDA User Manual, ver. 3.2, 2003.

I.U. Khudetsky et al., “Use of thermal imaging for control of the process hypothermia cardiac”, The Polish J. Appl. Sci., vol. 1, no. 3, pp. 93–96, 2015.

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