Mathematical and mechanical modeling of heat transport through the heart

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Abstract
Pulmonary artery blood temperature manifests large variations which obscure the measurement of cardiac parameters by thermodilution techniques. We have created three mathematical models of heat flow through the heart in order to better understand the origins of the temperature fluctuations in the pulmonary artery. These lumped parameter models are based on a serial connection of two mixing chambers, which correspond to the atrium and ventricle of the heart. We have used the models to predict temperature fluctuations in the outlet, based on measurements of inlet flow, inlet temperature, and the timing of the cardiac cycle, of a mechanical right artificial heart in a mock circulatory loop. The most complex model accurately predicts the outflow temperature from the input variables and provides a quantitative description of heat transport across the heart under many operating conditions. The simplified models illustrate the conditions under which is possible to predict the outflow temperature from the inflow temperatures alone.