Implementation of bioheat equation in lumped-parameter blood circulation model

Abstract

Whole-body cooling and warming are routinely employed during cardiopulmonary bypass and critical care procedures. Likewise, artificial blood pumps can generate excessive heat, potentially damaging blood and peripheral organs. Accurate system-level prediction of transient organ temperatures is essential to improve these vital applications. First, steady-state thermal resistance models were developed to include metabolic heat generation, blood perfusion, perspiration, and radiation at the boundary skin surface. These models were examined under both resting and exercise conditions and later extended to transient scenarios. The results obtained from our model were compared with corresponding analytical solutions and numerical simulations. The maximum errors observed were 0.4 ℃ at rest and 1 ℃ during exercise. The transient analysis also yielded temperature changes consistent with predictions from analytical specific heat-based formulations over a 20-min time span. Finally, the thermal resistances were integrated into a six-compartment whole-body adult cardiovascular lumped parameter model, incorporating an exposed left arm. For the first time in literature, this enabled computation of transient organ temperature changes under realistic boundary conditions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.