Using a Human Circulation Mathematical Model to Simulate the Effects of Hemodialysis and Therapeutic Hypothermia

Abstract

AbstractBackgroundThe human blood circulation is an intricate process regulated by multiple biophysical factors. Our patients often suffer from renal disease and atrial fibrillation, and are given treatments such as therapeutic hypothermia, exercise, and hemodialysis. In this work, a hemodynamic mathematical model of human circulation coupled to a representative dialysis machine is developed and used to explore causal mechanisms of our recent clinical observations.MethodsAn ordinary differential equation model consisting of human whole body circulation, baroreflex control, and a hemodialysis machine was implemented. Experimentally informed parameter alterations were used to implement hemodialysis and therapeutic hypothermia. By means of parameter perturbation, four model populations encompassing baseline, dialysed, hypothermia treated, and simultaneous dialysed with hypothermia were generated. In model populations, multiple conditions including atrial fibrillation, exercise, and renal failure were simulated. The effects of all conditions on clinically relevant non-invasive measurables such as heart rate and blood pressure were quantified. A parameter sensitivity analysis was implemented to rank model output influencing parameters in the presented model.ResultsResults were interpreted as alterations of the respective populations mean values and standard deviations of the clinical measurables, both in relation to the baseline population. A clinical measurable’s smaller standard deviation (in comparison to baseline population) was interpreted as a stronger association between a given clinical measure and the corresponding underlying process, which may permit the use of deducing one by observation of the other.The modelled dialysis was observed to increase systolic blood pressure, vessel shear, and heart rate. Therapeutic hypothermia was observed to reduce blood pressure as well as the intra-population standard deviation (heterogeneity) of blood flow in the large (aorta) and small (kidney) vasculature. Therapeutic hypothermia reduced shear in vessels, suggesting a potential benefit with respect to endothelial dysfunction and maintenance of microcirculatory blood flow. The action of therapeutic hypothermia under conditions such as atrial fibrillation, exercise, and renal failure was to reduce total blood flow, which was applicable in all simulated populations. Therapeutic hypothermia did not affect the dialysis function, but exercise improved the efficacy of dialysis by facilitating water removal.ConclusionsThis study illuminates some mechanisms of action for therapeutic hypothermia. It also suggests clinical measurables that may be used as surrogates to diagnose underlying diseases such as atrial fibrillation.