Background: Atrial fibrillation is a prevalent cardiac arrhythmia and may reduce cerebral blood perfusion augmenting the risk of dementia. We hypothesize that geometric variations in the cerebral arterial structure called the Circle of Willis (CoW) play an important role in influencing cerebral perfusion. The objective of this work was to develop a novel cardio-cerebral lumped parameter hemodynamic model to investigate the role of CoW variants on cerebral blood flow dynamics under atrial fibrillation conditions. Methods: A computational blood flow model was developed by coupling whole-body and detailed cerebral circulation descriptions, modified to represent six common variations of the CoW. Cerebral blood flow dynamics were simulated in common CoW variants, under control and imposed atrial fibrillation conditions. Risk was assessed based on the frequency of beat-wise hypoperfusion events, and sensitivity analysis was performed with respect to this model output. Results: It was found that the geometry of the CoW influenced the frequency of hypoperfusion events at different heart rates, with the variant missing a P1 segment having the highest risk. Sensitivity analysis revealed that intrinsic heart rate is most associated with the considered outcome. Conclusions: Our results suggest that CoW geometry plays an important role in influencing cerebral hemodynamics during atrial fibrillation. The presented study may assist in guiding our future clinical-imaging research.

Background: We developed a hemodynamic mathematical model of human circulation coupled to a virtual hemodialyzer. The model was used to explore mechanisms underlying our clinical observations involving hemodialysis. Methods: The model consists of whole body human circulation, baroreflex feedback control, and a hemodialyzer. Four model populations encompassing baseline, dialysed, therapeutic hypothermia treated, and simultaneous dialysed with hypothermia were generated. In all populations atrial fibrillation and renal failure as co-morbidities, and exercise as a treatment were simulated. Clinically relevant measurables were used to quantify the effects of each in silico experiment. Sensitivity analysis was used to uncover the most relevant parameters. Results: Relative to baseline, the modelled dialysis increased the population mean diastolic blood pressure by 5%, large vessel wall shear stress by 6%, and heart rate by 20%. Therapeutic hypothermia increased systolic blood pressure by 3%, reduced large vessel shear stress by 15%, and did not affect heart rate. Therapeutic hypothermia reduced wall shear stress by 15% in the aorta and 6% in the kidneys, suggesting a potential anti-inflammatory benefit. Therapeutic hypothermia reduced cardiac output under atrial fibrillation by 12% and under renal failure by 20%. Therapeutic hypothermia and exercise did not affect dialyser function, but increased water removal by approximately 40%. Conclusions: This study illuminates some mechanisms of the action of therapeutic hypothermia. It also suggests clinical measurables that may be used as surrogates to diagnose underlying diseases such as atrial fibrillation.

Background The 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. Methods An 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. Results Results 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. Conclusions This 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.

Atrial fibrillation is a prevalent cardiac arrhythmia, and may reduce cerebral blood perfusion augmenting the risk of dementia. It is thought that cer- ebral arterial geometry variants play an important role in cerebral perfusion. This computational work investigated the role of geometric variants on cerebral blood flow in the presence of cardiac atrial fibrillation.A model consisting of a detailed cerebral and whole-body circulation, along with baroreflex control mechanism was developed. Cerebral perfusion based on vasculature geometry variations, represented by Circle of Willis variants, was simulated in the presence of atrial fibrillation conditions. Perfusion and its heter- ogeneity were quantified using segment-wise hypoperfusion events and mean perfusion at terminals.It was found that cerebral perfusion and the rate of hypoperfusion events strongly depends geometry variation as well as atrial fibrillation induced stochas- tic heart rates. The hypoperfusion events were specific to particular arteries in each variant. Our results, based on biophysical principles, suggest that cerebral vascular geometries modulate the impact of atrial fibrillation in cerebral perfu- sion. Further, our findings suggest potential clinical assessment sites.