A Mathematical Model of Blood Loss during Renal Resection

Abstract

In 2021, approximately 51% of patients diagnosed with kidney tumors underwent surgical resections. One possible way to reduce complications from surgery is to minimise the associated blood loss, which, in the case of partial nephrectomy, is caused by the inadequate repair of branching arteries within the kidney cut during the tumor resection. The kidney vasculature is particularly complicated in nature, consisting of various interconnecting blood vessels and numerous bifurcation, trifurcation, tetrafurcation, and pentafurcation points. In this study, we present a mathematical lumped-parameter model of a whole kidney, assuming a non-Newtonian Carreau fluid, as a first approximation of estimating the blood loss arising from the cutting of single or multiple vessels. It shows that severing one or more blood vessels from the kidney vasculature results in a redistribution of the blood flow rates and pressures to the unaltered section of the kidney. The model can account for the change in the total impedance of the vascular network and considers a variety of multiple cuts. Calculating the blood loss for numerous combinations of arterial cuts allows us to identify the appropriate surgical protocols required to minimise blood loss during partial nephrectomy as well as enhance our understanding of perfusion and account for the possibility of cellular necrosis. This model may help renal surgeons during partial organ resection in assessing whether the remaining vascularisation is sufficient to support organ viability.

Computational Analysis of Blood Flow in Healthy Pulmonary Arteries in Comparison to Repaired Tetralogy of Fallot Results: A Small Cohort Study

“…The assumption of rigid walls is another limitation of this study, although previous studies that have investigated the effect of arterial wall compliance found no significant differences in the flow patterns [8,30,33,69,70]. Peripheral pulmonary vascular resistance [71] was also neglected but was compensated with the assignment of subject-specific flow splits at the models' outlets. Another limitation of this work was the inlet velocity, which only varied with time, while the spatial variability of the flow, induced by the movement of the valve, was not captured [72,73].…”