(H-284) Computational Modeling of Glomerular Capillary Flow Behavior with an Emphasis on Red Blood Cell Flow to Test the Hypothesis of Capillary Recruitment in Relaxin Administration.

To construct a mathematical model of glomerular capillary flow, we began with a simple model of a single capillary bifurcating into 2 daughter branches of the same diameter. A RBF of 1 L/min distributed across 2 million nephrons was used to determine parent vessel flow rate, with hematocrit of 40%. Resistances, flow rates, velocities, and hematocrit were calculated for each branch using known physical properties of glomerular capillaries (e.g. typical diameters, lengths), principles of flow networks, and previously established relationships between hematocrit and viscosity. We determined mean flow velocity for each branch using blood flow rates, and calculated red blood cell (RBC) velocity using the cell-to-capillary tube diameter ratio together with mean flow velocity. RBC velocity was shown to be faster than mean flow.

Viscosity depends on hematocrit, but hematocrit in each branch depends on relative branch resistances, which depend on viscosity,  posing a challenge when solving equations for the daughter branches. We addressed this by first using blood viscosity at normal hematocrit  to calculate daughter branch branch resistance and hematocrit, and then iteratively using the calculated hematocrit to recalculate viscosity, resistance, and new hematocrit until a stable solution was obtained. The viscosity calculated using hematocrit was much higher than the assumed plasma viscosity, thus validating the significance of their interdependency.

Our initial analysis demonstrates that for glomerular capillary branches with similar diameters but different lengths, both RBC and mean blood flow rate will be much lower in the longer branches than in the shorter branches (Figure 1). These findings support the possibility that longer capillary branches could be underperfused at normal RBCs, but further work is needed to represent more realistic glomerular capillary networks and to more fully account for rheological and hemodynamic factors affecting flow and filtration (e.g. the role of fluid loss due to filtration and the role of hemodynamic pressure differences around RBCs has not been accounted for), and to evaluate how these factors change when RBF increases. 

We also found that RBC effects on blood viscosity and flow are not negligible and thus must be considered when modeling blood flow through the glomerulus. Once further explored, this relationship between hematocrit and viscosity can allow for the consideration of RBC presence in the filtration and flow through the glomerulus, thus introducing a new factor into the GFR equation which could serve to explain how GFR could remain constant following an increase in plasma flow and decrease in glomerular pressure. 

Currently, the model is only developed to represent RBC behavior at capillary bifurcations into two daughter tubes of the same diameter, which limits its credibility. However, the hematocrit-viscosity linear relationship we found is consistent with previous studies of blood flow in microvascular networks (e.g. Pries et al., 1990). RBC flow has not been deeply investigated in the context of glomerular flow, so this research may introduce a new perspective to renal physiological phenomena. Additionally, this model may help explain how RBF changes with relaxin impact glomerular hemodynamics and filtration, which could be beneficial in treating kidney diseases and in understanding kidney disorders in pregnancy such as preeclampsia.