Multi-physics analysis of calcium dynamics of vascular endothelial cell response to the blood flow

Abstract

Vascular endothelial cell (VEC) responds to wall shear stress that has not only spatial variation, but also temporal gradient. Using a multi-physics mathematical model, the interaction between the intracellular calcium dynamics of VEC and the shear stress modulated by the vascular blood flow is simulated. A computational fluid dynamics (CFD) method was used to compute the shear stress distribution in a human artery and combined with the mathematical model of a VEC for physiological response. To simplify the problem, I first studied how the VEC responded to the steady wall shear stress of varying magnitude in a stenosed artery. I then studied how the VEC responded to the periodic shear stress that had temporal variation, as in the pulsatile blood flow. The CFD results showed that for the steady stenotic flow, the VECs showed spatially different responses to the disturbed flow due to stenosis. The wall shear stress in the recirculating flow was lower than the threshold value, 4 $dyne/cm^2$, at two particular points: flow separation and flow reattachment. For these subthreshold shear stresses, the peak value of the transient calcium response did not hit the normal saturated level, but reached a reduced magnitude. We investigated the effect of severity of stenosis (SOS) of the stenosed artery. For the pulsatile flow, the so-called shear stress slew rate or the temporal gradient of the first upsurge of the periodic flow was an important factor for the VEC response. The calcium response and hyperpolarization of membrane potential had a finite range of parameter for SOS and shear stress slew rate in which the calcium response was more sensitive than elsewhere, showing a sigmoid pattern. These multi-physics and mathematical approach is fresh and useful tool for the biomedical researchers.