|Qin (Maggie) Qi |
B.S., Chemical Engineering,
B.S., Operations Research,
Cornell University, 2013
Email: qinq @ stanford . edu
Coarse-grained theory to predict red blood cell concentration distribution in pressure-driven flow at zero Reynolds number
There exists clinical evidence that hematocrit (red blood cell concentration) greatly influences a personís bleeding time, which is important in the army as trauma is the leading cause of mortality of soldiers in combat. Therefore, it is worth investigating the concentration distribution of red blood cells (RBC) across the blood stream as well as platelet-cell interactions. Inspired by a coarse-grained theory by Vivek Narsimhan to predict RBC concentration distribution in wall-bounded Couette flow, this project aims to predict RBC concentration in pressure-driven flow, which resembles the flow condition inside blood vessels. Also, the theoretical method saves time and computational power as compared to the existing large-scale simulations.
Fig 1: RBC radial distribution profile. With capillary number = 1 and Hematrocrit = 20%, one can see that simulations and theory predict a peak in concentration profile at channel center as well as a boundary cell-free layer, albeit of different sizes.
Master equation of the new theory balances the flux from red blood cell lift with that from binary collisions. Small-scale simulations have been done to obtain cell lift velocities and post-collisional displacements, which are inputs for the master equation. Nonlocal corrections have been done to solve the singularity problem at the centerline of the channel. RBC concentration profile have been calculated from the master equation and is shown below. As compared with large-scale simulation, current theory is able to capture the peak concentration at the center (see Fig. 1.). However, the size of the cell-free layer at the boundary is larger than that from simulation, which is possibly caused by errors in interpolating collision data. Finding a more accurate way of analyzing collisional data would be the next step.