Modeling Filtration of Platelet-Rich Plasma in Fibrous Filters

Removing leukocytes (white cells) from blood products such as platelet-rich plasma (PRP) prevents serious problems for the PRP recipients. We present a model to study selective separation of leukocytes from a dilute suspension of leukocytes and platelets (PRP) using fibrous filters. A selective PRP filter permits platelets to pass but bars the way for leukocytes. In PRP filters, fine synthetic fibers are packed randomly and interstices are larger than cells. Interactive forces between the suspended cells and fibers determine cell capture yield, i.e., deep-bed filtration process. Our model is based on a hierarchical set of differential equations corresponding to porescale and macroscale. At the porescale, we model movement and interaction of cells with fibers. A single cell entering the interstitial space encounters drag and surface forces. We define a unit bed element (UBE) composed of a fiber and interstitial space, where fiber diameter corrected for the size of the cells. We add measured surface forces between cells and fibers (electrostatic, van der Waals, fluid expression resistance, and biological responses) to the cell velocity equation. We then transform pore scale events into macroscale continuum by imposing periodic boundary conditions for contiguous UBEs and applying macrotransport theory. At macroscale, two independent coefficients: mean cell velocity vector U* and mean cell capture yield constant K*characterize cell filtration efficiency. Our model showed reasonable match with experimental data. Model results showed that diameter of fibers, injection velocity, bed porosity, and bed thickness control selective capture of leukocytes. Our model showed that it is merely impossible to filter out all leukocytes without capturing platelets. Based on our model, an optimized filter can capture 90% of leukocytes and pass through 45% of platelets.