Modeling Filtration of Platelet-Rich Plasma in Fibrous Filters

Abstract

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. Nomenclature a&b Major diagonals of platelet, μm a The radius of a sphere with a volume equivalent to a platelet, μm a Cell radius, μm A A-function (Eq. 26) C Cell concentration, fraction D Fiber diameter, μm D m Diffusion coefficient of particle (cell), m 2 s E Bed porosity, fraction F rep Repulsive surface forces, nN F att Attractive surface forces, nN J ∞ 0 Asymptotic probability flux density, m −2 s −1 H Half width of the domain at the widest part of a pore channel (Sect. 4.2), μm k Boltzmann constant, 1.3805 × 10 −23 JK −1 K* Macroscopic cell capture yield constant, t −1 l UBE length, μm L Filter bed thickness, mm M 0 Moment of 0th order P ∞ 0 Steady-state conditional probability density, fraction rRadial distance from the center of a fiber (Fig. 7a) or narrowest part of a pore channel (Sect. 4.2), μm r Radial vector inside a UBE, μm R Fiber radius, μm R Macroscopic position vector, μm t Time, s T Temperature, K T Torque, Nm U Interfacial fluid velocity, ms −1 U* Macroscopic average cell velocity, ms −1 Greek symbols α Porosity-dependent coefficient in classical theory, dimensionless θ Coordination angle around a fiber, degree γ Perrin factor, dimensionless η cell...

The Effect of the Layered Internal Structure of Fibrous Beds on the Hydrodynamic Diffusive Behavior of Microparticles

“…J ( r ), R ( r ), and K ( r ) are expressed as follows: The value r represents r = x − x β , where x β is the center of particle β . Because the particle volume fraction is small, we used the F version of the SD method, in which only the translational motion of particles is considered [ 4 , 22 ]. From Faxèn’s law and Equation (1), in which the high-order terms are omitted because of the F version, the relationship between the relative velocity between the particles and the fluid, U − u ∞ , and the hydrodynamic force F exerted by each particle on the fluid is expressed as follows [ 23 ]: M is called the mobility matrix (or the Rotne−Prager tensor, particularly for the F version), which is determined by the positional relationship and size of all particles.…”

“…The representative amount of non-dimensionalization was determined based on platelet permeation in the PRP filter. Fluid viscosity μ = 1.0 mPa∙s, representative length (fiber radius) a = 1.5 μm, and representative velocity U = 300 μm/s [ 4 ] were used. In this study, where the fiber and microparticle volume fraction was loose, the particles did not get too close to each other.…”

“…Another example of cell separation using fibrous filters is the platelet-rich plasma (PRP) filter, which separates white blood cells from platelets in the blood to prepare a PRP solution [ 4 ]. Platelets have a healing function that repairs damaged tissues and are used to treat injuries.…”

“…However, a certain number of platelets are removed along with the white blood cells. In previous studies, the most optimized conditions that facilitate the collection of white blood cells and minimize the number of platelets removed have been discussed by examining the effects of fiber volume fraction, fiber diameter, fibrous filter thickness, and flow rate for injecting cells [ 4 ].…”

Multiscale Experimental Study of Selective Blood-Cell Filtration in Fibrous Porous Media

“…In PRP filtration, cell size is comparable in size to that of fibers; therefore, classical filtration theory (Tien 1989) may not be applicable. Macrotransport theory (Javadpour 2009;Brenner and Edwards 1993) is an elegant theory that relates pore-scale events to macroscopic cellcapture yield (Javadpour and Jeje 2011;Javadpour 2006). Using a verified model, we can study the effects of fiber size and orientations, along with bed porosity and thickness, for complete optimization.…”