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Modeling Filtration of Platelet-Rich Plasma in Fibrous Filters

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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.

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Abbreviations

a&b :

Major diagonals of platelet, μm

\({\bar{a}}\) :

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), m2s

E :

Bed porosity, fraction

F rep :

Repulsive surface forces, nN

F att :

Attractive surface forces, nN

\({{\bf J}_{0}^\infty }\) :

Asymptotic probability flux density, m−2s−1

H :

Half width of the domain at the widest part of a pore channel (Sect. 4.2), μm

k :

Boltzmann constant, \({1.3805 \times 10^{-23}\,{JK}^{-1}}\)JK−1

K*:

Macroscopic cell capture yield constant, t−1

l :

UBE length, μm

L :

Filter bed thickness, mm

M0 :

Moment of 0th order

\({P_0^\infty }\) :

Steady-state conditional probability density, fraction

r :

Radial 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

α :

Porosity-dependent coefficient in classical theory, dimensionless

θ :

Coordination angle around a fiber, degree

γ :

Perrin factor, dimensionless

η cell :

Cell capture yield (Eq. 34), fraction or %

η diff :

Fiber efficiency arising from diffusion in classical theory, %

η elec :

Fiber efficiency arising from electrostatic charges in classical theory, %

η iner :

Fiber efficiency arising from inertial impaction in classical theory, %

η inter :

Fiber efficiency arising from interception in classical theory, %

η tot :

Total fiber efficiency in classical filtration theory, %

κ :

Damping parameter in Eq. 8, m−2

μ :

Fluid viscosity, mPas

ψ :

Stream function, m2 s−1

\({\forall _0 }\) :

Superficial volume of a UBE, m3

\({\forall _g }\) :

Volume of fiber(s) in a UBE, m3

\({\forall _{\rm if}}\) :

Interstitial volume in a UBE, m3

\({\partial \forall _0 }\) :

Control surface of a UBE, m2

AFM:

Atomic force microscopy

CP2D:

Citrate phosphate double dextrose buffer

PRP:

Platelet-rich plasma

SEM:

Scanning electron microscope

UBE:

Unit bed element

vdW:

van der Waals forces

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Correspondence to Farzam Javadpour.

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Javadpour, F., Jeje, A. Modeling Filtration of Platelet-Rich Plasma in Fibrous Filters. Transp Porous Med 91, 677–696 (2012). https://doi.org/10.1007/s11242-011-9866-y

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