Design of microfluidic channels for magnetic separation of malaria-infected red blood cells

Abstract

This study is motivated by the development of a blood cell filtration device for removal of malaria-infected, parasitized red blood cells (pRBCs). The blood was modeled as a multi-component fluid using the computational fluid dynamics discrete element method (CFD-DEM), wherein plasma was treated as a Newtonian fluid and the red blood cells (RBCs) were modeled as soft-sphere solid particles which move under the influence of drag, collisions with other RBCs, and a magnetic force. The CFD-DEM model was first validated by a comparison with experimental data from Han and Frazier (Lab Chip 6:265–273, 2006) involving a microfluidic magnetophoretic separator for paramagnetic deoxygenated blood cells. The computational model was then applied to a parametric study of a parallel-plate separator having hematocrit of 40 % with 10 % of the RBCs as pRBCs. Specifically, we investigated the hypothesis of introducing an upstream constriction to the channel to divert the magnetic cells within the near-wall layer where the magnetic force is greatest. Simulations compared the efficacy of various geometries upon the stratification efficiency of the pRBCs. For a channel with nominal height of 100 µm, the addition of an upstream constriction of 80 % improved the proportion of pRBCs retained adjacent to the magnetic wall (separation efficiency) by almost twofold, from 26 to 49 %. Further addition of a downstream diffuser reduced remixing and hence improved separation efficiency to 72 %. The constriction introduced a greater pressure drop (from 17 to 495 Pa), which should be considered when scaling up this design for a clinical-sized system. Overall, the advantages of this design include its ability to accommodate physiological hematocrit and high throughput, which is critical for clinical implementation as a blood-filtration system.

Appendix: Symbol and explanation

Symbol	Explanation	Symbol	Explanation
ρ p	Density of plasma	$\varvec{\omega}$	Angular velocity
$\varvec{v}_{p}$	Velocity of plasma	$\tilde{\varvec{F}}_{contact}^{m,n}$	Tangential component of the contact force
ρ p0	Density of the plasma in the reference configuration	$\tilde{k}$	Tangential spring stiffness
ε	Volume fraction of plasma	$\tilde{\eta }$	Tangential damping coefficient
$\varvec{T}_{p}$	Constitutive equation of plasma	μ f	Friction coefficient
p	Pressure of the mixture	$\tilde{\varvec{v}}_{r}^{m,n}$	Relative tangential velocity
λ p	First coefficients of viscosity of the pure plasma	$\tilde{\delta }$	Tangential displacement
μ p	Second coefficients of viscosity of the pure plasma	$\varvec{t}^{m,n}$	Tangential unit vector
$\varvec{D}_{p}$	Symmetric part of the velocity gradient	$\hat{\delta }_{0}$	Tangential displacement in the previous time step
$\varvec{F}_{pr}$	Interaction forces	$\varvec{n}_{0}^{m.n}$	Normal direction in the previous time step
$\varvec{b}_{p}$	Body force	$\varvec{e}_{{z^{'} }}$	Unit vectors in the z
m r	Mass of a RBC	$\varvec{e}_{{y^{'} }}$	Unit vectors in the y
$\varvec{x}_{r}$	Instantial space position of RBCs	μ w	Magnetic permeability of the ferromagnetic wire
$\varvec{F}_{\text{contact}}$	Force of collision with other RBCs or boundaries	μ 0	Magnetic permeability of free space
$\varvec{F}_{pr}$	Interaction force with continuous phase	M s	Saturation magnetization field of the rectangular wire
$\varvec{F}_{ext}$	External force field	χ p	Magnetic susceptibility of the plasma
$\varvec{F}_{\text{contact}}^{m,n}$	The normal component of the contact force	χ rbc	Magnetic susceptibility of RBCs
$\hat{k}$	Normal “spring” stiffness	V rbc	Volume of the RBCs
$\hat{\eta }$	Normal damping coefficient	a	Nominal radius of the wire
δ	A (fictitious) overlap between two RBCs	H 0	The applied external magnetic field
R	Radius of a RBC	H c	Constriction height
$\varvec{n}$	Normal unit vector between two RBCs	L c	Constriction length
$\varvec{v}_{r}^{m,n}$	Relative velocity	L d	Diffuser length
$\hat{\varvec{v}}_{r}^{m,n}$	Normal relative velocity