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TECHNICAL PAPERS: Fluids/Heat/Transport

# Numerical Characterization of Diffusion-Based Extraction in Cell-Laden Flow Through a Microfluidic Channel

[+] Author and Article Information
K. K. Fleming

Department of Mechanical Engineering, University of Minnesota, 1100 Mechanical Engineering, 111 Church Street, Minneapolis, Minnesota 55455

E. K. Longmire

Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street SE, Minneapolis, Minnesota 55455

A. Hubel1

Department of Mechanical Engineering, University of Minnesota, 1100 Mechanical Engineering, 111 Church Street, Minneapolis, Minnesota 55455hubel001@umn.edu

1

Corresponding author.

J Biomech Eng 129(5), 703-711 (Dec 11, 2006) (9 pages) doi:10.1115/1.2768373 History: Received June 28, 2006; Revised December 11, 2006

## Abstract

Cells are routinely cryopreserved in dimethyl sulfoxide (DMSO), a cryoprotective agent, for medical applications. Infusion of a DMSO-laden cell suspension results in adverse patient reactions, but current DMSO extraction processes result in significant cell losses. A diffusion-based numerical model was employed to characterize DMSO extraction in fully developed channel flow containing a wash stream flowing parallel to a DMSO-laden cell suspension. DMSO was allowed to diffuse across cell membranes as well as across the channel depth. A variety of cases were considered with the ultimate goal of characterizing the optimal geometry and flow conditions to process clinical volumes of cell suspension in a reasonable time $(2–3ml∕min)$. The results were dependent on four dimensionless parameters: depth fraction of the DMSO-laden stream, Peclet number, cell volume fraction in the DMSO-laden stream, and cell membrane permeability parameter. Smaller depth fractions led to faster DMSO extraction but channel widths that were not practical. Higher Peclet numbers led to longer channels but smaller widths. For the Peclet values and channel depths considered $(⩾500μm)$ and appropriate permeability values, diffusion across cell membranes was significantly faster than diffusion across the channel depth. Cell volume fraction influenced the cross-stream diffusion of DMSO by limiting the fluid volume fraction available in the contaminant stream but did not play a significant role in channel geometry or operating requirements. The model was validated against preliminary experiments in which DMSO was extracted from suspensions of B-lymphoblast cells. The model results suggest that a channel device with practical dimensions can remove a sufficient level of contaminant within a mesoscale volume of cells in the required time.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic of the flow configuration. Two streams enter at left and flow in parallel toward the right as shown by the light arrows. The lower stream contains a DMSO-laden cell suspension. The upper stream is a wash solution that does not contain DMSO. Cross-stream molecular diffusion is shown by the dark arrow. Exploded view illustrates the diffusion of DMSO from the intracellular to the extracellular solution with the dark arrow.

Figure 7

(A) Normalized average extracellular concentration difference as a function of normalized streamwise location divided by Peclet in a DMSO-laden stream with cells. (B) Normalized average concentration for intracellular and extracellular compartments for Pe=625, Vi∕Vt=20%, B⋆=5, and fq(δ∕d)=0.10 (0.2).

Figure 2

Normalized concentration profiles at various streamwise locations (0⩽x∕d⩽100) for Pe=625(Re=0.5) and DMSO-laden stream volume fractions (δ∕d) of (A) 0.10 (0.2) and (B) 0.29 (0.36)

Figure 3

Normalized average concentration of contaminant stream versus normalized streamwise location for various volume fractions of DMSO-laden stream (fq=0.10–0.29). Pe=625(Re=0.5). Symbols on the right axis indicate equilibrium concentration for various DMSO-laden stream volume fractions: (∎) 0.29, (◆) 0.22, (▴) 0.17, and (●) 0.10. Stars ( ⋆) specify the TUL for a given fq.

Figure 4

(A) Normalized average concentration difference in the contaminant stream as a function of normalized streamwise location for varying Peclet numbers in a DMSO-laden stream without cells. (B) Normalized average concentration difference as a function of normalized streamwise location divided by Peclet number in a DMSO-laden stream without cells with Pe=625, B⋆=5, and fq(δ∕d)=0.10 (0.2).

Figure 5

Normalized concentration profiles for fq(δ∕d)=0.10 (0.2), Pe=625(Re=0.5), and Vi∕Vt=20% for (A) varying dimensionless permeability parameter B⋆ at x∕d=50 and (B) varying x∕d for B⋆=5.0

Figure 6

(A) Normalized intracellular concentration and (B) normalized extracellular concentration profiles for varying Vi∕Vt and streamwise location. fq(δ∕d)=0.10 (0.2), Pe=625, (Re=0.5), and B⋆=5.0. The normalized extracellular concentration for a DMSO-laden stream without cells is also included for comparison.

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