Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel

Abstract

It is well known that certain pathological conditions result in a decrease of red blood cells (RBCs) deformability and subsequently can significantly alter the blood flow in microcirculation, which may block capillaries and cause ischemia in the tissues. Microfluidic systems able to obtain reliable quantitative measurements of RBC deformability hold the key to understand and diagnose RBC related diseases. In this work, a microfluidic system composed of a microchannel with a hyperbolic-shaped contraction followed by a sudden expansion is presented. We provide a detailed quantitative description of the degree of deformation of human RBCs under a controlled homogeneous extensional flow field. We measured the deformation index (DI) as well as the velocity of the RBCs travelling along the centerline of the channel for four different flow rates and analyze the impact of the particle Reynolds number. The results show that human RBC deformation tends to reach a plateau value in the region of constant extensional rate, the value of which depends on the extension rate. Additionally, we observe that the presence of a sudden expansion downstream of the hyperbolic contraction modifies the spatial distribution of cells and substantially increases the cell free layer (CFL) downstream of the expansion plane similarly to what is seen in other expansion flows. Beyond a certain value of flow rate, there is only a weak effect of inlet flow rates on the enhancement of the downstream CFL. These in vitro experiments show the potential of using microfluidic systems with hyperbolic-shaped microchannels both for the separation of the RBCs from plasma and to assess changes in RBC deformability in physiological and pathological situations for clinical purposes. However, the selection of the geometry and the identification of the most suitable region to evaluate the changes on the RBC deformability under extensional flows are crucial if microfluidics is to be used as an in vitro clinical methodology to detect circulatory diseases.

Figures

Figure 1

Schematics of the hyperbolic contraction geometry used in the experiments. The channel depth, d, was 60 μm and the width of the upstream and downstream channels were the same, W1 = 406 μm. The minimum width in the contraction region was W2 = 17 μm, defining a total Hencky strain of εH = ln(W1/W2) = 3.17.

Figure 2

Experimental set-up consisting of an inverted microscope (IX71, Olympus, Japan), a high speed camera (Phantom v7.1, Vision Research, USA), a syringe pump (KD Scientific Inc., USA), and a thermo plate controller (Tokai Hit, Japan).

Figure 3

Images analysis sequence: (a) original image in which moving cells as well as microchannel boundaries and other static objects are visible, (b) background image containing only static objects, (c) original image after background subtraction showing only moving objects, and (d) final binary image.

Figure 4

Definition of the deformation index where L1 and L2 are the major (primary) and minor (secondary) axis lengths of the ellipse best fitted to the cell, Udt is the traveling length of RBC that is calculated by the RBC velocity (U) times the exposure time of the high speed camera (dt).

Figure 5

(a) RBC trajectories manually tracked by MTrackJ plug-in from ImageJ. (b) Image obtained after post-processing using the minimum intensity level option in ImageJ, Zproject operation for the measurement of the cell free layer and relevant variables: WC1 and WC2 are the widths of RBC core upstream and downstream of the hyperbolic region, respectively. WL1A and WL1B are the widths of CFL upstream of the contraction region, and WL2A and WL2B are the widths of CFL downstream of the contraction region. Each image is a combination of three separate images covering different parts of the channel. The dashed lines indicate the boundaries between images.

Figure 6

(a) Axial velocity profiles of flowing RBCs along the centerline for four flow rates (Q = 0.11 ml/h, Q = 1.11 ml/h, Q = 2.27 ml/h and Q = 4.2 ml/h). The solid lines represent the fit used to determine the strain rate in the linear region, calculated from the slope dux/dx. (b) Normalized axial velocity profile ux/U1, where ux refers to an instantaneous cell velocity average, and U1 is the cross-section overall mean velocity based on the large channel, U1 = Q/(d W1). The dashed lines indicate the start (x/Lc = 0), middle (x/Lc = 0.5) and end (x/Lc = 1) of the contraction region.

Figure 7

Evaluation of the deformation of the flowing RBCs at the centerline of the hyperbolic microchannel. (a) Illustration of the 12 regions used to analyze the RBCs deformation index. (b) Average DI in the 12 regions at four different volumetric flow rates: Q = 0.11 ml/h, Q = 1.11 ml/h, Q = 2.27 ml/h and Q = 4.2 ml/h. The measured values are expressed as the mean± standard deviation according to a t-test analysis at a 95% confidence interval.

Figure 8

RBCs DI as a function of Rep at the centerline of the hyperbolic microchannel for different volumetric flow rates: Q = 0.11 ml/h, Q = 1.11 ml/h, Q = 2.27 ml/h and Q = 4.2 ml/h. The Rep was calculated by assuming the average diameter of a human RBC (DRBC) = 8 μm.

Figure 9

Cell free layer measurements. (a) Width of CFLs upstream and downstream as a function of the flow rate: Q = 0.11 ml/h, Q = 1.11 ml/h, Q = 2.27 ml/h, and Q = 4.2 ml/h. (b) Effect of the flow rate on the ratio of the core RBC widths downstream and upstream of the contraction.