Statistical dynamics of flowing red blood cells by morphological image processing

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Original Entry by Michelle Borkin, AP225 Fall 2009


"Statistical dynamics of flowing red blood cells by morphological image processing."

J. Higgins, D. Eddington, S. Bhatia and L. Mahadevan. PLoS Computational Biology, 5, e1000288, 2009.


Fig. 1 Schematic of the experimental set-up.

This paper investigates the complex random motions of individual red blood cells to better understand the role of individual cell movements in nutrient transport, gas transport, clotting, and hematological diseases. With this microscopic view, versus studying just the bulk flow, they were able to see the importance of these random motions. For example, patients with sickle cell disease who have irregularly shaped cells, have decreased random cellular motions suggesting an increased risk of vessel occlusion. The experiments were conducted by passing blood through microfluidic devices with a cross-sectional area of 250 μm x 12 μm (red blood cells have a radius of ~4 μm and thickness of ~1-2 μm) thus confining the motion of the cells to one direction. Also, cells only in the middle fifth of the flow were studied since the shear rate (~10/sec) is in the human physiological range for microcirculation. This "quasi-2D" set-up allowed for easy video imaging of the cells and subsequent image analysis to determine the random motions.

Fig. 2 Top: Sample tracking image from video frame with the red blood cells segmented and numbered. Bottom: Centroid of each cell marked with vector arrow trajectory.

Soft Matter

Red blood cells, a major component of blood, are usually large enough that thermal fluctuation effects are negligible meaning their equilibrium diffusivity (<math>D_{thermal}</math>) is small:

<math>D_{thermal} = \frac{kT}{f} \sim 0.1 \frac{\mu m^2}{s}</math> (for a 4 μm flat disk at room temperature)

where <math>f</math> is the viscous drag coefficient. However, these soft cell suspensions when driven by pressure gradients or subject to shearing will result, via concentration variations and velocity gradients, in complex multi-particle interactions causing fluctuations in particle movements. Thus it is necessary to study this microscopic interactions to understand larger-scale observables such as clotting.

The observed fluctuations in cell movement seen in the experimental plane can be described in terms of the mean-squared displacement:

<math>\langle\Delta r^{2}(\tau)\rangle = \langle\big(r_{bulk}(\tau)-r_{cell}(\tau)^{2}\big)\rangle = D\tau</math>

where the diffusion constant <math>D</math> is larger than the equilibrium diffusivity.

characteristic length and time scales... shearing... clotting... [still finishing this section!]