Flow-induced segregation and dynamics of red blood cells in sickle cell disease

Blood flow in sickle cell disease (SCD) can substantially differ from normal blood flow due to significant alterations in the physical properties of the red blood cells (RBCs). Chronic complications, such as inflammation of the endothelial cells lining blood vessel walls, are associated with SCD, for reasons that are unclear. Here, detailed boundary integral simulations are performed to investigate an idealized model flow in SCD, a binary suspension of flexible biconcave discoidal fluid-filled capsules and stiff curved prolate capsules that represent healthy and sickle RBCs, respectively, subjected to pressure-driven flow in a planar slit. The stiff component is dilute. The key observation is that, unlike healthy RBCs that concentrate around the center of the channel and form an RBC-depleted layer (i.e., a cell-free layer) next to the walls, sickle cells are largely drained from the bulk of the suspension and aggregate inside the cell-free layer, displaying strong margination. These cells are found to undergo a rigid-body-like rolling orbit near the walls. A binary suspension of flexible biconcave discoidal capsules and stiff straight (noncurved) prolate capsules is also considered for comparison, and the curvature of the stiff component is found to play a minor role in the behavior. Additionally, by considering a mixture of flexible and stiff biconcave discoids, we reveal that rigidity difference by itself is sufficient to induce the segregation behavior in a binary suspension. Furthermore, the additional shear stress on the walls induced by the presence of cells is computed for the various cases. Compared to the small fluctuations in wall shear stress for a suspension of healthy RBCs, large local peaks in wall shear stress are observed for the binary suspensions, due to the proximity of the marginated stiff cells to the walls. This effect is most marked for the straight prolate capsules. As endothelial cells are known to mechanotransduce physical forces such as aberrations in shear stress and convert them to physiological processes such as activation of inflammatory signals, these results may aid in understanding mechanisms for endothelial dysfunction associated with SCD.

Figure 1

Schematic of the simulation domain.

Figure 2

Rest shapes of a biconcave discoidal capsule (top) as a model for healthy RBCs, a straight prolate capsule (bottom left), and a curved prolate capsule (bottom right) as a model for typical sickle cells.

Figure 3

(a) Wall-normal number density profile $\widehat{n}$ for healthy RBCs assuming different spontaneous shapes ($c_0$) in a homogeneous suspension at steady state. (b) Hematocrit profile for the healthy RBC suspension. The two positions at $y/a=0$ and 5 correspond to the wall and centerplane of the channel, respectively.

Figure 4

Simulation snapshots for a homogeneous suspension at steady state of flexible biconcave discoidal capsules (healthy RBCs) with $\mathrm{Ca}=1.6$ assuming either a biconcave discoidal (a) or an oblate spheroidal (b) spontaneous shape.

Figure 5

Time evolution of the parameter $s={〈{(y_{\text{cm}}-H)}^2〉}^{1/2}/a$ for (a) flexible (i.e., healthy) RBCs in suspension with stiff RBCs, and for (b) healthy RBCs in suspension with sickle cells and straight prolate capsules, respectively.

Figure 6

Wall-normal number density profiles $\widehat{n}$ for flexible (solid red) and stiff (dotted blue) RBCs in a binary suspension at steady state.

Figure 7

Simulation snapshots [(a) side view, (b) front view] for a binary suspension of flexible (red) and stiff (blue) RBCs at steady state.

Figure 8

Wall-normal number density profiles $\widehat{n}$ for (a) healthy RBCs in suspension with sickle cells (solid red) and straight prolate capsules (dotted red), and (b) sickle cells (solid blue) and straight prolate capsules (dotted blue) in suspension with healthy RBCs, respectively.

Figure 9

Simulation snapshots (left: side view; right: front view) for binary suspensions of healthy RBCs with sickle cells [(a), (b)] and straight prolate capsules [(c), (d)], respectively, at steady state.

Figure 10

Simulation snapshots [(a), (b)] for a steady-state binary suspension of healthy RBCs with sickle cells, as well as wall-normal number density profiles $\widehat{n}$ [(c), (d)] for both components, assuming a biconcave discoidal (a) and an oblate spheroidal (b) spontaneous shape ($c_0$) for healthy RBCs, respectively.

Figure 11

Magnitude of the $x\text{−}x$, $x\text{−}y$, $y\text{−}y$, and $z\text{−}z$ components of the tensor $\mathbf{S}=\langle \mathbf{pp}\rangle$ for sickle cells and straight prolate capsules inside the cell-free layer (labeled “CFL”) and in the bulk of the suspension (labeled “bulk”), respectively.

Figure 12

Examples of the spatial distribution of the additional wall shear stress ${\widehat{\tau }}_w$ on the bottom wall ($y=0$) induced by a homogeneous suspension of healthy RBCs (a) and binary suspensions of healthy (flexible) RBCs with stiff RBCs (b), sickle cells (c), and straight prolate capsules (d), respectively, at steady state.

Figure 13

Time evolution of the additional wall shear stress ${\widehat{\tau }}_w$ at a fixed wall position $(x,y,z)=(0.74a,0,1.67a)$ for the cases of a homogeneous suspension of healthy RBCs (a) and binary suspensions of healthy (flexible) RBCs with stiff RBCs (b), sickle cells (c), and straight prolate capsules (d), respectively, at steady state.

Figure 14

The spatially averaged RMS $\langle {\left({\widehat{\tau }}_w\right)}_{RMS}\rangle$ (a) and maximum $\langle {\left({\widehat{\tau }}_w\right)}_{max}\rangle$ (b) of the additional wall shear stress for different suspensions at steady state. For each quantity, the error bars represent standard error.

Figure 15

The ensemble-averaged magnitude $\langle {\left({\widehat{\tau }}_w\right)}_{\mathrm{pk}}\rangle$ (a), duration $\langle \mathrm{\Delta }{t}_{\mathrm{pk}}\rangle$ (b), and frequency $\langle f_{\mathrm{pk}}\rangle$ (c), respectively, of the wall shear stress peaks experienced by all wall positions for different suspensions at steady state, and the product $A_{\mathrm{pk}}$ of these three quantities (d). The error bars in (a), (b), and (c) represent standard error for each quantity.