Recent Advances in Computational Modeling of Biomechanics and Biorheology of Red Blood Cells in Diabetes

Figures

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  Figure 1. (A) Left: Young’s moduli of normal and diabetic RBCs reported from Fornal et al. [61] (crosses); Ciasca et al. [62] (triangles); Zhang et al. [63] (squares); Lekka et al. [64] (circles). Right: Particle-based models for RBCs with equilibrium biconcave (A/V = 1.44) and near-oblate (A/V = 1.04) shapes. (B) Comparison of stretching responses between normal and three T2DM RBC models. Experimental data by Suresh et al. [65], and stretching force at 100 pN are shown next to the figure. (C) Normal and diabetic RBC traversing velocities (v*) in a microfluidic channel with a width of 6.0 μm under difference pressure gradients (▵P). Experimental and simulation results from prior work of Quinn et al. [66] are plotted for comparison. (D) Tank-treading motion of normal and diabetic RBCs in Couette flow. Top: angular trajectories of marked particles on the cell membrane during the TT motion for different RBC models at a shear rate 105 s−1 are plotted. Bottom: Snapshots of diabetic RBC model at time t = 0.20 s, 0.25 s, 0.30 s, 0.35 s, and 0.40 s. Figures are adopted from [58] with permission.

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  Figure 4. (A) Variation of shear viscosity of suspensions of T2DM RBCs with different shear rates at hematocrit Ht = 45%. Circles represent data reported by Skovborg et al. [74]. Crosses represent data reported by Zingg et al. [75]. Diamonds represent data reported Peduzzi et al. [76]. Red symbols represent data computed from normal RBC suspension and green symbols represent data computed from diabetic RBC suspension. Figures are adopted from [58] with permission. (B) Side view of experimental setup for modeling the healthy and diabetic blood flow in a cylindrical vessel with diameter Dt= 40 μm and hematocrit = 15%. * signifies diabetic platelets. (C) A plug-like velocity profile is measured from the blood flow as compared with a parabolic curve (red line). (D) Front views of the blood cells in the vessel. Snapshots from left to right illustrate the distributions of RBCs+platelets, RBCs and platelets. Figures (B–D) are adopted from [72] with permission.

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  Figure 2. (A) A microfluidic device with periodic obstruction is designed for examination of the biomechanics of diabetic RBCs. (B) Schematic of a normal RBC (N-RBC) model, which stays as a biconcave shape with surface-to-volume ratio (A/V) of 1.44 whereas a T2DM RBC (D-RBC) model has a more oblate shape with A/V = 1.04. (C) An example of simulation results of a T2DM rouleaux travelling through microchannels. (D) Fibrinogen-dependent RBC aggregation model where blue vertices denoting “interactive vertices” (IVs) that is able to bind with vertices of the same type located on other RBCs. (E) Work pipeline employed to combine in-vivo and in-silico studies. Figures are adopted from [71] with permission.

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  Figure 3. (A) Experimental results of a T2DM doublet squeezing through microgates in experiment (left column) and companion simulation (right column). (B) Comparison on the percentage of rouleaux with different lengths detected from three different patients (* signifies that patients of obesity, not diabetes). (C) Doublet disaggregation rate measured from simulation and experiments; exp., experiment; sim., simulation. Different rouleaux breakup patterns of two 10-cell rouleaux of the rouleaux flow in (D) parallel to and (E) with a 21∘ inclination angle to the flow direction (t0=0 s,t1≈3 s,t2≈4.5 s). Bottom histograms show the accumulated results of five different runs. Figures are adopted from [71] with permission.

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  Figure 5. Platelet margination in blood containing healthy and diabetic RBC+platelet. Distributions of platelets and RBCs in the vessel for (A) NRBCs+PLTs, (B) DRBCs+PLTs (MPV = 6fL), and (C) DRBCs+PLT*s (MPV = 12 fL). * signifies the diabetic platelets. (D) Effect of MPV of platelets on platelet margination. (E–G) Effects of flow rate on platelet margination. Distribution of RBCs and platelets in the vessel with cell suspensions of (E) NRBCs+PLTs, (F) DRBCs+PLTs, and (G) DRBCs+PLT*. The percentage of marginated platelets ϕp for all three cases is summarized in (H). * signifies the diabetic platelets. Figures are adopted from [72] with permission.

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  Figure 6. (A) Normal and diabetic RBC and platelet models, validated in Chang et al. [58], are employed to simulate blood flow in (B) a 3D rectangular microchannel of size of 110 μm × 20 μm × 20 μm. Left: front view, right: side view. Solvent particles in the simulate carry 22 species for modeling the coagulation cascade that is initiated from two injury sites (highlighted with blue color lines) with a size of 40 μm located at the upper and bottom channel wall respectively. Figure is reproduced from [104].

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  Figure 7. (A) Simulation results of normal RBCs and platelets moving in the microchannel. Activated platelets adhere to the injury sites after they become activated by thrombin with concentration >1 nM. The number of bonds generated between platelets and injury sites for (B) normal and (C) diabetic blood as well as the number of adhered platelets for (D) normal and (E) diabetic blood are recorded for 40 s. Figure is reproduced from [104].

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  Figure 8. Simulation results of fibrin ([Ia]) concentration boundary layers in the middle cross-section of the microchannel for (A) normal and (B) diabetic blood. (C) Variation of fibrin concentration over time at three different sites of x=40,50,60μm for normal blood (solid lines) and diabetic blood (dashed lines). To investigate the effects of diabetic blood in promoting fibrin generation, an initial concentration of [I]0 = 7 μm is prescribed in normal blood model while [I]0 = 10.5 μm is used in the diabetic blood model. (N) represents normal blood whereas (D) designates diabetic blood. The figure is reproduced from [104].