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Modeling of Biomechanics and Biorheology of Red Blood Cells in Type 2 Diabetes Mellitus
Hung-Yu Chang, Xuejin Li, George Em Karniadakis Biophysical Journal Volume 113, Issue 2, Pages (July 2017) DOI: /j.bpj Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 1 (a) Young’s modulus of normal and diabetic RBCs measured in experiments, with data as follows: crosses, Fornal et al. (14); triangles, Ciasca et al. (15); squares, Zhang et al. (16); circles, Lekka et al. (90). (b) Sketch of the RBC models with equilibrium biconcave (S/V = 1.44) and near-oblate (S/V = 1.04) shapes. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 2 Stretching response of normal and T2DM RBC membrane at different values of the stretching force. The error bars are obtained by increasing or decreasing μ by 20% from the default values (Table 1). The experimental data are adopted from Suresh et al. (61), and the different stretched RBCs at stretching force Fs = 100 pN are presented on the right. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 3 Membrane fluctuation distributions of normal and T2DM RBCs. The solid red line represents experimental data for membrane fluctuation distribution of normal RBCs (62). The full-width, half-maximum fluctuation value is ∼128 nm for N-RBC, 110 nm for D-RBC1, 66 nm for D-RBC2, and 65 nm for D-RBC3. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 4 (a) Dynamic cell deformation and relaxation processes of different RBC models at the forces shown at top. (b) An apparent uncoupling between the lipid bilayer and cytoskeleton occurs by reducing the bilayer-cytoskeletal interaction of the D-RBC3 model in one or two orders of magnitude. (c) Estimated shape recovery time, tc, of different RBC models. t = 0 is the time when the external force is released and the cell starts to recover its original shape. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 5 TT motion of an RBC in shear flow. (a) Angular trajectory (θ) of a marked particle in the RBC membrane during the TT motion for different RBC models at shear rate γ˙ = 105 s−1. θ is the inclination angle between the position vector of the marked particle and the flow direction. (b) Corresponding snapshots of different RBC models at t = 0.20, 0.25, 0.30, 0.35, and 0.40 s. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 6 Functional dependence of RBC TT frequency with respect to shear rate γ˙. The error bars were obtained by increasing or decreasing ηm by 10% from their default values. Simulation results are compared with experimental data by Fischer (red circle) (74), by Tran-Son-Tay et al. (red cross) (77), and by Williamson et al. (green star) (59). The red and green lines show the linear fits for normal and diabetic RBCs, respectively, in experiments. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 7 RBC traversal across a microfluidic channel of 6.0 μm width at various values of pressure difference. The cell transit velocity, v, is defined as the transit distance divided by the average transit time for an RBC traversing the narrow channel, and ΔP is a local pressure gradient in the channel. For better comparison, the normalized cell transit velocity (v∗ = v/vs) and local pressure difference (ΔP∗ = ΔP/ΔPs) are adopted, where vs = 1.6 mm/s and ΔPs = 0.1 kPa. Experiments (open circles) and simulations (solid circles) of a normal RBC traversing a 6-μm -wide channel from Quinn et al. (79) are shown. (Inset) Schematic of the microfluidic channel with a symmetric converging-diverging geometry. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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Figure 8 Functional dependence of shear viscosity of T2DM RBC suspension on shear rate at hematocrit Ht=45.0%. Experimental data are as follows: circles are from Skovborg et al. (17), crosses from Zingg et al. (18), and diamonds from Peduzzi et al. (78); red symbols are for normal RBC suspension and green symbols for diabetic RBC suspension. To see this figure in color, go online. Biophysical Journal , DOI: ( /j.bpj ) Copyright © 2017 Biophysical Society Terms and Conditions
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