Table 1.
Model Parameters Extracted from Available Measured Data for RBCs in Normal and GD Conditions.
Fig 1.
Overview of simulation setup and Cell-Cell interaction models.
A) The front view of a typical simulation of blood viscosity at (corresponding to 698 RBCs) and the size of the simulation RBC populations (
m ×
m ×
m) employed in this study. Bi) Vertex-vertex interactions for the aggregation model. Bii) Representation of three different disaggregation thresholds through the Morse potential between constituents of different RBCs. Here, the presence of more blue vertices corresponds to a stronger RBC disaggregation threshold, which is commonly observed in blood with higher glucocerebroside accumulation levels. The severe condition corresponds to the highest RBC disaggregation threshold of 680 s−1 in the experiment; the moderate condition corresponds to a threshold of 250 s−1; and the mild condition corresponds to a threshold of 150 s−1. Detailed model parameters are provided in the Supporting Information and Methods section.
Fig 2.
Validation of shear modulus of GD RBC with adhesion assay.
A) X-axis length of CTR and GD RBCs from experiments at a shear stress of 1 dyn/cm2. The X-axis length measurements were performed on several images obtained from adhesion assay experiments conducted at a shear stress of 1 dyn/cm2, using CTR (n = 10) or GD (n = 11) RBCs. B) Morphology of CTR and GD RBC under shear flow. The left two figures are confocal images of adherent CTR and GD RBCs to laminin at a shear stress of 1 dyn/cm2. The right two figures are simulation images for CTR and GD RBCs at different shear modulus conditions at a shear stress of 1 dyn/cm2. Bar scale represents 1 μm.
Table 2.
Clinical and biological parameters of the studied patients with hemorheology experiment.
Fig 3.
Sequential snapshots of the disaggregation dynamics of GD RBCs (GD-RBC1) for a range of varied flow shear rates.
Fig 4.
Blood relative viscosity for GD evaluated in viscometric flows under physiologically relevant shear rates ranging from 22.5 to 225 s−1.
Experimental viscosity measurements for GD and CTR RBC suspension by Franco et al. [8]. The viscosity measurements were based on a hematocrit of ∼36% for GD RBCs and ∼40% for CTR RBCs. Open symbols represent experimental results, whereas solid symbols represent simulation results.
Fig 5.
Extension of blood relative viscosity for GD in shear flows under large shear rates ranging from 1 to 1000 s−1.
There are three distinct domains for blood viscosity based on the shear rate: the aggregation domain, ranging up to approximately 8 s−1; the transition area, spanning from around 8 to 100 s−1; and the stiffness domain, extending from approximately 100 s−1.
Fig 6.
Schematic diagram of different RBC disaggregation thresholds (A) and corresponding simulation results (B and C) of the relative viscosity of blood for different RBC disaggregation thresholds and hematocrit levels with shear modulus of 9Es0.
A) Representation of three different glucocerebroside accumulation through the Morse potential between constituents of different RBCs. Here, the presence of more blue vertices corresponds to a stronger RBC disaggregation threshold. The severe condition corresponds to the highest RBC disaggregation threshold of 680 s−1 in the experiment; the moderate condition corresponds to a threshold of 250 s−1; and the mild condition corresponds to a threshold of 150 s−1, as defined in Table 1.; B) The steady shear relative viscosity versus imposed shear rate for three different hematocrit levels and four different RBC disaggregation thresholds at each hematocrit. The viscosities are normalized by the plasma viscosity; the effect of RBC disaggregation thresholds disappears at high shear rates when it causes no stable cell-cell adhesion; C) Relative viscosity against hematocrit for different shear rates and four different RBC disaggregation thresholds of 150, 250, 350 and 680 s−1. In the simulation, we added an intermediate threshold of 350 s−1 to reduce the large gap between 250 s−1 and 680 s−1.
Fig 7.
Schematic diagram of different RBC stiffness (A) and corresponding simulation results (B and C) of the relative viscosity of blood for different RBC stiffness and hematocrit levels with disaggregation threshold of 250s−1.
A) Representation of three different levels of cell stiffness through different shear modulus conditions at a shear stress of 1 dyn/cm2. B) The steady shear relative viscosity versus imposed shear rate for three different hematocrit levels and three different cell stiffness at each hematocrit. The viscosities are normalized by the plasma viscosity; the effect of cell stiffness increases at high shear rates, and the deformation of cells becomes increasingly more dominant C) Relative viscosity against hematocrit for different shear rates and three different RBC stiffness of 20, 9, and 4 Es0.