# In Silico Investigation of the RBC Velocity Fluctuations in Ex Vivo Capillaries
## 3 Validation  
A series of validation studies was conducted to rigorously assess the predictive capacity of the proposed fluid-structure interaction model to capture the mechanics of RBCs under physiologically relevant conditions. These validations encompassed three canonical test cases: First, the stretching of a single RBC in a stationary fluid is investigated. Second, the shearing behavior of an RBC positioned at the center of a shear flow in which the velocity ranges from \(-\)u to u and zero at the middle is determined. Finally, we investigate the transport of a single RBC through a confined slit. The first two scenarios primarily served to verify the model's ability to reproduce the mechanical response of the RBCs to external forces and shear stress. However, the third case, involving cell transport near bounding walls, was particularly critical, since RBCs always move in the vicinity of the capillary walls, where confinement is always high. The accurate computation of wall effects is essential for a realistic simulation of microcirculatory flows. Unless stated otherwise, in all validation simulations, the lattice spacing is 0.5 um, while the single relaxation time is \(\tau=1\). The first validation study is conducted on the cell stretch experiment, in which a single RBC is placed in a stationary fluid. The RBC is fixed on one side and stretched by applying force on the other side. Figure 3(left) shows an example of a stretched RBC. This study was carried out experimentally by [PERSON] et al. [46], who used silica beads to fix the RBC on one side and stretch it by applying force on the other side. Figure 3(right) presents a comparison of the result with the data from [PERSON] et al. [46]. Our current simulation results are in agreement with the experimental data, where the axial diameter is accurately calculated, and the transverse diameter calculation is in the upper range of the measurements. However, the reason for the slightly less accurate transverse diameter in low-force regions (20-70 pN) lies in the shear modulus value. We have chosen the shear modulus in the upper range of the experimental values [35; 36; 37]; therefore, it could represent  
Figure 2: **(top)** An example snapshot of the periodic feeding channel. Blue rectangle shows the periodic domain, and the red rectangle shows the inlet portion in the main domain. Shaded lines show the intersection of these two regions. Data from the periodic section in the intersection region is extrapolated into the main simulation domain. **(bottom)** Simulation snapshot of the RBCs in a periodic domain, before they enter the main domain at two different times. a slightly more rigid RBC, which explains the higher transverse diameter in the low-force regime due to the slightly less deformed RBC behavior. The second validation study involves a single RBC in shear flow. A single RBC is placed in the center of a fully periodic domain, and Couette flow conditions are applied where the velocity is zero at the middle of the domain, and lowest and highest velocities are \(-\)u and u, respectively. The left image of Figure 4(left) shows an example simulation snapshot, while the right image of Figure 4(right) presents the comparison with the experimental study by [PERSON] et al. [47]. Our current results show good agreement with the experimental data and consistently fall within the measurement error range. The deviation from the curve fit line of the Yao (black) shows a larger deformation, which is caused again by the selected shear modulus value. A real RBC can have a shear modulus between 5 and 10 uN/m, but we use the shear modulus that is in the vicinity of the upper range of the experimental measurements. Therefore, a slightly lower deformation index observation is an expected outcome with the current material model constants. The final validation study examines the passage of the RBC through a 1.5 um slit, as illustrated in Figure 5(left). This particular study has been conducted numerically by both [PERSON] [48] and [PERSON] [49].