# In Silico Investigation of the RBC Velocity Fluctuations in Ex Vivo Capillaries
## 4 Results and Discussion
Although there is no linear correlation between \(I_{cc}\) and the deviation in ht or temporal average velocity; \(I_{cc}\) can be used to anticipate the highest fluctuations in the corresponding capillaries. The CoV is shared in Figure 8e,f. It is clear that all tube results are below 5%. That means that in tubes where (\(I_{cc}=1\)), the deviation is always small, whereas even in cases with high \(I_{cc}\), such as the S1 and S2 cases, the CoV varies near 15% and 10%, respectively. The S4 capillary on the other hand (\(I_{cc}=0.67\)) has a significantly higher CoV than other capillaries, even though the avarage hydraulic diameter of S3 and S4 is close. The difference in \(I_{cc}\) results in a nearly two-fold variance in CoV. This reinforces the idea that realistic capillary usage can change the result significantly even with capillaries that have similar average diameters and similar inlet conditions due to their unique shapes. One-way analysis of variance (ANOVA) and post hoc analysis revealed highly significant differences (\(p\approx 0\)) in RBC velocities compared between capillaries and tubes. Specifically, for the S2 capillary, the adjusted \(p\)-value was 0.0234 when comparing low-hematocrit (Ht) velocities and \(1\times 10^{-4}\) when comparing high-Ht velocities. These results indicate a significant departure from previous statistical analyses. This difference arises because the current analysis considers the temporal average velocity of individual RBCs, whereas prior analyses averaged the RBC velocities with respect to their spatial positions. This methodological distinction naturally strengthens the hypothesis that RBC velocities exhibit greater fluctuations along the capillary and demonstrate lower deviations within smaller temporal or spatial intervals. Figure 8: Temporal average velocity in each capillary and its equivalent tube for (**a**) S1, (**b**) S2, (**c**) S3, and (**d**) S4. Temporal average CoV for (**e**) each capillary and the tube (**f**) with different \(I_{cc}\) values. Finally, the effect of RDW was investigated by comparing the results of the high-ht cases in the capillaries. Our hypothesis was that due to the diameter (and possibly velocity) variance between individual RBCs, the overall capillary flow would fluctuate more, especially in the case of high-hematocrit conditions, which allow more interactions between RBCs. RDW cases were utilized by feeding 43% regular RBCs and 28.5% smaller (\(R=2.75\)\(\upmu\)m) and 28.5% larger (\(R=3.05\)\(\upmu\)m) RBCs to the capillaries. Figure 9a clearly shows that in high-\(I_{cc}\) capillaries (S1 and S2) RDW causes no significant change in the local RBC velocity distribution, yet in low-\(I_{cc}\) capillaries (S3 and S4), an increase in spatial RBC velocity is observed near the middle of the capillaries. In the S1 and S2 capillaries, the uniformity and high confinement of the capillaries cause each RBC to show parachuting behavior regardless of their diameter variation since the small RBCs are also larger than the channel diameter, and hence the RDW loses its effect on these capillaries with high \(I_{cc}\) values and low hydraulic diameters. The S3 and S4 results however (\(I_{cc}=0.84\) and 0.67) show a slight increase in the temporal average velocities while constraining the deviation from the temporal average. The reason behind this increase and the lower deviation can be explained by the RBC-RBC interaction and confinement. In the confined regions of these capillaries, smaller RBCs can accelerate more than regular or larger RBCs, increasing the average velocity. The CoV results are shown in Figure 9d, and using RDW does not cause a significant change in the CoV regardless of the \(I_{cc}\) of the capillary. The ANOVA test also shows no significance using RDW. The main emphasis of this study is on the critical need to consider the actual three-dimensional profile of a capillary, moving beyond simplified geometries that focus solely on the overall diameter.