# In Silico Investigation of the RBC Velocity Fluctuations in Ex Vivo Capillaries
## 4 Results and Discussion
(**b**) Ht with respect to the ht level in each capillary and the equivalent tube. (**c**) Average velocity distribution of the RBCs in each 5 \(\upmu\)m interval across the capillaries and the tubes (for the high-ht condition). In Figure 7, the second investigation is shown. The spatiotemporal profile of the average RBC velocity inside the capillary segments (Figure 7a-d) shows, unsurprisingly, that the mean RBC velocity can vary considerably, up to 30% on average, and higher locally, due to the effect of luminal irregularities. Tube channels show a uniform distribution of RBC velocity throughout their length, while in capillaries, RBCs tend to move faster in high-confinement regions. This trend is the most obvious for S4, the capillary with the lowest \(I_{cc}\). RBC velocity fluctuates more along this segment, where the increase in velocity is almost 80% near the center of the capillary. This velocity fluctuation increases as the hematocrit increases, pointing to the contribution of the RBC-RBC interactions to the RBC velocity profile in the capillaries. The spatial CoV distribution across the capillaries is shown in Figure 7e-h. It is clear that CoV is always below 4% for tube geometries. This indicates that the RBC velocity heterogeneity in the ideal tubes is always low, regardless of the ht level. However, in capillaries, even when \(I_{cc}\geq\) 0.91, a CoV between 5 and 7 can be observed in some regions of the capillary. In low \(I_{CC}\) cases, the CoV can reach 14% near high-confinement regions, and the CoV increases with increasing ht. It is important to point out that the highest CoV is not calculated at the highest-velocity regions, but near the highest-velocity regions. his suggests that the greatest heterogeneity does 349 not occur in areas of extreme confinement but rather as the RBC recovers its original shape 350 after leaving the highly confined region. Mixed ANOVA statistics revealed \(p\)-values of 0.392, 0.399, 0.0121, and approximately 0 for comparisons between capillaries and tubes in different ht configurations, with respect to segment number. This finding aligns with the observed velocity profiles, which indicate that velocity fluctuations are lower and more consistent with tube measurements in the S1 and S2 capillaries, whereas in S3 and S4, velocity fluctuations are higher and deviate significantly from the results obtained from the tubes. For the third step, the temporal average velocity of the RBCs for each simulation with respect to ht, as well as the deviation from the temporal average, is shown in Figure 8a-d. This temporal average was calculated by calculating the temporal average velocity of each individual RBC that traveled through the capillary and taking the arithmetic average of the temporal averages. The temporal average velocity of the RBCs in the S4 capillary shows the highest deviation, where it can reach a 75% difference for the highest ht and 35% for  
Figure 7: Spatiotemporal distribution of the velocity in (**a–d**). S1-S1T, S2-S2T, S3-S3T, and S4-S4T (**e–h**) CoV distributions that show the RBC velocity fluctuation over time, along the capillaries and their equivalent tubes. the lowest ht. Whereas in capillaries that have higher \(I_{cc}\) such as S1 and S2, temporal average velocity deviations are much smaller, and for the S2 capillary there is a negligible difference between different hematocrits, as well as the capillary and the tube. The average hydraulic diameters of the S1 and S2 capillaries are 4.89 and 5.22 \(\upmu\)m, respectively, and the confinement \(\chi\) is equal to almost unity across their length. This means that the RBCs are always forced to show parachuting behavior [53], and due to the restricting channel, the temporal average of each RBC is relatively the same. However, the S3 and S4 capillaries show a great deviation, while their equivalent tube results do not show a significant deviation. When \(I_{cc}\) values are compared, the S2 capillary has the highest \(I_{cc}\), and the S4 capillary has the lowest \(I_{cc}\).