# In Silico Investigation of the RBC Velocity Fluctuations in Ex Vivo Capillaries
## 4 Results and Discussion
This detailed approach is essential for accurately evaluating  
Figure 9: RDW effect on (**a**) spatial RBC velocity distribution, (**b**) spatial CoV distribution, (**c**) temporal average velocity, and (**d**) temporal average CoV. the velocity distribution in capillaries in both space and time. Computer simulations are crucial for revealing the velocity profiles of RBCs, which are currently inaccessible with available in vivo microscopy technologies. It should be noted that our model, although designed to be as realistic as possible in terms of mechanical RBC features and capillary geometries, completely omits the compliance of endotothelia and ignores the active or passive reactions in capillary torus and diameter to changes in flow. In reality, as cells are flowing inside a capillary segment, the vessel wall may passively respond to allow easier passage of the cell, and this is determined by endothelial rigidity or capillary tonus. Beyond the passive adaptability of the capillary wall, endothelial mechanosensors like Piezo1 channels can sense fluctuations in RBC flow or their forces applied to the capillary lumen and trigger appropriate effector responses to actively modulate the capillary tonus and geometry [54; 55]. This is mainly established by endothelial-pericyte signaling, which forms appropriate feedback mechanisms for this regulation [56]. Capillary pericytes that surround the endotothelia with their contractile machinery can monitor neuronal activity and oxygenation along with the mechanical status of the capillary lumen to calculate an adaptive contractile response that can result in either the constriction or dilation of the capillary lumen, and this immediately results in a change in RBC flow and the redistribution of pressure gradients in the adjacent capillary network [57; 58]. Finally, RBCs have been reported to actively respond and adapt to passages inside tight capillaries by adjusting their calcium level [59] or shape and size [60], which was not modeled in our simulations. This collective regulatory effort of RBCs themselves, endothelia, and pericytes can adjust the RBC flow fluctuations, dampening them with appropriate feedback mechanisms. Therefore, in reality, the measurements reported here that arise only from physical elements may not be observable in vivo to this extent, or in the case of excessive RBC slowing and aggregation, a reflex spontaneous dilatation of the capillary can help the resolution of the flow. A constant number of RBCs with a predetermined velocity are fed into the capillaries throughout the duration of simulations, which is a limitation. In reality, the capillary network continuously adjusts how many RBCs enter a specific capillary segment and at what velocity, depending on the hydraulic resistance of that specific capillary segment. Furthermore, passively, the interactions and dynamics of RBC-RBC and RBC-white blood cells at the capillary junctions affect the distribution of hematocrit in individual capillary segments [8]. Such network interactions are out of the scope of this study, as we focused only on single capillary segments to investigate a fundamental question. To extend this study, at least a network of some connected realistic capillaries must be investigated to reveal the full extent of the RBC velocity and hematocrit distributions. Finally, simulation times are limited to 1 s of physical time after examining the fluctuation on the RBC velocities. Although the RBC velocity deviation does not increase with respect to time, overextending the physical simulation time (such as 30 s) may demonstrate velocity fluctuations on a higher scale due to the random feeding of the RBCs.