## 3 Results  
### Effect of Moderate Mechanical Stress on RBC Deformability  
Figure 2 shows the impact of moderate mechanical stress (hemolysis \(<5\%\)) on the portion of rigid, undeformable cells (%UDFC) in both freshly-collected and cold-stored RBC. This figure demonstrated that the application of shear stress led to both an increase and a decrease in %UDFC. Furthermore, we did not observe a significant difference in the concentration of undeformable cells between samples obtained before and after the exposure to mechanical stress. Thus, the median value of %UDFC was 2.63% for cells before (RBC\({}_{\text{B}}\)) treatment and 3.68% for mechanically-treated cells (RBC\({}_{\text{MS}}\)), \(p=0.45\).  
In addition, we analyzed the impact of mechanical stress separately for freshly donated and stored RBCs. Figure 3 shows that the change in the proportion of rigid cells is primarily positive (\(\Delta\)UDFC \(>0\)) for freshly-donated cells and negative for stored RBC. Thus, mechanical stress leads predominantly to an increase in the fraction of non-deformable cells in the case of freshly donated RBCs, and, conversely, to a decrease in the fraction of rigid cells when stored RBCs are analyzed. The observed difference in the response to mechanical stress seems to be related to the fact that the initial concentration of undeformable cells is significantly higher for samples of stored RBCs than fresh ones. Furthermore, as we have previously shown [61], these are the rigid cells that are predominately destroyed as a result of mechanical impact. Therefore, the %UDFC predominately decreases when stored cells are exposed to mechanical stress.  
Figure 2: Percentage of undeformable cells (%UDFC) in samples collected before (RBC\({}_{\text{B}}\)) and after mechanical stress application (RBC\({}_{\text{MS}}\)). Mechanical stress was applied to cells by rolling freshly donated and stored RBCs with steel beads. Identical symbols designate the same RBC sample before and after applying mechanical stress. No significant difference between the two groups was observed, \(p=0.45\).  
Based on the results presented in Figure 2, we divided all the samples (whether fresh or stored) into two groups based on the percent of non-deformable RBCs before mechanical stress application. As a cutoff parameter, we chose the median value of the percentage of undeformable cells in the sample (2.63%, as mentioned earlier). As demonstrated in Figure 4, for both fresh and stored RBCs, the application of mechanical stress decreased the level of rigid cells (\(\Delta\)UDFC \(<\) 0) when its initial value (before treatment) was higher than the median (2.63%), and increased it (\(\Delta\)UDFC \(>\) 0) when the initial value was lower than the median.  
Thus, we found that samples with a low concentration of undeformable cells subjected to mechanical stress predominately showed an increase in this fraction, while samples with a high concentration of such cells (predominantly stored cells) mostly showed a decrease in this fraction.  
Furthermore, (Figure 5) the mechanical stress-induced change in the level of rigid cells (\(\Delta\)UDFC,%) showed a significant linear correlation (r = 0.87; \(p\) = 1.4 \(\times\) 10\({}^{-7}\)) with the proportion of the rigid cells before treatment (%UDFC\({}_{\rm B}\)).  
Figure 4: Alteration in the percentage of undeformable cells (\(\Delta\)UDFC, %) in the RBC population following mechanical stress (applied to cells by rolling with steel beads). \(p\) = 0.0007.  
Figure 3: Alteration (after rolling cells with steel beads) of the percentage of undeformable cells (\(\Delta\)UDFC, %) in the RBC population for fresh and stored samples. No significant difference between the two groups, \(p\) = 0.154.