## 3 Results
### Morpho-Rheological Properties of Sickle RBCs Are Patient-Specific
#### 3.1.2 Morphometry Post-Microcapillary-like Constrictions  
In the cascade of events that trigger VOC, polymerization of abnormal hemoglobin Hb5, leading to sickling, is a key step. To dynamically determine and quantify the extent of sickling and possible contribution to VOC, we measured the circularity, C, Equation (1) and roundness, \(R\), Equation (2), of RBCs at the exit channel of the MMM following advection. Figure 3 shows the results for circularity, and Figure 4 shows the results for roundness in one patient, patient 4 (P4). The heterogeneity of RBC morphology in the same patient is obvious from Figure 3a, where the histogram of steady-state circularity, P4, has two peaks as made clearer by the kernel smooth curve. The higher peak corresponds to normal RBCs and the lower to sickled RBCs, with a broad range that shows varying degrees of sickling. The distribution was altered when cells were treated with sodium metabisulfite (SM) to induce sickling, as seen in the P4 + SM result of Figure 3a. Finally, when the cells were treated with hydroxyurea (HU), the distribution again departed from the steady-state situation as seen in the P4 + HU result of Figure 3a. Box plots for the circularity data are shown in Figure 3b with statistically significant differences found among P4, P4 + SM and P4 + HU. Since we recorded videos of the MMM at various times post-advection, we could affirm the dynamic nature of morphological heterogeneity within the same patient, even for a specific condition such as P4 + SM or P4 + HU. Figure 3: Morphometry of cells from MMM outlet: circularity. (**a**) Histogram of circularity (Equation (1)) and kernel smooth curves for RBCs from patient 4, showing morphological heterogeneity in untreated cells, P4; in cells treated with sodium metabisulfite, P4 + SM; and cells treated with hydroxyurea, P4 + HU. (**b**) Box plots for the circularity data in (**a**). Cell numbers (\(n\)) and circularity (C) for each condition are: P4, \(n=114\), \(C=0.61\)\(\pm\) 0.02; P4 + SM (\(n=88\), \(C=0.64\)\(\pm\) 0.02); and P4 + HU (\(n=9\), \(C=0.50\)\(\pm\) 0.03). One-way ANOVA shows statistically significant (*** \(p<0.001\)) differences between P4 and P4 + HU and (* \(p<0.05\)) between P4 and P4 + SM. Again, the heterogeneity of RBC morphology in the same patient is made clear in Figure 4a, where the histogram of steady-state roundness, P4, has two peaks highlighted by the kernel smooth curve. Unlike circularity (Figure 3 and Equation (1)), roundness does not account for roughness of edges since it does not use the perimeter in its definition or calculation. It depicts the entire geometry of the object (cell). Here, it confirms the heterogeneity found in the circularity results. The higher peak in the roundness distribution (Figure 4) corresponds to normal RBCs and the lower to sickled RBCs. The distribution changed when cells were treated with sodium metabisulfite (SM) to induce sickling, as seen in the P4 + SM result of Figure 4a. When the cells were created with hydroxyurea (HU), the distribution again departed from the steady-state situation as seen in the P4 + HU result of Figure 4a. Box plots for the roundness data are shown in Figure 4b with statistically significant differences found among P4, P4 + SM (* \(p\) < 0.05) and P4 + HU (* \(p\) < 0.001). To quantify the morphological heterogeneity seen in RBCs of patient 4 in every condition measured, including steady state or normoxic (P4); induced hypoxic state, P4 + SM; and treatment state, P4 + HU, we measured the skewness and kurtosis of the circularity distributions in Figure 3 and the roundness distributions in Figure 4. Skewness measures the asymmetry of a distribution, and changes in skewness should enable the quantification of dynamic changes in proportions of sickled versus healthy RBCs in the same individual. Since kurtosis measures departure of a distribution from normality, it should enable the further quantification of heterogeneity based on outliers, even when homogeneity is approached.