## 3 Results and Discussion
### Evolution of RBC Morphology Characteristics during In-Vitro Storage
However, the \(SF\) of echinocyte I morphology at \(t=21\) (Days) is comparable to that of echinocyte I morphology obtained by echinocytogenic conditions. This discrepancy can be attributed to the cell details of the echinocyte I morphology obtained at these two shape-transforming scenarios. The echinocyte I at \(t=21\) (Days) has uneven undulation around its rim, whereas the echinocytogenic conditions produced echinocyte I has even undulations around its rim. This can influence \(SF\) estimation. In general, the evolution of \(SF\) of RBCs under both these shape-transforming scenarios indicate the rise of cell sphericity leading to lowered cell deformability [76]. These results agree with the experimentally observed deformability changes of RBCs [26; 78], and indicate the potential of \(SF\) as a quality measure of stored RBCs. At latter stages of in-vitro storage, the spicules on sphero-echinocyte RBC morphology form membrane budding and detach from the cell such that the spherocyte is formed. The progression of sphero-echinocyte to spherocyte is characterized by shortened spicules such that complete spheres are formed [77; 81]. The \(SF\) of a spherocyte is 1.0 and indicates the null deformability of the RBC, and it is important to predict and understand the progression of spherocyte formation during storage. The evolution of membrane spicules of echinocyte II, echinocyte III and sphero-echinocyte was therefore investigated to study the progression of a RBC towards a spherocyte during storage. Number of spicules (\(N_{Spicules}\)), average spicule height (\(H_{Spicules}\)), average spicule surface area (\(A_{Spicules}\)) and average spicule curvature (\(C_{Spicules}\)) of echinocyte II, echinocyte III and sphero-echinocyte at \(22\leq t\leq 42\) were studied and compared against that of the echinocytogenic conditions-produced echinocyte forms (refer to Figure 6). \(H_{Spicules}\) of the spiculated cells was estimated as follows;  
\[H_{Spicules}=\frac{1}{N_{Spicules}}\times\left[\sum_{kk=1}^{N_{Spicules}} \left(r_{kk,max}-r_{kk,min}\right)\right] \tag{4}\]  
where \(r_{kk,max}\) is the distance to the membrane vertex on the spicule that has the maximum \(C_{V,i}\) from the centroid of the cell, whereas \(r_{kk,min}\) is the distance to the membrane vertex on the spicule that has the minimum \(C_{V,i}\) from the centroid of the cell. \(C_{V,i}\) is the membrane curvature at \(i^{th}\) membrane vertex (refer to Equation (5)), and the maximum \(C_{V,i}\) is given by the membrane vertex at the peak of the spicule, whereas the minimum \(C_{V,i}\) is given by the membrane vertex at the foot of the spiculated cells was estimated according to Equation (6);  
\[C_{V,i}=\sum_{jj=1}^{N_{V-T,j}}\frac{M_{jj}}{\Delta A_{jj}} \tag{5}\]  
\[A_{Spicules}=\frac{1}{N_{Spicules}}\times\sum_{i=1}^{N_{V}} \begin{pmatrix} \sum_{jj=1}^{N_{V-T,j}}\Delta A_{jj},&C_{V,j}>0\\ 0,&C_{V,i}\ \leq\ 0\end{pmatrix}  \tag{6}\]  
where \(N_{V}\) is the number of membrane vertices, \(N_{V-T,i}\) is the number of neighbouring triangles to which the \(i^{th}\) vertex is attached to, and \(M_{jj}\) and \(\Delta A_{jj}\) are the membrane curvature and the membrane surface area at the triangle-pair that shares the \(jj^{th}\) triangle edge, respectively. In general, \(C_{V,i}>0\) occurs on the spicule surface, whereas \(C_{V,i}\ \leq\ 0\) occurs at the valleys between the membrane spicules. Similarly, \(C_{Spicules}\) of the spiculated cells was estimated according to Equation (7). \[C_{Spicules}=\frac{1}{N_{Spicules}}\times\sum_{i=1}^{N_{V}}\left\{ \begin{array}{cc} C_{V,i},&C_{V,i}>0\\ 0,&C_{V,i}\leq 0\end{array} \right. \tag{7}\]  
It can be observed (refer to Figure 6) that the number of spicules on echinocyte II and echinocyte III are similar for both shape-transforming scenarios. However, the number of spicules on the sphero-echinocyte at \(t\) (Days) = 28, 35 and 42 is less than the number of spicules on the sphero-echinocyte achieved under echinocytogenic conditions, and increases with the storage duration.