## 3 Results and Discussion
### Evolution of Deformation Behaviour of RBCs during In-Vitro Storage
The potential to form sharp projections increases with the increase of surface area of the lipid-bilayer segment that is unsupported by the cytoskeleton. Therefore, the loss of cytoskeleton and lipid-bilayer vertical interactions at adjacent actin junctional complexes promotes the formation of sharp projections on the cell surface, and can promote vesiculation at the tips of these sharp projections. This observation is in agreement with the experimental and computational predictions, which show that vesiculation does not require fragmentation of the cytoskeleton, although it can be enhanced by the uncoupling of the lipid-bilayer and the cytoskeleton [32; 82]. Therefore, the sphero-echinocyte cells at the latter stages of storage have increased potential for vesiculation due to the higher number of membrane spicules and depleted ATP levels. In addition, the deformation behaviour of stored RBCs at \(t\) (Days) = 0, 7, 14, 21, 23, 25, 28, 35 and 42 was also investigated for RBCs with a defective cytoskeleton of \(A_{Vertical}\) = 0, 1, 10 and 25 (%). The evolution of change in the axial (\(D_{A}\)) and transverse (\(D_{T}\)) diameters of stored RBCs with varying \(A_{Vertical}\) with respect to its analogous recovered cell state (i.e., recovered RBC shape at \(t\) and \(A_{Vertical}\) = 0%) at \(F^{ext}\) = 60.0 and 200.0 pN is presented in Figure 10.  
It can be observed (refer to Figure 10) that the change in \(D_{A}\) and \(D_{T}\) cell diameters in comparison to the recovered cell state increases with \(A_{Vertical}\), and indicates a similar form to that of the evolution of cell \(EI\) during storage. As expected, the change in \(D_{A}\) and \(D_{T}\) at equivalent \(A_{Vertical}\) increases with \(F^{ext}\) as a response to the increased external stretching forces. The increasing change in \(D_{A}\) and \(D_{T}\) with \(A_{Vertical}\) demonstrates the increased cell fluidity in the presence of decreased cytoskeleton and lipid-bilayer interactions. The cells showed a higher \(D_{A}\) than \(D_{T}\) to accommodate the applied stretching forces while maintaining cell reference conditions, and stretch along the axial direction of stretching. The observed lower change in \(D_{A}\) of echinocyte I morphology at \(t\) = 21 days can be attributed to the slight deviations of CG-RBC membrane model-predicted echinocyte I morphology at \(t\) = 21 days from an ideal echinocyte I morphology. However, it is difficult to distinguish any significant difference in the evolution of \(D_{A}\) of stored RBCs in the presence of high \(F^{ext}\) (= 200.0 pN) and \(A_{Vertical}\) (= 25%). This demonstrates the insignificant dependency of changes in cell morphology, \(\mu(t)\), \(\kappa(t)\), \(A_{0}(t)\), \(A_{k0}(t)\), and \(V_{0}(t)\) on RBC stretching response at very high \(F^{ext}\) and \(A_{Vertical}\), and the  
Figure 9: The equilibrium cell shapes of day 42 sphero-echinocytes with (**a**) \(A_{Vertical}\) = 0% and (**b**) \(A_{Vertical}\) = 25%, and the stretched cell state of (**a,b**) under optical tweezers stretching forces of \(F^{ext}\) = 200 pN; (**c,d**), respectively. The lines in black on the cell surface indicate the membrane surface supported by the cytoskeleton. The circled regions in black on day 42 sphero-echinocytes with \(A_{Vertical}\) = 25% indicate the sharp projections on the cell surface. probability of cell rupture is very high for these RBCs. The present CG-RBC membrane model does not consider cell rupture, but can be extended to investigate the mechanisms of cell rupture of defective cells subjected to mechanical deformation. Influence of Cytoskeletal Actin Junctional Defects during In-Vitro Storage on Cell Recovery following Deformations  
It is also important to investigate the influence of storage-induced membrane defects on cell recovery subjected to mechanical deformation.