## 3 Results and Discussion
### Evolution of Deformation Behaviour of RBCs during In-Vitro Storage  
The evolution of deformation behaviour of stored RBCs was investigated for CG-RBC membrane model-predicted RBC echinocytosis. RBC deformability is a measure of cell viability, and gradually decreases with storage duration [29; 83; 84]. The optical tweezers stretching forces were applied on the discocyte, echinocyte I, echinocyte II, echinocyte III and sphero-echinocyte morphologies at \(t\) (Days) = 0, 7, 14, 21, 23, 25, 28, 35 and 42, and the evolution of cell deformability in terms of elongation index (\(EI\)) during storage was determined. \(EI\) was estimated at the equilibrium cell stretched state based on axial (\(D_{A}\)) and transverse (\(D_{T}\)) diameters of the stretched cell [30; 62], such that \(EI=(D_{A}-D_{T})/(D_{A}+D_{T})\). The methods of implementation of optical tweezers stretching forces on the RBC and the estimation of \(EI\) are discussed in Appendix D: Implementation of Optical Tweezers Stretching. The effect on \(EI\) of the discocyte and echinocyte cells at echinocytogenic conditions undergoing optical tweezers stretching at varying membrane shear modulus, spectrin link extensibility, membrane bending modulus and \(\mathbf{d}\) RBC membrane-bead contact diameter, is discussed in [PERSON] et al. [85]. The evolution of \(EI\) of stored RBCs at the total stretching forces of \(F^{ext}=60\), 100 and 200 pN are presented in Figure 7.  
The \(EI\) of each RBC morphology increases with the increase of \(F^{ext}\), and reduces with the storage duration. The \(EI\) of day 42 sphero-echinocyte is significantly lower than that of the day 0 discocyte; 54.44% at \(F^{ext}=60\) pN, 43.39% at \(F^{ext}=100\) pN, and 29.19% at \(F^{ext}=200\) pN. Therefore, the stored RBCs demonstrate significantly lower deformability especially at low \(F^{ext}\). A rapid decrement in \(EI\) can be observed during the transition period (\(20\leq\ t<26\)), and demonstrates the reducing cell deformability with respect to its morphology transformation. These results indicate that the RBC deformability remained unaltered during \(0\leq\ t<20\), and RBCs become difficult to elongate when stored for longer periods and when morphology transformations occur. These observations are consistent with available analogous observations as well [9; 17; 26; 38]. The deformation behaviour of RBCs undergoing optical tweezers stretching is primarily due to the cytoskeletal stretching characteristics [86; 87], and therefore the evolution of \(EI\) is primarily lead by cytoskeletal stretching characteristics (i.e., membrane shear modulus (\(\mu\)) and maximum extensibility of spectrin links (\(x_{0}\))). The gap between \(EI\) values at \(t\) decreases with increasing \(F^{ext}\), and can be attributed to the influence of \(x_{0}\) such that the stretchability of the cell is inhibited at higher \(F^{ext}\). The \(EI\) of echinocyte I morphology at \(t=21\) (Days) indicates a lower \(EI\) in comparison to the predicted general \(EI\) evolution during storage. The definition of \(EI\) becomes less suitable for irregular shapes [26], and therefore this observation may result from the uneven undulations on the rim of echinocyte I cells at \(t=21\) (Days). A slight increment in \(EI\) was observed between similar morphologies with respect to the storage duration; for the discocyte morphology at \(t\) (Days) = 0, 7 and 14, and also for the sphero-echinocyte morphology at \(t\) (Days) = 28, 35 and 42. Figure 7: Evolution of elongation index (\(EI\)) of stored RBCs (discocyte at \(0\leq\ t<20\); echinocyte I at \(20\leq\ t<22\); echinocyte II at \(22\leq\ t<24\); echinocyte III at \(24\leq\ t<26\); and sphero-echinocyte at \(26\leq\ t\leq 42\)) at the total optical tweezers stretching forces of \(F^{ext}=60\), 100 and 200 pN. The evolution of \(\mu(t)\) and \(\kappa(t)\) during storage is comparable with the morphology transition (refer to Section 2).