## 3 Results and Discussion
### Evolution of Deformation Behaviour of RBCs during In-Vitro Storage
Among those factors that influence the cell stretching response (e.g., spectrin network, intracellular viscosity and cholesterol content), the cytoskeletal spectrin network is the primary contributor for cell stretching response, and differences in cytoskeletal spectrin densities can be observed for different RBC morphologies [28]. During the cell recovery process, the cell can achieve equilibrium and corresponding reference conditions (i.e., \(\Delta A_{0}(t)\), \(C_{0}(t)\), \(A_{0}(t)\), \(A_{k,0}(t)\), and \(V_{0}(t)\)) at different cell features to that of the original state. However, a minimal change in cell features indicates a higher integrity of the cell. Therefore, the recoverability of stretched cells at \(t\) storage-period with a defective cytoskeleton of \(A_{Vertical}=0\), 1, 10 and 25 (%) to its original cell state with \(A_{Vertical}=0\%\) was investigated in terms of cell dimensions. \(H_{1}\), \(H_{2}\) and \(H_{3}\) cell dimensions were estimated and used to estimate the average percentage error (\(\varepsilon\)) for \(H_{1}\), \(H_{2}\) and \(H_{3}\) for the analogous original and recovered cell. The evolution of \(\varepsilon\) of recovered stretched 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 11.  
Figure 10: The change in axial (\(D_{A}\)) and transverse (\(D_{T}\)) diameters of stored RBCs with 0%, 1%, 10% and 25% defective vertical interactions (\(A_{Vertical}\)) with respect to their analogous recovered cell state at optical tweezers stretching forces of (**a**) \(F^{ext}=60.0\) pN and (**b**) \(F^{ext}=200.0\) pN. It can be observed (refer to Figure 11) that the trend of evolution of \(\varepsilon\) increases with storage-period for similar morphologies and decreases during the transition period where irregular RBC morphologies occur. The discocyte morphology during \(0\leq\ t\ <20\) and sphero-echinocyte morphology during \(26\leq\ t\ \leq 42\) each has equivalent \(\mu(t)\), \(\kappa(t)\), \(\Delta A_{0}(t)\) and \(C_{0}(t)\), but varying \(A_{0}(t)\), \(A_{k,0}(t)\), and \(V_{0}(t)\). The cytoskeletal reference state of the CG-RBC membrane model is considered to be an ellipsoidal shape at around 0.94 of the volume of a healthy RBC. Therefore, the cell recovery process after direct axial cell stretching is affected by the increasing cell sphericity and cytoskeletal reference state such that a cell with increased cell thickness results. In addition, the stretching response of cells with similar morphology indicates increasing change in cell diameters with respect to the applied stretching forces. Therefore, the discocyte at day 19 and the sphero-echinocyte at day 42 need to recover a higher change in cell diameters than that of the day 0 discocyte and day 26 sphero-echinocyte, which can be difficult. Similarly, the decreasing cell stretchability with the storage time with respect to increasing \(\mu(t)\) reduces the cell elongation to be recovered, and therefore indicates better cell recoverability during the transition period. In addition, the cell sphericity increases with echinocyte I, echinocyte II, echinocyte III and sphero-echinocyte morphologies, and therefore the cytoskeletal reference state and the evolution of \(A_{0}(t)\), \(A_{k,0}(t)\), and \(V_{0}(t)\) supports better cell recovery during the transition period. The sphero-echinocyte during \(26\leq\ t\leq 42\) with increasing \(A_{Vertical}\) at \(F^{ext}=60.0\) pN indicates better recoverability than that of a healthy RBC. Similarly, it is difficult to achieve a trend to represent the evolution of \(\varepsilon\) for sphero-echinocytes during \(26\leq\ t\ \leq 42\) at \(A_{Vertical}=0\%\), \(1\%\) and \(10\%\) and at \(F^{ext}=200.0\) pN, such that all the numerically predicted \(\varepsilon\) values are contained within.