## 2 Methods
### CG-RBC Membrane Model-Predicted RBC Morphologies during In-Vitro Storage  
The in-vitro storage effects were implemented on a CG-RBC membrane model to predict the analogous RBC time-dependent echinocytosis process. Identical model parameters and constraint coefficients as in Appendix B: Prediction of Discocyte, Echinocyte I, Echinocyte II, Echinocyte III and Sphero-Echinocyte RBC Morphologies, except for \(\mu(t)\), \(\kappa(t)\), \(A_{0}(t)\), \(A_{k,0}(t)\), \(V_{0}(t)\), \(\Delta A_{0}(t)\) and \(C_{0}(t)\), were adopted to predict the RBC morphology at \(t\) (Days) = 0, 7, 14, 21, 23, 25, 28, 35 and 42. The RBC morphology at the above time points during in-vitro storage was predicted as the stable minimum energy configuration at equivalent reference conditions, and is presented in Table 1. The numerically predicted RBC morphologies at day \(t\) qualitatively agree well with both the corresponding morphology characteristics given by [PERSON]'s classification [75,77] and with the corresponding experimental observations [74,75,76,77] for discocyte, echinocyte I, echinocyte III and sphero-echinocyte morphologies. It can be observed that the thickness of the biconcavity of the discocyte morphology increases with \(t\), and the cell diameter reduces in response to the increased reduced cell volume at \(t\)  
Figure 4: The evolution of the CG-RBC membrane model predicted a **(a)** reference bilayer-leaflet-area-difference (\(\Delta A_{0}(t)\)), and **(b)** reference total-membrane-curvature (\(C_{0}(t)\)) during in-vitro RBC storage. Figure 3: Evolution of **(a)** cell surface area (\(A_{0}(t)\)), and **(b)** cell volume (\(V_{0}(t)\)) of in-vitro stored RBCs. In addition, the discocyte cell shape at \(t=7\) (Days) and \(t=14\) (Days) indicate uneven cell thickness on its rim, and the echinocyte I at \(t=21\) (Days) has uneven undulations around its rim. The loss of RBC membrane surface area during in-vitro storage induces increased levels of stress on cytoskeletal spectrin links, and this may affect the equilibrium cell state and morphology at \(t\). Moreover, the cytoskeletal reference state is predicted at an equivalent membrane shear modulus (\(\mu(t_{0})\)), membrane bending modulus (\(\kappa(t_{0})\)), membrane surface area (\(A_{0}(t_{0})\)) and cell volume (\(V_{0}(t_{0})\)) of a healthy RBC at \(t=0\). Therefore, the cytoskeleton is subjected to increased lateral compression due to the loss of membrane surface area during storage. These changes during in-vitro storage may have influenced the predicted RBC morphology at \(t\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Days**} & \multicolumn{6}{c}{**CG-RBC Membrane Model Parameters at \(t\)**} \\ \cline{2-7}  & \(\frac{\mu(t)}{\mu(t_{0})}\) & \(\frac{\kappa(t)}{\kappa(t_{0})}\) & \(\frac{A_{0}(t)}{A_{0}(t_{0})}\) & \(\frac{V_{0}(t)}{\overline{V}_{0}(t_{0})}\) & \(\frac{\Delta A_{0}(t)}{A_{0}(t_{0})}\) & \(\frac{C_{0}(t)}{A_{0}(t_{0})}\) \\  & & & & & & \\ \hline
0 & 1.000 & 1.000 & 1.000 & 1.000 & 0.120 & 0.185 \\ \hline
7 & 1.000 & 1.000 & 0.976 & 0.974 & 0.120 & 0.185 \\ \hline
14 & 1.000 & 1.000 & 0.953 & 0.947 & 0.120 & 0.185 \\ \hline
21 & 1.452 & 1.956 & 0.929 & 0.921 & 0.135 & 0.200 \\ \hline
23 & 1.905 & 2.911 & 0.923 & 0.913 & 0.190 & 0.550 \\ \hline
25 & 2.357 & 3.867 & 0.916 & 0.906 & 0.225 & 0.600 \\ \hline
28 & 2.583 & 4.345 & 0.906 & 0.895 & 0.300 & 0.900 \\ \hline
35 & 2.583 & 4.345 & 0.862 & 0.835 & 0.300 & 0.900 \\ \hline
42 & 2.583 & 4.345 & 0.818 & 0.775 & 0.300 & 0.900 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The CG-RBC membrane model-predicted morphology of in-vitro stored RBC. Shear modulus (\(\mu(t)\)), bending modulus (\(\kappa(t)\)), cell surface area (\(A_{0}(t)\)) and cell volume (\(V_{0}(t)\)) during in-vitro storage are presented in the form of multiplications of \(\mu(t_{0})\), \(\kappa(t_{0})\), \(A_{0}(t_{0})\), \(V_{0}(t_{0})\), respectively, which represent the corresponding parameters at \(t=0\) (Days) (refer to Figures 2 and 3).