## 2 Methods
### Evolution of Coarse-Grained (CG)-RBC Membrane Model Parameters during In-Vitro Storage
The \(\mu(t)\) corresponding to echinocyte I, echinocyte II and echinocyte III during the transition period was determined through linear interpolation of \(\mu(t)\). Similarly, the evolution of \(\kappa(t)\) was determined based on the measurements of RBC membrane mechanics by [PERSON] et al. [47]. It can be observed (refer to Figure 4a of [PERSON] et al. [47]) that the spherocyte morphology has the highest membrane bending modulus, whereas the echinocyte has an intermediate membrane bending modulus. The evolution of \(\kappa(t)\) was determined in agreement with these observations such that the measured membrane bending modulus of the discocyte [47] is  
Figure 2: The evolution of the Coarse-Grained (CG)-RBC membrane: (**a**) shear modulus (\(\mu(t)\)) and (**b**) bending modulus (\(\kappa(t)\)) during in-vitro storage. \(\mu(t)\) and \(\kappa(t)\) are presented in the form of multiplications of \(\mu(t_{0})\) and \(\kappa(t_{0})\), respectively. comparable with a \(\kappa(t)\) of up to 20 days of in-vitro storage (i.e., bending modulus of the discocyte \(\propto\kappa(t)\); \(0\leq t<\)20) and the measured membrane bending modulus of the spherocyte [47] is comparable with a \(\kappa(t)\) from day 26 of in-vitro storage (i.e., bending modulus of the spherocyte \(\propto\kappa(t);26\leq t\leq 42\)). The \(\kappa(t)\) corresponding to echinocyte I, echinocyte II and echinocyte III during the transition period was determined through linear interpolation of \(\kappa(t)\). The evolution of \(\kappa(t)\) during in-vitro storage is presented in Figure 2b. The cell surface area is an important property of RBCs as the exchange of oxygen and carbon dioxide takes place at the cell surface. A higher cell surface area is required for improved gas exchange in the lungs and body tissues [78]. However, RBCs lose their cell membrane during cell aging, and the cell becomes smaller and denser during storage [38]. The evolution of \(A_{0}(t)\) and \(V_{0}(t)\) was determined based on the data extracted from 3D confocal microscopy imaging of RBCs during in-vitro storage ([PERSON], personal communication, 10 October 2018). The RBC surface area and volume measurements for the discocyte, echinocyte I, echinocyte II and echinocyte III cell morphologies corresponding to three donors during 42 days of in-vitro storage in SAGM additive solution are presented in Appendix C: Measurements of Cell Surface Area and Volume of RBC during In-Vitro Storage--Experimental Observations. Figure 3 represents the general evolution of cell surface area and volume during in-vitro storage. The loss of membrane surface area and volume results in an increased concentration of micro-particles in the extracellular additive solution, and a notable increase of micro-particle concentration is observed from day 28 onwards [9; 20; 79]. In agreement with these observations, the evolution of cell surface area and cell volume was considered for two in-vitro storage durations such that \(0\leq\ t\ <28\) and \(28\leq\ t\ \leq 42\), and the expressions as in Equations (1) and (2) respectively, were established to reflect this evolution. The coefficients of Equations (1) and (2) are estimated based on the linear regression relationships between storage duration (i.e., dependent variable) and cell surface area and volume (i.e., independent variable) for the two in-vitro storage durations (i.e., \(0\leq\ t\ <28\) and \(28\leq\ t\ \leq 42\)). The local surface area of the RBC membrane was assumed to follow the evolution of \(A_{0}(t)\), and the reference area of the \(k^{th}\) triangle of the CG-RBC membrane model (\(A_{k,0}(t)\)) was estimated according to Equation (3). \(A_{k,0}(t_{0})\) is the reference area of the \(k^{th}\) triangle at day 0, and is adopted from Appendix B: Prediction of Discocyte, Echinocyte I, Echinocyte II, Echinocyte III and Sphero-Echinocyte RBC Morphologies. \[A_{0}(t)= \begin{cases}\frac{-0.4232\ t+A_{0}(t_{0})}{A_{0}(t_{0})}&0\ \leq\ t<28\\ \frac{-0.7907\ t+1.08\ A_{0}(t_{0})}{A_{0}(t_{0})}&28\ \leq\ t\ \leq\ 42\\ \end{cases}  \tag{1}\]  
\[V_{0}(t)=