## 2 Materials and Methods
### Analysis of Stretching Behavior of the Planar Specimens  
To compare Patterns A and B in mechanical performance, a single unit was taken out of each of the stent patterns to characterize the shape of the peak-to-valley struts, as shown in Figure 1. We labelled these struts unit A (in stent design Pattern A) and unit B (in stent design Pattern B).  
The mechanical responses of these two stent design patterns in the planar form were analyzed using FEA. Considering the geometric features of the stent design patterns, the pattern unit was modeled using beam elements. The same material properties of the AZ31 alloy, given in Section 2.1, and the same boundary conditions were applied in the FE models of the single unit of the two planar patterns. Stretching deformation of the strut unit of the patterns was performed in an FE analyzer ABAQUS/Standard (Dassault Systemes Simulia Corp., Johnston, RI, US). The strut unit was fixed in the x and y directions at the peak, and a displacement of 0.1 mm in the x direction at the valley was applied.  
Assuming the single unit acted like a spring with a displacement-dependent stiffness coefficient, the whole mesh of the pattern could be considered to be springs hooked together either in a series combination or in a parallel combination. The displacement-dependent stiffness coefficients of the single unit of the stent patterns were calculated from the simulated force \(F\) and displacement \(x\) at the valley:  
\[\text{Stiffness coefficient}:k_{\text{unit}}=\frac{dF}{dx} \tag{1}\]  
The stiffness coefficients of the planar stent patterns, \(k_{\text{s}}\) and \(k_{\text{p}}\), were calculated from the stiffness coefficients of the cell unit:  
\[\text{In series (in a stent ring)}:k_{\text{s}}=\frac{k_{1}k_{2}}{k_{1}+k_{2}} \tag{2}\]  
\[\text{In parallel (in a plurality of stent rings)}:k_{\text{p}}=k_{\text{S1}}+k_{\text{S2}} \tag{3}\]  
where \(k_{1}\) and \(k_{2}\) are the stiffness coefficients of the single unit in series in a stent ring, \(k_{1}=k_{2}=k_{\text{a}}\) in Pattern A and \(k_{1}=k_{2}=k_{\text{b}}\) in Pattern B. \(k_{\text{s1}}\) and \(k_{\text{s2}}\) are the stiffness coefficients of the single unit in a plurality of rings in parallel.  
Figure 2: Tensile stress-strain curves of the magnesium alloys AZ31 and AE21.  
To arrange a plurality of stent rings over a length of 16-18 mm (representing the typical length of a coronary artery stent), nineteen rings could be laid out in the axial direction with Pattern A and eight rings with Pattern B. The ring with Pattern A contained twelve units and the ring with Pattern B contained eight units. Thus, the stiffness coefficients of the whole planar meshes with Patterns A and B could be calculated using Equations (4) and (5), respectively.  
\[\text{Pattern A}:k_{\text{A}}=\frac{1}{12}k_{\text{a}}\times 19=\frac{19}{12}k_{ \text{a}} \tag{4}\]  
\[\text{Pattern B}:k_{\text{B}}=\frac{1}{8}k_{\text{b}}\times 8=k_{\text{b}} \tag{5}\]  
The stent mesh with Pattern A would have a much higher stiffness value than that with Pattern B. Patterns A and B would have individual advantages in mechanical performance, i.e., higher stiffness for Pattern A and better deformability for Pattern B.