# A Workflow for Creating Gastric Computational Models from SPARC Scaffolds
## 3 Results  
### Generation of Computational Models  
Three FEM models generated from the rat stomach scaffold had varying mesh properties (see Table 1) and have been made publicly available ([[https://doi.org/10.6084/m9.figshare.25241770.v2](https://doi.org/10.6084/m9.figshare.25241770.v2)]([https://doi.org/10.6084/m9.figshare.25241770.v2](https://doi.org/10.6084/m9.figshare.25241770.v2)), accessed on 7 November 2024). The 2D surface model had approximately 24 thousand nodes (i.e., solution points) and 47 thousand elements. The 3D volume models had a much higher number of nodes and elements. While the fixed thickness model had 1.5 million nodes and 6.7 million elements, these numbers were nearly doubled in the varying thickness model with 2.5 million nodes and 11.5 million elements. The ratio of the longest edge to the shortest edge in an element (known as the aspect ratio) was between 1 and 2 for all elements in the 2D surface model with an average edge length of 0.33 \(\pm\) 0.03 mm (see Figure 3). Similarly, the aspect ratio was between 1 and 4 for more than 90% of the elements in both fixed and varying thickness volume meshes each with average edge lengths of 0.07 \(\pm\) 0.04 mm and 0.05 \(\pm\) 0.04 mm, respectively.  
The three FEM models had notable differences in the density of nodes and elements as seen in Figure 4a-c. The color in each figure corresponds to the total wall thickness (i.e., the combined thickness of the LM and CM layers) across the stomach. While the 2D surface model had no thickness, the fixed thickness 3D model had a total wall thickness of 115 \(\upmu\)m (LM: 25 \(\upmu\)m and CM: 90 \(\upmu\)m) in the entire stomach. The varying thickness mesh, on the other hand, had the thickest wall near the lower esophageal sphincter mainly due to the CM layer thickness, which was as high as 268 \(\upmu\)m in this region. The corpus region on the greater curvature had the lowest total wall thickness with around 61 \(\upmu\)m, nearly half of the thickness the scaffold had in that region. The root-mean-squared error of thickness fitting computed for the 30 fiducial points from the experimental data was 0.3 \(\upmu\)m and 1.6 \(\upmu\)m for the LM and CM layers, respectively.  
The fiber orientations computed for the longitudinal and circular muscle layer were displayed in Figure 4d,e. The LM fibers were consistent with experimental observations and generally oriented along the stomach axis while they rotated toward the middle in the fundus, creating a fingerprint-like structure [14]. The CM fibers had an orientation from the greater curvature to the lesser curvature in the corpus and antrum and encircled the fundic cap as reported in [14] (see Figure 4e). While the 2D surface model contained only the circular muscle fibers, both the LM and CM fibers were included in the two 3D volume models.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Number of Nodes** & **Number of Elements** & \
\begin{tabular}{c} **Average Edge Length** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **Solution Time** \\ **(hours)** \\ \end{tabular} \\ \hline
2D Surface Mesh & 23,510 & 46,894 & 0.33 \(\pm\) 0.03 & 0.1 \\ \hline
3D Fixed Thickness Mesh & 1,488,257 & 6,677,962 & 0.07 \(\pm\) 0.04 & 26 \\ \hline
3D Varying Thickness Mesh & 2,534,889 & 11,466,050 & 0.05 \(\pm\) 0.04 & 38 \\ \hline \end{tabular}
\end{table}
Table 1: Mesh properties of the three computational meshes with the solution times of a 200 s slow wave simulation.  
Figure 3: The distribution of element aspect ratios (i.e., the ratio of the longest edge to the shortest edge within an element) in the computational meshes. While all the elements in the 2D surface model had aspect ratios between 1 and 2, more than 90% of the elements in the two 3D volume models had aspect ratios between 1 and 4.