## 2 Materials and Methods
### Vocal Fold Agent-based Models
#### 2.2.2 Sensitivity Analysis  
The goal of sensitivity analysis was to determine the influence of model parameters on the ABM cell count outputs in order to reduce the number of parameters for calibration by selecting the most important parameters. Random Forests were chosen as the sensitivity analysis method herein because it does not require many samples for the implementation and thus makes the computational cost feasible for the notable scale of VF-ABM. Random Forests use an ensemble method with decision trees that are constructed using bootstrapping [94] (see Figure S2 for the workflow of Random Forests in Supplementary Materials). To split the node on any variable (or parameter) within a tree, the GINI impurity criterion (GINI Index) is used [95; 96]. The GINI Index for two descendent nodes should be less than that of the parent node. A node is split if the change in GINI Index is significant [95], i.e.,  
\[\Delta i(t)=i(t)-\ \frac{N_{L}}{N}i(t_{L})-\ \frac{N_{R}}{N}i(t_{R}) \tag{1}\]  
where, \(t_{L}\) is the node on the left, and \(t_{R}\) the node on the right, \(N_{L}\) is the number of samples on left node and \(N_{R}\) is the number of samples on right node. The importance of any variable (or parameter) is determined by Mean decrease GINI, given by [95]  
\[I(P)=\ \sum_{T}\sum_{N}\Delta i_{P}\ (N,\ T) \tag{2}\]  
The mean decrease GINI (_I_) for a parameter (_P_) is evaluated by adding up the weighted GINI indices (_i_) for all nodes (_N_) where parameter \(P\) is used (averaged over all trees \(T\) in the forest) [95]. This quantity indicates how often a parameter \(P\) was selected for a split and provides a relative ranking of the parameters. \begin{table}
\begin{tabular}{c c c c} \hline
**Item** & **Unit** & **Size** & **Reference** \\ \hline \multirow{2}{*}{Vocal Fold Width} & mm & 1 & [35] \\  & patches & 142 & \\ \hline \multirow{2}{*}{Vocal Fold Height} & mm & 1 & [35] \\  & patches & 142 & \\ \hline \multirow{2}{*}{Vocal Fold Thickness} & mm & 0.2 & [35] \\  & patches & 28 & \\ \hline \multirow{2}{*}{Vocal Fold Epithelium Thickness} & mm & 0.01 & [31] \\  & patches & 1 & \\ \hline \multirow{2}{*}{Capillary Diameter} & \(\mu\)m & 7 & [28] \\  & patches & 1 & \\ \hline \multirow{2}{*}{Capillary Gap} & \(\mu\)m & 12.89 & [28] \\  & patches & 1 & \\ \hline \multirow{2}{*}{Patch size} & \(\mu\)m & \(7\times 7\times 7\) & \\ \hline \multirow{2}{*}{Total number of patches} & patches & 564,592 & - \\ \hline \multirow{2}{*}{Total number of non-epi patches} & patches & 544,428 & - \\ \hline \multirow{2}{*}{Total number of capillary patches} & patches & 138,450 & - \\ \hline \multirow{2}{*}{Total number of tissue patches} & patches & 405,978 & - \\ \hline \multirow{2}{*}{Simulated time-step Neutrophils} & Minutes & 30 & - \\  & \(\mu\)m & 7 & [29] \\  & Cells & 517 & Flow data \\ \hline \multirow{2}{*}{Macrophages} & \(\mu\)m & 6 & [30] \\  & Cells & 316 & Flow data \\ \hline \multirow{2}{*}{Fibroblasts} & \(\mu\)m & 6 & [29] \\  & Cells & 3594 & Flow data \\ \hline \end{tabular}
\end{table} 
Table 4: Initial configurations of VF-ABM. To find the suitable number of iterations, \(n\) for our sensitivity analysis, pilot tests were implemented with \(n\) = 3000, 4000, 4500, 5000, and 5500. It was observed that after 4500, the top three parameters for each cell type and time-point were identical and thus \(n\) = 5000 was chosen for this study. Sensitivity analysis using Random Forest was then implemented independently for the first four time-points (Day 1, Day 2, Day 3 and Day 5) as these time points would be used for the subsequent calibration. The R package _RandomForest_ was implemented in our computations (Algorithm 2) [97]. The user setting was set as (1) Number of Input parameters = 213, (2) Number of Output Parameters = Neutrophils, Macrophages, or Fibroblasts and (3) Number of Samples/ Number of Iterations of Model = 5000. The ranking of parameter importance was then obtained by sorting the parameters according to their Mean Decrease GINI.