## 2 Materials and Methods
### Vocal Fold Agent-based Models
#### 2.2.3 Model Calibration  
The Statistical Parameter Optimization Tool for Python (SPOTPY) package was used for parameter calibration [98]. The SPOTPY package has a library of algorithms and objective functions for model calibration and verification. The algorithm has five major steps: (1) Sampling, (2) Simulation, (3) Evaluation, (4) Objective Function and (5) Parameter Estimation. Sampling was implemented for the most important parameters based on the sensitivity analysis using a uniform distribution and a predefined range. After sampling was done, the simulation was executed with the generated parameter set using the sampling function and the output was stored as simulated data. In our case, the empirical flow cytometry data were used as evaluation data. An objective function was then used to estimate the performance of the model for that given parameter set. The root mean square error (RMSE) was then used as the objective function, which determines the fitness of simulated data to evaluated data. RMSE is given by  
\[RMSE=\sqrt{1/m\sum_{i}^{m}(e(i)-s(i))^{2}} \tag{3}\]  
Here, \(e(i)\) is evaluated data, \(s(i)\) is simulated data and \(m\) is the total number of parameters. Lastly, the Robust Parameter Estimation (ROPE) algorithm was used for parameter optimization based on the concept of data depth [98]. Data depth refers to a statistical method that assigns a numerical value to a data point with respect to a set of points based on its centrality. It is a non-parametric multivariate statistical method that no distributional assumptions are needed [98; 99]. ROPE was selected for VF-ABM calibration because it accelerates the calibration process by iteratively using information from previous simulations to estimate the outputs of subsequent ones [98; 100]. The principle of ROPE is to identify a set of parameter vectors with the high model performance and subsequently generate a set of parameter vectors with high data depth with respect to the first set [98; 100]. Instead of requiring thousands of random parameter sets, ROPE uses the results from the previous simulation as knowledge to define the parameter sets for the subsequent simulations. ROPE is recommended when the model requires parallel computing and the simulations are expensive, as the case of VF-ABM herein [98; 100]. According to ROPE, the top 10% results are used to generate the next parameter sets. After estimating the best set of parameters, the algorithm repeats the sampling again. This time, the algorithm uses parameter sets learned from previous runs to determine the parameter set for the next run. The procedure repeats either until the defined number of iterations is reached or the RMSE reaches zero. In the present study, flow cytometry data from the first four time-points (Day 1, Day 2, Day 3 and Day 5) was used and the VF-ABM was run 800 times iteratively for each calibration step (Figure 1). Figure 1: Workflow of VF-ABM Calibration. A total of 36 top parameters were ranked for each cell type at each time point. Twelve of them were overlapped across conditions. As a result, a total of 24 unique parameters were used for calibration. The top three parameters for each cell type (neutrophils, macrophages and fibroblasts) for each time point were used to proceed for calibration. Hence, a total of 36 top parameters were ranked for each cell type at each time point (3 parameters x 3 cell types x 4 time points); however, 12 of these parameters were found to be the same across certain conditions. As a result, a set of 24 unique parameters was calibrated iteratively with all other parameters being fixed as constants until the model eventually yielded a satisfactory match between simulation data and empirical data. All four time points (Day 1, Day 2, Day 3 and Day 5) were first calibrated for each cell type individually and calibrated values of parameter sets for each cell type were determined.