# A 3D Agent-Based Model of Lung Fibrosis
## 4 Discussion  
In this study, we outlined the development of a hybrid 3D ABM of lung fibrosis. The disease has been shown to be triggered by many factors, and its pathophysiology has not been fully understood yet. Within this context, mathematical models and computational  
Figure 7: Relative parameter sensitivity map showing the impact of changes in the parameters on the characteristics. For each pair of characteristic \(c\) and parameter \(p\), \(r_{c,p}\) indicates the ratio between the sensitivity \(S_{c,p}\) and the maximum absolute value of \(S_{c,p}\) for that particular characteristic (i.e., computed over an entire row). simulations have the potential to shed light on its mechanistic progression and allow for the testing of potential treatment candidates beforehand without the need for laboratories. The simulation space of our model consists of a partial acinus built from morphometric data, in which stationary alveolar ducts act as agents whose behaviors are derived from biological findings and previous computational models. Each agent encompasses six distinct cell types secreting ten different extracellular substances. The results that we provide show that the model can qualitatively simulate the onset of fibrosis and represent a valuable extendable framework that can reproduce further scenarios on smaller and larger spatial and temporal scales. It should be noted that while the model may be seen as static, the shared extracellular space acts as a mutable environment, thus making it a time-varying network in which geometry plays a strong role. We first calibrated the parameters of our model so that it could reproduce stationary homeostatic conditions for a time frame of 30 days. Specifically, we adjusted the secretion, proliferation, differentiation, and apoptotic rates of the cells within the agents in order to reproduce and maintain the initial conditions provided by [PERSON] et al. [48]. To assess whether the model was able to reach its steady-state and that both the concentration of the extracellular mediators and the number of cells did not drift from the experimental values, we measured their time evolution along with their relative change. We showed that the simulated values never exceeded the 10% threshold, while their relative change remained below 0.005% for the entire simulated time frame. It should be noted that the concentration of the substances shown in Figures 4-6 is the average concentration measured within the cell-hosting voxels of the diffusion grids. We performed a parameter sensitivity analysis on 5 selected parameters and assessed their impact on 14 different characteristics (namely, the number of cells and the substances' concentration) in steady-state and homeostatic conditions. The analysis showed that, among the selected parameters, \(\lambda_{M01}\) had the greatest impact on the majority of the simulation readouts, highlighting the central role of macrophages in the model. The second step introduced the external damage: we investigated the effect of different fractions \(\overline{f}\) of damaged AEC2 cells at the beginning of the simulations and simulated heterogeneous damage by drawing those fractions from normal distributions with average \(\overline{f}\) and \(\sigma=1\%\). It has to be noted that incorporating heterogeneous damage allowed our model to run more realistic simulations as the amount of damage is randomly distributed in human fibrotic lungs. Moreover, the presence of randomness in individual behavior is a distinctive feature of ABM that cannot be implemented within traditional averaging methods (such as EBMs). Heterogenous fractions of damaged AEC2 cells result in different distributions of MCP1 that, in turn, show different chemoattractant effects on M1 cells. This indirectly affects the number of M2 cells within each alveolar duct and alters the amount of secreted TGF\(\beta_{\alpha}\), which is reflected by different ECM patterns.