# A 3D Agent-Based Model of Lung Fibrosis
## 3 Results
### Inflammation  
To simulate the onset of fibrosis, our model is run with an initial amount of damaged AEC2 cells and replicates a time frame of 300 days. Different runs are performed for different initial (average) fractions \(\overline{f}\) of damaged AEC2, where \(\overline{f}\in\{6.25,10,20,30,40,50,60,70,80,90\}\%\) and the damage is heterogeneously spread over the simulation space (i.e., the fraction of damaged AEC2 cells within each alveolar duct is drawn from a normal distribution with average \(\overline{f}\) and \(\sigma=1\%\)). More specifically, the value \(\overline{f}=6.25\%\) allows us to compare the  
Figure 4: Time evolution of the extracellular mediators’ average local concentration (**a**) and the average number of cells per alveolus (**b**) in homeostatic conditions. Red bands show the steady-states from the literature \(\pm 10\%\). results from our simulations against those shown in [48] since the study reports the steady-state ratio \(\frac{ActCatCatACE}{InitialACE}=0.0625\). Rather than a continuous damage (as proposed in [48]), healthy AEC2 cells in our model are damaged only at the beginning of the simulation and the active AEC2 cells cannot undergo apoptosis (i.e., they are never removed from the simulation). We make this assumption as our model aims to simulate the onset of lung fibrosis regardless of the cause for the damage to the AEC2 cells. The initial conditions are listed in Table S1, and the results, shown in Figure 5, are expressed in Section 3.1. Figure 5: Time evolution of the extracellular mediators’ average local concentration (**a**) and the average number of cells per alveolus (**b**) with initial heterogeneous damage. Different colors show different initial average fractions of damaged AEC2, and the thicker lines are used for \(\overline{f}=6.25\%\). Though with slower dynamics, our results (for \(\overline{f}=6.25\%\)) are in agreement with those provided by [PERSON] et al. [48]. ECM accumulation, a surrogate of lung fibrosis severity, shows incremental rises for \(\overline{f}\leq 40\%\). On the other hand, for \(\overline{f}>40\%\), the healthy AEC2 cells are unable to support the mesenchymal population, whose drop leads to a progressive decline in the final ECM concentration. This notwithstanding, we show that the loss of AEC2 progenitor cells is reflected by a sharp decline in the number of AEC1 cells that has been experimentally detected in lung fibrosis patients as a depletion in epithelial integrity [9]. In order to assess how the degree of damage correlates with the ECM distribution across the simulation space, the ECM concentration in each cell-hosting voxel of the diffusion grid is measured during the last time step of the 300-days simulated time frame. By taking the ECM concentration as a surrogate for the attenuation coefficient (the use of which to monitor lung fibrosis is ordinary in the clinic [59]), we show the results through density distribution histograms in Figure 6.  
Although Figure 6 provides the density distribution histograms for a late fibrotic phase only, the trends shown are qualitatively in agreement with the results provided in [59; 60], where lung fibrosis is induced by radiotherapy in mice. As expected, a right shift is observed for \(\overline{f}\leq 40\%\), while the ECM density distributions progressively shift towards left for higher \(\overline{f}\) values. It should be noted here that this kind of simulation output could be compared (after an appropriate conversion) against clinical lung CT readings, a feature that cannot be provided by 2D models and/or averaging methods. The three-dimensionality of our model enables the emergence of peculiar patterns and provides additional information to the curves showing the average ECM concentration. Interestingly, multiple animal and human studies [59; 60; 61; 62; 63; 64] have shown that higher irradiation doses (corresponding to  
Figure 6: ECM distribution histograms for different initial fractions of damaged AEC2 cells (damage is heterogeneous).