**3. Results**

We proposed two experiments to validate the in silico model. In the first experiment, we compared cell sedimentation velocity to validate the mechanical model as well as the ECM and cell interactions considering a few cells in a large-scale ECM. The duration of the experiment was adapted to the time required for cell sedimentation. In the second experiment, we compared cell proliferation in a reduced slice of the ECM, starting with the same cell concentration as described in Section 2.2, considering four days of cell–cell and cell–ECM interactions. In this experiment, we increased the number of cells and the geometry to study tumor aggregates' growth.

### *3.1. Cell Sedimentation*

The velocity of cell sedimentation was compared to that of in vitro models found in the literature [44]. We compared the evolution of cell sedimentation velocity using a reference portion of the ECM with a base of 30 × 30 μm and a height of 4.5 mm. The results were compared using the mean values from five cases with different initial cell distributions. In all cases, cells were seeded in the ECM with a random distribution, with an equivalent initial cell concentration in the in vitro experiment used as a reference (5 × 10<sup>5</sup> cells/mL) [44]. The time step increment was decoupled for cell position tracking (0.1 s) and fluid time step (5 s), and the cell sedimentation velocity was obtained for all cells over a simulation time of 15 min.

The mean cell sedimentation velocity for both computational models was around 13 mm/h (Figure 2), which is consistent with the experimental results [44]. The obtained curves with both models have been compared with the reference data, through the value of the mean square error (MSE), obtaining values of 0.0026, and 0.0029 for the ABQ and ANS models, respectively. As the objective of the case was the calibration and validation of the models, it is possible to conclude that both models give a valid approximation. In addition, the difference between them is not significant. Higher velocities were obtained using the ANS model, which considered the inertial effects of cells, as well as the changes in cell diameter, which is related to the cell maturation state. The ABQ model was unable to reproduce the maximum velocity (16 mm/h), and the cell distribution velocity observed was more homogeneous.

**Figure 2.** Distribution of mean cell sedimentation velocity per unit cell. The results obtained were compared to the in vitro results (red). The results of the ANS model showed a wider cell sedimentation velocity due to variational inertial forces and a non-homogeneous cell diameter (MSE = 0.0029), while the ABQ model revealed a lower distribution of the cell velocity due to the more homogeneous conditions considered (MSE = 0.0026).

### *3.2. Cell Proliferation*

Cell proliferation was compared to the experimental data detailed in Section 2.2 [38]. Similarly to the first case (cell sedimentation) the results were compared with five different initial cell distributions. Based on the initial cell concentration described in Section 2.2, 20 MMCs were randomly seeded in an ECM of 200 × 200 × 200 μm, with their initial state of maturation being randomly assigned. Due to differences in the timescale of the various events, different time step increments were considered for the fluid domain (0.5 h), cell position tracking (1 s), and cell processes (0.5 h), for a total time of 96 h.

The cell distribution and initial state of maturation were randomly assigned for both computational models (Figure 3 top). After 10–30 h, depending on the initial state of maturation considered in each case, a few cells proliferated. The proliferated cells were randomly scattered around the mother cells. After four days of simulation, several cell distributions were observed in all cases (Figure 3 bottom), although the final number of cells was always comparable (240–260 cells). The results of cell proliferation were normalized with respect to the initial cell number and compared with the in vitro experiments (Figure 4a). In general, cell proliferation was consistent with the experimental data, and the ANS model exhibited greater homogeneity in terms of cell proliferation. An increase in the variability of cell proliferation was observed at later times, with a higher number of cells and higher variability in terms of the specific conditions of each cell (Figure 4b).

**Figure 3.** MI during 96 h of simulation using the ABQ (**a**) and ANS (**b**) models. MMCs were seeded in a random initial distribution, and at a random initial state of maturation (**top**). After 96 h of cell-in-culture simulation, MMC aggregates started to form (**bottom**) (see also Supplementary Material Videos S1 and S2).

**Figure 4.** Cell doubling. (**a**) Comparison of the mean values after 96 h in a cells-in-culture simulation using the ANS and ABQ models, with results of the in vitro model (Section 2.2). (**b**) Dispersion of the results due to the random nature of the experiment.

### *3.3. Tumor Aggregation Growth*

After calibration and validation of the initial model, the formation of tumor aggregates, due to the proliferation of individual cells, was studied in a long-term case. Cells were initially distributed into groups to form cell aggregates in an ECM of 400 × 400 × 50 μm, then were simulated for 360 h.

The number of cells in each cluster increased due to cell proliferation and, after 30 h, all clusters were considered to be tumor aggregates (minimum of 30 cells). Given the increase in the number of cell–cell contacts (∼6.1% per hour), the internal cells in these aggregates showed the highest increase in maturation rate (∼30.3%). However, once the cell was completely surrounded, cell proliferation was inhibited due to the lack of space (Figure 5). After 60 h, tumor aggregates started to merge with each other, and by the end of the simulation, all cells had joined together to form a single cluster. The cell proliferation

rate was higher in the first 48 h, when exponential cell growth was observed, and then progressively reduced as more cells became completely surrounded (Figure 5d).

**Figure 5.** Tumor aggregate growth. (**a**) Initially, cells were randomly distributed into groups of 20–30 cells. (**b**) After 48 h, cell groups merged, and the inner cells of the aggregates lost their ability to proliferate. (**c**) Surface cells continued to proliferate up until 360 h of simulation. (**d**) Cell growth for 360 h of simulation (log scale) (see also Supplementary Material Video S3).
