**5. Conclusions**

We have presented a new computational model to study MMC behavior and tumor growth. The model was compared to a previous in-house ABQ computational model [29], as wel as with the experimental results obtained by the authors and from the literature [9,10,38,44,46,47]. The results obtained are qualitatively consistent with the literature. The obtained results show that the initial cell concentration has a clear effect on MMC growth, with cell proliferation increasing as the numbers of cell–cell and cell–ECM interactions increase. As such, we observed faster cell maturation for cells with more cell–cell and cell–ECM interactions (reduction in maturation time of up to 69.7%), while cell proliferation was inhibited when a lack of space was observed.

From a computational viewpoint, the ANS model offers several advantages when compared with the model developed previously. Better results for the MMC sedimentation velocity and tumor growth were obtained due to the more representative definition of the fluidic environment and the consideration of a non-homogeneous cell volume. Compared with the ABQ model, we observed reduced computational costs for adequately simulating cells and the cell microenvironment. The maximum number of cells in the ABQ model was limited and proportional to the number of discretized elements in the ECM. In this case, increasing the ECM implied increasing the number of elements, which dramatically increased computational costs. As the ANS model simulation time step seems to be the main responsible of these computational costs, using a decoupled calculation time step for the cells and fluid reduced them. Thus, the model developed herein has significant advantages compared to the previous model in computation, as it results in a significant reduction (84–91%) in computational costs, which allows a more realistic simulation. Although not considered in this model, additional advantages can be added to the ANS model, such as the consideration of nutrient diffusion and consumption, non-stationary fluid flow and pressure gradients, or the presence of blood vessels in an in vivo analysis.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/math11081824/s1, Video S1: Video\_Fig\_3(a); Video S2: Video\_Fig\_3(b); Video S3: Video\_Fig\_5.

**Author Contributions:** Conceptualization, P.U. and M.H.D.; methodology, P.U. and M.H.D.; in vitro analysis, S.C.-T. and J.L.G.R., software, P.U. and M.H.D.; validation, P.U., S.C.-T., J.L.G.R. and M.H.D.; formal analysis, P.U. and M.H.D.; investigation, P.U. and M.H.D.; resources, J.L.G.R. and M.H.D.; data curation, P.U., S.C.-T., J.L.G.R. and M.H.D.; writing—original draft preparation, P.U. and S.C.-T.; writing—review and editing, J.L.G.R. and M.H.D.; visualization, P.U.; supervision, J.L.G.R. and M.H.D.; project administration, J.L.G.R. and M.H.D.; funding acquisition, J.L.G.R. and M.H.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Spanish State Research Agency (AEI/10.13039/501100011033) through the projects PID2019-106099RB-C44 and C41, and the Government of Aragon (DGA-T24 20R). This work was also supported by the Spanish Ministry of Science, Innovation and Universities through Grant N- FPU17/05810 awarded to Sandra Clara-Trujillo.

**Data Availability Statement:** All the data and results are included within the manuscript.

**Acknowledgments:** The authors would like to thank the anonymous reviewers for their thorough reading and professional comments that helped improve the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
