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Characterizing the dynamics of multi-cellular tumor spheroids (MCTS) within biomimetic environments is essential for identifying the physical factors affecting cancer proliferation and invasive behavior. While Cellular Capsule Technology (CCT) serves as a robust tool for monitoring these dynamics through microfluidic encapsulation, current mathematical frameworks are limited by their focus on specific growth stages. The model proposed by Le Maout et al. (2020) effectively utilizes a phase-field approach, based on Cahn-Hilliard theory, to resolve the diffuse interface and chemical potential of early-stage growth. Cahn-Hilliard theory is a mathematical framework used to describe the phase separation of a mixture, such as tumor cells and culture medium, by defining a chemical potential that drives the system toward an equilibrium state. By minimizing the system's free energy, this theory treats the tumor boundary as a smooth, diffuse interface rather than a sharp edge, which naturally accounts for surface tension and early-stage kinetics. However, this phase-field approach assumes small deformations of the alginate capsule and does not explicitly account for the mechanical deformability of the alginate capsule in its numerical analysis.
Conversely, the poro-mechanical model developed by Urcun et al. (2021) provides a precise "digital twin" of post-confluence dynamics, where the MCTS deforms the capsule wall. By treating the tumor as a triphasic continuum consisting of tumor cells, extracellular matrix, and interstitial fluid, this approach is more accurate for assessing capsule deformation and growth in the post-confluence stage. This approach is however not reliable in the pre-confluence stage, i.e. before contact with the alginate shell.
In this study, we propose a novel, unified mechanistic model that integrates the Cahn-Hilliard chemical potential into a multiphase poro-mechanical framework. This integration allows for a seamless prediction of cellular growth across the entire lifecycle, from initial aggregation to high-pressure confinement. We perform a thorough quantitative comparison of the accuracy and computational efficiency of our complete model specifically against the individual frameworks of Le Maout and Urcun. Our results demonstrate that this unified approach not only improves predictive precision throughout all stages but also offers a more computationally robust solution for real-time digital twinning of CCT experiments. This work provides an advanced theoretical framework for interpreting the interplay between mechanical stress and biochemical factors in tumor progression.
| References | Urcun et al. (2021): Urcun, S., Rohan, P. Y., Skalli, W., Nassoy, P., Bordas, S. P. A., & Sciumè, G. (2021). Digital twinning of Cellular Capsule Technology: Emerging outcomes from the perspective of porous media mechanics. PLOS ONE, 16(7), e0254512. Le Maout et al. (2020): Le Maout, V., Alessandri, K., Gurchenkov, B., Bertin, H., Nassoy, P., & Sciumè, G. (2020). Role of mechanical cues and hypoxia on the growth of tumor cells in strong and weak confinement: A dual in vitro-in silico approach. Science Advances, 6(13), eaaz7130. |
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| Country | France |
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