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Continuum Simulations of Multi-Cellular Tumor Spheroids using Two-phase Flow Models


Cancer growth and invasion is a problem that has been studied for several decades, particularly due to high mortality rates among patients. Despite this, large gaps in our understanding of cancer remain. The traditional approach for studying cancer has been largely from the biological perspective. But, recently, the biophysical properties of cancer have proven to complement these traditional studies and enhance our understanding of cancer. Are there mechanical gradients developed inside tumor aggregates? Do these gradients represent a solid-to-fluid phase transition inside the spheroid? If so, does it af- fect its behavior? How does the growth of the tumor aggregate affect its surface features? If so, are these features that could initiate tumor invasion? What is the involvement of the forces that the tumor exerts on its surroundings?

This study attempts to answer these questions by developing a simplified Stokes’ flow model using the commercial Multiphysics package — COMSOL Multiphysics versions (5.3) and (5.4). It begins by highlighting the relevance of mechanics in cancer and no- table attempts to model them mathematically. The internal mechanics of the tumor and the evolution of the spheroid contour as it grows has been discussed. We studied curva- ture dependent active stresses normal to the spheroid surface. Growth induced surface instabilities have also been explored. Experimental techniques that could be used to confirm these hypotheses have been described and finally, the potential future work in this domain has been elucidated.

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