Numerical analysis of mechanical stress in a spherical cancerous tissue

Abstract

The complexity of cancer growth makes cancer treatment an active open field for research despite the decades of studies. Cancer growth does not only depend on biological and chemical factors, but also in physical and mechanical factors and the local environment. The analysis of the mechanical effects of cancerous tumor to its local environment could provide medical practitioners insights to improve tumor management. In this study, we simulate cancer growth on a spherical surface and analyze its mechanical effect to the other normal cells. We report that the empirical relationship between the stress-level of normal cells against its distance from the nearest cancerous cell is obtained for the 3D surface. The same powerlaw, with exponent α, is consistently obtained over the growth curve of the cancer mass (for different cancer areas) N_c. This means that stress (therefore pain) has long-range effect over the whole tissues. Moreover, the stress distribution can be more localized for more negative α-values. The α is also found to approximately vary quadratically with α_c having a minimum (most negative) at N_c ≈ 0.20N (20%). This implies that the stress distribution is most local whenever the cancer size is about 20% of the tissue size. Our results could have important implication in tumor pain management as well as its growth monitoring.