In vivo mimicking multiphase model towards impact of host on avascular tumour growth

Tumour growth involves dynamic interactions among tumour cells, extracellular materials, and host tissue. The tumour exerts mechanical stresses on the host tissue and simultaneously experiences compression across the tumour-host interface. This article presents a mathematical model that mimics an in vivo set-up, where an avascular tumour is surrounded by healthy/normal tissue, utilizing conservation principles for the constituents in each region. Tumour and host tissues are separately treated as biphasic mixtures comprising cells and extracellular materials. This study incorporates the diffusion-dominated transport and metabolism of cell-nourishing agents (CNA), such as oxygen, nutrients, and growth factors. The mechanical impact of normal host tissue on tumour growth dynamics while maintaining stress continuity at the tumour-host interface is analysed through numerical simulations. The key findings are that when CNA levels decline below a specific threshold, the tumour cell volume fraction decreases from the periphery to the centre, resulting in necrotic cell death alongside apoptosis. This study indicates that host tissue reduces CNA tension, accelerating tumour necrosis. The increased viscosity of normal host cells indicates stronger intercellular bonds, causing the cells to adhere more tightly and stiffen the host. With increasing viscosity-induced resistance, the host tissue more effectively impedes tumour expansion, thereby slowing tumour growth due to rising compressive stress. Analytical results for a solvable scenario are also provided to explore the comparative behaviour with numerical simulations of the complete model. Furthermore, analytical results indicate that an increased viscosity of normal host tissue may delay the initiation of necrotic cell death.