Co-evolution of solid stress and interstitial fluid pressure in tumors during progression: Implications for vascular collapse

Abstract

The stress harbored by the solid phase of tumors is known as solid stress. Solid stress can be either applied externally by the surrounding normal tissue or induced by the tumor itself due to its growth. Fluid pressure is the isotropic stress exerted by the fluid phase. We recently demonstrated that growth-induced solid stress is on the order of 1.3-13.0 kPa (10-100 mmHg) - high enough to cause compression of fragile blood vessels resulting in poor perfusion and hypoxia. However, the evolution of growth-induced stress with tumor progression and its effect on cancer cell proliferation in vivo is not understood. To this end, we developed a mathematical model for tumor growth that takes into account all three types of stresses: growth-induced stress, externally applied stress and fluid pressure. First, we performed in vivo experiments and found that growth-induced stress is related to tumor volume through a bi-exponential relationship. Then, we incorporated this information into our mathematical model and showed that due to the evolution of growth-induced stress, total solid stress levels are higher in the tumor interior and lower in the periphery. Elevated compressive solid stress in the interior of the tumor is sufficient to cause the collapse of blood vessels and results in a lower growth rate of cancer cells compared to the periphery, independently from that caused by the lack of nutrients due to vessel collapse. Furthermore, solid stress in the periphery of the tumor causes blood vessels in the surrounding normal tissue to deform to elliptical shapes. We present histological sections of human cancers that demonstrate such vessel deformations. Finally, we found that fluid pressure increases with tumor growth due to increased vascular permeability and lymphatic impairment, and is governed by the microvascular pressure. Crucially, fluid pressure does not cause vessel compression of tumor vessels. Major Findings. Growth-induced solid stress is accumulated in tumors during growth. Growth-induced and externally applied solid stresses are additive and might affect cancer cell growth in two ways: directly by compressing cancer cells and indirectly by deforming blood vessels and thus, reducing delivery of nutrients.