The conjecture of carrying capacity in cancer: Thermodynamic implications

In this study, we explore Deisboeck and Z. Wang's conjecture from 2007, which establishes a quantitative relationship between the spatial expansion of tumours and the volume constraints as well as functional variations of the surrounding host tissue. By integrating the physical properties of cells into this mechanistic framework, we provide a robust thermodynamic interpretation based on cellular internal energy. Our findings decisively characterise the conditions that facilitate coexistence between tumours and host organs at first, while also identifying the factors that eventually drive the competitive transformation of tumour cells through spatial dissemination-specifically, local invasion into healthy tissue followed by distant metastasis. We underscore the critical necessity of vascularisation from an energetic perspective and highlight the existence of an `entropy threshold' for cancer invasion, which mirrors a phase transition in physics, as revealed through the application of the second law of thermodynamics.