||Uterine myomas are common, benign smooth-muscle tumours that can grow to 10cm or more in diameter and are routinely removed surgically. They are typically slow growing, well-vascularised, spherical tumours that, on a macro-scale, are a structurally uniform, hard elastic material. We present a multi-phase mathematical model of a fully vascularised myoma growing within a surrounding elastic tissue. Adopting a continuum approach, the model assumes the conservation of mass and momentum of four phases, namely cells/collagen, extracellular fluid, arterial and venous phases. The cell/collagen phase is treated as a poro-elastic material and Darcy's law is applied to describe flow in the extracellular fluid and the two vascular phases. The supply of extracellular fluid is dependent on the capillary flow rate and mean capillary pressure expressed in terms of the arterial and venous pressures. Cell growth and division is limited to the myoma domain and dependent on the local stress in the material. The resulting model consists of a system of non-linear partial differential equations with two moving boundaries.
Numerical solutions of the model reproduce qualitatively the clinically observed three-phase "fast-slow-fast" growth profile that is typical for myomas. The results suggest that this growth profile requires stress-induced resistance to growth by the surrounding tissue and a switch like cell growth response to stress. Analysis of large-time solutions reveal that whilst there is a functioning vasculature throughout the myoma exponential growth results, otherwise power-law growth is predicted. An extensive survey of the effect of parameters on model solutions is carried out and, in particular, the enhanced growth caused by factors such as oestrogen is predicted by the model.