Mathematical modeling of cancer cell migration - from in vitro to in vivo

Abstract

Tumors has been the object of computational model studies for nearly five decades. The early models considered simple tumor growth based on nutrients, whereas models now can simulate from microscale gene expressions in cells to the larger scale tissue, and even a combination of micro and macroscale models in hybrid models. In this thesis we apply a continuum model to capture different mechanisms that cause tumor cells to move. More precisely, the interaction between different cells and the flowing fluid in tissue through forces are investigated upon. The first versions of the model attempt to capture behavior found in experimental work performed in controlled environments, and evolves to better align with how a realistic tumor may act. The first paper (Paper I) in this thesis formulates a two-phase model consisting of a tumor cell and interstitial fluid phase. It relies upon the experience gained from creeping flow in petroleum reservoirs with regards to the interaction forces and how fluid flow is described. The model in Paper 1 is motivated by the experimental work by Shields et al. 2007 that identifies a tumor cell migration mechanism called autologous chemotaxis. This means that due to interstitial fluid flow, tumor cells creates a chemical gradient in the flow direction of its own fruition, letting cancer cells migrate downstream. The second part of this thesis (Paper II & III) extends the two-phase model in Paper I to include a new mechanism. Paper II maintains autologous chemotaxis as a migration mechanism and introduces a new one, rheotaxis. Rheotaxis is considered a competing mechanism to chemotaxis in the study by Polacheck et al. 2011, where fluid flow imposes a stress on the cancer cells and causes them to migrate in the upstream direction. These two competing mechanisms are explored in a computational context in Paper II. After in-depth investigation into the different parameters in the model in Paper II, the model is extended to a two-dimensional domain. This allows for better visualization, while at the same time illustrating the potential of the model as a tool to explore how tumor cells may escape from the primary tumor to metastasize. In the next part (Paper IV & V) a new phase in introduced, resulting in a three-phase model. The new phase is a common component of both normal and cancerous tissue, namely fibroblast cells. In our model we look at tumor-associated fibroblasts (TAFs) which behave differently from their normal counterpart. Motivated by the experimental work by Gaggioli et al. 2007; Labernadie et al. 2017; Shieh et al. 2011, we investigate two different methods TAFs use to enhance tumor cell migration, in the presence of interstitial fluid flow (Paper IV). In Paper V the model is used in a 2D setting, showing that fibroblasts may lead cancer cells in a collective manner towards draining lymphatics as a means for metastasis. It is also suggested targeting fibroblast-cancer cell interaction as a method to decrease metastasis. In the last part (Paper VI) the three-phase model is used to elucidate that ECM structures within the tumor can cause heterogeneous interstitial fluid pressure based on preclinical data from xenograft models in Hansem et al. 2019. One important aspect of the computational model is to achieve a realistic interstitial fluid pressure and fluid velocity, which is measured in the experimental data. We achieve similar results with regards to the pressure under the various circumstances explored in Hansem et al. 2019, and give rise to heterogeneous migration pattern with possibility for formation of isolated islands of tumor cells.