Particle methods to solve modelling problems in wound healing and tumor growth

Abstract

The paper deals with a compilation of several of our modelling studies on particle methods used for simulation of wound healing and tumor growth processes. The paper serves as an introduction of our modelling approaches to researchers with interest in biological cell-based models that use particle-based modelling approaches. The particles that we consider in the present models mimic either cells or points on cell boundaries that are allowed to migrate as a result of several chemical and mechanical factors. A distinct feature of our modelling frameworks with respect to conventional particle models, is that cells, mimicked by particles, are allowed to divide, differentiate and to die as a result of apoptosis or any causes for cell death. The paper is merely descriptive, rather than written in full mathematical rigor, and will show some of the potentials of the applied modelling.

Mathematical modelling of angiogenesis using continuous cell-based models

“…In the future, we want to combine the current angiogenesis model with modelling of cancer development, such as in Vermolen (2015), where the necrotic core of the tumour releases growth factors (Tumour Necrosis Growth factor) that trigger the angiogenesis response of the endothelial cells.…”

“…(2015). A recent review on particle methods applied to wound healing and tumour growth can be found in Vermolen (2015). Regarding cancer initiation, growth and invasion of cancer cells, and the use of cell-based modelling, we refer to the studies by Schlüter et al.…”

Computational modeling of therapy on pancreatic cancer in its early stages

“…Cell proliferation, mutation and death are some of the fundamental processes of cells regulated by genes, intracellular interaction and microenvironment. To simplify the model, stochastic processes are considered to simulate the probability of cell division, mutation and death (Vermolen 2015). We hypothesize that the probability of cell division, mutation and death is only influenced by the total strain energy density one cell endures.…”

Modeling migration in cell colonies in two and three dimensional substrates with varying stiffnesses

“…This continuous cellular approach was developed in earlier studies by Byrne and Drasdo [34], Groh and Louis [35] and in Neilson et al [36]. A review on particle methods applied to tumor growth and wound healing is given in Vermolen [37]. Various cell migration models with cell-cell contacts have been developed and focus mainly on group migration and single cell movement rather than interactions between (proximal or distant) neighboring cells.…”