Journal Article10.1007/S00285-008-0218-7
Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications.
Luigi Preziosi,Andrea Tosin +1 more
TL;DR: The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM.
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Abstract: Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis.
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Citations
Nonlinear modelling of cancer: Bridging the gap between cells and tumours
John Lowengrub,Hermann B. Frieboes,Hermann B. Frieboes,Fang Jin,Fang Jin,Yao-Li Chuang,Xiangrong Li,Paul Macklin,Steven M. Wise,Vittorio Cristini +9 more
TL;DR: In this paper, the authors provide an overview of multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis, and limit the scope further by considering models of tumor progression that do not distinguish tumour cells by their age and do not consider immune system interactions nor do they describe models of therapy.
600
Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method.
TL;DR: This is the first paper in a two-part series in which a diffuse interface continuum model of multispecies tumor growth and tumor-induced angiogenesis in two and three dimensions is developed, analyzed, and simulated.
554
Individual-based and continuum models of growing cell populations: a comparison.
Helen M. Byrne,Dirk Drasdo +1 more
TL;DR: A quantitative analysis of both a biophysical agent-based and a continuum mechanical model shows that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress.
351
Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results
TL;DR: An overview of agent-based models that are used to simulate mechanical and physiological phenomena in cells and tissues is presented, and the underlying concepts, limitations, and future perspectives of these models are discussed.
Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): From microscopic measurements to macroscopic predictions of clinical progression
Paul Macklin,Paul Macklin,Paul Macklin,Mary E. Edgerton,Alastair M. Thompson,Vittorio Cristini,Vittorio Cristini +6 more
TL;DR: A mechanistic, agent-based cell model is developed and applied to DCIS that is the first to account for cell calcification and introduces the first patient-specific calibration method to fully constrain the model based upon clinically-accessible histopathology data.
259
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