A fully continuous individual-based model of tumor cell evolution

Gómez-Mourelo, Pablo; Sánchez, Esteban Morcillo; Casasús, Luis; Webb, Glenn

doi:10.1016/j.crvi.2008.08.010

Cited by 5 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Simulations show finger-like invasions of tumour cells where the leading cells degrade the extracellular matrix to form a channel and the trailing cells follow a gradient of chemoattractant released by the degraded ECM in their wake. Another stochastic agent-based model of tumour growth was developed recently by Gomez-Mourelo et al [245]. Their model extends the Anderson cellular automaton model by removing the lattice-based constraint, and incorporating an age-structure.…”

Section: Discrete Modellingmentioning

confidence: 99%

Nonlinear modelling of cancer: bridging the gap between cells and tumours

et al. 2009

View full text Add to dashboard Cite

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

show abstract

Section: Discrete Modellingmentioning

confidence: 99%

Nonlinear modelling of cancer: bridging the gap between cells and tumours

et al. 2009

View full text Add to dashboard Cite

show abstract

“…For instance, the way to obtain this equivalent PDE from a particular IBM has already been explained in two different cases: a cancer tumour invasion in a healthy surrounding tissue [46] , and a yeast population growth in a liquid medium [47] . …”

Section: General Considerationsmentioning

confidence: 99%

A connection between discrete individual-based and continuous population-based models: A forest modelling case study

Gómez-Mourelo

Gisbert

2013

AIR

Self Cite

View full text Add to dashboard Cite

Modelling is perceived as a way of dealing with real life activities. The aim of this work is to compare two approaches to study forest dynamics, namely discrete individual-based and continuous population-based models, in order to contribute to an improvement in their use among researchers. An analysis of the strengths, weaknesses, opportunities and threats of the two different approaches, jointly with a mention of the state-of-the-art, allows us to illustrate this discussion. We will also provide a bridge or connection between these two modelling methodologies. This link will be developed in detail in a particular study case. Firstly, an individual-tree based model to deal with dynamics of forests is presented. Secondly, this model is scaled up to a system of partial differential equations, which represents the limiting behaviour of the individualbased model.

show abstract

“…There is an extensive literature of spatial models of tumor growth that have included many of these processes in both continuum and discrete frameworks. Our objective here is to continue the study of a continuum model of tumor growth first proposed in [5] (see also [3] and [4]), and later developed in [6], [7], [8], [18], and [19]. The salient feature of this model is the use of cell age to track passage of individual cells through the cell cycle.…”

Section: Introductionmentioning

confidence: 99%

A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes

Dyson

Villella-Bressan

Webb

2007

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

Abstract.A model of tumor growth in a spatial environment is analyzed. The model includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments of tumor cells, extracellular matrix, matrix degradative enzyme, and oxygen. The existence, uniqueness, positivity, regularity, and growth characteristics of the solutions are investigated.

show abstract

A fully continuous individual-based model of tumor cell evolution

Cited by 5 publications

References 25 publications

Nonlinear modelling of cancer: bridging the gap between cells and tumours

Nonlinear modelling of cancer: bridging the gap between cells and tumours

A connection between discrete individual-based and continuous population-based models: A forest modelling case study

A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes

Contact Info

Product

Resources

About