A Mathematical Model of Glioblastoma Tumor Spheroid Invasion in a Three-Dimensional In Vitro Experiment

Stein, Andrew M.; Demuth, Tim; Mobley, David L.; Berens, Michael E.; Sander, Leonard M.

doi:10.1529/biophysj.106.093468

Cited by 222 publications

(236 citation statements)

References 41 publications

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“…When the adhesion strength between leading-edge cells and followers is weakened, the leading cells can migrate individually (data not shown), as is typically observed in glioma cell invasion in vitro (Kim et al 2009;Stein et al 2007). How this is controlled in different cell types is not understood.…”

Section: The Cell-based Modelmentioning

confidence: 95%

A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer

Kim

Othmer

2013

Bull Math Biol

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Ductal carcinoma in situ (DCIS) is an early stage noninvasive breast cancer that originates in the epithelial lining of the milk ducts, but it can evolve into comedo DCIS and ultimately, into the most common type of breast cancer, invasive ductal carcinoma. Understanding the progression and how to effectively intervene in it presents a major scientific challenge. The extracellular matrix (ECM) surrounding a duct contains several types of cells and several types of growth factors that are known to individually affect tumor growth, but at present the complex biochemical and mechanical interactions of these stromal cells and growth factors with tumor cells is poorly understood. Here we develop a mathematical model that incorporates the cross-talk between stromal and tumor cells, which can predict how perturbations of the local biochemical and mechanical state influence tumor evolution. We focus on the EGF and TGF-β signaling pathways and show how upor down-regulation of components in these pathways affects cell growth and proliferation. We then study a hybrid model for the interaction of cells with the tumor microenvironment (TME), in which epithelial cells (ECs) are modeled individually while the ECM is treated as a continuum, and show how these interactions affect the early development of tumors. Finally, we incorporate breakdown of the epithelium into the model and predict the early stages of tumor invasion into the stroma. Our results shed light on the interactions between growth factors, mechanical properties of the ECM, and feedback signaling loops between stromal and tumor cells, and suggest how epigenetic changes in transformed cells affect tumor progression.

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Section: The Cell-based Modelmentioning

confidence: 95%

A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer

Kim

Othmer

2013

Bull Math Biol

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“…This has been generalised in numerous investigations, for example in off-lattice models (Lipkova et al, 2011), whereby the framework at the individual level does not rely upon a discretisation of space and/or time, as well as the incorporation of numerous physical and biological features. Examples in this popular field (Chowdhury et al, 2005;Othmer and Stevens, 1997;Hillen and Othmer, 2000;Deroulers et al, 2009) include the consideration of exclusion processes (Landman and Fernando, 2011), motility biases such as chemotaxis (Hillen and Painter, 2009), competing cell populations (Penington et al, 2011), contact interactions (Lushnikov et al, 2008;Painter and Sherratt, 2003) and cell-cell adhesions (Stein et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

Modelling biological invasions: Individual to population scales at interfaces

Belmonte-Beitia

Woolley

Scott

et al. 2013

Journal of Theoretical Biology

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We explore the influence of spatial heterogeneity in biological systems. We consider how local transport mechanisms impact behaviour near interfaces. We study cell movement between white and grey matter in the brain, as an example. Profound differences in population behaviour emerge in the presence of interface. The commonly used Fickian diffusion transport model cannot predict this dynamics. a r t i c l e i n f o b s t r a c tExtracting the population level behaviour of biological systems from that of the individual is critical in understanding dynamics across multiple scales and thus has been the subject of numerous investigations. Here, the influence of spatial heterogeneity in such contexts is explored for interfaces with a separation of the length scales characterising the individual and the interface, a situation that can arise in applications involving cellular modelling. As an illustrative example, we consider cell movement between white and grey matter in the brain which may be relevant in considering the invasive dynamics of glioma. We show that while one can safely neglect intrinsic noise, at least when considering glioma cell invasion, profound differences in population behaviours emerge in the presence of interfaces with only subtle alterations in the dynamics at the individual level. Transport driven by local cell sensing generates predictions of cell accumulations along interfaces where cell motility changes. This behaviour is not predicted with the commonly used Fickian diffusion transport model, but can be extracted from preliminary observations of specific cell lines in recent, novel, cryo-imaging. Consequently, these findings suggest a need to consider the impact of individual behaviour, spatial heterogeneity and especially interfaces in experimental and modelling frameworks of cellular dynamics, for instance in the characterisation of glioma cell motility.

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“…This makes them harder to adapt to specific patient cases. Macroscopic models on the other hand, describe the average behavior of tumor cells and model the evolution of local tumor cell densities rather than individual cells [39,8,18,9,16,45,10,13,26,37]. Therefore, it is harder for them to capture the stochastic characteristic of tumor growth.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the macroscopic models, [39,8,18,16,37], are based on the reactiondiffusion formalism Murray introduced in the early 1990 and later formulated as a conservation equation [27,40]. This formalism uses the general class of partial differential equations (PDEs) called the reaction-diffusion and reactiondiffusion-advection type.…”

Section: Introductionmentioning

confidence: 99%

Extrapolating glioma invasion margin in brain magnetic resonance images: Suggesting new irradiation margins

Konukoğlu

Clatz

Bondiau

et al. 2010

Medical Image Analysis

116

122

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Radiotherapy for brain glioma treatment relies on magnetic resonance (MR) and computed tomography (CT) images. These images provide information on the spatial extent of the tumor, but can only visualize parts of the tumor where cancerous cells are dense enough, masking the low density infiltration. In radiotherapy, a 2 cm constant margin around the tumor is taken to account for this uncertainty. This approach however, does not consider the growth dynamics of gliomas, particularly the differential motility of tumor cells in the white and in the gray matter. In this article, we propose a novel method for estimating the full extent of the tumor infiltration starting from its visible mass in the patients' MR images. This estimation problem is a time independent problem where we do not have information about the temporal evolution of the pathology nor its initial conditions. Based on the reaction-diffusion models widely used in the literature, we derive a method to solve this extrapolation problem. Later, we use this formulation to tailor new tumor specific variable irradiation margins. We perform geometrical comparisons between the conventional constant and the proposed variable margins through determining the amount of targeted tumor cells and healthy tissue in the case of synthetic tumors. Results of these experiments suggest that the variable margin could be more effective at targeting cancerous cells and preserving healthy tissue. *

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A Mathematical Model of Glioblastoma Tumor Spheroid Invasion in a Three-Dimensional In Vitro Experiment

Cited by 222 publications

References 41 publications

A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer

A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer

Modelling biological invasions: Individual to population scales at interfaces

Extrapolating glioma invasion margin in brain magnetic resonance images: Suggesting new irradiation margins

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