Modeling Diffusely Invading Brain Tumors An Individualized Approach to Quantifying Glioma Evolution and Response to Therapy

Rockne, Russell; Alvord, Ellsworth C.; Szeto, Mindy D; Gu, Stanley; Chakraborty, Gargi; Swanson, Kristin R.

doi:10.1007/978-0-8176-4713-1_8

Cited by 17 publications

(13 citation statements)

References 34 publications

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“…On passing through the interface the diffusivity increases by a factor of 25, as depicted in Fig. 3(a), which is consistent with an upper estimate of the ratio of cell diffusion coefficients in grey and white matter (Rockne et al, 2008;Konukoglu et al, 2010b). One can immediately note that the deterministic simulation, within the left column of the plots, accurately approximates the stochastic simulation, in the right column.…”

Section: A Single Transition Region In One Spatial Dimensionsupporting

confidence: 81%

“…For definiteness, we use values of D w dim ∼0:25 mm 2 per day, following estimates by Konukoglu et al (2010b) with the ratio D w dim =D g dim in the range of 5-25, which is consistent with the ranges estimated in previous modelling (Rockne et al, 2008;Konukoglu et al, 2010b). Similarly, we use ρ dim ¼ 0:012=day (Konukoglu et al, 2010b); though this parameter varies substantially (Wang et al, 2009), it influences only the time scales of the predictions.…”

Section: Appendix B Parameter Estimationmentioning

confidence: 85%

“…Ratio of white to grey matter diffusion coefficient 5-25 Rockne et al (2008), Konukoglu et al (2010b).…”

Section: Appendix C Analysis Of Anisotropic Nonlinear Fickian Diffusmentioning

confidence: 99%

“…In addition, and as recognised in current modelling frameworks (Konukoglu et al, 2010a(Konukoglu et al, , 2010bRockne et al, 2008), invading gliomas infiltrate highly heterogeneous brain tissue, due to the presence of disparate levels of myelin within white and grey matter. This, in turn, result in substantially different motilities estimated for each of these two phases, differing by a factor of between 5 and 25 according to the parameter estimation method (Rockne et al, 2008;Konukoglu et al, 2010b), with faster motility in white matter.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Single Transition Region In One Spatial Dimensionsupporting

confidence: 81%

Section: Appendix B Parameter Estimationmentioning

confidence: 85%

“…Ratio of white to grey matter diffusion coefficient 5-25 Rockne et al (2008), Konukoglu et al (2010b).…”

Section: Appendix C Analysis Of Anisotropic Nonlinear Fickian Diffusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling biological invasions: Individual to population scales at interfaces

Belmonte-Beitia

Woolley

Scott

et al. 2013

Journal of Theoretical Biology

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“…Treatment simulation results are then directly applicable to the corresponding clinical case. Simulations of the model reveal that the radiotherapy model parameter a is correlated with net proliferation rate k c (/year) in such a way that response to radiation, measured in terms of changes to gross tumor volume, can be predicted prior to treatment (Rockne et al 2008(Rockne et al , 2009) in individual patients. The model can be further extended to incorporate resistance factors such as acute or chronic oxygen depletion (hypoxia) using an oxygen enhancement ratio (OER) to the a/b ratio in the linear-quadratic model.…”

Section: Continuous Tumor Growth Models and Radiotherapymentioning

confidence: 99%

Quantitative Modeling of Tumor Dynamics and Radiotherapy

2010

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Cancer is a complex disease, necessitating research on many different levels; at the subcellular level to identify genes, proteins and signaling pathways associated with the disease; at the cellular level to identify, for example, cell-cell adhesion and communication mechanisms; at the tissue level to investigate disruption of homeostasis and interaction with the tissue of origin or settlement of metastasis; and finally at the systems level to explore its global impact, e.g. through the mechanism of cachexia. Mathematical models have been proposed to identify key mechanisms that underlie dynamics and events at every scale of interest, and increasing effort is now being paid to multi-scale models that bridge the different scales. With more biological data becoming available and with increased interdisciplinary efforts, theoretical models are rendering suitable tools to predict the origin and course of the disease. The ultimate aims of cancer models, however, are to enlighten our concept of the carcinogenesis process and to assist in the designing of treatment protocols that can reduce mortality and improve patient quality of life. Conventional treatment of cancer is surgery combined with radiotherapy or chemotherapy for localized tumors or systemic treatment of advanced cancers, respectively. Although radiation is widely used as treatment, most scheduling is based on empirical knowledge and less on the predictions of sophisticated growth dynamical models of treatment response. Part of the failure to translate modeling research to the clinic may stem from language barriers, exacerbated by often esoteric model renderings with inaccessible parameterization. Here we discuss some ideas for combining tractable dynamical tumor growth models with radiation response models using biologically accessible parameters to provide a more intuitive and exploitable framework for understanding the complexity of radiotherapy treatment and failure.

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New alternative numerical approaches for solving the glioma model and their efficiencies

Korkut

2021

Math Sci

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Modeling Diffusely Invading Brain Tumors An Individualized Approach to Quantifying Glioma Evolution and Response to Therapy

Cited by 17 publications

References 34 publications

Modelling biological invasions: Individual to population scales at interfaces

Modelling biological invasions: Individual to population scales at interfaces

Quantitative Modeling of Tumor Dynamics and Radiotherapy

New alternative numerical approaches for solving the glioma model and their efficiencies

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