Invasion in Malignant Glioma

Mikkelsen, Tom; Enam, Ather; Rosenblum, Mark L.

doi:10.1016/b978-1-4160-5316-3.00105-2

Cited by 2 publications

(1 citation statement)

References 169 publications

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“…Ballistic front length was largest for low values of p 0 and high values of D 0 , because as p 0 increases, more cells become jammed. In general, the non-overlapping model predicts reasonable edge lengths that are of order 0.1–1 mm, corresponding to the approximate length scale of a diffuse GBM tumor margin [57]. Likewise, the time to reach a jammed configuration depends on the input parameters, as shown in figure 5(D).…”

Section: Resultsmentioning

confidence: 99%

A Brownian dynamics tumor progression simulator with application to glioblastoma

Klank

Rosenfeld

Odde

2018

Converg. Sci. Phys. Oncol.

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Tumor progression modeling offers the potential to predict tumor-spreading behavior to improve prognostic accuracy and guide therapy development. Common simulation methods include continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumor spreading behavior and discrete agent-based (AB) approaches which capture individual cell events such as proliferation or migration. The brain cancer glioblastoma (GBM) is especially appropriate for such proliferation-migration modeling approaches because tumor cells seldom metastasize outside of the central nervous system and cells are both highly proliferative and migratory. In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from computed tomography or magnetic resonance images. However, these estimates of glioblastoma cell migration rates, modeled as a diffusion coefficient, are approximately 1–2 orders of magnitude larger than single-cell measurements in animal models of this disease. To identify possible sources for this discrepancy, we evaluated the fundamental RD simulation assumptions that cells are point-like structures that can overlap. To give cells physical size (~10 μm), we used a Brownian dynamics approach that simulates individual single-cell diffusive migration, growth, and proliferation activity via a gridless, off-lattice, AB method where cells can be prohibited from overlapping each other. We found that for realistic single-cell parameter growth and migration rates, a non-overlapping model gives rise to a jammed configuration in the center of the tumor and a biased outward diffusion of cells in the tumor periphery, creating a quasi-ballistic advancing tumor front. The simulations demonstrate that a fast-progressing tumor can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates. Thus, modeling with the assumption of physically-grounded volume conservation can account for the apparent discrepancy between estimated and measured diffusion of GBM cells and provide a new theoretical framework that naturally links single-cell growth and migration dynamics to tumor-level progression.

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Section: Resultsmentioning

confidence: 99%

A Brownian dynamics tumor progression simulator with application to glioblastoma

Klank

Rosenfeld

Odde

2018

Converg. Sci. Phys. Oncol.

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What mathematical models can or cannot do in glioma description and understanding

Perrillat-Mercerot¹,

Miranville²,

Bourmeyster³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

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Our aim in this article is not to provide a review of the existing literature but to make a critical analysis on glioma behavior mathematical modeling. We present here mathematical modeling history, interests, modalities and limitations on the study of glioma growth. We also make a point on model consideration according to glioma comportments. We finally introduce medical imaging coupled with in silico models as the next step in glioma research. We do not claim completeness of the bibliography but we tried to cover a large amount of mathematical considerations for glioma behavior illustrated with selected representative papers.

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Invasion in Malignant Glioma

Cited by 2 publications

References 169 publications

A Brownian dynamics tumor progression simulator with application to glioblastoma

A Brownian dynamics tumor progression simulator with application to glioblastoma

What mathematical models can or cannot do in glioma description and understanding

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