Bright solitary waves in malignant gliomas.

@article{PrezGarca2011BrightSW,
  title={Bright solitary waves in malignant gliomas.},
  author={Victor Manuel P{\'e}rez-Garc{\'i}a and Gabriel Fern{\'a}ndez Calvo and Juan Belmonte-Beitia and David Diego and Luis A. P{\'e}rez-Romasanta},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2011},
  volume={84 2 Pt 1},
  pages={
          021921
        }
}
We put forward a nonlinear wave model describing the fundamental dynamical features of an aggressive type of brain tumors. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis, and exact solutions we prove that bright solitary tumor waves develop in such systems. Possible implications of our model… 
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References

SHOWING 1-10 OF 59 REFERENCES
Dynamics and pattern formation in invasive tumor growth.
TLDR
A model is formulated for this sort of growth of the malignant brain tumor glioblastoma multiforme using two coupled reaction-diffusion equations for the cell and nutrient concentrations that determines the instability threshold and the full phase-plane diagram in the parameter space.
Extrapolating glioma invasion margin in brain magnetic resonance images: Suggesting new irradiation margins
TLDR
A novel method is proposed for estimating the full extent of the tumor infiltration starting from its visible mass in the patients' MR images and it is suggested that the variable margin could be more effective at targeting cancerous cells and preserving healthy tissue.
Computer simulation of glioma growth and morphology
TLDR
This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment and on the cellular phenotypes, and can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy.
A reaction-diffusion model of cancer invasion.
We present mathematical analyses, experimental data, and clinical observations which support our novel hypothesis that tumor-induced alteration of microenvironmental pH may provide a simple but
Biocomputing: numerical simulation of glioblastoma growth using diffusion tensor imaging.
TLDR
This work has demonstrated that modeling the complex behavior of brain tumors is feasible and will account for further validation of this new conceptual approach.
Virtual glioblastoma: growth, migration and treatment in a three‐dimensional mathematical model
TLDR
Through mathematical modelling, the process of invasion is model and the relative importance of mechanisms contributing to malignant invasion is predicted and patterns of tumour recurrence following various modes of therapeutic intervention are predicted.
Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model.
TLDR
This is the first report indicating that dynamic insight from routinely obtained pretreatment imaging may be quantitatively useful in characterizing the survival of individual patients with glioblastoma.
A new mathematical model for avascular tumour growth
TLDR
A new model is developed, formulated in terms of continuum densities of proliferating, quiescent and necrotic cells, together with a generic nutrient/growth factor, which allows for nutrient supply from underlying tissue, which will arise in the two-dimensional setting of a tumour growing within an epithelium.
Collective behavior of brain tumor cells: the role of hypoxia.
TLDR
A discrete stochastic model for cell dynamics is formulated and suggests that hypoxia decreases both the motility of cells and the strength of cell-cell adhesion.
Exciting New Advances in Neuro‐Oncology: The Avenue to a Cure for Malignant Glioma
TLDR
There is definite hope that by 2020, new cocktails of drugs will be available to target the key molecular pathways involved in gliomas and reduce their mortality and morbidity, a positive development for patients, their families, and medical professionals alike.
...
1
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3
4
5
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