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Mathematical modeling of human glioma growth based on brain topological structures: study of two clinical cases.

ABSTRACT: Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor), and an advanced state when infiltration starts (malign tumor). Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality.

SUBMITTER: Suarez C

PROVIDER: S-EPMC3386273 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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Mathematical modeling of human glioma growth based on brain topological structures: study of two clinical cases.

Suarez Cecilia C Maglietti Felipe F Colonna Mario M Breitburd Karina K Marshall Guillermo G

PloS one 20120628 6

Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from bra ...[more]

PMID: 22761843

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Project description:BackgroundTumor-infiltrated immune cells compose a significant component of many cancers. They have been observed to have contradictory impacts on tumors. Although the primary reasons for these observations remain elusive, it is important to understand how immune cells infiltrating into tumors is regulated. Recently our group conducted a series of experimental studies, which showed that muIDH1 gliomas have a significant global reduction of immune cells and suggested that the longer survival time of mice with CIMP gliomas may be due to the IDH mutation and its effect on reducing of the tumor-infiltrated immune cells. However, to comprehend how IDH1 mutants regulate infiltration of immune cells into gliomas and how they affect the aggressiveness of gliomas, it is necessary to integrate our experimental data into a dynamical system to acquire a much deeper understanding of subtle regulation of immune cell infiltration.MethodsThe method is integration of mathematical modeling and experiments. According to mass conservation laws and assumption that immune cells migrate into the tumor site along a chemotactic gradient field, a mathematical model is formulated. Parameters are estimated from our experiments. Numerical methods are developed to solve the problem. Numerical predictions are compared with experimental results.ResultsOur analysis shows that the net rate of increase of immune cells infiltrated into the tumor is approximately proportional to the 4/5 power of the chemoattractant production rate, and it is an increasing function of time while the percentage of immune cells infiltrated into the tumor is a decreasing function of time. Our model predicts that wtIDH1 mice will survive longer if the immune cells are blocked by reducing chemotactic coefficient. For more aggressive gliomas, our model shows that there is little difference in their survivals between wtIDH1 and muIDH1 tumors, and the percentage of immune cells infiltrated into the tumor is much lower. These predictions are verified by our experimental results. In addition, wtIDH1 and muIDH1 can be quantitatively distinguished by their chemoattractant production rates, and the chemotactic coefficient determines possibilities of immune cells migration along chemoattractant gradient fields.ConclusionsThe chemoattractant gradient field produced by tumor cells may facilitate immune cells migration to the tumor cite. The chemoattractant production rate may be utilized to classify wtIDH1 and muIDH1 tumors. The dynamics of immune cells infiltrating into tumors is largely determined by tumor cell chemoattractant production rate and chemotactic coefficient.

Dataset Information

Mathematical modeling of human glioma growth based on brain topological structures: study of two clinical cases.

Publications

Mathematical modeling of human glioma growth based on brain topological structures: study of two clinical cases.

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