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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:BACKGROUND:Tumor-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. METHODS:The 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. RESULTS:Our 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. CONCLUSIONS:The 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.

Project description:In many countries, patients with mild coronavirus disease 2019 (COVID-19) are told to self-isolate at home, but imperfect compliance and shared living space with uninfected people limit the effectiveness of home-based isolation. We examine the impact of facility-based isolation compared to self-isolation at home on the continuing epidemic in the USA. We developed a compartment model to simulate the dynamic transmission of COVID-19 and calibrated it to key epidemic measures in the USA from March to September 2020. We simulated facility-based isolation strategies with various capacities and starting times under different diagnosis rates. Our primary model outcomes are new infections and deaths over 2 months from October 2020 onwards. In addition to national-level estimations, we explored the effects of facility-based isolation under different epidemic burdens in major US Census Regions. We performed sensitivity analyses by varying key model assumptions and parameters. We find that facility-based isolation with moderate capacity of 5 beds per 10 000 total population could avert 4.17 (95% credible interval 1.65-7.11) million new infections and 16 000 (8000-23 000) deaths in 2 months compared with home-based isolation. These results are equivalent to relative reductions of 57% (44-61%) in new infections and 37% (27-40%) in deaths. Facility-based isolation with high capacity of 10 beds per 10 000 population could achieve reductions of 76% (62-84%) in new infections and 52% (37-64%) in deaths when supported by expanded testing with an additional 20% daily diagnosis rate. Delays in implementation would substantially reduce the impact of facility-based isolation. The effective capacity and the impact of facility-based isolation varied by epidemic stage across regions. Timely facility-based isolation for mild COVID-19 cases could substantially reduce the number of new infections and effectively curb the continuing epidemic in the USA. Local epidemic burdens should determine the scale of facility-based isolation strategies.

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

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

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