Dataset Information

Mathematical modelling of spatio-temporal glioma evolution.

ABSTRACT:

Background

Gliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression.

Methods

Building and expanding on existing approaches, this paper develops a continuous three-dimensional model of avascular glioma spatio-temporal evolution. The proposed spherical model incorporates the interactions between the populations of four different glioma cell phenotypes (proliferative, hypoxic, hypoglychemic and necrotic) and their tissue microenvironment, in order to investigate how they affect tumor growth and invasion in an isotropic and homogeneous medium. The model includes two key variables involved in the proliferation and invasion processes of cancer cells; i.e. the extracellular matrix and the matrix-degradative enzymes concentrations inside the tumor and its surroundings. Additionally, the proposed model focuses on innovative features, such as the separate and independent impact of two vital nutrients, namely oxygen and glucose, in tumor growth, leading to the formation of cell populations with different metabolic profiles. The model implementation takes under consideration the variations of particular factors, such as the local cell proliferation rate, the variable conversion rates of cells from one category to another and the nutrient-dependent thresholds of conversion. All model variables (cell densities, ingredients concentrations) are continuous and described by reaction-diffusion equations.

Results

Several simulations were performed using combinations of growth and invasion rates, for different evolution times. The model results were evaluated by medical experts and validated on experimental glioma models available in the literature, revealing high agreement between simulated and experimental results.

Conclusions

Based on the experimental validation, as well as the evaluation by clinical experts, the proposed model may provide an essential tool for the patient-specific simulation of different tumor evolution scenarios and reliable prognosis of glioma spatio-temporal progression.

SUBMITTER: Papadogiorgaki M

PROVIDER: S-EPMC3734056 | biostudies-literature | 2013 Jul

REPOSITORIES: biostudies-literature

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Publications

Mathematical modelling of spatio-temporal glioma evolution.

Papadogiorgaki Maria M Koliou Panagiotis P Kotsiakis Xenofon X Zervakis Michalis E ME

Theoretical biology & medical modelling 20130724

<h4>Background</h4>Gliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression.<h4>Methods</h4>Building and expanding on existing approaches, this paper develops a continuous three-dimens ...[more]

PMID: 23880133

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Project description:BackgroundThe Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) was first detected in China at the end of 2019 and it has since spread in few months all over the World. Italy was one of the first Western countries who faced the health emergency and is one of the countries most severely affected by the pandemic. The diffusion of Coronavirus disease 2019 (COVID-19) in Italy has followed a peculiar spatial pattern, however the attention of the scientific community has so far focussed almost exclusively on the prediction of the evolution of the disease over time.MethodsOfficial freely available data about the number of infected at the finest possible level of spatial areal aggregation (Italian provinces) are used to model the spatio-temporal distribution of COVID-19 infections at local level. An endemic-epidemic time-series mixed-effects generalized linear model for areal disease counts has been implemented to understand and predict spatio-temporal diffusion of the phenomenon.ResultsThree subcomponents characterize the fitted model. The first describes the transmission of the illness within provinces; the second accounts for the transmission between nearby provinces; the third is related to the evolution of the disease over time. At the local level, the provinces first concerned by containment measures are those that are not affected by the effects of spatial neighbours. On the other hand, the component accounting for the spatial interaction with surrounding areas is prevalent for provinces that are strongly involved by contagions. Moreover, the proposed model provides good forecasts for the number of infections at local level while controlling for delayed reporting.ConclusionsA strong evidence is found that strict control measures implemented in some provinces efficiently break contagions and limit the spread to nearby areas. While containment policies may potentially be more effective if planned considering the peculiarities of local territories, the effective and homogeneous enforcement of control measures at national level is needed to prevent the disease control being delayed or missed as a whole. This may also apply at international level where, as it is for the European Union or the United States, the internal border checks among states have largely been abolished.

Project description:BackgroundVector-borne diseases are important public health issues and, consequently, in silico models that simulate them can be useful. The susceptible-infected-recovered (SIR) model simulates the population dynamics of an epidemic and can be easily adapted to vector-borne diseases, whereas the Hardy-Weinberg model simulates allele frequencies and can be used to study insecticide resistance evolution. The aim of the present study is to develop a coupled system that unifies both models, therefore enabling the analysis of the effects of vector population genetics on the population dynamics of an epidemic.MethodsOur model consists of an ordinary differential equation system. We considered the populations of susceptible, infected and recovered humans, as well as susceptible and infected vectors. Concerning these vectors, we considered a pair of alleles, with complete dominance interaction that determined the rate of mortality induced by insecticides. Thus, we were able to separate the vectors according to the genotype. We performed three numerical simulations of the model. In simulation one, both alleles conferred the same mortality rate values, therefore there was no resistant strain. In simulations two and three, the recessive and dominant alleles, respectively, conferred a lower mortality.ResultsOur numerical results show that the genetic composition of the vector population affects the dynamics of human diseases. We found that the absolute number of vectors and the proportion of infected vectors are smaller when there is no resistant strain, whilst the ratio of infected people is larger in the presence of insecticide-resistant vectors. The dynamics observed for infected humans in all simulations has a very similar shape to real epidemiological data.ConclusionThe population genetics of vectors can affect epidemiological dynamics, and the presence of insecticide-resistant strains can increase the number of infected people. Based on the present results, the model is a basis for development of other models and for investigating population dynamics.

Dataset Information

Mathematical modelling of spatio-temporal glioma evolution.

Background

Methods

Results

Conclusions

Publications

Mathematical modelling of spatio-temporal glioma evolution.

Similar Datasets

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