Mathematical modelling of spatio-temporal glioma evolution.

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.

Glioma growth modeling based on the effect of vital nutrients and metabolic products.

Glioma brain tumors exhibit considerably aggressive behavior leading to high mortality rates. Mathematical modeling of tumor growth aims to explore the interactions between glioma cells and tissue microenvironment, which affect tumor evolution. Leveraging this concept, we present a three-dimensional model of glioma spatio-temporal evolution based on existing continuum approaches, yet incorporating novel factors of the phenomenon. The proposed model involves the interactions between different tumor cell phenotypes and their microenvironment, investigating how tumor growth is affected by complex biological exchanges. It focuses on the separate and combined effect of vital nutrients and cellular wastes on tumor expansion, leading to the formation of cell populations with different metabolic, proliferative, and diffusive profiles. Several simulations were performed on a virtual and a real glioma, using combinations of proliferation and diffusion rates for different evolution times. The model results were validated on a glioma model available in the literature and a real case of tumor progression. The experimental observations indicate that our model estimates quite satisfactorily the expansion of each region and the overall tumor growth. Based on the individual results, the proposed model may provide an important research tool for patient-specific simulation of different tumor evolution scenarios and reliable estimation of glioma evolution. Graphical Abstract Outline of the mathematical model functionality and application to glioma growth with indicative results.

A Glycolysis-Based In Silico Model for the Solid Tumor Growth.

Cancer-tumor growth is a complex process depending on several biological factors, such as the chemical microenvironment of the tumor, the cellular metabolic profile, and its proliferation rate. Several mathematical models have been developed for identifying the interactions between tumor cells and tissue microenvironment, since they play an important role in tumor formation and progression. Toward this direction we propose a new continuum model of avascular glioma-tumor growth, which incorporates a new factor, namely, the glycolytic potential of cancer cells, to express the interactions of three different tumor-cell populations (proliferative, hypoxic, and necrotic) with their tissue microenvironment. The glycolytic potential engages three vital nutrients, i.e., oxygen, glucose, and lactate, which provide cells with the necessary energy for their survival and proliferation. Extensive simulations are performed for different evolution times and various proliferation rates, in order to investigate how the tumor growth is affected. According to medical experts, the experimental observations indicate that the model predicts quite satisfactorily the overall tumor growth as well as the expansion of each region separately. Following extensive evaluation, the proposed model may provide an essential tool for patient-specific tumor simulation and reliable prediction of glioma spatiotemporal expansion.

High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases.

Glioma, especially glioblastoma, is a leading cause of brain cancer fatality involving highly invasive and neoplastic growth. Diffusive models of glioma growth use variations of the diffusion-reaction equation in order to simulate the invasive patterns of glioma cells by approximating the spatiotemporal change of glioma cell concentration. The most advanced diffusive models take into consideration the heterogeneous velocity of glioma in gray and white matter, by using two different discrete diffusion coefficients in these areas. Moreover, by using diffusion tensor imaging (DTI), they simulate the anisotropic migration of glioma cells, which is facilitated along white fibers, assuming diffusion tensors with different diffusion coefficients along each candidate direction of growth. Our study extends this concept by fully exploiting the proportions of white and gray matter extracted by normal brain atlases, rather than discretizing diffusion coefficients. Moreover, the proportions of white and gray matter, as well as the diffusion tensors, are extracted by the respective atlases; thus, no DTI processing is needed. Finally, we applied this novel glioma growth model on real data and the results indicate that prognostication rates can be improved.

In-depth analysis and evaluation of diffusive glioma models.

Glioma is one of the most aggressive types of brain tumor. Several mathematical models have been developed during the past two decades, toward simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. Nevertheless, despite the applications presented, there has been little work on studying the details of the mathematical solution and implementation of the 3-D diffusion model and presenting a qualitative analysis of the algorithmic results. This paper presents a complete mathematical framework on the solution of the DRE using different numerical schemes. This framework takes into account all characteristics of the latest models, such as brain tissue heterogeneity, anisotropic tumor cell migration, chemotherapy, and resection modeling. The different numerical schemes presented have been evaluated based upon the degree to which the DRE exact solution is approximated. Experiments have been conducted both on real datasets and a test case for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the accuracy of the different models.

Integration of gene signatures using biological knowledge.

OBJECTIVE: Gene expression patterns that distinguish clinically significant disease subclasses may not only play a prominent role in diagnosis, but also lead to the therapeutic strategies tailoring the treatment to the particular biology of each disease. Nevertheless, gene expression signatures derived through statistical feature-extraction procedures on population datasets have received rightful criticism, since they share few genes in common, even when derived from the same dataset. We focus on knowledge complementarities conveyed by two or more gene-expression signatures by means of embedded biological processes and pathways, which alternatively form a meta-knowledge platform of analysis towards a more global, robust and powerful solution. METHODS: The main contribution of this work is the introduction and study of an approach for integrating different gene signatures based on the underlying biological knowledge, in an attempt to derive a unified global solution. It is further recognized that one group's signature does not perform well on another group's data, due to incompatibilities of microarray technologies and the experimental design. We assess this cross-platform aspect, showing that a unified solution derived on the basis of both statistical and biological validation may also help in overcoming such inconsistencies. RESULTS: Based on the proposed approach we derived a unified 69-gene signature, which outperforms significantly the performance of the initial signatures succeeding a 0.73 accuracy metric on 234 new patients with 81% sensitivity and 64% specificity. The same signature manages to reveal the two prognostic groups on an additional dataset of 286 new patients obtained through a different experimental protocol and microarray platform. Furthermore, it manages to derive two clusters in a dataset from a different platform, showing remarkable difference on both gene-expression and survival-prediction levels.

Complementary gene signature integration in multiplatform microarray experiments.

The concept of gene signature overlap has been addressed previously in a number of research papers. A common conclusion is the absence of significant overlap. In this paper, we verify the aforementioned fact, but we also assess the issue of similarities not on the gene level, but on the biology level hidden underneath a given signature. We proceed by taking into account the biological knowledge that exists among different signatures, and use it as a means of integrating them and refining their statistical significance on the datasets. In this form, by integrating biological knowledge with information stemming from data distributions, we derive a unified signature that is significantly improved over its predecessors in terms of performance and robustness. Our motive behind this approach is to assess the problem of evaluating different signatures not in a competitive but rather in a complementary manner, where one is treated as a pool of knowledge contributing to a global and unified solution.

Comparison and unification of genomic signatures in breast cancer.

The concept of deriving a gene signature in breast cancer has been addressed by different research groups, each one proposing a different solution with minor overlap among them. There is still an open issue of unifying results among different research groups. In this study we evaluate two published signatures, namely the 70 gene signature of Netherlands group and a 57 gene signature published in our previous study and propose an evaluation platform under which the underlined signatures could be compared effectively. After such an evaluation, we proceed with a unified signature and assess its performance with improved efficiency over the initial signatures.

Assessment of linear and nonlinear synchronization measures for analyzing EEG in a mild epileptic paradigm.

Epilepsy is one of the most common brain disorders and may result in brain dysfunction and cognitive disturbances. Epileptic seizures usually begin in childhood without being accommodated by brain damage and are tolerated by drugs that produce no brain dysfunction. In this study, cognitive function is evaluated in children with mild epileptic seizures controlled with common antiepileptic drugs. Under this prism, we propose a concise technical framework of combining and validating both linear and nonlinear methods to efficiently evaluate (in terms of synchronization) neurophysiological activity during a visual cognitive task consisting of fractal pattern observation. We investigate six measures of quantifying synchronous oscillatory activity based on different underlying assumptions. These measures include the coherence computed with the traditional formula and an alternative evaluation of it that relies on autoregressive models, an information theoretic measure known as minimum description length, a robust phase coupling measure known as phase-locking value, a reliable way of assessing generalized synchronization in state-space and an unbiased alternative called synchronization likelihood. Assessment is performed in three stages; initially, the nonlinear methods are validated on coupled nonlinear oscillators under increasing noise interference; second, surrogate data testing is performed to assess the possible nonlinear channel interdependencies of the acquired EEGs by comparing the synchronization indexes under the null hypothesis of stationary, linear dynamics; and finally, synchronization on the actual data is measured. The results on the actual data suggest that there is a significant difference between normal controls and epileptics, mostly apparent in occipital-parietal lobes during fractal observation tests.

Classifier fusion approaches for diagnostic cancer models.

Classifier ensembles have produced promising results, improving accuracy, confidence and most importantly feature space coverage in many practical applications. The recent trend is to move from heuristic combinations of classifiers to more statistically sound integrated schemes to produce quantifiable results as far as error bounds and overall generalization capability are concerned. In this study, we are evaluating the use of an ensemble of 8 classifiers based on 15 different fusion strategies on two medical problems. We measure the base classifiers correlation using 11 commonly accepted metrics and provide the grounds for choosing an improved hyper-classifier.

Laparoscopic image analysis for robotic arm guidance.

Some of the most important problems arising during a laparoscopic surgery relate to the limited perception of depth and field of view (fov). In this paper we explore the possibilities of dealing with these problems using appropriate re-modeling of the laparoscopic equipment and image processing algorithms, as to increase the perception ability of the surgeon within the operation space. We demonstrate that by using two camera units and appropriate estimation of the epipolar geometry between the camera views, we can acquire an accurate 3D map of the scene, as well as increased field of view. The benefits for the surgeon include the enhancement of the visible operating space and the increased perception of this space, with the ability of accurately estimating distances of sensitive abdomen regions and organs from the end of the laparoscope tip. Several simulation and real-world experiments are presented as to validate the potential of the proposed scheme.