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Applying diffusive models for simulating the spatiotemporal change of concentration of tumour cells is a modern application of predictive oncology. Diffusive models are used for modelling glioblastoma, the most aggressive type of glioma. This paper presents the results of applying a linear quadratic model for simulating the effects of radiotherapy on an advanced diffusivegliomamodel. This diffusive model takes into consideration the heterogeneous velocity of glioma in gray and white matter and the anisotropic migration of tumor cells, which is facilitated along white fibers. This work uses normal brain atlases for extracting the proportions of white and gray matter and the diffusion tensors used for anisotropy. The paper also presents the results of applying this glioma model on real clinical datasets., 1. Introduction Cancer causes more than 13% of all deaths worldwide with an estimation of 12 million deaths in 2030 [1, 2]. In United States, 2.5% of cancer deaths are [...]

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. [ABSTRACT FROM PUBLISHER]

During the last decades, especially via the EU initiative related to the Virtual Physiological Human, significant progress has been made in advancing "in-silico" computational models to produce accurate and reliable tumor growth simulations. However, currently most attempts to validate the outcome of the models are either done in-vitro or ex-vivo after tumor resection. In this work, we incorporate information provided by fluorescence molecular tomography performed in-vivo into a mathematical model that describes tumor growth. The outcome is validated against tumor evolution snapshots captured in-vivo using advanced molecular probes in laboratory animals. The simulations are inline with the actual in-vivo growth and although alternative modeling parameters can lead to similar results challenging for additional microscopic information and imaging modalities to drive the in-silico models, they all show that hypoxia plays a dominant role in the evolution of the tumor under study.

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., (© 2012 IEEE)

This paper investigates the applicability of multilevel macroscopic models for simulating solid tumor growth in the invasive glioblastoma multiforme (GBM) case. The continuum case approach tumor model based on the diffusion reaction equation is evaluated on a pre-segmented tomographic atlas where all tissue properties are known a priori. The atlas is further registered on a real clinical case where the tumor invasion status is gauged in two successive points in time. Based on the latter, the model attempts to fully replicate tumor growth taking into account tissue based properties as identified from the atlas template. The whole process is performed on a clinical platform specially designed to facilitate precise identification and delineation of tumors of large number of 3D tomographic datasets by an expert clinician. The promising results presented encourage the potential clinical applicability of the proposed model in the glioma case and identify crucial points and direction of further model refinement and research.

Glioma is the most aggressive type of brain tumor. Several mathematical models have been developed during the last two decades, towards 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. The proposed diffusive models have mainly used finite differences (FDs) or finite elements (FEs) for the approximation of the solution of the partial differential DRE. This paper presents experimental results on the comparison of the FEs and FDs, especially focused on the glioma model case. It is studied how the different meshes of brain can affect computational consistency, simulation time and efficiency of the model. The experiments have been studied on a test case, for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the error that the different models yield.

Glioma is the most aggressive type of brain cancer. Several mathematical models have been developed towards identifying the mechanism of tumor growth. The most successful models have used variations of the diffusion-reaction equation, with the recent ones taking into account brain tissue heterogeneity and anisotropy. However, to the best of our knowledge, there hasn't been any work studying in detail the mathematical solution and implementation of the 3D diffusion model, addressing related heterogeneity and anisotropy issues. To this end, this paper introduces a complete mathematical framework on how to derive the solution of the equation using different numerical approximation of finite differences. It indicates how different proliferation rate schemes can be incorporated in this solution and presents a comparative study of different numerical approaches.