Image guided personalization of reaction-diffusion type tumor growth models using modified anisotropic eikonal equations
Reaction-diffusion based tumor growth models have been widely used in the literature for
modeling the growth of brain gliomas. Lately, recent models have started integrating medical …
modeling the growth of brain gliomas. Lately, recent models have started integrating medical …
A recursive anisotropic fast marching approach to reaction diffusion equation: Application to tumor growth modeling
Bridging the gap between clinical applications and mathematical models is one of the new
challenges of medical image analysis. In this paper, we propose an efficient and accurate …
challenges of medical image analysis. In this paper, we propose an efficient and accurate …
An image-driven parameter estimation problem for a reaction–diffusion glioma growth model with mass effects
C Hogea, C Davatzikos, G Biros - Journal of mathematical biology, 2008 - Springer
We present a framework for modeling gliomas growth and their mechanical impact on the
surrounding brain tissue (the so-called, mass-effect). We employ an Eulerian continuum …
surrounding brain tissue (the so-called, mass-effect). We employ an Eulerian continuum …
Predicting in vivo glioma growth with the reaction diffusion equation constrained by quantitative magnetic resonance imaging data
Reaction–diffusion models have been widely used to model glioma growth. However, it has
not been shown how accurately this model can predict future tumor status using model …
not been shown how accurately this model can predict future tumor status using model …
Glioma dynamics and computational models: a review of segmentation, registration, and in silico growth algorithms and their clinical applications
Tracking gliomas dynamics on MRI has became more and more important for therapeutic
management. Powerful computational tools have been recently developed in this context …
management. Powerful computational tools have been recently developed in this context …
A generative approach for image-based modeling of tumor growth
Extensive imaging is routinely used in brain tumor patients to monitor the state of the
disease and to evaluate therapeutic options. A large number of multi-modal and multi …
disease and to evaluate therapeutic options. A large number of multi-modal and multi …
An inverse problem formulation for parameter estimation of a reaction–diffusion model of low grade gliomas
We present a numerical scheme for solving a parameter estimation problem for a model of
low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor …
low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor …
The integration of quantitative multi-modality imaging data into mathematical models of tumors
NC Atuegwu, JC Gore… - Physics in Medicine & …, 2010 - iopscience.iop.org
Quantitative imaging data obtained from multiple modalities may be integrated into
mathematical models of tumor growth and treatment response to achieve additional insights …
mathematical models of tumor growth and treatment response to achieve additional insights …
A mechanically coupled reaction–diffusion model that incorporates intra-tumoural heterogeneity to predict in vivo glioma growth
DA Hormuth, JA Weis, SL Barnes… - Journal of The …, 2017 - royalsocietypublishing.org
While gliomas have been extensively modelled with a reaction–diffusion (RD) type equation
it is most likely an oversimplification. In this study, three mathematical models of glioma …
it is most likely an oversimplification. In this study, three mathematical models of glioma …
Hybrid mathematical model of glioma progression
ML Tanaka, W Debinski, IK Puri - Cell proliferation, 2009 - Wiley Online Library
Objectives: Gliomas are an important form of brain cancer, with high mortality rate.
Mathematical models are often used to understand and predict their behaviour. However …
Mathematical models are often used to understand and predict their behaviour. However …