Coupling time series of MR Images with reaction-diffusion-based models has provided interesting ways to better understand the proliferative-invasive aspect of glial cells in tumors. In this paper, we address a different formulation of the inverse problem: from a single time point image of a non-swollen brain tumor, estimate the tumor source location and the diffusivity ratio between white and grey matter, while exploring the possibility to predict the further extent of the observed tumor at later time points in low-grade gliomas. The synthetic and clinical results show the stability of the located source and its varying distance from the tumor barycenter and how the estimated ratio controls the spikiness of the tumor.

Tumor growth models based on the FisherKolmogorov reactiondiffusion equation (FK) have shown convincing results in reproducing and predicting the invasion patterns of gliomas brain tumors. Diffusion tensor images (DTIs) were suggested to model the anisotropic diffusion of tumor cells in the brain white matter. However, clinical patient-DTIs are expensive and often acquired with low resolution, which compromises the accuracy of the tumor growth models. In this work, we used the traveling wave approximation model to describe the evolution of the visible boundary of the tumor modeled by the FK equation to investigate the impact of replacing the patient DTI by (i) an isotropic diffusion map or (ii) an anisotropic high-resolution DTI atlas formed by averaging DTIs of multiple patients. We quantify the impact of replacing the patient DTI using three metrics: the shape of the simulated glioma, the estimation of the tumor growth parameters, and the prediction performance on clinical cases.

Abstract. We propose a method for estimating the location of glioma recurrence after surgical resection. This method consists of a pipeline including the registration of images at different time points, the estimation of the tumor infiltration map, and the prediction of tumor regrowth using a reaction-diffusion model. A data set acquired on a patient with a low-grade glioma and post surgery MRIs is considered to evaluate the accuracy of the estimated recurrence locations found using our method. We observed good agreement in tumor volume prediction and qualitative matching in regrowth locations. Therefore, the proposed method seems adequate for modeling low-grade glioma recurrence. This tool could help clinicians anticipate tumor regrowth and better characterize the radiologically non-visible infiltrative extent of the tumor. Such information could pave the way for model-based personalization of treatment planning in a near future.

Biomathematical modeling of glioma growth has been developed to optimize treatments delivery and to evaluate their efficacy. Simulations currently make use of anatomical knowledge from standard MRI atlases. For example, cerebrospinal fluid (CSF) spaces are obtained by automatic thresholding of the MNI atlas, leading to an approximate representation of real anatomy. To correct such inaccuracies, an expert-revised CSF segmentation map of the MNI atlas was built. Several virtual glioma growth patterns of different locations were generated, with and without using the expert-revised version of the MNI atlas. The adequacy between virtual and radiologically observed growth patterns was clearly higher when simulations were based on the expert-revised atlas. This work emphasizes the need for close collaboration between clinicians and researchers in the field of brain tumor modeling.