Low-grade gliomas (LGGs) are a group of primary brain tumours usually encountered in young patient populations. These tumours represent a difficult challenge because many patients survive a decade or more and may be at a higher risk for treatment-related complications. Specifically, radiation therapy is known to have a relevant effect on survival but in many cases it can be deferred to avoid side effects while maintaining its beneficial effect. However, a subset of LGGs manifests more aggressive clinical behaviour and requires earlier intervention. Moreover, the effectiveness of radiotherapy depends on the tumour characteristics. Recently Pallud et al. (2012. Neuro-Oncology, 14: , 1-10) studied patients with LGGs treated with radiation therapy as a first-line therapy and obtained the counterintuitive result that tumours with a fast response to the therapy had a worse prognosis than those responding late. In this paper, we construct a mathematical model describing the basic facts of glioma progression and response to radiotherapy. The model provides also an explanation to the observations of Pallud et al. Using the model, we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate tumour malignancy while at the same time reducing the toxicity associated to the treatment.
• Three-dimensional segmentation on magnetic resonance images allows the study of geometric measures. • Patients with small width of contrast enhancing areas have better prognosis. • The irregularity of contrast enhancing areas predicts survival in glioblastoma patients.
We put forward a nonlinear wave model describing the fundamental dynamical features of an aggressive type of brain tumors. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis, and exact solutions we prove that bright solitary tumor waves develop in such systems. Possible implications of our model as a tool to extract relevant patient specific tumor parameters in combination with standard preoperative clinical imaging are also discussed.
Objective: The main objective of this retrospective work was the study of three-dimensional (3D) heterogeneity measures of post-contrast pre-operative MR images acquired with T 1 weighted sequences of patients with glioblastoma (GBM) as predictors of clinical outcome. Methods: 79 patients from 3 hospitals were included in the study. 16 3D textural heterogeneity measures were computed including run-length matrix (RLM) features (regional heterogeneity) and co-occurrence matrix (CM) features (local heterogeneity). The significance of the results was studied using Kaplan-Meier curves and Cox proportional hazards analysis. Correlation between the variables of the study was assessed using the Spearman's correlation coefficient.Results: Kaplan-Meyer survival analysis showed that 4 of the 11 RLM features and 4 of the 5 CM features considered were robust predictors of survival. The median survival differences in the most significant cases were of over 6 months. Conclusion: Heterogeneity measures computed on the post-contrast pre-operative T 1 weighted MR images of patients with GBM are predictors of survival. Advances in knowledge: Texture analysis to assess tumour heterogeneity has been widely studied. However, most works develop a two-dimensional analysis, focusing only on one MRI slice to state tumour heterogeneity. The study of fully 3D heterogeneity textural features as predictors of clinical outcome is more robust and is not dependent on the selected slice of the tumour. INTRODUCTIONGlioblastoma (GBM) is the most frequent malignant brain tumour in adults and the most lethal type, with a median survival of 14.6 months for patients receiving the standard of care, i.e. maximal safe surgery plus radiotherapy and chemotherapy.1 Pre-operative MRI is routinely used for diagnosis, treatment planning, response evaluation and follow-up.The typical GBM appearance upon diagnosis on MRI consists of an enhanced ring with a central non-enhanced core of necrosis observed mainly on contrast-enhanced T 1 weighted images. Recently, there has been an increased use of advanced imaging techniques alone or in combination with conventional MRI modalities to characterize the connection of the so-called radio phenotype with the tumour genotype, the so-called radiogenomics (e.g. recent reviews for GBM 2,3 ). However, the use of those techniques requires further research and validation to achieve a broad clinical applicability. Thus, in clinical practice and trials, T 1 contrast-enhanced and T 2 /fluid-attenuated inversionrecovery images are still the gold standard for diagnosis and treatment planning. 4 One of the most important characteristics of GBM is its marked intratumour heterogeneity. In fact, these tumours are usually referred to as "glioblastoma multiforme", in order to highlight their heterogeneous nature. GBM tumours are formed by tumour cells which differ in their morphology, genetics and biological behaviour and may underlie the inability of conventional therapies to significantly impact patient outcomes.5 It is well known that ...
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