Hypoxic Cell Waves around Necrotic Cores in Glioblastoma: A Biomathematical Model and its Therapeutic Implications

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hiperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.Comment: 29 pages, 9 figure

Delay effects in the response of low-grade gliomas to radiotherapy: a mathematical model and its therapeutical implications

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 treatmen

Combined therapies of antithrombotics and antioxidants delay in silico brain tumor progression

Glioblastoma multiforme, the most frequent type of primary brain tumor, is a rapidly evolving and spatially heterogeneous high-grade astrocytoma that presents areas of necrosis, hypercellularity and microvascular hyperplasia. The aberrant vasculature leads to hypoxic areas and results in an increase of the oxidative stress selecting for more invasive tumor cell phenotypes. In our study we assay in silico different therapeutic approaches which combine antithrombotics, antioxidants and standard radiotherapy. To do so, we have developed a biocomputational model of glioblastoma multiforme that incorporates the spatio-temporal interplay among two glioma cell phenotypes corresponding to oxygenated and hypoxic cells, a necrotic core and the local vasculature whose response evolves with tumor progression. Our numerical simulations predict that suitable combinations of antithrombotics and antioxidants may diminish, in a synergetic way, oxidative stress and the subsequent hypoxic response. This novel therapeutical strategy, with potentially low or no toxicity, might reduce tumor invasion and further sensitize glioblastoma multiforme to conventional radiotherapy or other cytotoxic agents, hopefully increasing median patient overall survival time.Comment: 8 figure

Functional imaging in radiation therapy planning for head and neck cancer

Functional imaging and its application to radiotherapy (RT) is a rapidly expanding field with new modalities and techniques constantly developing and evolving. As technologies improve, it will be important to pay attention to their implementation. This review describes the main achievements in the field of head and neck cancer (HNC) with particular remarks on the unsolved problems

Tumour heterogeneity in glioblastoma assessed by MRI texture analysis: a potential marker of survival

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 T1 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 T1 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

Optimal Combinations of Chemotherapy and Radiotherapy in Low-Grade Gliomas: A Mathematical Approach.

Low-grade gliomas (LGGs) are brain tumors characterized by their slow growth and infiltrative nature. Treatment options for these tumors are surgery, radiation therapy and chemotherapy. The optimal use of radiation therapy and chemotherapy is still under study. In this paper, we construct a mathematical model of LGG response to combinations of chemotherapy, specifically to the alkylating agent temozolomide and radiation therapy. Patient-specific parameters were obtained from longitudinal imaging data of the response of real LGG patients. Computer simulations showed that concurrent cycles of radiation therapy and temozolomide could provide the best therapeutic efficacy in-silico for the patients included in the study. The patient cohort was extended computationally to a set of 3000 virtual patients. This virtual cohort was subject to an in-silico trial in which matching the doses of radiotherapy to those of temozolomide in the first five days of each cycle improved overall survival over concomitant radio-chemotherapy according to RTOG 0424. Thus, the proposed treatment schedule could be investigated in a clinical setting to improve combination treatments in LGGs with substantial survival benefits

Stereotactic Radiotherapy for Hepatocellular Carcinoma, Radiosensitization Strategies and Radiation-Immunotherapy Combination

Stereotactic body radiotherapy (SBRT) is an emerging ablative modality for hepatocellular carcinoma (HCC). Most patients with HCC have advanced disease at the time of diagnosis, and therefore, are not candidates for definitive-intent therapies such as resection or transplantation. For this reason, various alternative local and regional therapies have been used to prevent disease progression, palliate symptoms, and delay liver failure. Stereotactic body radiation therapy is a non-invasive technique of delivering ablative doses of radiation to tumors while sparing normal or non-tumor hepatic tissue. Incorporation of SBRT in multidisciplinary HCC management is gradual, initially applied when other liver-directed therapies have failed or are contraindicated, and tried in combination with other locoregional or systemic therapies for more unfavorable conditions by more experienced teams. In order to improve SBRT therapeutic ratio, there has been much interest in augmenting the effect of radiation on tumors by combining it with chemotherapy, molecularly targeted therapeutics, nanoparticles, and immunotherapy. This review aims to synthesize available evidence to evaluate the clinical feasibility and efficacy of SBRT for HCC, and to explore novel radio-potentiation concepts by combining SBRT with novel therapeutics. It is expected that those approaches would result in improved therapeutic outcomes, even though many questions remain with regard to the optimal way to assemble treatments. Further trials are needed to evaluate and consolidate these promising therapies for HCC

Delay effects in the response of low-grade gliomas to radiotherapy: a mathematical model and its therapeutical implications

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

Applied mathematics and nonlinear sciences in the war on cancer

Cancer is a major health problem in the industrialized world being the second leading cause of death in the USA and EU after heart disease. A huge quantity of resources is spent every year on cancer research, resulting in a small, yet sustained, reduction in cancer death rates (in the last ten years this was about 1 − 2% per year in the US) [1]. However, there is a widespread concern about the slow pace at which these discoveries in fundamental biology are translated into safe and effective clinical interventions. Statistics is already considered to be a basic ingredient of medical education and routinely used in research, specifically in clinical studies. This is so even when many physicians have a limited understanding of statistics and risk analysis [2]. However, the potential of other mathematical tools such as differential equations, advanced numerical methods, optimization, etc, have not been broadly incorporated into medical research on clinical care. This is so in spite of the fact that these methods are part of the standard toolbox of the applied mathematician that have proven useful in many other fields of science and engineering.VMP-G is partially supported by Ministerio de Economía y Competitividad/FEDER (MINECO), Spain [grant numbers: MTM2012-31073 and MTM2015-71200-R], Consejería de Educación Cultura y Deporte from Junta de Comunidades de Castilla-La Mancha (Spain) [grant number PEII-2014-031-P] and James S. Mc. Don-nell Foundation (USA) 21st Century Science Initiative in Mathematical and Complex Systems Approaches for Brain Cancer (Special Initiative Collaborative - Planning Grant 220020420 and Collaborative award 220020450). PSG is supported by MINECO under grants RD12/0036/0027 and SAF2015-65175-R. We would like to acknowledge MôLAB members (Universidad de Castilla-La Mancha, Spain) Juan Belmonte-Beitia, Gabriel F. Calvo and Alicia Martínez-González for a critical reading of the manuscript.S