Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications

Multiscale modelling of palisade formation in gliobastoma multiforme

Palisades are characteristic tissue aberrations that arise in glioblastomas. Observation of palisades is considered as a clinical indicator of the transition from a noninvasive to an invasive tumour. In this paper we propose a computational model to study the influence of the hypoxic switch in palisade formation. For this we produced three-dimensional realistic simulations, based on a multiscale hybrid model, coupling the evolution of tumour cells and the oxygen diffusion in tissue, that depict the shape of palisades during its formation. Our results can be summarized as follows: (1) the presented simulations can provide clinicians and biologists with a better understanding of three-dimensional structure of palisades as well as of glioblastomas growth dynamics; (2) we show that heterogeneity in cell response to hypoxia is a relevant factor in palisade and pseudopalisade formation; (3) we show how selective processes based on the hypoxia switch influence the tumour proliferation.

Towards the Personalized Treatment of Glioblastoma: Integrating Patient-Specific Clinical Data in a Continuous Mechanical Model

Glioblastoma multiforme (GBM) is the most aggressive and malignant among brain tumors. In addition to uncontrolled proliferation and genetic instability, GBM is characterized by a diffuse infiltration, developing long protrusions that penetrate deeply along the fibers of the white matter. These features, combined with the underestimation of the invading GBM area by available imaging techniques, make a definitive treatment of GBM particularly difficult. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of GBM evolution in every single patient throughout his/her oncological history, in order to target therapeutic weapons in a patient-specific manner. In this work, we propose a continuous mechanical model and we perform numerical simulations of GBM invasion combining the main mechano-biological characteristics of GBM with the micro-structural information extracted from radiological images, i.e. by elaborating patient-specific Diffusion Tensor Imaging (DTI) data. The numerical simulations highlight the influence of the different biological parameters on tumor progression and they demonstrate the fundamental importance of including anisotropic and heterogeneous patient-specific DTI data in order to obtain a more accurate prediction of GBM evolution. The results of the proposed mathematical model have the potential to provide a relevant benefit for clinicians involved in the treatment of this particularly aggressive disease and, more importantly, they might drive progress towards improving tumor control and patient’s prognosis.

Optimal radiation fractionation for low-grade gliomas: Insights from a mathematical model

We study optimal radiotherapy fractionations for low-grade glioma using mathematical models. Both space-independent and space-dependent models are studied. Two different optimization criteria have been developed, the first one accounting for the global effect of the tumor mass on the disease symptoms and the second one related to the delay of the malignant transformation of the tumor. The models are studied theoretically and numerically using the method of feasible directions. We have searched for optimal distributions of the daily doses dj in the standard protocol of 30 fractions using both models and the two different optimization criteria. The optimal results found in all cases are minor deviations from the standard protocol and provide only marginal potential gains. Thus, our results support the optimality of current radiation fractionations over the standard 6 week treatment period. This is also in agreement with the observation that minor variations of the fractionation have failed to provide measurable gains in survival or progression free survival, pointing out to a certain optimality of the current approach.

Extreme protraction for low-grade gliomas: theoretical proof of concept of a novel therapeutical strategy

Grade II gliomas are slowly growing primary brain tumours that affect mostly young patients and become fatal after a variable time period. Current clinical handling includes surgery as first-line treatment. Cytotoxic therapies (radiotherapy RT or chemotherapy QT) are used initially only for patients having a bad prognosis. Therapies are administered following the 'maximum dose in minimum time' principle, which is the same schedule used for high-grade brain tumours. Using mathematical models describing the growth of these tumours in response to radiotherapy, we find that an extreme protraction therapeutical strategy, i.e. enlarging substantially the time interval between RT fractions, may lead to better tumour control. Explicit formulas are found providing the optimal spacing between doses in a very good agreement with the simulations of the full 3D mathematical model approximating the tumour spatiotemporal dynamics. This idea, although breaking the well-established paradigm, has biological meaning since, in these slowly growing tumours, it may be more favourable to treat the tumour as the tumour cells leave the quiescent compartment and move into the cell cycle.

A combined gene signature of hypoxia and notch pathway in human glioblastoma and its prognostic relevance

Hypoxia is a hallmark of solid tumors including glioblastoma (GBM). Its synergism with Notch signaling promotes progression in different cancers. However, Notch signaling exhibits pleiotropic roles and the existing literature lacks a comprehensive understanding of its perturbations under hypoxia in GBM with respect to all components of the pathway. We identified the key molecular cluster(s) characteristic of the Notch pathway response in hypoxic GBM tumors and gliomaspheres. Expression of Notch and hypoxia genes was evaluated in primary human GBM tissues by q-PCR. Clustering and statistical analyses were applied to identify the combination of hypoxia markers correlated with upregulated Notch pathway components. We found well-segregated tumor—clusters representing high and low HIF-1α/PGK1-expressors which accounted for differential expression of Notch signaling genes. In combination, a five-hypoxia marker set (HIF-1α/PGK1/VEGF/CA9/OPN) was determined as the best predictor for induction of Notch1/Dll1/Hes1/Hes6/Hey1/Hey2. Similar Notch-axis genes were activated in gliomaspheres, but not monolayer cultures, under moderate/severe hypoxia (2%/0.2% O₂). Preliminary evidence suggested inverse correlation between patient survival and increased expression of constituents of the hypoxia-Notch gene signature. Together, our findings delineated the Notch-axis maximally associated with hypoxia in resected GBM, which might be prognostically relevant. Its upregulation in hypoxia-exposed gliomaspheres signify them as a better in-vitro model for studying hypoxia-Notch interactions than monolayer cultures.

Quantitative modeling of clinical, cellular, and extracellular matrix variables suggest prognostic indicators in cancer: a model in neuroblastoma

BACKGROUND

Risk classification and treatment stratification for cancer patients is restricted by our incomplete picture of the complex and unknown interactions between the patient's organism and tumor tissues (transformed cells supported by tumor stroma). Moreover, all clinical factors and laboratory studies used to indicate treatment effectiveness and outcomes are by their nature a simplification of the biological system of cancer, and cannot yet incorporate all possible prognostic indicators.

METHODS

A multiparametric analysis on 184 tumor cylinders was performed. To highlight the benefit of integrating digitized medical imaging into this field, we present the results of computational studies carried out on quantitative measurements, taken from stromal and cancer cells and various extracellular matrix fibers interpenetrated by glycosaminoglycans, and eight current approaches to risk stratification systems in patients with primary and nonprimary neuroblastoma.

RESULTS

New tumor tissue indicators from both fields, the cellular and the extracellular elements, emerge as reliable prognostic markers for risk stratification and could be used as molecular targets of specific therapies.

CONCLUSION

The key to dealing with personalized therapy lies in the mathematical modeling. The use of bioinformatics in patient-tumor-microenvironment data management allows a predictive model in neuroblastoma.

Mathematical modelling of spatio-temporal glioma evolution

Background

Gliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression.

Methods

Building and expanding on existing approaches, this paper develops a continuous three-dimensional model of avascular glioma spatio-temporal evolution. The proposed spherical model incorporates the interactions between the populations of four different glioma cell phenotypes (proliferative, hypoxic, hypoglychemic and necrotic) and their tissue microenvironment, in order to investigate how they affect tumor growth and invasion in an isotropic and homogeneous medium. The model includes two key variables involved in the proliferation and invasion processes of cancer cells; i.e. the extracellular matrix and the matrix-degradative enzymes concentrations inside the tumor and its surroundings. Additionally, the proposed model focuses on innovative features, such as the separate and independent impact of two vital nutrients, namely oxygen and glucose, in tumor growth, leading to the formation of cell populations with different metabolic profiles. The model implementation takes under consideration the variations of particular factors, such as the local cell proliferation rate, the variable conversion rates of cells from one category to another and the nutrient-dependent thresholds of conversion. All model variables (cell densities, ingredients concentrations) are continuous and described by reaction-diffusion equations.

Results

Several simulations were performed using combinations of growth and invasion rates, for different evolution times. The model results were evaluated by medical experts and validated on experimental glioma models available in the literature, revealing high agreement between simulated and experimental results.

Conclusions

Based on the experimental validation, as well as the evaluation by clinical experts, the proposed model may provide an essential tool for the patient-specific simulation of different tumor evolution scenarios and reliable prognosis of glioma spatio-temporal progression.