Skeletal and Dental Morphological Characteristics of the Maxillary in Patients with Impacted Canines Using Cone Beam Computed Tomography: A Retrospective Clinical Study.

The aim of this study is to analyze the skeletal and dentoalveolar morphological characteristics of the maxillary in subjects with a unilateral palatally impacted canine using Cone Beam Computed Tomography (CBCT). A retrospective clinical study was conducted of 100 adult patients divided into two groups: one consisting of patients with a unilaterally palatally impacted maxillary canine (GI), with the subgroups in the right and left hemiarches (GI-R and GI-L), and the second, without impacted canine, as the control group (CG). The CBCT measured skeletal variables (maxillary basal width and alveolar crest height) and dentoalveolar variables (inclination of the upper incisor, tooth lengths of incisors and canines, arch length, tooth size and bone dental discrepancy). In skeletal variables, statistically significant differences were found in alveolar crest height (ACH) in all groups and subgroups (p < 0.01). In the dentoalveolar variables, there were differences in the angle of the upper incisor (II) and lateral incisor length (LLIL) between the GI and GC and the angle of the upper incisor (II'), arch length (AL') and arch length-tooth size discrepancy (ATD') among the GI subgroups (p < 0.01). There are skeletal and dentoalveolar differences in patients with unilateral palatally impacted maxillary canines, with lower angular and linear measurements compared with patients without impaction.

Pretreatment inflammatory indices predict Bevacizumab response in recurrent Glioma.

Aim: It remains unclear what the best therapeutic option for recurrent glioma patients after Stupp treatment is. Bevacizumab (BVZ) is commonly administered in progression, but it appears that only some patients benefit. It would be useful to find biomarkers that determine beforehand who these patients are. Methods: The protocol included 31 high-risk progressing glioma patients after Stupp treatment who received BVZ 5-10 mg/kg every 14 days and temozolomide (3-19 cycles, 150-200 mg five days each 28-day cycle) during a mean of eight cycles of BVZ or until tumor progression or unacceptable toxicity. We analyzed the clinical outcome values of inflammatory indices measured before BVZ administration. Results: Lymphocyte level before BVZ administration was the best independent predictor of overall survival (HR = 0.34; 95%CI: 0.145-0.81; P = 0.015). The area under the receiver operating characteristic (ROC) curve was 0.823, with 1.645 being the optimal cut-off value, and 0.80 and 0.85 the sensitivity and specificity values, respectively. Responder and non-responder survival curves were also significantly different, considering the first and second tertiles as cut-off points. The number of BVZ cycles was not related to lymphopenia. Pretreatment neutrophil, platelet levels, platelet-to-lymphocyte ratio (PLR), and neutrophil-to-lymphocyte ratio (NLR) did not have independent predictive value. Inflammatory variables were not correlated with each other. However, patients with high NLR and PLR simultaneously (double positive PLR-NLR) showed a worse clinical outcome than the rest (P = 0.043). Conclusion: Pretreatment lymphocyte levels and double positive PLR-NLR could be used as non-invasive hematological prognostic markers for recurrent gliomas treated with bevacizumab. A close relationship emerged between inflammation and angiogenesis.

Morphological MRI-based features provide pretreatment survival prediction in glioblastoma.

OBJECTIVES: We wished to determine whether tumor morphology descriptors obtained from pretreatment magnetic resonance images and clinical variables could predict survival for glioblastoma patients. METHODS: A cohort of 404 glioblastoma patients (311 discoveries and 93 validations) was used in the study. Pretreatment volumetric postcontrast T1-weighted magnetic resonance images were segmented to obtain the relevant morphological measures. Kaplan-Meier, Cox proportional hazards, correlations, and Harrell's concordance indexes (c-indexes) were used for the statistical analysis. RESULTS: A linear prognostic model based on the outstanding variables (age, contrast-enhanced (CE) rim width, and surface regularity) identified a group of patients with significantly better survival (p < 0.001, HR = 2.57) with high accuracy (discovery c-index = 0.74; validation c-index = 0.77). A similar model applied to totally resected patients was also able to predict survival (p < 0.001, HR = 3.43) with high predictive value (discovery c-index = 0.81; validation c-index = 0.92). Biopsied patients with better survival were well identified (p < 0.001, HR = 7.25) by a model including age and CE volume (c-index = 0.87). CONCLUSIONS: Simple linear models based on small sets of meaningful MRI-based pretreatment morphological features and age predicted survival of glioblastoma patients to a high degree of accuracy. The partition of the population using the extent of resection improved the prognostic value of those measures. KEY POINTS: • A combination of two MRI-based morphological features (CE rim width and surface regularity) and patients' age outperformed previous prognosis scores for glioblastoma. • Prognosis models for homogeneous surgical procedure groups led to even more accurate survival prediction based on Kaplan-Meier analysis and concordance indexes.

Correction to: Morphological MRI-based features provide pretreatment survival prediction in glioblastoma.

The original version of this article, published on 15 October 2018, unfortunately contained a mistake. The following correction has therefore been made in the original: The name of Mariano Amo-Salas and the affiliation of Ismael Herruzo were presented incorrectly.

Intratumoral heterogeneity in 18F-FDG PET/CT by textural analysis in breast cancer as a predictive and prognostic subrogate.

AIM: To assess the predictive and prognostic value of textural parameters in locally advanced breast cancer (LABC) obtained by 18F-FDG PET/CT. METHODS: Prospective study including 68 patients with LABC, neoadjuvant chemotherapy (NC) indication and a baseline 18F-FDG PET/CT. Breast specimens were grouped into molecular phenotypes and classified as responders or non-responders after completion of NC. Patients underwent standard follow-up to obtain the disease-free survival (DFS) and overall survival (OS). After breast tumor segmentation, three-dimensional (3D) textural measures were computed based on run-length matrices (RLM) and co-occurrence matrices (CM). Relations between textural features with risk categories attending to molecular phenotypes were explored. Kaplan-Meier analysis and univariate and multivariate Cox proportional hazard analysis were used to study the potential of textural variables, molecular phenotypes and histologic response to predict DFS and OS. Receiver operating characteristic (ROC) analysis was used to obtain the best cut-off value, the area under the curve (AUC) and sensitivity and specificity considering OS and DFS. RESULTS: Eighteen patients were classified as responders. Mean ± SD of DFS and OS was 70.87 ± 21.85 and 76.77 ± 18.80 months, respectively. Long run emphasis (LRE) and long run high gray-level emphasis (LRHGE) showed a relation with risk categories. Low gray-level run emphasis (LGRE), LRHGE and run-length non-uniformity (RLNU) showed association with the NC response. Textural variables were significantly associated with OS and DFS in univariate analysis. Regarding the multivariate Cox regression analysis, PET stage with short run high gray-level emphasis (SRHGE) was significantly associated with OS, and PET stage and high gray-level run emphasis (HGRE) with DFS. CONCLUSION: Textural variables obtained with 18F-FDG PET/CT were predictors of neoadjuvant chemotherapy response and prognosis, being as relevant as PET stage at diagnosis for OS and DFS prediction.

Regulation of the oxidative balance with coenzyme Q10 sensitizes human glioblastoma cells to radiation and temozolomide.

OBJECTIVES: To investigate how the modulation of the oxidative balance affects cytotoxic therapies in glioblastoma, in vitro. MATERIAL AND METHODS: Human glioblastoma U251 and T98 cells and normal astrocytes C8D1A were loaded with coenzyme Q10 (CoQ). Mitochondrial superoxide ion (O2-) and H2O2 were measured by fluorescence microscopy. OXPHOS performance was assessed in U251 cells with an oxytherm Clark-type electrode. Radio- and chemotherapy cytotoxicity was assessed by immunostaining of γH2AX (24 h), annexin V and nuclei morphology, at short (72 h) and long (15 d) time. Hif-1α, SOD1, SOD2 and NQO1 were determined by immunolabeling. Catalase activity was measured by classic enzymatic assay. Glutathione levels and total antioxidant capacity were quantified using commercial kits. RESULTS: CoQ did not affect oxygen consumption but reduced the level of O2- and H2O2 while shifted to a pro-oxidant cell status mainly due to a decrease in catalase activity and SOD2 level. Hif-1α was dampened, echoed by a decrease lactate and several key metabolites involved in glutathione synthesis. CoQ-treated cells were twofold more sensitive than control to radiation-induced DNA damage and apoptosis in short and long-term clonogenic assays, potentiating TMZ-induced cytotoxicity, without affecting non-transformed astrocytes. CONCLUSIONS: CoQ acts as sensitizer for cytotoxic therapies, disarming GBM cells, but not normal astrocytes, against further pro-oxidant injuries, being potentially useful in clinical practice for this fatal pathology.

Textural features and SUV-based variables assessed by dual time point 18F-FDG PET/CT in locally advanced breast cancer.

AIM: To study the influence of dual time point 18F-FDG PET/CT in textural features and SUV-based variables and their relation among them. METHODS: Fifty-six patients with locally advanced breast cancer (LABC) were prospectively included. All of them underwent a standard 18F-FDG PET/CT (PET-1) and a delayed acquisition (PET-2). After segmentation, SUV variables (SUVmax, SUVmean, and SUVpeak), metabolic tumor volume (MTV), and total lesion glycolysis (TLG) were obtained. Eighteen three-dimensional (3D) textural measures were computed including: run-length matrices (RLM) features, co-occurrence matrices (CM) features, and energies. Differences between all PET-derived variables obtained in PET-1 and PET-2 were studied. RESULTS: Significant differences were found between the SUV-based parameters and MTV obtained in the dual time point PET/CT, with higher values of SUV-based variables and lower MTV in the PET-2 with respect to the PET-1. In relation with the textural parameters obtained in dual time point acquisition, significant differences were found for the short run emphasis, low gray-level run emphasis, short run high gray-level emphasis, run percentage, long run emphasis, gray-level non-uniformity, homogeneity, and dissimilarity. Textural variables showed relations with MTV and TLG. CONCLUSION: Significant differences of textural features were found in dual time point 18F-FDG PET/CT. Thus, a dynamic behavior of metabolic characteristics should be expected, with higher heterogeneity in delayed PET acquisition compared with the standard PET. A greater heterogeneity was found in bigger tumors.

A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications.

Gliomas are the most frequent type of primary brain tumours. Low grade gliomas (LGGs, WHO grade II gliomas) may grow very slowly for the long periods of time, however they inevitably cause death due to the phenomenon known as the malignant transformation. This refers to the transition of LGGs to more aggressive forms of high grade gliomas (HGGs, WHO grade III and IV gliomas). In this paper we propose a mathematical model describing the spatio-temporal transition of LGGs into HGGs. Our modelling approach is based on two cellular populations with transitions between them being driven by the tumour microenvironment transformation occurring when the tumour cell density grows beyond a critical level. We show that the proposed model describes real patient data well. We discuss the relationship between patient prognosis and model parameters. We approximate tumour radius and velocity before malignant transformation as well as estimate the onset of this process.

Lack of robustness of textural measures obtained from 3D brain tumor MRIs impose a need for standardization.

PURPOSE: Textural measures have been widely explored as imaging biomarkers in cancer. However, their robustness under dynamic range and spatial resolution changes in brain 3D magnetic resonance images (MRI) has not been assessed. The aim of this work was to study potential variations of textural measures due to changes in MRI protocols. MATERIALS AND METHODS: Twenty patients harboring glioblastoma with pretreatment 3D T1-weighted MRIs were included in the study. Four different spatial resolution combinations and three dynamic ranges were studied for each patient. Sixteen three-dimensional textural heterogeneity measures were computed for each patient and configuration including co-occurrence matrices (CM) features and run-length matrices (RLM) features. The coefficient of variation was used to assess the robustness of the measures in two series of experiments corresponding to (i) changing the dynamic range and (ii) changing the matrix size. RESULTS: No textural measures were robust under dynamic range changes. Entropy was the only textural feature robust under spatial resolution changes (coefficient of variation under 10% in all cases). CONCLUSION: Textural measures of three-dimensional brain tumor images are not robust neither under dynamic range nor under matrix size changes. Standards should be harmonized to use textural features as imaging biomarkers in radiomic-based studies. The implications of this work go beyond the specific tumor type studied here and pose the need for standardization in textural feature calculation of oncological images.

Non-standard radiotherapy fractionations delay the time to malignant transformation of low-grade gliomas.

Grade II gliomas are slowly growing primary brain tumors that affect mostly young patients. Cytotoxic therapies (radiotherapy and/or chemotherapy) are used initially only for patients having a bad prognosis. These therapies are planned following the "maximum dose in minimum time" principle, i. e. the same schedule used for high-grade brain tumors in spite of their very different behavior. These tumors transform after a variable time into high-grade gliomas, which significantly decreases the patient's life expectancy. In this paper we study mathematical models describing the growth of grade II gliomas in response to radiotherapy. We find that protracted metronomic fractionations, i.e. therapeutical schedules enlarging the time interval between low-dose radiotherapy fractions, may lead to a better tumor control without an increase in toxicity. Other non-standard fractionations such as protracted or hypoprotracted schemes may also be beneficial. The potential survival improvement depends on the tumor's proliferation rate and can be even of the order of years. A conservative metronomic scheme, still being a suboptimal treatment, delays the time to malignant progression by at least one year when compared to the standard scheme.

Glioblastoma on a microfluidic chip: Generating pseudopalisades and enhancing aggressiveness through blood vessel obstruction events.

Background: Glioblastoma (GBM) is one of the most lethal tumor types. Hypercellular regions, named pseudopalisades, are characteristic in these tumors and have been hypothesized to be waves of migrating glioblastoma cells. These "waves" of cells are thought to be induced by oxygen and nutrient depletion caused by tumor-induced blood vessel occlusion. Although the universal presence of these structures in GBM tumors suggests that they may play an instrumental role in GBM's spread and invasion, the recreation of these structures in vitro has remained challenging. Methods: Here we present a new microfluidic model of GBM that mimics the dynamics of pseudopalisade formation. To do this, we embedded U-251 MG cells within a collagen hydrogel in a custom-designed microfluidic device. By controlling the medium flow through lateral microchannels, we can mimic and control blood-vessel obstruction events associated with this disease. Results: Through the use of this new system, we show that nutrient and oxygen starvation triggers a strong migratory process leading to pseudopalisade generation in vitro. These results validate the hypothesis of pseudopalisade formation and show an excellent agreement with a systems-biology model based on a hypoxia-driven phenomenon. Conclusions: This paper shows the potential of microfluidic devices as advanced artificial systems capable of modeling in vivo nutrient and oxygen gradients during tumor evolution.

Glioblastoma: does the pre-treatment geometry matter? A postcontrast T1 MRI-based study.

BACKGROUND: The potential of a tumour's volumetric measures obtained from pretreatment MRI sequences of glioblastoma (GBM) patients as predictors of clinical outcome has been controversial. Mathematical models of GBM growth have suggested a relation between a tumour's geometry and its aggressiveness. METHODS: A multicenter retrospective clinical study was designed to study volumetric and geometrical measures on pretreatment postcontrast T1 MRIs of 117 GBM patients. Clinical variables were collected, tumours segmented, and measures computed including: contrast enhancing (CE), necrotic, and total volumes; maximal tumour diameter; equivalent spherical CE width and several geometric measures of the CE "rim". The significance of the measures was studied using proportional hazards analysis and Kaplan-Meier curves. RESULTS: Kaplan-Meier and univariate Cox survival analysis showed that total volume [p = 0.034, Hazard ratio (HR) = 1.574], CE volume (p = 0.017, HR = 1.659), spherical rim width (p = 0.007, HR = 1.749), and geometric heterogeneity (p = 0.015, HR = 1.646) were significant parameters in terms of overall survival (OS). Multivariable Cox analysis for OS provided the later two parameters as age-adjusted predictors of OS (p = 0.043, HR = 1.536 and p = 0.032, HR = 1.570, respectively). CONCLUSION: Patients with tumours having small geometric heterogeneity and/or spherical rim widths had significantly better prognosis. These novel imaging biomarkers have a strong individual and combined prognostic value for GBM patients. KEY POINTS: • 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.

Metabolic Tumor Burden Assessed by Dual Time Point [18F]FDG PET/CT in Locally Advanced Breast Cancer: Relation with Tumor Biology.

PURPOSE: The aim of the study was to investigate the influence of dual time point 2-deoxy-2-[18F]fluoro-D-glucose ([18F]FDG) positron emission tomography/x-ray computed tomography (PET/CT) on the standard uptake value (SUV) and volume-based metabolic variables of breast lesions and their relation with biological characteristics and molecular phenotypes. PROCEDURES: Retrospective analysis including 67 patients with locally advanced breast cancer (LABC). All patients underwent a dual time point [18F]FDG PET/CT, 1 h (PET-1) and 3 h (PET-2) after [18F]FDG administration. Tumors were segmented following a three-dimensional methodology. Semiquantitative metabolic variables (SUVmax, SUVmean, and SUVpeak) and volume-based variables (metabolic tumor volume, MTV, and total lesion glycolysis, TLG) were obtained. Biologic prognostic parameters, such as the hormone receptors status, p53, HER2 expression, proliferation rate (Ki-67), and grading were obtained. Molecular phenotypes and risk-classification [low: luminal A, intermediate: luminal B HER2 (-) or luminal B HER2 (+), and high: HER2 pure or triple negative] were established. Relations between clinical and biological variables with the metabolic parameters were studied. The relevance of each metabolic variable in the prediction of phenotype risk was assessed using a multivariate analysis. RESULTS: SUV-based variables and TLG obtained in the PET-1 and PET-2 showed high and significant correlations between them. MTV and SUV variables (SUVmax, SUVmean, and SUVpeak) where only marginally correlated. Significant differences were found between mean SUV variables and TLG obtained in PET-1 and PET-2. High and significant associations were found between metabolic variables obtained in PET-1 and their homonymous in PET-2. Based on that, only relations of PET-1 variables with biological tumor characteristics were explored. SUV variables showed associations with hormone receptors status (p < 0.001 and p = 0.001 for estrogen and progesterone receptor, respectively) and risk-classification according to phenotype (SUVmax, p = 0.003; SUVmean, p = 0.004; SUVpeak, p = 0.003). As to volume-based variables, only TLG showed association with hormone receptors status (estrogen, p < 0.001; progesterone, p = 0.031), risk-classification (p = 0.007), and grade (p = 0.036). Hormone receptor negative tumors, high-grade tumors, and high-risk phenotypes showed higher TLG values. No association was found between the metabolic variables and Ki-67, HER2, or p53 expression. CONCLUSION: Statistical differences were found between mean SUV-based variables and TLG obtained in the dual time point PET/CT. Most of PET-derived parameters showed high association with molecular factors of breast cancer. However, dual time point PET/CT did not offer any added value to the single PET acquisition with respect to the relations with biological variables, based on PET-1 SUV, and volume-based variables were predictors of those obtained in PET-2.

Influence of gray level and space discretization on brain tumor heterogeneity measures obtained from magnetic resonance images.

PURPOSE: Tumor heterogeneity in medical imaging is a current research trend due to its potential relationship with tumor malignancy. The aim of this study is to analyze the effect of dynamic range and matrix size changes on the results of different heterogeneity measures. MATERIALS AND METHODS: Four patients harboring three glioblastomas and one metastasis were considered. Sixteen textural heterogeneity measures were computed for each patient, with a configuration including co-occurrence matrices (CM) features (local heterogeneity) and run-length matrices (RLM) features (regional heterogeneity). The coefficient of variation measured agreement between the textural measures in two types of experiments: (i) fixing the matrix size and changing the dynamic range and (ii) fixing the dynamic range and changing the matrix size. RESULTS: None of the measures considered were robust under dynamic range changes. The CM Entropy and the RLM high gray-level run emphasis (HGRE) were the outstanding textural features due to their robustness under matrix size changes. Also, the RLM low gray-level run emphasis (LGRE) provided robust results when the dynamic range considered was sufficiently high (more than 8 levels). All of the remaining textural features were not robust. CONCLUSION: Tumor texture studies based on images with different characteristics (e.g. multi-center studies) should first fix the dynamic range to be considered. For studies involving images of different resolutions either (i) only robust measures should be used (in our study CM entropy, RLM HGRE and/or RLM LGRE) or (ii) images should be resampled to match those of the lowest resolution before computing the textural features.

Geometrical Measures Obtained from Pretreatment Postcontrast T1 Weighted MRIs Predict Survival Benefits from Bevacizumab in Glioblastoma Patients.

BACKGROUND: Antiangiogenic therapies for glioblastoma (GBM) such as bevacizumab (BVZ), have been unable to extend survival in large patient cohorts. However, a subset of patients having angiogenesis-dependent tumors might benefit from these therapies. Currently, there are no biomarkers allowing to discriminate responders from non-responders before the start of the therapy. METHODS: 40 patients from the randomized GENOM009 study complied the inclusion criteria (quality of images, clinical data available). Of those, 23 patients received first line temozolomide (TMZ) for eight weeks and then concomitant radiotherapy and TMZ. 17 patients received BVZ+TMZ for seven weeks and then added radiotherapy to the treatment. Clinical variables were collected, tumors segmented and several geometrical measures computed including: Contrast enhancing (CE), necrotic, and total volumes; equivalent spherical CE width; several geometric measures of the CE 'rim' geometry and a set of image texture measures. The significance of the results was studied using Kaplan-Meier and Cox proportional hazards analysis. Correlations were assessed using Spearman correlation coefficients. RESULTS: Kaplan-Meier and Cox proportional hazards analysis showed that total, CE and inner volume (p = 0.019, HR = 4.258) and geometric heterogeneity of the CE areas (p = 0.011, HR = 3.931) were significant parameters identifying response to BVZ. The group of patients with either regular CE areas (small geometric heterogeneity, median difference survival 15.88 months, p = 0.011) or those with small necrotic volume (median survival difference 14.50 months, p = 0.047) benefited substantially from BVZ. CONCLUSION: Imaging biomarkers related to the irregularity of contrast enhancing areas and the necrotic volume were able to discriminate GBM patients with a substantial survival benefit from BVZ. A prospective study is needed to validate our results.

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.

Combined therapies of antithrombotics and antioxidants delay in silico brain tumour progression.

Glioblastoma multiforme (GBM), the most frequent type of primary brain tumour, 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 in oxidative stress, selecting for more invasive tumour cell phenotypes. In our study, we assay in silico different therapeutic approaches which combine antithrombotics (ATs), antioxidants and standard radiotherapy (RT). To do so, we have developed a biocomputational model of GBM 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 tumour progression. Our numerical simulations predict that suitable combinations of ATs and antioxidants may diminish, in a synergistic way, oxidative stress and the subsequent hypoxic response. This novel therapeutical strategy, with potentially low or no toxicity, might reduce tumour invasion and further sensitize GBM to conventional RT or other cytotoxic agents, hopefully increasing median patient overall survival time.

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.

Glucose-lactate metabolic cooperation in cancer: insights from a spatial mathematical model and implications for targeted therapy.

A recent study has hypothesised a glucose-lactate metabolic symbiosis between adjacent hypoxic and oxygenated regions of a developing tumour, and proposed a treatment strategy to target this symbiosis. However, in vivo experimental support remains inconclusive. Here we develop a minimal spatial mathematical model of glucose-lactate metabolism to examine, in principle, whether metabolic symbiosis is plausible in human tumours, and to assess the potential impact of inhibiting it. We find that symbiosis is a robust feature of our model system-although on the length scale at which oxygen supply is diffusion-limited, its occurrence requires very high cellular metabolic activity-and that necrosis in the tumour core is reduced in the presence of symbiosis. Upon simulating therapeutic inhibition of lactate uptake, we predict that targeted treatment increases the extent of tissue oxygenation without increasing core necrosis. The oxygenation effect is correlated strongly with the extent of wild-type hypoxia and only weakly with wild-type symbiotic behaviour, and therefore may be promising for radiosensitisation of hypoxic, lactate-consuming tumours even if they do not exhibit a spatially well-defined symbiosis. Finally, we conduct in vitro experiments on the U87 glioblastoma cell line to facilitate preliminary speculation as to where highly malignant tumours might fall in our parameter space, and find that these experiments suggest a weakly symbiotic regime for U87 cells, thus raising the new question of what relationship might exist between symbiosis and tumour malignancy.

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 hyperplasia. 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.