Modeling Tumor-Associated Edema in Gliomas during Anti-Angiogenic Therapy and Its Impact on Imageable Tumor

Noninvasive Autopsy-Validated Tumor Probability Maps Identify Glioma Invasion Beyond Contrast Enhancement

BACKGROUND AND OBJECTIVES

This study identified a clinically significant subset of patients with glioma with tumor outside of contrast enhancement present at autopsy and subsequently developed a method for detecting nonenhancing tumor using radio-pathomic mapping. We tested the hypothesis that autopsy-based radio-pathomic tumor probability maps would be able to noninvasively identify areas of infiltrative tumor beyond traditional imaging signatures.

METHODS

A total of 159 tissue samples from 65 subjects were aligned to MRI acquired nearest to death for this retrospective study. Demographic and survival characteristics for patients with and without tumor beyond the contrast-enhancing margin were computed. An ensemble algorithm was used to predict pixelwise tumor presence from pathological annotations using segmented cellularity (Cell), extracellular fluid, and cytoplasm density as input (6 train/3 test subjects). A second level of ensemble algorithms was used to predict voxelwise Cell, extracellular fluid, and cytoplasm on the full data set (43 train/22 test subjects) using 5-by-5 voxel tiles from T1, T1 + C, fluid-attenuated inversion recovery, and apparent diffusion coefficient as input. The models were then combined to generate noninvasive whole brain maps of tumor probability.

RESULTS

Tumor outside of contrast was identified in 41.5% of patients, who showed worse survival outcomes (hazard ratio = 3.90, P < .001). Tumor probability maps reliably tracked nonenhancing tumor on a range of local and external unseen data, identifying tumor outside of contrast in 69% of presurgical cases that also showed reduced survival outcomes (hazard ratio = 1.67, P = .027).

CONCLUSION

This study developed a multistage model for mapping gliomas using autopsy tissue samples as ground truth, which was able to identify regions of tumor beyond traditional imaging signatures.

KCa channel targeting impairs DNA repair and invasiveness of patient-derived glioblastoma stem cells in culture and orthotopic mouse xenografts which only in part is predictable by KCa expression levels

Prognosis of glioblastoma patients is still poor despite multimodal therapy. The highly brain-infiltrating growth in concert with a pronounced therapy resistance particularly of mesenchymal glioblastoma stem-like cells (GSCs) has been proposed to contribute to therapy failure. Recently, we have shown that a mesenchymal-to-proneural mRNA signature of patient derived GSC-enriched (pGSC) cultures associates with in vitro radioresistance and gel invasion. Importantly, this pGSC mRNA signature is prognostic for patients' tumor recurrence pattern and overall survival. Two mesenchymal markers of the mRNA signature encode for IKCa and BKCa Ca2+-activated K+ channels. Therefore, we analyzed here the effect of IKCa- and BKCa-targeting concomitant to (fractionated) irradiation on radioresistance and glioblastoma spreading in pGSC cultures and in pGSC-derived orthotopic xenograft glioma mouse models. To this end, in vitro gel invasion, clonogenic survival, in vitro and in vivo residual DNA double strand breaks (DSBs), tumor growth, and brain invasion were assessed in the dependence on tumor irradiation and K+ channel targeting. As a result, the IKCa- and BKCa-blocker TRAM-34 and paxilline, respectively, increased number of residual DSBs and (numerically) decreased clonogenic survival in some but not in all IKCa- and BKCa-expressing pGSC cultures, respectively. In addition, BKCa- but not IKCa-blockade slowed-down gel invasion in vitro. Moreover, systemic administration of TRAM-34 or paxilline concomitant to fractionated tumor irradiation increased in the xenograft model(s) residual number of DSBs and attenuated glioblastoma brain invasion and (numerically) tumor growth. We conclude, that KCa-blockade concomitant to fractionated radiotherapy might be a promising new strategy in glioblastoma therapy.

Automated glioblastoma patient classification using hypoxia levels measured through magnetic resonance images

INTRODUCTION

The challenge of treating Glioblastoma (GBM) tumors is due to various mechanisms that make the tumor resistant to radiation therapy. One of these mechanisms is hypoxia, and therefore, determining the level of hypoxia can improve treatment planning and initial evaluation of its effectiveness in GBM. This study aimed to design an intelligent system to classify glioblastoma patients based on hypoxia levels obtained from magnetic resonance images with the help of an artificial neural network (ANN).

MATERIAL AND METHOD

MR images and PET measurements were available for this study. MR images were downloaded from the Cancer Imaging Archive (TCIA) database to classify glioblastoma patients based on hypoxia. The images in this database were prepared from 27 patients with glioblastoma on T1W + Gd, T2W-FLAIR, and T2W. Our designed algorithm includes various parts of pre-processing, tumor segmentation, feature extraction from images, and matching these features with quantitative parameters related to hypoxia in PET images. The system's performance is evaluated by categorizing glioblastoma patients based on hypoxia.

RESULTS

The results of classification with the artificial neural network (ANN) algorithm were as follows: the highest sensitivity, specificity, and accuracy were obtained at 86.71, 85.99 and 83.17%, respectively. The best specificity was related to the T2W-EDEMA image with the tumor to blood ratio (TBR) as a hypoxia parameter. T1W-NECROSIS image with the TBR parameter also showed the highest sensitivity and accuracy.

CONCLUSION

The results of the present study can be used in clinical procedures before treating glioblastoma patients. Among these treatment approaches, we can mention the radiotherapy treatment design and the prescription of effective drugs for the treatment of hypoxic tumors.

Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

Deep Learning for Reaction-Diffusion Glioma Growth Modeling: Towards a Fully Personalized Model?

Simple Summary

Mathematical tumor growth models have been proposed for decades to capture the growth of gliomas, an aggressive form of brain tumor. However, the estimation of the tumor cell-density distribution at diagnosis and model parameters from partial observations provided by magnetic resonance imaging are ill-posed problems. In this work, we propose a deep learning-based approach to address these problems. 1200 synthetic tumors are first generated using the mathematical model over brain geometries of 6 volunteers. Two deep convolutional neural networks are then trained to (i) reconstruct a whole tumor cell-density distribution and (ii) evaluate the model parameters from partial observations provided in the form of threshold-like imaging contours, with state-of-the-art results. From the estimated cell-density distribution and parameter values, the spatio-temporal evolution of the tumor can ultimately be accurately captured by the mathematical model. Such an approach could be of great interest for glioma characterization and therapy planning.

Abstract

Reaction-diffusion models have been proposed for decades to capture the growth of gliomas, the most common primary brain tumors. However, ill-posedness of the initialization at diagnosis time and parameter estimation of such models have restrained their clinical use as a personalized predictive tool. In this work, we investigate the ability of deep convolutional neural networks (DCNNs) to address commonly encountered pitfalls in the field. Based on 1200 synthetic tumors grown over real brain geometries derived from magnetic resonance (MR) data of six healthy subjects, we demonstrate the ability of DCNNs to reconstruct a whole tumor cell-density distribution from only two imaging contours at a single time point. With an additional imaging contour extracted at a prior time point, we also demonstrate the ability of DCNNs to accurately estimate the individual diffusivity and proliferation parameters of the model. From this knowledge, the spatio-temporal evolution of the tumor cell-density distribution at later time points can ultimately be precisely captured using the model. We finally show the applicability of our approach to MR data of a real glioblastoma patient. This approach may open the perspective of a clinical application of reaction-diffusion growth models for tumor prognosis and treatment planning.

Radio-Pathomic Maps of Cell Density Identify Brain Tumor Invasion beyond Traditional MRI-Defined Margins

BACKGROUND AND PURPOSE

Currently, contrast-enhancing margins on T1WI are used to guide treatment of gliomas, yet tumor invasion beyond the contrast-enhancing region is a known confounding factor. Therefore, this study used postmortem tissue samples aligned with clinically acquired MRIs to quantify the relationship between intensity values and cellularity as well as to develop a radio-pathomic model to predict cellularity using MR imaging data.

MATERIALS AND METHODS

This single-institution study used 93 samples collected at postmortem examination from 44 patients with brain cancer. Tissue samples were processed, stained with H&E, and digitized for nuclei segmentation and cell density calculation. Pre- and postgadolinium contrast T1WI, T2 FLAIR, and ADC images were collected from each patient's final acquisition before death. In-house software was used to align tissue samples to the FLAIR image via manually defined control points. Mixed-effects models were used to assess the relationship between single-image intensity and cellularity for each image. An ensemble learner was trained to predict cellularity using 5 × 5 voxel tiles from each image, with a two-thirds to one-third train-test split for validation.

RESULTS

Single-image analyses found subtle associations between image intensity and cellularity, with a less pronounced relationship in patients with glioblastoma. The radio-pathomic model accurately predicted cellularity in the test set (root mean squared error = 1015 cells/mm²) and identified regions of hypercellularity beyond the contrast-enhancing region.

CONCLUSIONS

A radio-pathomic model for cellularity trained with tissue samples acquired at postmortem examination is able to identify regions of hypercellular tumor beyond traditional imaging signatures.

Initial Condition Assessment for Reaction-Diffusion Glioma Growth Models: A Translational MRI-Histology (In)Validation Study

Reaction-diffusion models have been proposed for decades to capture the growth of gliomas. Nevertheless, these models require an initial condition: the tumor cell density distribution over the whole brain at diagnosis time. Several works have proposed to relate this distribution to abnormalities visible on magnetic resonance imaging (MRI). In this work, we verify these hypotheses by stereotactic histological analysis of a non-operated brain with glioblastoma using a 3D-printed slicer. Cell density maps are computed from histological slides using a deep learning approach. The density maps are then registered to a postmortem MR image and related to an MR-derived geodesic distance map to the tumor core. The relation between the edema outlines visible on T2-FLAIR MRI and the distance to the core is also investigated. Our results suggest that (i) the previously proposed exponential decrease of the tumor cell density with the distance to the core is reasonable but (ii) the edema outlines would not correspond to a cell density iso-contour and (iii) the suggested tumor cell density at these outlines is likely overestimated. These findings highlight the limitations of conventional MRI to derive glioma cell density maps and the need for other initialization methods for reaction-diffusion models to be used in clinical practice.

Improving personalized tumor growth predictions using a Bayesian combination of mechanistic modeling and machine learning

BACKGROUND

In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient's pathology producing a variety of clinical data. However, investigation of these data faces two major challenges. Firstly, we lack the knowledge of the mechanisms involved in regulating these data variables, and secondly, data collection is sparse in time since it relies on patient's clinical presentation. The former limits the predictive accuracy of clinical outcomes for any mechanistic model. The latter restrains any machine learning algorithm to accurately infer the corresponding disease dynamics.

METHODS

Here, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning, aiming at improving individualized predictions by addressing the aforementioned challenges.

RESULTS

We evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two relevant clinical outputs. The method results in improved predictions in almost all simulated patients, especially for those with a late clinical presentation (>95% patients show improvements compared to standard mathematical modeling). In addition, we test the methodology in two additional settings dealing with real patient cohorts. In both cases, namely cancer growth in chronic lymphocytic leukemia and ovarian cancer, predictions show excellent agreement with reported clinical outcomes (around 60% reduction of mean squared error).

CONCLUSIONS

We show that the combination of machine learning and mathematical modeling approaches can lead to accurate predictions of clinical outputs in the context of data sparsity and limited knowledge of disease mechanisms.

Comparison of In Vivo and Ex Vivo Magnetic Resonance Imaging in a Rat Model for Glioblastoma-Associated Epilepsy

Magnetic resonance imaging (MRI) is frequently used for preclinical treatment monitoring in glioblastoma (GB). Discriminating between tumors and tumor-associated changes is challenging on in vivo MRI. In this study, we compared in vivo MRI scans with ex vivo MRI and histology to estimate more precisely the abnormal mass on in vivo MRI. Epileptic seizures are a common symptom in GB. Therefore, we used a recently developed GB-associated epilepsy model from our group with the aim of further characterizing the model and making it useful for dedicated epilepsy research. Ten days after GB inoculation in rat entorhinal cortices, in vivo MRI (T2w and mean diffusivity (MD)), ex vivo MRI (T2w) and histology were performed, and tumor volumes were determined on the different modalities. The estimated abnormal mass on ex vivo T2w images was significantly smaller compared to in vivo T2w images, but was more comparable to histological tumor volumes, and might be used to estimate end-stage tumor volumes. In vivo MD images displayed tumors as an outer rim of hyperintense signal with a core of hypointense signal, probably reflecting peritumoral edema and tumor mass, respectively, and might be used in the future to distinguish the tumor mass from peritumoral edema—associated with reactive astrocytes and activated microglia, as indicated by an increased expression of immunohistochemical markers—in preclinical models. In conclusion, this study shows that combining imaging techniques using different structural scales can improve our understanding of the pathophysiology in GB.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Image-based personalization of computational models for predicting response of high-grade glioma to chemoradiation

High-grade gliomas are an aggressive and invasive malignancy which are susceptible to treatment resistance due to heterogeneity in intratumoral properties such as cell proliferation and density and perfusion. Non-invasive imaging approaches can measure these properties, which can then be used to calibrate patient-specific mathematical models of tumor growth and response. We employed multiparametric magnetic resonance imaging (MRI) to identify tumor extent (via contrast-enhanced T1-weighted, and T2-FLAIR) and capture intratumoral heterogeneity in cell density (via diffusion-weighted imaging) to calibrate a family of mathematical models of chemoradiation response in nine patients with unresected or partially resected disease. The calibrated model parameters were used to forecast spatially-mapped individual tumor response at future imaging visits. We then employed the Akaike information criteria to select the most parsimonious member from the family, a novel two-species model describing the enhancing and non-enhancing components of the tumor. Using this model, we achieved low error in predictions of the enhancing volume (median: - 2.5%, interquartile range: 10.0%) and a strong correlation in total cell count (Kendall correlation coefficient 0.79) at 3-months post-treatment. These preliminary results demonstrate the plausibility of using multiparametric MRI data to inform spatially-informative, biologically-based predictive models of tumor response in the setting of clinical high-grade gliomas.

Fully Automatic Calibration of Tumor-Growth Models Using a Single mpMRI Scan

Our objective is the calibration of mathematical tumor growth models from a single multiparametric scan. The target problem is the analysis of preoperative Glioblastoma (GBM) scans. To this end, we present a fully automatic tumor-growth calibration methodology that integrates a single-species reaction-diffusion partial differential equation (PDE) model for tumor progression with multiparametric Magnetic Resonance Imaging (mpMRI) scans to robustly extract patient specific biomarkers i.e., estimates for (i) the tumor cell proliferation rate, (ii) the tumor cell migration rate, and (iii) the original, localized site(s) of tumor initiation. Our method is based on a sparse reconstruction algorithm for the tumor initial location (TIL). This problem is particularly challenging due to nonlinearity, ill-posedeness, and ill conditioning. We propose a coarse-to-fine multi-resolution continuation scheme with parameter decomposition to stabilize the inversion. We demonstrate robustness and practicality of our method by applying the proposed method to clinical data of 206 GBM patients. We analyze the extracted biomarkers and relate tumor origin with patient overall survival by mapping the former into a common atlas space. We present preliminary results that suggest improved accuracy for prediction of patient overall survival when a set of imaging features is augmented with estimated biophysical parameters. All extracted features, tumor initial positions, and biophysical growth parameters are made publicly available for further analysis. To our knowledge, this is the first fully automatic scheme that can handle multifocal tumors and can localize the TIL to a few millimeters.

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence.

STAT3-PTTG11 abrogation inhibits proliferation and induces apoptosis in malignant glioma cells

Pituitary tumor transforming gene 1 (PTTG11) is abundantly expressed in glioma. Our previous study demonstrated that the downregulation of PTTG11 gene expression significantly inhibited the proliferation, migration and invasion ability, and increased the apoptosis of SHG44 glioma cells. However, the molecular mechanisms that regulate PTTG11 and its actions remain elusive. In the present study, CCK-8 and flow cytometry assays were used to assess the proliferation/viability and apoptosis, respectively, of the human glioma U251 cell line. STAT3-PTTG1 signals were further evaluated by western blotting. The findings of the present study revealed that STAT3 induced PTTG11 expression, which subsequently induced downstream c-Myc and Bcl-2 expression while inhibiting Bax expression, thereby promoting cell viability and inhibiting apoptosis. PTTG11 suppression via siRNA inhibited the viability and increased the apoptosis of glioma cells induced by the STAT3 activator S3I-201. c-Myc and Bcl-2 expression was suppressed by PTTG11 inhibition. The findings of the present study suggest that the STAT3-PTTG11 signaling pathway may play an important role in glioma progression by regulating cell proliferation and apoptosis.

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

How heterogeneity drives tumour growth: a computational study

Although cancerous tumours usually originate from a single cell, they normally evolve into a remarkably heterogeneous agglomeration of cells. Heterogeneity is a pervasive and almost universal feature of tumours, but its origin and consequences remain poorly understood. Tumour heterogeneity has been usually associated with poor prognosis, but a better understanding of it may lead to more personalized diagnosis and therapy. Here, we study tumour heterogeneity developing a computational model in which different cell subpopulations compete for space. The model suggests that aggressive tumour subpopulations may become even more aggressive when they grow with a non-aggressive subpopulation. The model also provides a mechanistic explanation of how heterogeneity drives growth. In particular, we observed that even a mild heterogeneity in the proliferation rates of different cell subpopulations leads to a much faster overall tumour growth when compared to a homogeneous tumour. The proposed model may be a starting point to study tumour heterogeneity computationally and to suggest new hypotheses to be tested experimentally. This article is part of the theme issue 'Patterns in soft and biological matters'.

Speed Switch in Glioblastoma Growth Rate due to Enhanced Hypoxia-Induced Migration

We analyze the wave speed of the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model that was previously created and applied to simulate the growth and spread of glioblastoma (GBM), a particularly aggressive primary brain tumor. We extend the PIHNA model by allowing for different hypoxic and normoxic cell migration rates and study the impact of these differences on the wave-speed dynamics. Through this analysis, we find key variables that drive the outward growth of the simulated GBM. We find a minimum tumor wave-speed for the model; this depends on the migration and proliferation rates of the normoxic cells and is achieved under certain conditions on the migration rates of the normoxic and hypoxic cells. If the hypoxic cell migration rate is greater than the normoxic cell migration rate above a threshold, the wave speed increases above the predicted minimum. This increase in wave speed is explored through an eigenvalue and eigenvector analysis of the linearized PIHNA model, which yields an expression for this threshold. The PIHNA model suggests that an inherently faster-diffusing hypoxic cell population can drive the outward growth of a GBM as a whole, and that this effect is more prominent for faster-proliferating tumors that recover relatively slowly from a hypoxic phenotype. The findings presented here act as a first step in enabling patient-specific calibration of the PIHNA model.

A novel in silico platform for a fully automatic personalized brain tumor growth

Glioblastoma Multiforme is the most common and most aggressive type of brain tumors. Although accurate prediction of Glioblastoma borders and shape is absolutely essential for neurosurgeons, there are not many in silico platforms that can make such predictions. In the current study, an automatic patient-specific simulation of Glioblastoma growth would be described. A finite element approach is used to analyze the magnetic resonance images from patients in the early stages of their tumors. For segmentation of the tumor, the Support Vector Machine (SVM) method, which is an automatic segmentation algorithm, is used. Using in situ and in vivo data, the main parameters of tumor prediction and growth are estimated with high precision in proliferation-invasion partial differential equation, using the genetic algorithm optimization method. The results show that for a C57BL mouse, the differences between the area and perimeter of in vivo test and simulation prediction data, as the objective function, are 3.7% and 17.4%, respectively.

Forecasting tumor and vasculature response dynamics to radiation therapy via image based mathematical modeling

BACKGROUND

Intra-and inter-tumoral heterogeneity in growth dynamics and vascularity influence tumor response to radiation therapy. Quantitative imaging techniques capture these dynamics non-invasively, and these data can initialize and constrain predictive models of response on an individual basis.

METHODS

We have developed a family of 10 biologically-based mathematical models describing the spatiotemporal dynamics of tumor volume fraction, blood volume fraction, and response to radiation therapy. To evaluate this family of models, rats (n = 13) with C6 gliomas were imaged with magnetic resonance imaging (MRI) three times before, and four times following a single fraction of 20 Gy or 40 Gy whole brain irradiation. The first five 3D time series data of tumor volume fraction, estimated from diffusion-weighted (DW-) MRI, and blood volume fraction, estimated from dynamic contrast-enhanced (DCE-) MRI, were used to calibrate tumor-specific model parameters. The most parsimonious and well calibrated of the 10 models, selected using the Akaike information criterion, was then utilized to predict future growth and response at the final two imaging time points. Model predictions were compared at the global level (percent error in tumor volume, and Dice coefficient) as well as at the local or voxel level (concordance correlation coefficient).

RESULT

The selected model resulted in < 12% error in tumor volume predictions, strong spatial agreement between predicted and observed tumor volumes (Dice coefficient > 0.74), and high level of agreement at the voxel level between the predicted and observed tumor volume fraction and blood volume fraction (concordance correlation coefficient > 0.77 and > 0.65, respectively).

CONCLUSIONS

This study demonstrates that serial quantitative MRI data collected before and following radiation therapy can be used to accurately predict tumor and vasculature response with a biologically-based mathematical model that is calibrated on an individual basis. To the best of our knowledge, this is the first effort to characterize the tumor and vasculature response to radiation therapy temporally and spatially using imaging-driven mathematical models.

ENvironmental Dynamics Underlying Responsive Extreme Survivors (ENDURES) of Glioblastoma: A Multidisciplinary Team-based, Multifactorial Analytical Approach

Although glioblastoma (GBM) is a fatal primary brain cancer with short median survival of 15 months, a small number of patients survive >5 years after diagnosis; they are known as extreme survivors (ES). Because of their rarity, very little is known about what differentiates these outliers from other patients with GBM. For the purpose of identifying unknown drivers of extreme survivorship in GBM, the ENDURES consortium (ENvironmental Dynamics Underlying Responsive Extreme Survivors of GBM) was developed. This consortium is a multicenter collaborative network of investigators focused on the integration of multiple types of clinical data and the creation of patient-specific models of tumor growth informed by radiographic and histologic parameters. Leveraging our combined resources, the goals of the ENDURES consortium are 2-fold: (1) to build a curated, searchable, multilayered repository housing clinical and outcome data on a large cohort of ES patients with GBM; and (2) to leverage the ENDURES repository for new insights into tumor behavior and novel targets for prolonging survival for all patients with GBM. In this article, the authors review the available literature and discuss what is already known about ES. The authors then describe the creation of their consortium and some preliminary results.

An autopsy case of widespread brain dissemination of glioblastoma unnoticed by magnetic resonance imaging after treatment with bevacizumab

Background:

Although glioblastoma has been shown to be able to disseminate widely in the intracranially after treatment with bevacizumab without any significant radiological findings, reports on such cases with subsequent autopsy findings are lacking.

Case Description:

A 36-year-old man presented with a general seizure and a mass of the right frontal lobe, which was diagnosed as diffuse astrocytoma (WHO Grade II). The patient underwent a total of four surgeries from 2005 to 2017. He showed tumor recurrence, progression, and malignant transformation to glioblastoma (GBM) (WHO Grade IV) despite repeated tumor resections, radiotherapy, and chemotherapies with temozolomide and carmustine wafers. Bevacizumab (10 mg/kg body weight) was started following the fourth surgery. After bevacizumab administration, the patient’s clinical condition improved to a Karnofsky performance status (KPS) score of 50–60, and he was stable for several months before finally deteriorating and passing away. Although sequential magnetic resonance imaging (MRI) showed shrinkage of the lesion and a reduction of edema, an autopsy showed widespread tumor invasion that was not revealed on MRI. Neoplastic foci were identified extensively in the cerebral cortex, basal ganglia, pituitary gland, cerebellum, and brainstem, imposing as gliomatosis cerebri.

Conclusion:

Imaging follow-up of malignant gliomas needs to be interpreted with caution as marked improvement in radiological response after bevacizumab treatment may not be indicating tumor regression. Despite the notable lack of evidence to increase overall survival in GBM patients with bevacizumab, the increase in progression-free survival and the observed relief of symptoms due to a decrease in edema should be considered relevant for patient management.

Simulation of glioblastoma growth using a 3D multispecies tumor model with mass effect

In this article, we present a multispecies reaction-advection-diffusion partial differential equation coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so-called "mass effect", a term-of-art that refers to the deformation of brain tissue due to the presence of the tumor. The multispecies model accounts for proliferating, invasive and necrotic tumor cells as well as a simple model for nutrition consumption and tumor-induced brain edema. The coupling of the model with linear elasticity equations with variable coefficients allows us to capture the mechanical deformations due to the tumor growth on surrounding tissues. We present the overall formulation along with a novel operator-splitting scheme with components that include linearly-implicit preconditioned elliptic solvers, and a semi-Lagrangian method for advection. We also present results showing simulated MRI images which highlight the capability of our method to capture the overall structure of glioblastomas in MRIs.

Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [18F]fluorodeoxyglucose positron emission tomography, and [18F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.

Characterizing Glioblastoma Heterogeneity via Single-Cell Receptor Quantification

Dysregulation of tyrosine kinase receptor (RTK) signaling pathways play important roles in glioblastoma (GBM). However, therapies targeting these signaling pathways have not been successful, partially because of drug resistance. Increasing evidence suggests that tumor heterogeneity, more specifically, GBM-associated stem and endothelial cell heterogeneity, may contribute to drug resistance. In this perspective article, we introduce a high-throughput, quantitative approach to profile plasma membrane RTKs on single cells. First, we review the roles of RTKs in cancer. Then, we discuss the sources of cell heterogeneity in GBM, providing context to the key cells directing resistance to drugs. Finally, we present our provisionally patented qFlow cytometry approach, and report results of a "proof of concept" patient-derived xenograft GBM study.

A mechanically coupled reaction-diffusion model that incorporates intra-tumoural heterogeneity to predict in vivo glioma growth

While gliomas have been extensively modelled with a reaction-diffusion (RD) type equation it is most likely an oversimplification. In this study, three mathematical models of glioma growth are developed and systematically investigated to establish a framework for accurate prediction of changes in tumour volume as well as intra-tumoural heterogeneity. Tumour cell movement was described by coupling movement to tissue stress, leading to a mechanically coupled (MC) RD model. Intra-tumour heterogeneity was described by including a voxel-specific carrying capacity (CC) to the RD model. The MC and CC models were also combined in a third model. To evaluate these models, rats (n = 14) with C6 gliomas were imaged with diffusion-weighted magnetic resonance imaging over 10 days to estimate tumour cellularity. Model parameters were estimated from the first three imaging time points and then used to predict tumour growth at the remaining time points which were then directly compared to experimental data. The results in this work demonstrate that mechanical-biological effects are a necessary component of brain tissue tumour modelling efforts. The results are suggestive that a variable tissue carrying capacity is a needed model component to capture tumour heterogeneity. Lastly, the results advocate the need for additional effort towards capturing tumour-to-tissue infiltration.

Clinical implications of in silico mathematical modeling for glioblastoma: a critical review

Glioblastoma remains a clinical challenge in spite of years of extensive research. Novel approaches are needed in order to integrate the existing knowledge. This is the potential role of mathematical oncology. This paper reviews mathematical models on glioblastoma from the clinical doctor's point of view, with focus on 3D modeling approaches of radiation response of in vivo glioblastomas based on contemporary imaging techniques. As these models aim to provide a clinically useful tool in the era of personalized medicine, the integration of the latest advances in molecular and imaging science and in clinical practice by the in silico models is crucial for their clinical relevance. Our aim is to indicate areas of GBM research that have not yet been addressed by in silico models and to point out evidence that has come up from in silico experiments, which may be worth considering in the clinic. This review examines how close these models have come in predicting the outcome of treatment protocols and in shaping the future of radiotherapy treatments.

Quantitative analysis of the proliferative-to-invasive transition of hypoxic glioma cells

Impact of the proliferative-to-invasive transformation of glioma cells on the global growth kinetics of the tumor.

Fast and high temperature hyperthermia coupled with radiotherapy as a possible new treatment for glioblastoma

Background

A new transcranial focused ultrasound device has been developed that can induce hyperthermia in a large tissue volume. The purpose of this work is to investigate theoretically how glioblastoma multiforme (GBM) can be effectively treated by combining the fast hyperthermia generated by this focused ultrasound device with external beam radiotherapy.

Methods/Design

To investigate the effect of tumor growth, we have developed a mathematical description of GBM proliferation and diffusion in the context of reaction–diffusion theory. In addition, we have formulated equations describing the impact of radiotherapy and heat on GBM in the reaction–diffusion equation, including tumor regrowth by stem cells. This formulation has been used to predict the effectiveness of the combination treatment for a realistic focused ultrasound heating scenario.

Our results show that patient survival could be significantly improved by this combined treatment modality.

Discussion

High priority should be given to experiments to validate the therapeutic benefit predicted by our model.

Electronic supplementary material

The online version of this article (doi:10.1186/s40349-016-0078-3) contains supplementary material, which is available to authorized users.

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.

MRI Based Bayesian Personalization of a Tumor Growth Model

The mathematical modeling of brain tumor growth has been the topic of numerous research studies. Most of this work focuses on the reaction-diffusion model, which suggests that the diffusion coefficient and the proliferation rate can be related to clinically relevant information. However, estimating the parameters of the reaction-diffusion model is difficult because of the lack of identifiability of the parameters, the uncertainty in the tumor segmentations, and the model approximation, which cannot perfectly capture the complex dynamics of the tumor evolution. Our approach aims at analyzing the uncertainty in the patient specific parameters of a tumor growth model, by sampling from the posterior probability of the parameters knowing the magnetic resonance images of a given patient. The estimation of the posterior probability is based on: 1) a highly parallelized implementation of the reaction-diffusion equation using the Lattice Boltzmann Method (LBM), and 2) a high acceptance rate Monte Carlo technique called Gaussian Process Hamiltonian Monte Carlo (GPHMC). We compare this personalization approach with two commonly used methods based on the spherical asymptotic analysis of the reaction-diffusion model, and on a derivative-free optimization algorithm. We demonstrate the performance of the method on synthetic data, and on seven patients with a glioblastoma, the most aggressive primary brain tumor. This Bayesian personalization produces more informative results. In particular, it provides samples from the regions of interest and highlights the presence of several modes for some patients. In contrast, previous approaches based on optimization strategies fail to reveal the presence of different modes, and correlation between parameters.

DEMARCATE: Density-based magnetic resonance image clustering for assessing tumor heterogeneity in cancer

Tumor heterogeneity is a crucial area of cancer research wherein inter- and intra-tumor differences are investigated to assess and monitor disease development and progression, especially in cancer. The proliferation of imaging and linked genomic data has enabled us to evaluate tumor heterogeneity on multiple levels. In this work, we examine magnetic resonance imaging (MRI) in patients with brain cancer to assess image-based tumor heterogeneity. Standard approaches to this problem use scalar summary measures (e.g., intensity-based histogram statistics) that do not adequately capture the complete and finer scale information in the voxel-level data. In this paper, we introduce a novel technique, DEMARCATE (DEnsity-based MAgnetic Resonance image Clustering for Assessing Tumor hEterogeneity) to explore the entire tumor heterogeneity density profiles (THDPs) obtained from the full tumor voxel space. THDPs are smoothed representations of the probability density function of the tumor images. We develop tools for analyzing such objects under the Fisher-Rao Riemannian framework that allows us to construct metrics for THDP comparisons across patients, which can be used in conjunction with standard clustering approaches. Our analyses of The Cancer Genome Atlas (TCGA) based Glioblastoma dataset reveal two significant clusters of patients with marked differences in tumor morphology, genomic characteristics and prognostic clinical outcomes. In addition, we see enrichment of image-based clusters with known molecular subtypes of glioblastoma multiforme, which further validates our representation of tumor heterogeneity and subsequent clustering techniques.

In silico analysis suggests differential response to bevacizumab and radiation combination therapy in newly diagnosed glioblastoma

Recently, two phase III studies of bevacizumab, an anti-angiogenic, for newly diagnosed glioblastoma (GBM) patients were released. While they were unable to statistically significantly demonstrate that bevacizumab in combination with other therapies increases the overall survival of GBM patients, there remains a question of potential benefits for subpopulations of patients. We use a mathematical model of GBM growth to investigate differential benefits of combining surgical resection, radiation and bevacizumab across observed tumour growth kinetics. The differential hypoxic burden after gross total resection (GTR) was assessed along with the change in radiation cell kill from bevacizumab-induced tissue re-normalization when starting therapy for tumours at different diagnostic sizes. Depending on the tumour size at the time of treatment, our model predicted that GTR would remove a variable portion of the hypoxic burden ranging from 11% to 99.99%. Further, our model predicted that the combination of bevacizumab with radiation resulted in an additional cell kill ranging from 2.6×10⁷ to 1.1×10¹⁰ cells. By considering the outcomes given individual tumour kinetics, our results indicate that the subpopulation of patients who would receive the greatest benefit from bevacizumab and radiation combination therapy are those with large, aggressive tumours and who are not eligible for GTR.

Multimodal imaging based on MRI and PET reveals [(18)F]FLT PET as a specific and early indicator of treatment efficacy in a preclinical model of recurrent glioblastoma

PURPOSE

The primary objective of this study was to compare the ability of PET and MRI biomarkers to predict treatment efficacy in a preclinical model of recurrent glioblastoma multiforme.

METHODS

MRI (anatomical, diffusion, vasculature and oxygenation) and PET ([(18)F]FDG and [(18)F]FLT) parameters were obtained 3 days after the end of treatment and compared with late tumour growth and survival.

RESULTS

Early after tumour recurrence, no effect of treatment with temozolomide combined with bevacizumab was observed on tumour volume as assessed by T2-W MRI. At later times, the treatment decreased tumour volume and increased survival. Interestingly, at the earlier time, temozolomide + bevacizumab decreased [(18)F]FLT uptake, cerebral blood volume and oedema. [(18)F]FLT uptake, oedema and cerebral blood volume were correlated with overall survival but [(18)F]FLT uptake had the highest specificity and sensitivity for the early prediction of treatment efficacy.

CONCLUSION

The present investigation in a preclinical model of glioblastoma recurrence underscores the importance of multimodal imaging in the assessment of oedema, tumour vascular status and cell proliferation. Finally, [(18)F]FLT holds the greatest promise for the early assessment of treatment efficacy. These findings may translate clinically in that individualized treatment for recurrent glioma could be prescribed for patients selected after PET/MRI examinations.

Recombinant interleukin-1 receptor antagonist conjugated to superparamagnetic iron oxide nanoparticles for theranostic targeting of experimental glioblastoma

Cerebral edema commonly accompanies brain tumors and contributes to neurologic symptoms. The role of the interleukin-1 receptor antagonist conjugated to superparamagnetic iron oxide nanoparticles (SPION-IL-1Ra) was assessed to analyze its anti-edemal effect and its possible application as a negative contrast enhancing agent for magnetic resonance imaging (MRI). Rats with intracranial C6 glioma were intravenously administered at various concentrations of IL-1Ra or SPION-IL-1Ra. Brain peritumoral edema following treatment with receptor antagonist was assessed with high-field MRI. IL-1Ra administered at later stages of tumor progression significantly reduced peritumoral edema (as measured by MRI) and prolonged two-fold the life span of comorbid animals in a dose-dependent manner in comparison to control and corticosteroid-treated animals (P < .001). Synthesized SPION-IL-1Ra conjugates had the properties of negative contrast agent with high coefficients of relaxation efficiency. In vitro studies of SPION-IL-1Ra nanoparticles demonstrated high intracellular incorporation and absence of toxic influence on C6 cells and lymphocyte viability and proliferation. Retention of the nanoparticles in the tumor resulted in enhanced hypotensive T2-weighted images of glioma, proving the application of the conjugates as negative magnetic resonance contrast agents. Moreover, nanoparticles reduced the peritumoral edema confirming the therapeutic potency of synthesized conjugates. SPION-IL-1Ra nanoparticles have an anti-edemal effect when administered through a clinically relevant route in animals with glioma. The SPION-IL-1Ra could be a candidate for theranostic approach in neuro-oncology both for diagnosis of brain tumors and management of peritumoral edema.

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.

An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas

We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor diffusion. We use a constrained optimization formulation with a reaction-diffusion model that results in a system of nonlinear partial differential equations. In our formulation, we estimate the parameters using partially observed, noisy tumor concentration data at two different time instances, along with white matter fiber directions derived from diffusion tensor imaging. The optimization problem is solved with a Gauss-Newton reduced space algorithm. We present the formulation and outline the numerical algorithms for solving the resulting equations. We test the method using a synthetic dataset and compute the reconstruction error for different noise levels and detection thresholds for monofocal and multifocal test cases.

Patient-specific mathematical neuro-oncology: using a simple proliferation and invasion tumor model to inform clinical practice

Glioblastoma multiforme (GBM) is the most common malignant primary brain tumor associated with a poor median survival of 15–18 months, yet there is wide heterogeneity across and within patients. This heterogeneity has been the source of significant clinical challenges facing patients with GBM and has hampered the drive toward more precision or personalized medicine approaches to treating these challenging tumors. Over the last two decades, the field of Mathematical Neuro-oncology has grown out of desire to use (often patient-specific) mathematical modeling to better treat GBMs. Here, we will focus on a series of clinically relevant results using patient-specific mathematical modeling. The core model at the center of these results incorporates two hallmark features of GBM, proliferation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\rho )$$\end{document}(ρ) and invasion (D), as key parameters. Based on routinely obtained magnetic resonance images, each patient’s tumor can be characterized using these two parameters. The Proliferation-Invasion (PI) model uses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document}ρ and D to create patient-specific growth predictions. The PI model, its predictions, and parameters have been used in a number of ways to derive biological insight. Beyond predicting growth, the PI model has been utilized to identify patients who benefit from different surgery strategies, to prognosticate response to radiation therapy, to develop a treatment response metric, and to connect clinical imaging features and genetic information. Demonstration of the PI model’s clinical relevance supports the growing role for it and other mathematical models in routine clinical practice.

Advanced magnetic resonance imaging of the physical processes in human glioblastoma

The most common malignant primary brain tumor, glioblastoma multiforme (GBM) is a devastating disease with a grim prognosis. Patient survival is typically less than two years and fewer than 10% of patients survive more than five years. Magnetic resonance imaging (MRI) can have great utility in the diagnosis, grading, and management of patients with GBM as many of the physical manifestations of the pathologic processes in GBM can be visualized and quantified using MRI. Newer MRI techniques such as dynamic contrast enhanced and dynamic susceptibility contrast MRI provide functional information about the tumor hemodynamic status. Diffusion MRI can shed light on tumor cellularity and the disruption of white matter tracts in the proximity of tumors. MR spectroscopy can be used to study new tumor tissue markers such as IDH mutations. MRI is helping to noninvasively explore the link between the molecular basis of gliomas and the imaging characteristics of their physical processes. We, here, review several approaches to MR-based imaging and discuss the potential for these techniques to quantify the physical processes in glioblastoma, including tumor cellularity and vascularity, metabolite expression, and patterns of tumor growth and recurrence. We conclude with challenges and opportunities for further research in applying physical principles to better understand the biologic process in this deadly disease. See all articles in this Cancer Research section, "Physics in Cancer Research."

Genetic modification of neurons to express bevacizumab for local anti-angiogenesis treatment of glioblastoma

The median survival of glioblastoma multiforme (GBM) approximately 1 yr. Following surgical removal, systemic therapies are limited by the blood-brain barrier. To circumvent this, we developed a method to modify neurons with the genetic sequence for therapeutic monoclonal antibodies using adeno-associated virus (AAV) gene transfer vectors, directing persistent, local expression in the tumor milieu. The human U87MG GBM cell line or patient-derived early passage GBM cells were administered to the striatum of NOD/SCID immunodeficient mice.

AAVrh.10BevMab, an AAVrh.10-based vector coding for bevacizumab (Avastin^®), an anti-human vascular endothelial growth factor (VEGF) monoclonal antibody, was delivered to the area of the GBM xenograft. Localized expression of bevacizumab was demonstrated by quantitative PCR, ELISA and Western. Immunohistochemistry showed the bevacizumab was expressed in neurons. Concurrent administration of AAVrh.10BevMab with the U87MG tumor reduced tumor blood vessel density, and tumor volume and increased survival. Administration of AAVrh.10BevMab 1 wk after U87MG xenograft reduced growth and increased survival. Studies with patient-derived early passage GBM primary cells showed a reduction in primary tumor burden with an increased survival. This data supports the strategy of AAV-mediated CNS gene therapy to treat GBM, overcoming the blood-brain barrier through local, persistent delivery of an anti-angiogenesis monoclonal antibody.

Oedema-based model for diffuse low-grade gliomas: application to clinical cases under radiotherapy

OBJECTIVES

Diffuse low-grade gliomas are characterized by slow growth. Despite appropriate treatment, they change inexorably into more aggressive forms, jeopardizing the patient's life. Optimizing treatments, for example with the use of mathematical modelling, could help to prevent tumour regrowth and anaplastic transformation. Here, we present a model of the effect of radiotherapy on such tumours. Our objective is to explain observed delay of tumour regrowth following radiotherapy and to predict its duration.

MATERIALS AND METHODS

We have used a migration-proliferation model complemented by an equation describing appearance and draining of oedema. The model has been applied to clinical data of tumour radius over time, for a population of 28 patients.

RESULTS

We were able to show that draining of oedema accounts for regrowth delay after radiotherapy and have been able to fit the clinical data in a robust way. The model predicts strong correlation between high proliferation coefficient and low progression-free gain of lifetime, due to radiotherapy among the patients, in agreement with clinical studies. We argue that, with reasonable assumptions, it is possible to predict (precision ~20%) regrowth delay after radiotherapy and the gain of lifetime due to radiotherapy.

CONCLUSIONS

Our oedema-based model provides an early estimation of individual duration of tumour response to radiotherapy and thus, opens the door to the possibility of personalized medicine.

Emergence of spatial structure in the tumor microenvironment due to the Warburg effect

Drastic metabolic alterations, such as the Warburg effect, are found in most if not all types of malignant tumors. Emerging evidence shows that cancer cells benefit from these alterations, but little is known about how they affect noncancerous stromal cells within the tumor microenvironment. Here we show that cancer cells are better adapted to metabolic changes in the microenvironment, leading to the emergence of spatial structure. A clear example of tumor spatial structure is the localization of tumor-associated macrophages (TAMs), one of the most common stromal cell types found in tumors. TAMs are enriched in well-perfused areas, such as perivascular and cortical regions, where they are known to potentiate tumor growth and invasion. However, the mechanisms of TAM localization are not completely understood. Computational modeling predicts that gradients--of nutrients, gases, and metabolic by-products such as lactate--emerge due to altered cell metabolism within poorly perfused tumors, creating ischemic regions of the tumor microenvironment where TAMs struggle to survive. We tested our modeling prediction in a coculture system that mimics the tumor microenvironment. Using this experimental approach, we showed that a combination of metabolite gradients and differential sensitivity to lactic acid is sufficient for the emergence of macrophage localization patterns in vitro. This suggests that cancer metabolic changes create a microenvironment where tumor cells thrive over other cells. Understanding differences in tumor-stroma sensitivity to these alterations may open therapeutic avenues against cancer.