A multilayer grow-or-go model for GBM: effects of invasive cells and anti-angiogenesis on growth

Chemotaxis effects on the vascular tumor growth: Phase-field model and simulations

In this paper, we propose a vascular tumor growth model that combines a phase-field tumor model with a phase-field angiogenesis model. By incorporating various tumor cell species, we capture the instabilities of the tumor in the presence of evolving neovasculature. The model not only considers different dynamics of tumor cell phase conversions, movement, and pressure effects but also provides a comprehensive representation of angiogenesis, encompassing chemotaxis of endothelial cells, sprouting, anastomoses, and blood flow in capillaries. This study evaluates the impact of chemotaxis on tumor cell movement in both avascular and vascular tumor growth scenarios. The results highlight the acceleration of tumor growth when angiogenesis is stimulated. Additionally, the investigation explores various initial distances of the tumor from neighboring vessels, revealing a critical threshold distance beyond which the angiogenesis factor fails to stimulate angiogenesis, resulting in the tumor maintaining a stable state. The integration of chemotaxis into the growth model induces instabilities, leading to increased nutrient availability and faster growth for the tumor. Furthermore, the study considers anti-angiogenesis therapy as an ideal approach, assuming complete inhibition of angiogenesis from the early stages. In this scenario, the tumor persists in a steady state, adhering to the avascular size limit in the absence of neovasculature. Conversely, when considering chemotaxis, anti-angiogenesis therapy loses efficiency, enabling unrestrained tumor growth towards neighboring vessels. This work sheds light on the intricate interplay among chemotaxis, angiogenesis, and anti-angiogenesis therapy in the context of vascular tumor growth, providing valuable insights for the development of targeted treatment strategies.

Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans. Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patient-specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion partial differential equation (PDE) model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic non-dimensional parameters, a pre-training step that utilizes the non-dimensional parameters and a fine-tuning step to determine the patient specific parameters. Additionally, the diffuse-domain method is employed to handle the complex brain geometry within the PINN framework. The method is validated on both synthetic and patient datasets, showing promise for personalized GBM treatment through parametric inference within clinically relevant timeframes.

Life history dynamics of evolving tumors: insights into task specialization, trade-offs, and tumor heterogeneity

The evolution of cancer cells parallels species evolution in numerous ways. Variations arise and spread under the pressure of competition between cancer cells. Current investigations of tumor evolution echo earlier debates between biologists. These include the role of non-Darwinian mechanisms, the contribution of neutral evolution, and life history dynamics. The trade-off between proliferation and metastasis is the most well-studied application of life history theory to cancer evolution. This article briefly introduces some parallels between cancer and species evolution, focusing on the life history of evolving tumors. Next, we review evidence from simulation and experimental studies supporting task specialization and trade-offs in cancer. We also cover recent work on inferring tumor tasks from data. We then turn to the implications of multi-tasking and the utility of the theory in explaining critical aspects of tumor heterogeneity. Finally, we discuss some of the criticism and future directions of this research topic.

Phenotypic switching mechanisms determine the structure of cell migration into extracellular matrix under the 'go-or-grow' hypothesis

A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell population, in-line with the 'go-or-grow' hypothesis (Hatzikirou et al., 2012; Stepien et al., 2018), they regularly overlook the role that the environment may play in determining the cells' phenotype during migration. Comparing a previously studied volume-filling model for a homogeneous population of generalist cells that can proliferate, move and degrade extracellular matrix (ECM) (Crossley et al., 2023) to a novel model for a heterogeneous population comprising two distinct sub-populations of specialist cells that can either move and degrade ECM or proliferate, this study explores how different hypothetical phenotypic switching mechanisms affect the speed and structure of the invading cell populations. Through a continuum model derived from its individual-based counterpart, insights into the influence of the ECM and the impact of phenotypic switching on migrating cell populations emerge. Notably, specialist cell populations that cannot switch phenotype show reduced invasiveness compared to generalist cell populations, while implementing different forms of switching significantly alters the structure of migrating cell fronts. This key result suggests that the structure of an invading cell population could be used to infer the underlying mechanisms governing phenotypic switching.

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

CD57 defines a novel cancer stem cell that drive invasion of diffuse pediatric-type high grade gliomas

BACKGROUND

Diffuse invasion remains a primary cause of treatment failure in pediatric high-grade glioma (pHGG). Identifying cellular driver(s) of pHGG invasion is needed for anti-invasion therapies.

METHODS

Ten highly invasive patient-derived orthotopic xenograft (PDOX) models of pHGG were subjected to isolation of matching pairs of invasive (HGGINV) and tumor core (HGGTC) cells.

RESULTS

pHGGINV cells were intrinsically more invasive than their matching pHGGTC cells. CSC profiling revealed co-positivity of CD133 and CD57 and identified CD57+CD133- cells as the most abundant CSCs in the invasive front. In addition to discovering a new order of self-renewal capacities, i.e., CD57+CD133- > CD57+CD133+ > CD57-CD133+ > CD57-CD133- cells, we showed that CSC hierarchy was impacted by their spatial locations, and the highest self-renewal capacities were found in CD57+CD133- cells in the HGGINV front (HGGINV/CD57+CD133- cells) mediated by NANOG and SHH over-expression. Direct implantation of CD57+ (CD57+/CD133- and CD57+/CD133+) cells into mouse brains reconstituted diffusely invasion, while depleting CD57+ cells (i.e., CD57-CD133+) abrogated pHGG invasion.

CONCLUSION

We revealed significantly increased invasive capacities in HGGINV cells, confirmed CD57 as a novel glioma stem cell marker, identified CD57+CD133- and CD57+CD133+ cells as a new cellular driver of pHGG invasion and suggested a new dual-mode hierarchy of HGG stem cells.

Diagnostic and Therapeutic Issues in Glioma Using Imaging Data: The Challenge of Numerical Twinning

Glial tumors represent the leading etiology of primary brain tumors. Their particularities lie in (i) their location in a highly functional organ that is difficult to access surgically, including for biopsy, and (ii) their rapid, anisotropic mode of extension, notably via the fiber bundles of the white matter, which further limits the possibilities of resection. The use of mathematical tools enables the development of numerical models representative of the oncotype, genotype, evolution, and therapeutic response of lesions. The significant development of digital technologies linked to high-resolution NMR exploration, coupled with the possibilities offered by AI, means that we can envisage the creation of digital twins of tumors and their host organs, thus reducing the use of physical sampling.

Predicting the spatio-temporal response of recurrent glioblastoma treated with rhenium-186 labelled nanoliposomes

Rhenium-186 (186Re) labeled nanoliposome (RNL) therapy for recurrent glioblastoma patients has shown promise to improve outcomes by locally delivering radiation to affected areas. To optimize the delivery of RNL, we have developed a framework to predict patient-specific response to RNL using image-guided mathematical models.

Methods

We calibrated a family of reaction-diffusion type models with multi-modality imaging data from ten patients (NCR01906385) to predict the spatio-temporal dynamics of each patient's tumor. The data consisted of longitudinal magnetic resonance imaging (MRI) and single photon emission computed tomography (SPECT) to estimate tumor burden and local RNL activity, respectively. The optimal model from the family was selected and used to predict future growth. A simplified version of the model was used in a leave-one-out analysis to predict the development of an individual patient's tumor, based on cohort parameters.

Results

Across the cohort, predictions using patient-specific parameters with the selected model were able to achieve Spearman correlation coefficients (SCC) of 0.98 and 0.93 for tumor volume and total cell number, respectively, when compared to the measured data. Predictions utilizing the leave-one-out method achieved SCCs of 0.89 and 0.88 for volume and total cell number across the population, respectively.

Conclusion

We have shown that patient-specific calibrations of a biology-based mathematical model can be used to make early predictions of response to RNL therapy. Furthermore, the leave-one-out framework indicates that radiation doses determined by SPECT can be used to assign model parameters to make predictions directly following the conclusion of RNL treatment.

Statement of Significance

This manuscript explores the application of computational models to predict response to radionuclide therapy in glioblastoma. There are few, to our knowledge, examples of mathematical models used in clinical radionuclide therapy. We have tested a family of models to determine the applicability of different radiation coupling terms for response to the localized radiation delivery. We show that with patient-specific parameter estimation, we can make accurate predictions of future glioblastoma response to the treatment. As a comparison, we have shown that population trends in response can be used to forecast growth from the moment the treatment has been delivered.In addition to the high simulation and prediction accuracy our modeling methods have achieved, the evaluation of a family of models has given insight into the response dynamics of radionuclide therapy. These dynamics, while different than we had initially hypothesized, should encourage future imaging studies involving high dosage radiation treatments, with specific emphasis on the local immune and vascular response.

Modelling microtube driven invasion of glioma

Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of predictive partial differential equation models, formulated at varying levels of detail, and including (i) "proliferation-infiltration" models, (ii) "go-or-grow" models, and (iii) anisotropic diffusion models. Often, these models use macroscopic observations of a diffuse tumour interface to motivate a phenomenological description of invasion, rather than performing a detailed and mechanistic modelling of glioma cell invasion processes. Here we close this gap. Based on experiments that support an important role played by long cellular protrusions, termed tumour microtubes, we formulate a new model for microtube-driven glioma invasion. In particular, we model a population of tumour cells that extend tissue-infiltrating microtubes. Mitosis leads to new nuclei that migrate along the microtubes and settle elsewhere. A combination of steady state analysis and numerical simulation is employed to show that the model can predict an expanding tumour, with travelling wave solutions led by microtube dynamics. A sequence of scaling arguments allows us reduce the detailed model into simpler formulations, including models falling into each of the general classes (i), (ii), and (iii) above. This analysis allows us to clearly identify the assumptions under which these various models can be a posteriori justified in the context of microtube-driven glioma invasion. Numerical simulations are used to compare the various model classes and we discuss their advantages and disadvantages.

Ensemble Inversion for Brain Tumor Growth Models With Mass Effect

We propose a method for extracting physics-based biomarkers from a single multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor. We account for mass effect, the deformation of brain parenchyma due to the growing tumor, which on its own is an important radiographic feature but its automatic quantification remains an open problem. In particular, we calibrate a partial differential equation (PDE) tumor growth model that captures mass effect, parameterized by a single scalar parameter, tumor proliferation, migration, while localizing the tumor initiation site. The single-scan calibration problem is severely ill-posed because the precancerous, healthy, brain anatomy is unknown. To address the ill-posedness, we introduce an ensemble inversion scheme that uses a number of normal subject brain templates as proxies for the healthy precancer subject anatomy. We verify our solver on a synthetic dataset and perform a retrospective analysis on a clinical dataset of 216 glioblastoma (GBM) patients. We analyze the reconstructions using our calibrated biophysical model and demonstrate that our solver provides both global and local quantitative measures of tumor biophysics and mass effect. We further highlight the improved performance in model calibration through the inclusion of mass effect in tumor growth models-including mass effect in the model leads to 10% increase in average dice coefficients for patients with significant mass effect. We further evaluate our model by introducing novel biophysics-based features and using them for survival analysis. Our preliminary analysis suggests that including such features can improve patient stratification and survival prediction.

Traveling wave speed and profile of a "go or grow" glioblastoma multiforme model

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction-diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction-diffusion GBM model based on the 'go or grow' hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

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.

Simulating the behaviour of glioblastoma multiforme based on patient MRI during treatments

Glioblastoma multiforme is a brain cancer that still shows poor prognosis for patients despite the active research for new treatments. In this work, the goal is to model and simulate the evolution of tumour associated angiogenesis and the therapeutic response to glioblastoma multiforme. Multiple phenomena are modelled in order to fit different biological pathways, such as the cellular cycle, apoptosis, hypoxia or angiogenesis. This leads to a nonlinear system with 4 equations and 4 unknowns: the density of tumour cells, the [Formula: see text] concentration, the density of endothelial cells and the vascular endothelial growth factor concentration. This system is solved numerically on a mesh fitting the geometry of the brain and the tumour of a patient based on a 2D slice of MRI. We show that our numerical scheme is positive, and we give the energy estimates on the discrete solution to ensure its existence. The numerical scheme uses nonlinear control volume finite elements in space and is implicit in time. Numerical simulations have been done using the different standard treatments: surgery, chemotherapy and radiotherapy, in order to conform to the behaviour of a tumour in response to treatments according to empirical clinical knowledge. We find that our theoretical model exhibits realistic behaviours.

Inducing Biomechanical Heterogeneity in Brain Tumor Modeling by MR Elastography: Effects on Tumor Growth, Vascular Density and Delivery of Therapeutics

Simple Summary

Biomechanical forces aggravate brain tumor progression. In this study, magnetic resonance elastography (MRE) is employed to extract tissue biomechanical properties from five glioblastoma patients and a healthy subject, and data are incorporated in a mathematical model that simulates tumor growth. Mathematical modeling enables further understanding of glioblastoma development and allows patient-specific predictions for tumor vascularity and delivery of drugs. Incorporating MRE data results in a more realistic intratumoral distribution of mechanical stress and anisotropic tumor growth and a better description of subsequent events that are closely related to the development of stresses, including heterogeneity of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Abstract

The purpose of this study is to develop a methodology that incorporates a more accurate assessment of tissue mechanical properties compared to current mathematical modeling by use of biomechanical data from magnetic resonance elastography. The elastography data were derived from five glioblastoma patients and a healthy subject and used in a model that simulates tumor growth, vascular changes due to mechanical stresses and delivery of therapeutic agents. The model investigates the effect of tumor-specific biomechanical properties on tumor anisotropic growth, vascular density heterogeneity and chemotherapy delivery. The results showed that including elastography data provides a more realistic distribution of the mechanical stresses in the tumor and induces anisotropic tumor growth. Solid stress distribution differs among patients, which, in turn, induces a distinct functional vascular density distribution—owing to the compression of tumor vessels—and intratumoral drug distribution for each patient. In conclusion, incorporating elastography data results in a more accurate calculation of intratumoral mechanical stresses and enables a better mathematical description of subsequent events, such as the heterogeneous development of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Non-local multiscale approach for the impact of go or grow hypothesis on tumour-viruses interactions

We propose and study computationally a novel non-local multiscale moving boundary mathematical model for tumour and oncolytic virus (OV) interactions when we consider the go or grow hypothesis for cancer dynamics. This spatio-temporal model focuses on two cancer cell phenotypes that can be infected with the OV or remain uninfected, and which can either move in response to the extracellular-matrix (ECM) density or proliferate. The interactions between cancer cells, those among cancer cells and ECM, and those among cells and OV occur at the macroscale. At the micro-scale, we focus on the interactions between cells and matrix degrading enzymes (MDEs) that impact the movement of tumour boundary. With the help of this multiscale model we explore the impact on tumour invasion patterns of two different assumptions that we consider in regard to cell-cell and cell-matrix interactions. In particular we investigate model dynamics when we assume that cancer cell fluxes are the result of local advection in response to the density of extracellular matrix (ECM), or of non-local advection in response to cell-ECM adhesion. We also investigate the role of the transition rates between mainly-moving and mainly-growing cancer cell sub-populations, as well as the role of virus infection rate and virus replication rate on the overall tumour dynamics.

Modeling of Glioma Growth with Mass Effect by Longitudinal Magnetic Resonance Imaging

It is well-known that expanding glioblastomas typically induce significant deformations of the surrounding parenchyma (i.e., the so-called ?mass effect?). In this study, we evaluate the performance of three mathematical models of tumor growth: 1) a reaction-diffusion-advection model which accounts for mass effect (RDAM), 2) a reaction-diffusion model with mass effect that is consistent only in the case of small deformations (RDM), and 3) a reaction-diffusion model that does not include the mass effect (RD). The models were calibrated with magnetic resonance imaging (MRI) data obtained during tumor development in a murine model of glioma (n = 9). We obtained T₂-weighted and contrast-enhanced T₁-weighted MRI at 6 time points over 10 days to determine the spatiotemporal variation in the mass effect and tumor concentration, respectively. We calibrated the three models using data 1) at the first four, 2) only at the first and fourth, and 3) only at the third and fourth time points. Each of these calibrations were run forward in time to predict the volume fraction of tumor cells at the conclusion of the experiment. The diffusion coefficient for the RDAM model (median of 10.65 ? 10^-3 mm²d^-1) is significantly less than those for the RD and RDM models (17.46 ? 10^-3 mm²d^-1 and 19.38 ? 10^-3 mm²d^-1, respectively). The tumor concentrations for the RD, RDM, and RDAM models have medians of 40.2%, 32.1%, and 44.7%, respectively, for the calibration using data from the first four time points. The RDM model most accurately predicts tumor growth, while the RDAM model presents the least variation in its estimates of the diffusion coefficient and proliferation rate. This study demonstrates that the mathematical models capture both tumor development and mass effect observed in experiments.

In Silico Mathematical Modelling for Glioblastoma: A Critical Review and a Patient-Specific Case

Glioblastoma extensively infiltrates the brain; despite surgery and aggressive therapies, the prognosis is poor. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of glioblastoma evolution in every single patient, with the aim of tailoring therapeutic weapons. In particular, the ultimate goal of biomathematics for cancer is the identification of the most suitable theoretical models and simulation tools, both to describe the biological complexity of carcinogenesis and to predict tumor evolution. In this report, we describe the results of a critical review about different mathematical models in neuro-oncology with their clinical implications. A comprehensive literature search and review for English-language articles concerning mathematical modelling in glioblastoma has been conducted. The review explored the different proposed models, classifying them and indicating the significative advances of each one. Furthermore, we present a specific case of a glioblastoma patient in which our recently proposed innovative mechanical model has been applied. The results of the mathematical models have the potential to provide a relevant benefit for clinicians and, more importantly, they might drive progress towards improving tumor control and patient's prognosis. Further prospective comparative trials, however, are still necessary to prove the impact of mathematical neuro-oncology in clinical practice.

Dichotomy in Growth and Invasion from Low- to High-Grade Glioma Cellular Variants

Glial dysfunction outraging CNS plasticity and integrity results in one of the most dangerous cancers, namely glioma, featuring little median survival period and high recurrence. The hallmark properties of proliferation, invasion and angiogenesis with the infiltrated macrophages in glioma are expected to be tightly coupled or cross-linked, but not properly related so far. The present study is aimed to find a relationship between this featured quadrangle from lower to higher grades (HG) of post-operative glioma tissues and their invading subsets. Elevated Ki67-associated proliferation in lower grades (LG) was supported with VEGF dependent angiogenic maintenance which found a decrease unlikely in HG. In contrast, MMP 2 and 9-associated invasions augmented high in HG with the dominant presence of CD204⁺ M2 polarized macrophages and a general increase in global DNMT1-associated methylation. Marked differences found in ECM invading cellular subsets of HG showing high proliferative capacity indicating rationally for recurrence, contrasting the nature of gross tumor tissue of the same grade. Thus in LG, the neoplastic lesion is more inclined to its growth while in higher grade more disposed towards tissue wreckage in support with cellular environmental milieu whereas the cellular variants and subsets of invaded cells showed different trends. Therefore, some operational dichotomy or coupling among cellular variants in glioma is active in determining its low- to high-grade transition and aggressive progression.

Feasibility and clinical usefulness of modelling glioblastoma migration in adjuvant radiotherapy

Glioblastoma (GBM) is one of the most common primary brain tumours in adults, with a dismal prognosis despite aggressive multimodality treatment by a combination of surgery and adjuvant radiochemotherapy. A detailed knowledge of the spreading of glioma cells in the brain might allow for more targeted escalated radiotherapy, aiming to reduce locoregional relapse. Recent years have seen the development of a large variety of mathematical modelling approaches to predict glioma migration. The aim of this study is hence to evaluate the clinical applicability of a detailed micro- and meso-scale mathematical model in radiotherapy. First and foremost, a clinical workflow is established, in which the tumour is automatically segmented as input data and then followed in time mathematically based on the diffusion tensor imaging data. The influence of several free model parameters is individually evaluated, then the full model is retrospectively validated for a collective of 3 GBM patients treated at our institution by varying the most important model parameters to achieve optimum agreement with the tumour development during follow-up. Agreement of the model predictions with the real tumour growth as defined by manual contouring based on the follow-up MRI images is analyzed using the dice coefficient. The tumour evolution over 103-212 days follow-up could be predicted by the model with a dice coefficient better than 60% for all three patients. In all cases, the final tumour volume was overestimated by the model by a factor between 1.05 and 1.47. To evaluate the quality of the agreement between the model predictions and the ground truth, we must keep in mind that our gold standard relies on a single observer's (CB) manually-delineated tumour contours. We therefore decided to add a short validation of the stability and reliability of these contours by an inter-observer analysis including three other experienced radiation oncologists from our department. In total, a dice coefficient between 63% and 89% is achieved between the four different observers. Compared with this value, the model predictions (62-66%) perform reasonably well, given the fact that these tumour volumes were created based on the pre-operative segmentation and DTI.

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.

Spatial mechanistic modeling for prediction of the growth of asymptomatic meningiomas

BACKGROUND AND OBJECTIVE

Mathematical modeling of tumor growth draws interest from the medical community as they have the potential to improve patients' care and the use of public health resources. The main objectives of this work are to model the growth of meningiomas - slow-growing benign tumors requiring extended imaging follow-up - and to predict tumor volume and shape at a later desired time using only two times examinations.

METHODS

We develop two variants of a 3D partial differential system of equations (PDE) which yield after a spatial integration systems of ordinary differential equations (ODE) that relate tumor volume with time. Estimation of models parameters is a crucial step to obtain a personalized model for a patient that can be used for descriptive or predictive purposes. As PDE and ODE systems share the same parameters, they are both estimated by fitting the ODE systems to the tumor volumes obtained from MRI examinations acquired at different times. A population approach allows to compensate for sparse sampling times and measurement uncertainties by constraining the variability of the parameters in the population.

RESULTS

Description capabilities of the models are investigated in 39 patients with benign asymptomatic meningiomas who had had at least three surveillance MRI examinations. The two models can fit to the data accurately and more realistically than a naive linear regression. Prediction performances are validated for 33 patients using a population approach. Mean relative errors in volume predictions are less than 10% with ODE systems versus 12.5% with the naive linear model using only two times examinations. Concerning the shape, the mean Sørensen-Dice coefficients are 85% with the PDE systems in a subset of 10 representative patients.

CONCLUSIONS

Our strategy - based on personalization of mathematical model - provides a good insight on meningioma growth and may help decide whether to extend the follow-up or to treat the tumor.

BrainSeg-Net: Brain Tumor MR Image Segmentation via Enhanced Encoder-Decoder Network

Efficient segmentation of Magnetic Resonance (MR) brain tumor images is of the utmost value for the diagnosis of tumor region. In recent years, advancement in the field of neural networks has been used to refine the segmentation performance of brain tumor sub-regions. The brain tumor segmentation has proven to be a complicated task even for neural networks, due to the small-scale tumor regions. These small-scale tumor regions are unable to be identified, the reason being their tiny size and the huge difference between area occupancy by different tumor classes. In previous state-of-the-art neural network models, the biggest problem was that the location information along with spatial details gets lost in deeper layers. To address these problems, we have proposed an encoder–decoder based model named BrainSeg-Net. The Feature Enhancer (FE) block is incorporated into the BrainSeg-Net architecture which extracts the middle-level features from low-level features from the shallow layers and shares them with the dense layers. This feature aggregation helps to achieve better performance of tumor identification. To address the problem associated with imbalance class, we have used a custom-designed loss function. For evaluation of BrainSeg-Net architecture, three benchmark datasets are utilized: BraTS2017, BraTS 2018, and BraTS 2019. Segmentation of Enhancing Core (EC), Whole Tumor (WT), and Tumor Core (TC) is carried out. The proposed architecture have exhibited good improvement when compared with existing baseline and state-of-the-art techniques. The MR brain tumor segmentation by BrainSeg-Net uses enhanced location and spatial features, which performs better than the existing plethora of brain MR image segmentation approaches.

BU-Net: Brain Tumor Segmentation Using Modified U-Net Architecture

The semantic segmentation of a brain tumor is of paramount importance for its treatment and prevention. Recently, researches have proposed various neural network-based architectures to improve the performance of segmentation of brain tumor sub-regions. Brain tumor segmentation, being a challenging area of research, requires improvement in its performance. This paper proposes a 2D image segmentation method, BU-Net, to contribute to brain tumor segmentation research. Residual extended skip (RES) and wide context (WC) are used along with the customized loss function in the baseline U-Net architecture. The modifications contribute by finding more diverse features, by increasing the valid receptive field. The contextual information is extracted with the aggregating features to get better segmentation performance. The proposed BU-Net was evaluated on the high-grade glioma (HGG) datasets of the BraTS2017 Challenge—the test datasets of the BraTS 2017 and 2018 Challenge datasets. Three major labels to segmented were tumor core (TC), whole tumor (WT), and enhancing core (EC). To compare the performance quantitatively, the dice score was utilized. The proposed BU-Net outperformed the existing state-of-the-art techniques. The high performing BU-Net can have a great contribution to researchers from the field of bioinformatics and medicine.

Cell – extracellular matrix interaction in glioma growth. In silico model

The study aims to investigate the role of viscoelastic interactions between cells and extracellular matrix (ECM) in avascular tumor growth. Computer simulations of glioma multicellular tumor spheroid (MTS) growth are being carried out for various conditions. The calculations are based on a continuous model, which simulates oxygen transport into MTS; transitions between three cell phenotypes, cell transport, conditioned by hydrostatic forces in cell–ECM composite system, cell motility and cell adhesion. Visco-elastic cell aggregation and elastic ECM scaffold represent two compressible constituents of the composite. Cell–ECM interactions form a Transition Layer on the spheroid surface, where mechanical characteristics of tumor undergo rapid transition. This layer facilitates tumor progression to a great extent. The study demonstrates strong effects of ECM stiffness, mechanical deformations of the matrix and cell–cell adhesion on tumor progression. The simulations show in particular that at certain, rather high degrees of matrix stiffness a formation of distant multicellular clusters takes place, while at further increase of ECM stiffness subtumors do not form. The model also illustrates to what extent mere mechanical properties of cell–ECM system may contribute into variations of glioma invasion scenarios.

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.

Self-organization in brain tumors: How cell morphology and cell density influence glioma pattern formation

Modeling cancer cells is essential to better understand the dynamic nature of brain tumors and glioma cells, including their invasion of normal brain. Our goal is to study how the morphology of the glioma cell influences the formation of patterns of collective behavior such as flocks (cells moving in the same direction) or streams (cells moving in opposite direction) referred to as oncostream. We have observed experimentally that the presence of oncostreams correlates with tumor progression. We propose an original agent-based model that considers each cell as an ellipsoid. We show that stretching cells from round to ellipsoid increases stream formation. A systematic numerical investigation of the model was implemented in [Formula: see text]. We deduce a phase diagram identifying key regimes for the dynamics (e.g. formation of flocks, streams, scattering). Moreover, we study the effect of cellular density and show that, in contrast to classical models of flocking, increasing cellular density reduces the formation of flocks. We observe similar patterns in [Formula: see text] with the noticeable difference that stream formation is more ubiquitous compared to flock formation.

WHERE DID THE TUMOR START? AN INVERSE SOLVER WITH SPARSE LOCALIZATION FOR TUMOR GROWTH MODELS

We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

Using mathematics in MRI data management for glioma assesment

Our aim is to review the mathematical tools usefulness in MR data management for glioma diagnosis and treatment optimization. MRI does not give access to organs variations in hours or days. However a lot of multiparametric data are generated. Mathematics could help to override this paradox, the aim of this article is to show how. We first make a review on mathematical modelling using equations. Afterwards we present statistical analysis. We provide detailed examples in both sections. We finally conclude, giving some clues on in silico models.

Monoamines in glioblastoma: complex biology with therapeutic potential

Glioblastoma (GBM) is characterized by extremely poor prognoses, despite the use of gross surgical resection, alkylating chemotherapeutic agents, and radiotherapy. Evidence increasingly highlights the role of the tumor microenvironment in enabling this aggressive phenotype. Despite this interest, the role of neurotransmitters, brain-specific messengers underlying synaptic transmission, remains murky. These signaling molecules influence a complex network of molecular pathways and cellular behaviors in many CNS-resident cells, including neural stem cells and progenitor cells, neurons, and glia cells. Critically, available data convincingly demonstrate that neurotransmitters can influence proliferation, quiescence, and differentiation status of these cells. This ability to affect progenitors and glia-GBM-initiating cells-and their availability in the CNS strongly support the notion that neurotransmitters participate in the onset and progression of GBM. This review will focus on dopamine and serotonin, as studies indicate they contribute to gliomagenesis. Particular attention will be paid to how these neurotransmitters and their receptors can be utilized as novel therapeutic targets. Overall, this review will analyze the complex biology governing the interaction of GBM with neurotransmitter signaling and highlight how this interplay shapes the aggressive nature of GBM.

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.

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.

Personalized Radiotherapy Planning Based on a Computational Tumor Growth Model

In this article, we propose a proof of concept for the automatic planning of personalized radiotherapy for brain tumors. A computational model of glioblastoma growth is combined with an exponential cell survival model to describe the effect of radiotherapy. The model is personalized to the magnetic resonance images (MRIs) of a given patient. It takes into account the uncertainty in the model parameters, together with the uncertainty in the MRI segmentations. The computed probability distribution over tumor cell densities, together with the cell survival model, is used to define the prescription dose distribution, which is the basis for subsequent Intensity Modulated Radiation Therapy (IMRT) planning. Depending on the clinical data available, we compare three different scenarios to personalize the model. First, we consider a single MRI acquisition before therapy, as it would usually be the case in clinical routine. Second, we use two MRI acquisitions at two distinct time points in order to personalize the model and plan radiotherapy. Third, we include the uncertainty in the segmentation process. We present the application of our approach on two patients diagnosed with high grade glioma. We introduce two methods to derive the radiotherapy prescription dose distribution, which are based on minimizing integral tumor cell survival using the maximum a posteriori or the expected tumor cell density. We show how our method allows the user to compute a patient specific radiotherapy planning conformal to the tumor infiltration. We further present extensions of the method in order to spare adjacent organs at risk by re-distributing the dose. The presented approach and its proof of concept may help in the future to better target the tumor and spare organs at risk.

Evaluation Expression of Microrna-93 and Integrin Β8 in Different Types of Glioma Tumors

MicroRNAs (miRNAs), are a type of small non-coding RNAs, that induce mRNA degradation or repress translation by binding to the 3′-untranslated region (UTR) of its target mRNA. Some specific miRNAs, e.g. miR-93, have been discovered to be involved in pathological procedures by targeting some oncogenes or tumor suppressors in glioma. In the present study, real-time RT-PCR data was indicated the expression pattern and prognostic value of miR-93 in patients with types of Glioma. MiR-93 expression was significantly decreased in tumor tissue compared with normal group brain tissues (P<0.001). Low miR-93 expression was significantly correlated with progressive tumor grade (P=0.02). Moreover, multivariate analysis showed that miR-93 decreased expression (HR, 4.3; 95% CI, 0.8–17.2, P=0.02), advanced tumor grade (HR, 3.1; 95% CI, 0.2–13.9, P=0.04), for integrinβ8, level expression was inverse. Our data was shown that the down regulation of miR-93 was significantly correlated with unfavorable pathological features in patients with Glioma. Suggesting that decreased expression of miR-93can be used as a novel prognostic factor for this disease.

Towards the Design of a Patient-Specific Virtual Tumour

The design of a patient-specific virtual tumour is an important step towards Personalized Medicine. However this requires to capture the description of many key events of tumour development, including angiogenesis, matrix remodelling, hypoxia, and cell state heterogeneity that will all influence the tumour growth kinetics and degree of tumour invasiveness. To that end, an integrated hybrid and multiscale approach has been developed based on data acquired on a preclinical mouse model as a proof of concept. Fluorescence imaging is exploited to build case-specific virtual tumours. Numerical simulations show that the virtual tumour matches the characteristics and spatiotemporal evolution of its real counterpart. We achieved this by combining image analysis and physiological modelling to accurately described the evolution of different tumour cases over a month. The development of such models is essential since a dedicated virtual tumour would be the perfect tool to identify the optimum therapeutic strategies that would make Personalized Medicine truly reachable and achievable.

Extended Modality Propagation: Image Synthesis of Pathological Cases

This paper describes a novel generative model for the synthesis of multi-modal medical images of pathological cases based on a single label map. Our model builds upon i) a generative model commonly used for label fusion and multi-atlas patch-based segmentation of healthy anatomical structures, ii) the Modality Propagation iterative strategy used for a spatially-coherent synthesis of subject-specific scans of desired image modalities. The expression Extended Modality Propagation is coined to refer to the extension of Modality Propagation to the synthesis of images of pathological cases. Moreover, image synthesis uncertainty is estimated. An application to Magnetic Resonance Imaging synthesis of glioma-bearing brains is i) validated on the training dataset of a Multimodal Brain Tumor Image Segmentation challenge, ii) compared to the state-of-the-art in glioma image synthesis, and iii) illustrated using the output of two different tumor growth models. Such a generative model allows the generation of a large dataset of synthetic cases, which could prove useful for the training, validation, or benchmarking of image processing algorithms.

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.

Computational Trials: Unraveling Motility Phenotypes, Progression Patterns, and Treatment Options for Glioblastoma Multiforme

Glioblastoma multiforme is a malignant brain tumor with poor prognosis and high morbidity due to its invasiveness. Hypoxia-driven motility and concentration-driven motility are two mechanisms of glioblastoma multiforme invasion in the brain. The use of anti-angiogenic drugs has uncovered new progression patterns of glioblastoma multiforme associated with significant differences in overall survival. Here, we apply a mathematical model of glioblastoma multiforme growth and invasion in humans and design computational trials using agents that target angiogenesis, tumor replication rates, or motility. The findings link highly-dispersive, moderately-dispersive, and hypoxia-driven tumors to the patterns observed in glioblastoma multiforme treated by anti-angiogenesis, consisting of progression by Expanding FLAIR, Expanding FLAIR + Necrosis, and Expanding Necrosis, respectively. Furthermore, replication rate-reducing strategies (e.g. Tumor Treating Fields) appear to be effective in highly-dispersive and moderately-dispersive tumors but not in hypoxia-driven tumors. The latter may respond to motility-reducing agents. In a population computational trial, with all three phenotypes, a correlation was observed between the efficacy of the rate-reducing agent and the prolongation of overall survival times. This research highlights the potential applications of computational trials and supports new hypotheses on glioblastoma multiforme phenotypes and treatment options.

Current Challenges in Glioblastoma: Intratumour Heterogeneity, Residual Disease, and Models to Predict Disease Recurrence

Glioblastoma (GB) is the most common primary malignant brain tumor, and despite the availability of chemotherapy and radiotherapy to combat the disease, overall survival remains low with a high incidence of tumor recurrence. Technological advances are continually improving our understanding of the disease, and in particular, our knowledge of clonal evolution, intratumor heterogeneity, and possible reservoirs of residual disease. These may inform how we approach clinical treatment and recurrence in GB. Mathematical modeling (including neural networks) and strategies such as multiple sampling during tumor resection and genetic analysis of circulating cancer cells, may be of great future benefit to help predict the nature of residual disease and resistance to standard and molecular therapies in GB.

Effects of anti-angiogenesis on glioblastoma growth and migration: model to clinical predictions

Glioblastoma multiforme (GBM) causes significant neurological morbidity and short survival times. Brain invasion by GBM is associated with poor prognosis. Recent clinical trials of bevacizumab in newly-diagnosed GBM found no beneficial effects on overall survival times; however, the baseline health-related quality of life and performance status were maintained longer in the bevacizumab group and the glucocorticoid requirement was lower. Here, we construct a clinical-scale model of GBM whose predictions uncover a new pattern of recurrence in 11/70 bevacizumab-treated patients. The findings support an exception to the Folkman hypothesis: GBM grows in the absence of angiogenesis by a cycle of proliferation and brain invasion that expands necrosis. Furthermore, necrosis is positively correlated with brain invasion in 26 newly-diagnosed GBM. The unintuitive results explain the unusual clinical effects of bevacizumab and suggest new hypotheses on the dynamic clinical effects of migration by active transport, a mechanism of hypoxia-driven brain invasion.