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

Evolution of phenotypic plasticity leads to tumor heterogeneity with implications for therapy

Cancer is a significant global health issue, with treatment challenges arising from intratumor heterogeneity. This heterogeneity stems mainly from somatic evolution, causing genetic diversity within the tumor, and phenotypic plasticity of tumor cells leading to reversible phenotypic changes. However, the interplay of both factors has not been rigorously investigated. Here, we examine the complex relationship between somatic evolution and phenotypic plasticity, explicitly focusing on the interplay between cell migration and proliferation. This type of phenotypic plasticity is essential in glioblastoma, the most aggressive form of brain tumor. We propose that somatic evolution alters the regulation of phenotypic plasticity in tumor cells, specifically the reaction to changes in the microenvironment. We study this hypothesis using a novel, spatially explicit model that tracks individual cells' phenotypic and genetic states. We assume cells change between migratory and proliferative states controlled by inherited and mutation-driven genotypes and the cells' microenvironment. We observe that cells at the tumor edge evolve to favor migration over proliferation and vice versa in the tumor bulk. Notably, different genetic configurations can result in this pattern of phenotypic heterogeneity. We analytically predict the outcome of the evolutionary process, showing that it depends on the tumor microenvironment. Synthetic tumors display varying levels of genetic and phenotypic heterogeneity, which we show are predictors of tumor recurrence time after treatment. Interestingly, higher phenotypic heterogeneity predicts poor treatment outcomes, unlike genetic heterogeneity. Our research offers a novel explanation for heterogeneous patterns of tumor recurrence in glioblastoma patients.

A simple agent-based hybrid model to simulate the biophysics of glioblastoma multiforme cells and the concomitant evolution of the oxygen field

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is one of the most aggressive cancers of the central nervous system. It is characterized by a high mitotic activity and an infiltrative ability of the glioma cells, neovascularization and necrosis. GBM evolution entails the continuous interplay between heterogeneous cell populations, chemotaxis, and physical cues through different scales. In this work, an agent-based hybrid model is proposed to simulate the coupling of the multiscale biological events involved in the GBM invasion, specifically the individual and collective migration of GBM cells and the concurrent evolution of the oxygen field and phenotypic plasticity. An asset of the formulation is that it is conceptually and computationally simple but allows to reproduce the complexity and the progression of the GBM micro-environment at cell and tissue scales simultaneously.

METHODS

The migration is reproduced as the result of the interaction between every single cell and its micro-environment. The behavior of each individual cell is formulated through genotypic variables whereas the cell micro-environment is modeled in terms of the oxygen concentration and the cell density surrounding each cell. The collective behavior is formulated at a cellular scale through a flocking model. The phenotypic plasticity of the cells is induced by the micro-environment conditions, considering five phenotypes.

RESULTS

The model has been contrasted by benchmark problems and experimental tests showing the ability to reproduce different scenarios of glioma cell migration. In all cases, the individual and collective cell migration and the coupled evolution of both the oxygen field and phenotypic plasticity have been properly simulated. This simple formulation allows to mimic the formation of relevant hallmarks of glioblastoma multiforme, such as the necrotic cores, and to reproduce experimental evidences related to the mitotic activity in pseudopalisades.

CONCLUSIONS

In the collective migration, the survival of the clusters prevails at the expense of cell mitosis, regardless of the size of the groups, which delays the formation of necrotic foci and reduces the rate of oxygen consumption.

Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics

We here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differential equations (PDEs). A differential equation finally governs the local degradation of the extracellular matrix (ECM) by the malignant mass. Numerical realizations of the model are run to reproduce tumor growth and invasion in a number scenarios that differ for cell properties (adhesiveness, duplication potential, proteolytic activity) and/or environmental conditions (level of tissue oxygenation and matrix density pattern). In particular, our simulations suggest that tumor aggressiveness, in terms of invasive depth and extension of necrotic tissue, can be reduced by (i) stable cell-cell contact interactions, (ii) poor tendency of malignant agents to chemotactically move upon oxygen gradients, and (iii) presence of an overdense matrix, if coupled by a disrupted proteolytic activity of the disease.

A Mathematical Modelling Study of Chemotactic Dynamics in Cell Cultures: The Impact of Spatio-temporal Heterogeneity

As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell chemotaxis waves in heterogeneous fields of chemoattractant from the underlying partial differential equation models. In particular, such chemotactic waves are not in general translationally invariant travelling waves, but possess a spatial variation that evolves in time, and may even oscillate back and forth in time, according to the details of the chemotactic gradients. The analytical framework exploits the observation that unbiased cellular diffusive flux is typically small compared to chemotactic fluxes and is first developed and validated for a range of exemplar scenarios. The framework is subsequently applied to more complex models considering the chemoattractant dynamics under more general settings, potentially including those of relevance for representing pathophysiology scenarios in microdevice studies. In particular, even though solutions cannot be constructed in all cases, a wide variety of scenarios can be considered analytically, firstly providing global insight into the important mechanisms and features of cell motility in complex spatiotemporal fields of chemoattractant. Such analytical solutions also provide a means of rapid evaluation of model predictions, with the prospect of application in computationally demanding investigations relating theoretical models and experimental observation, such as Bayesian parameter estimation.

Data driven modeling of pseudopalisade pattern formation

Pseudopalisading is an interesting phenomenon where cancer cells arrange themselves to form a dense garland-like pattern. Unlike the palisade structure, a similar type of pattern first observed in schwannomas by pathologist J.J. Verocay (Wippold et al. in AJNR Am J Neuroradiol 27(10):2037-2041, 2006), pseudopalisades are less organized and associated with a necrotic region at their core. These structures are mainly found in glioblastoma (GBM), a grade IV brain tumor, and provide a way to assess the aggressiveness of the tumor. Identification of the exact bio-mechanism responsible for the formation of pseudopalisades is a difficult task, mainly because pseudopalisades seem to be a consequence of complex nonlinear dynamics within the tumor. In this paper we propose a data-driven methodology to gain insight into the formation of different types of pseudopalisade structures. To this end, we start from a state of the art macroscopic model for the dynamics of GBM, that is coupled with the dynamics of extracellular pH, and formulate a terminal value optimal control problem. Thus, given a specific, observed pseudopalisade pattern, we determine the evolution of parameters (bio-mechanisms) that are responsible for its emergence. Random histological images exhibiting pseudopalisade-like structures are chosen to serve as target pattern. Having identified the optimal model parameters that generate the specified target pattern, we then formulate two different types of pattern counteracting ansatzes in order to determine possible ways to impair or obstruct the process of pseudopalisade formation. This provides the basis for designing active or live control of malignant GBM. Furthermore, we also provide a simple, yet insightful, mechanism to synthesize new pseudopalisade patterns by linearly combining the optimal model parameters responsible for generating different known target patterns. This particularly provides a hint that complex pseudopalisade patterns could be synthesized by a linear combination of parameters responsible for generating simple patterns. Going even further, we ask ourselves if complex therapy approaches can be conceived, such that some linear combination thereof is able to reverse or disrupt simple pseudopalisade patterns; this is investigated with the help of numerical simulations.

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data

Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models' performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions.

A mechanobiological model for tumor spheroid evolution with application to glioblastoma: A continuum multiphysics approach

BACKGROUND

Spheroids are in vitro quasi-spherical structures of cell aggregates, eventually cultured within a hydrogel matrix, that are used, among other applications, as a technological platform to investigate tumor formation and evolution. Several interesting features can be replicated using this methodology, such as cell communication mechanisms, the effect of gradients of nutrients, or the creation of realistic 3D biological structures. The main objective of this work is to link the spheroid evolution with the mechanical activity of cells, coupled with nutrient consumption and the subsequent cell dynamics.

METHOD

We propose a continuum mechanobiological model which accounts for the most relevant phenomena that take place in tumor spheroid evolution under in vitro suspension, namely, nutrient diffusion in the spheroid, kinetics of cellular growth and death, and mechanical interactions among the cells. The model is qualitatively validated, after calibration of the model parameters, versus in vitro experiments of spheroids of different glioblastoma cell lines.

RESULTS

Our model is able to explain in a novel way quite different setups, such as spheroid growth (up to six times the initial configuration for U-87 MG cell line) or shrinking (almost half of the initial configuration for U-251 MG cell line); as the result of the mechanical interplay of cells driven by cellular evolution.

CONCLUSIONS

Glioblastoma tumor spheroid evolution is driven by mechanical interactions of the cell aggregate and the dynamical evolution of the cell population. All this information can be used to further investigate mechanistic effects in the evolution of tumors and their role in cancer disease.

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.

Therapy-induced shaping of the glioblastoma microenvironment: Macrophages at play

The intricate cross-talks between tumor cells and their microenvironment play a key role in cancer progression and resistance to treatment. In recent years, targeting pro-tumorigenic components of the tumor microenvironment (TME) has emerged as a tantalizing strategy to improve the efficacy of standard-of-care (SOC) treatments, particularly for hard-to-treat cancers such as glioblastoma. In this review, we explore how the distinct microenvironmental niches characteristic of the glioblastoma TME shape response to therapy. In particular, we delve into the interplay between tumor-associated macrophages (TAM) and glioblastoma cells within angiogenic and hypoxic niches, and interrogate their dynamic co-evolution upon SOC therapies that fuels malignancy. Resolving the complexity of therapy-induced alterations in the glioblastoma TME and their impact on disease relapse is a stepping stone to identify targetable pro-tumorigenic pathways and TAM subsets, and may open the way to efficient combination therapies that will improve clinical outcomes.

The low affinity A2B adenosine receptor enhances migratory and invasive capacity in vitro and angiogenesis in vivo of glioblastoma stem-like cells

Glioblastoma (GBM) is the most common and deadly malignant brain tumor, with a median survival of 15 to 17 months for a patient. GBM contains a cellular subpopulation known as GBM stem-like cells (GSCs) that persist in hypoxic niches and are capable of infiltrating into healthy brain tissue. For this reason, GSCs are considered one of the main culprits for GBM recurrence. A hypoxic microenvironment increases extracellular adenosine levels, activating the low affinity A2B adenosine receptor (A_2BAR). Adenosine, through A_2BAR, is capable of modulating invasiveness. However, its role in the invasion/migration of hypoxic-GSCs is still unknown. This study aims to understand the importance of A_2BAR in modulating the migratory/invasive capacity of GSCs under hypoxia. Data analysis from The Cancer Genome Atlas (TCGA) program correlates A_2BAR expression with high-grade glioma and hypoxic necrotic areas. U87MG and primary culture-derived GSCs under hypoxic conditions (0.5% O₂) increased A_2BAR mRNA and protein levels. As expected, the migratory and invasive capacity of GSCs increased under hypoxia, which was counteracted by blocking A_2BAR, through the downregulation of MMP9 activity and epithelial–mesenchymal transition marker expression. Finally, in a xenograft mouse model, we demonstrate that treatment with MRS1754 did not affect the tumor volume but could decrease blood vessel formation and VEGF expression. Our results suggest that extracellular adenosine, through the activation of A_2BAR, enhances the migratory and invasive capacity of GSCs in vitro under hypoxic conditions. Targeting A_2BAR can be an effective therapy for GBM recurrence.

Type-I Collagen/Collagenase Modulates the 3D Structure and Behavior of Glioblastoma Spheroid Models

Multicellular tumor spheroids have emerged as well-structured, three-dimensional culture models that resemble and mimic the complexity of the dense and hypoxic cancer microenvironment. However, in brain tumor studies, a variety of glioblastoma multiforme (GBM) cell lines only self-assemble into loose cellular aggregates, lacking the properties of actual glioma tumors in humans. In this study, we used type-I collagen as an extracellular matrix component to promote the compaction of GBM aggregates forming tight spheroids to understand how collagen influences the properties of tumors, such as their growth, proliferation, and invasion, and collagenase to promote collagen degradation. The GBM cell lines U87MG, T98G, and A172, as well as the medulloblastoma cell line UW473, were used as standard cell lines that do not spontaneously self-assemble into spheroids, and GBM U251 was used as a self-assembling cell line. According to the findings, all cell lines formed tight spheroids at collagen concentrations higher than 15.0 μg mL^-1. Collagen was distributed along the spheroid, similarly to that observed in invasive GBM tumors, and decreased cell migration with no effect on the cellular uptake of small active molecules, as demonstrated by uptake studies using the photosensitizer verteporfin. The enzymatic cleavage of collagen affected spheroid morphology and increased cell migration while maintaining cell viability. Such behaviors are relevant to the physiological models of GBM tumors and are useful for better understanding cell migration and the in vivo infiltration path, drug screening, and kinetics of progression of GBM tumors.

A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment

We here propose a one-dimensional spatially explicit phenotype-structured model to analyze selected aspects of avascular tumor progression. In particular, our approach distinguishes viable and necrotic cell fractions. The metabolically active part of the disease is, in turn, differentiated according to a continuous trait, that identifies cell variants with different degrees of motility and proliferation potential. A parabolic partial differential equation (PDE) then governs the spatio-temporal evolution of the phenotypic distribution of active cells within the host tissue. In this respect, active tumor agents are allowed to duplicate, move upon haptotactic and pressure stimuli, and eventually undergo necrosis. The mutual influence between the emerging malignancy and its environment (in terms of molecular landscape) is implemented by coupling the evolution law of the viable tumor mass with a parabolic PDE for oxygen kinetics and a differential equation that accounts for local consumption of extracellular matrix (ECM) elements. The resulting numerical realizations reproduce tumor growth and invasion in a number scenarios that differ for cell properties (i.e., individual migratory behavior, duplication and mutation potential) and environmental conditions (i.e., level of tissue oxygenation and homogeneity in the initial matrix profile). In particular, our simulations show that, in all cases, more mobile cell variants occupy the front edge of the tumor, whereas more proliferative clones are selected at the more internal regions. A necrotic core constantly occupies the bulk of the mass due to nutrient deprivation. This work may eventually suggest some biomedical strategies to partially reduce tumor aggressiveness, i.e., to enhance necrosis of malignant tissue and to promote the presence of more proliferative cell phenotypes over more invasive ones.

Predicting cell behaviour parameters from glioblastoma on a chip images. A deep learning approach

The broad possibilities offered by microfluidic devices in relation to massive data monitoring and acquisition open the door to the use of deep learning technologies in a very promising field: cell culture monitoring. In this work, we develop a methodology for parameter identification in cell culture from fluorescence images using Convolutional Neural Networks (CNN). We apply this methodology to the in vitro study of glioblastoma (GBM), the most common, aggressive and lethal primary brain tumour. In particular, the aim is to predict the three parameters defining the go or grow GBM behaviour, which is determinant for the tumour prognosis and response to treatment. The data used to train the network are obtained from a mathematical model, previously validated with in vitro experimental results. The resulting CNN provides remarkably accurate predictions (Pearson's ρ > 0.99 for all the parameters). Besides, it proves to be sound, to filter noise and to generalise. After training and validation with synthetic data, we predict the parameters corresponding to a real image of a microfluidic experiment. The obtained results show good performance of the CNN. The proposed technique may set the first steps towards patient-specific tools, able to predict in real-time the tumour evolution for each particular patient, thanks to a combined in vitro-in silico approach.

Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment

Gliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .

High-pressure oxygen rewires glucose metabolism of patient-derived glioblastoma cells and fuels inflammasome response

Human glioblastoma (GBM) is one of the most feared primary malignant brain tumors. We investigated the effect of hyperbaric oxygen (HBO) on GBM patient-derived cells and on microglia cell biology (CHME-5). HBO administered to GBM cells inhibited cell proliferation, downregulated hypoxia-inducible factor 1 α (HIF-1α) expression, and induced glucose metabolism reprogramming (glucose rewiring). It also affected the ability of a cell to perpetuate its lineage, give rise to differentiated cells and interact with its environment to maintain a balance between quiescence, proliferation and regeneration (stemness features). Such an effect may be ascribable to an increase in intracellular ROS levels and to the triggering of inflammasome signaling by HBO itself through caspase1 activation. Moreover, the results obtained from the combination of HBO and radiotherapy (RT) clearly showed a radiosensitising effect of HBO on GBM cells grown in both 2D and 3D, and a radioprotective effect of HBO in CHME-5. In addition, the exposure of M0 microglia cells to exhausted medium or extracellular vesicles (EVs) of HBO-treated GBM cells upregulated the expression of pro-inflammatory cytokines IL1β, IL6 and STAT1, whilst also downregulating the anti-inflammatory cytokine PPARγ. Collectively, these data provide a scientific rationale for the use of HBO in combination with RT for the treatment of patients with GBM.

A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors

Increasingly complex in silico modeling approaches offer a way to simultaneously access cancerous processes at different spatio-temporal scales. High-level models, such as those based on partial differential equations, are computationally affordable and allow large tumor sizes and long temporal windows to be studied, but miss the discrete nature of many key underlying cellular processes. Individual-based approaches provide a much more detailed description of tumors, but have difficulties when trying to handle full-sized real cancers. Thus, there exists a trade-off between the integration of macroscopic and microscopic information, now widely available, and the ability to attain clinical tumor sizes. In this paper we put forward a stochastic mesoscopic simulation framework that incorporates key cellular processes during tumor progression while keeping computational costs to a minimum. Our framework captures a physical scale that allows both the incorporation of microscopic information, tracking the spatio-temporal emergence of tumor heterogeneity and the underlying evolutionary dynamics, and the reconstruction of clinically sized tumors from high-resolution medical imaging data, with the additional benefit of low computational cost. We illustrate the functionality of our modeling approach for the case of glioblastoma, a paradigm of tumor heterogeneity that remains extremely challenging in the clinical setting.

A Review of Newly Diagnosed Glioblastoma

Glioblastoma is an aggressive and inevitably recurrent primary intra-axial brain tumor with a dismal prognosis. The current mainstay of treatment involves maximally safe surgical resection followed by radiotherapy over a 6-week period with concomitant temozolomide chemotherapy followed by temozolomide maintenance. This review provides a summary of the epidemiological, clinical, histologic and genetic characteristics of newly diagnosed disease as well as the current standard of care and potential future therapeutic prospects.

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.

Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution

In silico models and computer simulation are invaluable tools to better understand complex biological processes such as cancer evolution. However, the complexity of the biological environment, with many cell mechanisms in response to changing physical and chemical external stimuli, makes the associated mathematical models highly non-linear and multiparametric. One of the main problems of these models is the determination of the parameters' values, which are usually fitted for specific conditions, making the conclusions drawn difficult to generalise. We analyse here an important biological problem: the evolution of hypoxia-driven migratory structures in Glioblastoma Multiforme (GBM), the most aggressive and lethal primary brain tumour. We establish a mathematical model considering the interaction of the tumour cells with oxygen concentration in what is called the go or grow paradigm. We reproduce in this work three different experiments, showing the main GBM structures (pseudopalisade and necrotic core formation), only changing the initial and boundary conditions. We prove that it is possible to obtain versatile mathematical tools which, together with a sound parametric analysis, allow to explain complex biological phenomena. We show the utility of this hybrid "biomimetic in vitro-in silico" platform to help to elucidate the mechanisms involved in cancer processes, to better understand the role of the different phenomena, to test new scientific hypotheses and to design new data-driven experiments.

A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

We propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of which the former infers flux limitation both in the self-diffusion and taxis terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor vascularization on the establishment and maintenance of these histological patterns which are typical for high-grade brain cancer. Numerical simulations of the population level dynamics are performed to investigate several model scenarios containing this and further effects.

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.

Successful Free Tissue Transfer in the Profoundly Hypercoagulable Glioblastoma Multiforme Patient: Surgical Experience and Anticoagulation Protocol

Background Glioblastoma multiforme (GBM) produces a hypercoagulable environment and is associated the highest rates of deep venous thrombosis (DVT) and pulmonary emboli (PE) of any malignancy. The use of postoperative radiation in this generally compromised patient group is associated with the development of complex scalp wounds. Free tissue transfer reconstruction will be essential in selected cases despite the presence of an underlying hypercoagulable state.

Methods A 67-year-old female with a history of previous DVT presented with osteoradionecrosis and infected scalp wound following GBM treatment. She underwent reconstruction with a free vastus lateralis flap and skin graft. Initial anticoagulation was provided with intravenous heparin and transitioned to oral apixaban. Wound cultures demonstrated coagulase-negative Staphylococcus, Actinomyces neuii, and Peptoniphilus harei and were treated with a 6-week course of intravenous cefepime and vancomycin.

Results Despite the initial failure of a local scalp rotation flap, successful wound healing was achieved with a free muscle flap and a course of culture specific antibiotics. The patient succumbed to recurrent disease 22 months after surgery, underscoring the importance of limiting hospitalization and maximizing quality of life in this group of patients.

Conclusion Free tissue transfer can be successfully achieved in the hypercoagulable GBM patient. Heparin and apixaban were employed successfully in the prevention of thrombotic events. Antiplatelet therapy should also be considered to counteract platelet aggregation induced by the transmembrane glycoprotein (podoplanin) that is expressed on GBM tumor cells. Enzyme-linked immunosorbent assay testing (ELISA) of blood soluble podoplanin may help determine the degree of hypercoagulability and guide therapy.

Pretreatment inflammatory indices predict Bevacizumab response in recurrent Glioma

Aim: It remains unclear what the best therapeutic option for recurrent glioma patients after Stupp treatment is. Bevacizumab (BVZ) is commonly administered in progression, but it appears that only some patients benefit. It would be useful to find biomarkers that determine beforehand who these patients are.

Methods: The protocol included 31 high-risk progressing glioma patients after Stupp treatment who received BVZ 5-10 mg/kg every 14 days and temozolomide (3-19 cycles, 150-200 mg five days each 28-day cycle) during a mean of eight cycles of BVZ or until tumor progression or unacceptable toxicity. We analyzed the clinical outcome values of inflammatory indices measured before BVZ administration.

Results: Lymphocyte level before BVZ administration was the best independent predictor of overall survival (HR = 0.34; 95%CI: 0.145-0.81; P = 0.015). The area under the receiver operating characteristic (ROC) curve was 0.823, with 1.645 being the optimal cut-off value, and 0.80 and 0.85 the sensitivity and specificity values, respectively. Responder and non-responder survival curves were also significantly different, considering the first and second tertiles as cut-off points. The number of BVZ cycles was not related to lymphopenia. Pretreatment neutrophil, platelet levels, platelet-to-lymphocyte ratio (PLR), and neutrophil-to-lymphocyte ratio (NLR) did not have independent predictive value. Inflammatory variables were not correlated with each other. However, patients with high NLR and PLR simultaneously (double positive PLR-NLR) showed a worse clinical outcome than the rest (P = 0.043).

Conclusion: Pretreatment lymphocyte levels and double positive PLR-NLR could be used as non-invasive hematological prognostic markers for recurrent gliomas treated with bevacizumab. A close relationship emerged between inflammation and angiogenesis.

Investigating the Physical Effects in Bacterial Therapies for Avascular Tumors

Tumor-targeting bacteria elicit anticancer effects by infiltrating hypoxic regions, releasing toxic agents and inducing immune responses. Although current research has largely focused on the influence of chemical and immunological aspects on the mechanisms of bacterial therapy, the impact of physical effects is still elusive. Here, we propose a mathematical model for the anti-tumor activity of bacteria in avascular tumors that takes into account the relevant chemo-mechanical effects. We consider a time-dependent administration of bacteria and analyze the impact of bacterial chemotaxis and killing rate. We show that active bacterial migration toward tumor hypoxic regions provides optimal infiltration and that high killing rates combined with high chemotactic values provide the smallest tumor volumes at the end of the treatment. We highlight the emergence of steady states in which a small population of bacteria is able to constrain tumor growth. Finally, we show that bacteria treatment works best in the case of tumors with high cellular proliferation and low oxygen consumption.

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.

NFкB is a critical transcriptional regulator of atypical cadherin FAT1 in glioma

Background

Overexpression of FAT1 gene and its oncogenic effects have been reported in several cancers. Previously, we have documented upregulation of FAT1 gene in glioblastoma (GBM) tumors which was found to increase the expression of proinflammatory markers, HIF-1α, stemness genes and EMT markers in glioma cells. Here, we reveal NFкB (RelA)/RelA/p65 as the transcriptional regulator of FAT1 gene in GBM cells.

Methods

In-silico analysis of FAT1 gene promoter was performed using online bioinformatics tool Promo alggen (Transfac 8.3) to identify putative transcription factor(s) binding motifs. A 4.0 kb FAT1 promoter (− 3220 bp to + 848 bp w.r.t. TSS + 1) was cloned into promoter less pGL3Basic reporter vector. Characterization of FAT1 promoter for transcriptional regulation was performed by in-vitro functional assays using promoter deletion constructs, site directed mutagenesis and ChIP in GBM cells.

Results

Expression levels of NFкB (RelA) and FAT1 were found to be increased and positively correlated in GBM tumors (n = 16), REMBRANDT GBM-database (n = 214) and TCGA GBM-database (n = 153). In addition to glioma, positive correlation between NFкB (RelA) and FAT1 expression was also observed in other tumors like pancreatic, hepatocellular, lung and stomach cancers (data extracted from TCGA tumor data). A 4.0 kb FAT1-promoter-construct [− 3220 bp/+ 848 bp, transcription start site (TSS) + 1, having 17 NFкB (RelA) motifs] showed high FAT1 promoter luciferase-activity in GBM cells (U87MG/A172/U373MG). FAT1 promoter deletion-construct pGL3F1 [− 200 bp/+ 848 bp, with 3-NFкB (RelA)-motifs] showed the highest promoter activity. Exposure of GBM cells to known NFкB (RelA)-activators [severe-hypoxia/TNF-α/ectopic-NFкB (RelA) + IKBK vectors] led to increased pGL3F1-promoter activity and increased endogenous-FAT1 expression. Conversely, siRNA-mediated NFкB (RelA) knockdown led to decreased pGL3F1-promoter activity and decreased endogenous-FAT1 expression. Deletion of NFкB (RelA)-motif at − 90 bp/− 80 bp [pGL3F1δ1-construct] showed significant decrease in promoter activity. Site directed mutagenesis at -90 bp/− 80 bp and ChIP assay for endogenous-NFкB (RelA) confirmed the importance of this motif in FAT1 expression regulation. Significant reduction in the migration, invasion as well as colony forming capacity of the U87MG glioma cells was observed on siRNA-mediated knockdown of NFкB (RelA).

Conclusion

Since FAT1 and NFкB (RelA) are independently known to promote pro-tumorigenic inflammation and upregulate the expression of HIF-1α/EMT/stemness in tumors, targeting the NFкB (RelA)-FAT1 axis may attenuate an important tumor-promoting pathway in GBM. This may also be applicable to other tumors.

Radiation protraction schedules for low-grade gliomas: a comparison between different mathematical models

We optimize radiotherapy (RT) administration strategies for treating low-grade gliomas. Specifically, we consider different tumour growth laws, both with and without spatial effects. In each scenario, we find the optimal treatment in the sense of maximizing the overall survival time of a virtual low-grade glioma patient, whose tumour progresses according to the examined growth laws. We discover that an extreme protraction therapeutic strategy, which amounts to substantially extending the time interval between RT sessions, may lead to better tumour control. The clinical implications of our results are also presented.

The immune suppressive microenvironment of human gliomas depends on the accumulation of bone marrow-derived macrophages in the center of the lesion

BACKGROUND

Systemic and local immune suppression plays a significant role in glioma progression. Glioma microenvironment contains both brain-resident microglial cells (MG) and bone marrow-derived macrophages (BMDM), but the study of their functional and immune regulatory activity has been hampered until now by the lack of markers allowing a proper identification and isolation to collect pure populations.

METHODS

Myeloid and lymphoid infiltrate were characterized in grade II, III and IV gliomas by multicolor flow cytometry, along with the composition of the cell subsets of circulating myeloid cells. Macrophages were sorted and tested for their immunosuppressive ability. Moreover, following preoperative administration of 5-aminolevulinic acid to patients, distinct areas of tumor lesion were surgically removed and analyzed, based on protoporphyrin IX fluorescence emission.

RESULTS

The immune microenvironment of grade II to grade IV gliomas contains a large proportion of myeloid cells and a small proportion of lymphocytes expressing markers of dysfunctional activity. BMDM and resident MG cells were characterized through a combination of markers, thus permitting their geographical identification in the lesions, their sorting and subsequent analysis of the functional characteristics. The infiltration by BMDM reached the highest percentages in grade IV gliomas, and it increased from the periphery to the center of the lesion, where it exerted a strong immunosuppression that was, instead, absent in the marginal area. By contrast, MG showed little or no suppression. Functional differences, such as iron metabolism and phagocytosis, characterized resident versus blood-derived macrophages. Significant alterations in circulating monocytes were present in grade IV patients, correlating with accumulation of tumor macrophages.

CONCLUSIONS

Grade IV gliomas have an alteration in both circulating and tumor-associated myeloid cells and, differently from grade II and III gliomas, show a significant presence of blood-derived, immune suppressive macrophages. BMDM and MG have different functional properties.

Pericytes in Glioblastomas: Multifaceted Role Within Tumor Microenvironments and Potential for Therapeutic Interventions

Glioblastoma (GBM) is an aggressive and lethal disease that often results in a poor prognosis. Unlike most solid tumors, GBM is characterized by diffuse infiltrating margins, extensive angiogenesis, hypoxia, necrosis, and clonal heterogeneity. Recurrent disease is an unavoidable consequence for many patients as standard treatment options such as surgery, radiotherapy, and chemotherapy have proven to be insufficient in causing long-term survival benefits. Systemic delivery of promising drugs is hindered due to the blood-brain barrier and non-uniform perfusion within GBM tissue. In recent years, many investigations have highlighted the role of GBM stem cells (GSCs) and their microenvironment in the initiation and maintenance of tumor tissue. Preclinical and early clinical studies to target GSCs and microenvironmental components are currently underway. Of these strategies, immunotherapy using checkpoint inhibitors and redirected cytotoxic T cells have shown promising results in early investigations. But, GBM microenvironment is heterogenous and recent investigations have shown cell populations within this microenvironment to be plastic. These studies underline the importance of identifying the role of and targeting multiple cell populations within the GBM microenvironment which could have a synergistic effect when combined with novel therapies. Pericytes are multipotent perivascular cells that play a vital role within the GBM microenvironment by assisting in tumor initiation, survival, and progression. Due to their role in regulating the blood-brain barrier permeability, promoting angiogenesis, tumor growth, clearing extracellular matrix for infiltrating GBM cells and in helping GBM cells evade immune surveillance, pericytes could be ideal therapeutic targets for stymieing or exploiting their role within the GBM microenvironment. This chapter will introduce hallmarks of GBM and elaborate on the contributions of pericytes to these hallmarks by examining recent findings. In addition, the chapter also highlights the therapeutic value of targeting pericytes, while discussing conventional and novel GBM therapies and obstacles to their efficacy.

The biology and mathematical modelling of glioma invasion: a review

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

Glioma growth modeling based on the effect of vital nutrients and metabolic products

Glioma brain tumors exhibit considerably aggressive behavior leading to high mortality rates. Mathematical modeling of tumor growth aims to explore the interactions between glioma cells and tissue microenvironment, which affect tumor evolution. Leveraging this concept, we present a three-dimensional model of glioma spatio-temporal evolution based on existing continuum approaches, yet incorporating novel factors of the phenomenon. The proposed model involves the interactions between different tumor cell phenotypes and their microenvironment, investigating how tumor growth is affected by complex biological exchanges. It focuses on the separate and combined effect of vital nutrients and cellular wastes on tumor expansion, leading to the formation of cell populations with different metabolic, proliferative, and diffusive profiles. Several simulations were performed on a virtual and a real glioma, using combinations of proliferation and diffusion rates for different evolution times. The model results were validated on a glioma model available in the literature and a real case of tumor progression. The experimental observations indicate that our model estimates quite satisfactorily the expansion of each region and the overall tumor growth. Based on the individual results, the proposed model may provide an important research tool for patient-specific simulation of different tumor evolution scenarios and reliable estimation of glioma evolution. Graphical Abstract Outline of the mathematical model functionality and application to glioma growth with indicative results.

A Brownian dynamics tumor progression simulator with application to glioblastoma

Tumor progression modeling offers the potential to predict tumor-spreading behavior to improve prognostic accuracy and guide therapy development. Common simulation methods include continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumor spreading behavior and discrete agent-based (AB) approaches which capture individual cell events such as proliferation or migration. The brain cancer glioblastoma (GBM) is especially appropriate for such proliferation-migration modeling approaches because tumor cells seldom metastasize outside of the central nervous system and cells are both highly proliferative and migratory. In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from computed tomography or magnetic resonance images. However, these estimates of glioblastoma cell migration rates, modeled as a diffusion coefficient, are approximately 1-2 orders of magnitude larger than single-cell measurements in animal models of this disease. To identify possible sources for this discrepancy, we evaluated the fundamental RD simulation assumptions that cells are point-like structures that can overlap. To give cells physical size (~10 μm), we used a Brownian dynamics approach that simulates individual single-cell diffusive migration, growth, and proliferation activity via a gridless, off-lattice, AB method where cells can be prohibited from overlapping each other. We found that for realistic single-cell parameter growth and migration rates, a non-overlapping model gives rise to a jammed configuration in the center of the tumor and a biased outward diffusion of cells in the tumor periphery, creating a quasi-ballistic advancing tumor front. The simulations demonstrate that a fast-progressing tumor can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates. Thus, modeling with the assumption of physically-grounded volume conservation can account for the apparent discrepancy between estimated and measured diffusion of GBM cells and provide a new theoretical framework that naturally links single-cell growth and migration dynamics to tumor-level progression.

Hypoxia activates cadherin-22 synthesis via eIF4E2 to drive cancer cell migration, invasion and adhesion

Hypoxia is a driver of cell movement in processes such as development and tumor progression. The cellular response to hypoxia involves a transcriptional program mediated by hypoxia-inducible factors, but translational control has emerged as a significant contributor. In this study, we demonstrate that a cell-cell adhesion molecule, cadherin-22, is upregulated in hypoxia via mTORC1-independent translational control by the initiation factor eIF4E2. We identify new functions of cadherin-22 as a hypoxia-specific cell-surface molecule involved in cancer cell migration, invasion and adhesion. Silencing eIF4E2 or cadherin-22 significantly impaired MDA-MB-231 breast carcinoma and U87MG glioblastoma cell migration and invasion only in hypoxia, while reintroduction of the respective exogenous gene restored the normal phenotype. Cadherin-22 was evenly distributed throughout spheroids and required for their formation and support of a hypoxic core. Conversely, E-cadherin translation was repressed by hypoxia and only expressed in the oxygenated cells of U87MG spheroids. Furthermore, immunofluorescence on paraffin-embedded human tissue from 40 glioma and 40 invasive ductal breast carcinoma patient specimens revealed that cadherin-22 expression colocalized with areas of hypoxia and significantly correlated with tumor grade and progression-free survival or stage and tumor size, respectively. This study broadens our understanding of tumor progression and metastasis by highlighting cadherin-22 as a potential new target of cancer therapy to disable hypoxic cancer cell motility and adhesion.

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

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

Hypoxia in Gliomas: Opening Therapeutical Opportunities Using a Mathematical-Based Approach

This chapter explores the use of mathematical models as promising and powerful tools to understand the complexity of tumors and their, frequently, hypoxic environment. We focus on gliomas, which are primary brain tumors derived from glial cells, mainly astrocytes and/or oligodendrocytes. A variety of mathematical models, based on ordinary and/or partial differential equations, have been developed both at the micro and macroscopic levels. The aim here is to describe in a quantitative way key physiopathological mechanisms relevant in these types of malignancies and to suggest optimal therapeutical strategies. More specifically, we consider novel therapies targeting thromboembolic phenomena to decrease cell invasion in high grade glioma or to delay the malignant transformation in low grade gliomas. This study has been the basis of a multidisciplinary collaboration involving, among others, neuro-oncologists, radiation oncologists, pathologists, cancer biologists, surgeons and mathematicians.

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

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

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

Background

Glioblastoma (GBM) is one of the most lethal tumor types. Hypercellular regions, named pseudopalisades, are characteristic in these tumors and have been hypothesized to be waves of migrating glioblastoma cells. These "waves" of cells are thought to be induced by oxygen and nutrient depletion caused by tumor-induced blood vessel occlusion. Although the universal presence of these structures in GBM tumors suggests that they may play an instrumental role in GBM's spread and invasion, the recreation of these structures in vitro has remained challenging.

Methods

Here we present a new microfluidic model of GBM that mimics the dynamics of pseudopalisade formation. To do this, we embedded U-251 MG cells within a collagen hydrogel in a custom-designed microfluidic device. By controlling the medium flow through lateral microchannels, we can mimic and control blood-vessel obstruction events associated with this disease.

Results

Through the use of this new system, we show that nutrient and oxygen starvation triggers a strong migratory process leading to pseudopalisade generation in vitro. These results validate the hypothesis of pseudopalisade formation and show an excellent agreement with a systems-biology model based on a hypoxia-driven phenomenon.

Conclusions

This paper shows the potential of microfluidic devices as advanced artificial systems capable of modeling in vivo nutrient and oxygen gradients during tumor evolution.

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.

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.

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

Background

Antiangiogenic therapies for glioblastoma (GBM) such as bevacizumab (BVZ), have been unable to extend survival in large patient cohorts. However, a subset of patients having angiogenesis-dependent tumors might benefit from these therapies. Currently, there are no biomarkers allowing to discriminate responders from non-responders before the start of the therapy.

Methods

40 patients from the randomized GENOM009 study complied the inclusion criteria (quality of images, clinical data available). Of those, 23 patients received first line temozolomide (TMZ) for eight weeks and then concomitant radiotherapy and TMZ. 17 patients received BVZ+TMZ for seven weeks and then added radiotherapy to the treatment. Clinical variables were collected, tumors segmented and several geometrical measures computed including: Contrast enhancing (CE), necrotic, and total volumes; equivalent spherical CE width; several geometric measures of the CE ‘rim’ geometry and a set of image texture measures. The significance of the results was studied using Kaplan-Meier and Cox proportional hazards analysis. Correlations were assessed using Spearman correlation coefficients.

Results

Kaplan-Meier and Cox proportional hazards analysis showed that total, CE and inner volume (p = 0.019, HR = 4.258) and geometric heterogeneity of the CE areas (p = 0.011, HR = 3.931) were significant parameters identifying response to BVZ. The group of patients with either regular CE areas (small geometric heterogeneity, median difference survival 15.88 months, p = 0.011) or those with small necrotic volume (median survival difference 14.50 months, p = 0.047) benefited substantially from BVZ.

Conclusion

Imaging biomarkers related to the irregularity of contrast enhancing areas and the necrotic volume were able to discriminate GBM patients with a substantial survival benefit from BVZ. A prospective study is needed to validate our results.

Monte-Carlo model development for evaluation of current clinical target volume definition for heterogeneous and hypoxic glioblastoma

Clinical target volume (CTV) determination may be complex and subjective. In this work a microscopic-scale tumour model was developed to evaluate current CTV practices in glioblastoma multiforme (GBM) external radiotherapy. Previously, a Geant4 cell-based dosimetry model was developed to calculate the dose deposited in individual GBM cells. Microscopic extension probability (MEP) models were then developed using Matlab-2012a. The results of the cell-based dosimetry model and MEP models were combined to calculate survival fractions (SF) for CTV margins of 2.0 and 2.5 cm. In the current work, oxygenation and heterogeneous radiosensitivity profiles were incorporated into the GBM model. The genetic heterogeneity was modelled using a range of α/β values (linear-quadratic model parameters) associated with different GBM cell lines. These values were distributed among the cells randomly, taken from a Gaussian-weighted sample of α/β values. Cellular oxygen pressure was distributed randomly taken from a sample weighted to profiles obtained from literature. Three types of GBM models were analysed: homogeneous-normoxic, heterogeneous-normoxic, and heterogeneous-hypoxic. The SF in different regions of the tumour model and the effect of the CTV margin extension from 2.0-2.5 cm on SFs were investigated for three MEP models. The SF within the beam was increased by up to three and two orders of magnitude following incorporation of heterogeneous radiosensitivities and hypoxia, respectively, in the GBM model. However, the total SF was shown to be overdominated by the presence of tumour cells in the penumbra region and to a lesser extent by genetic heterogeneity and hypoxia. CTV extension by 0.5 cm reduced the SF by a maximum of 78.6  ±  3.3%, 78.5  ±  3.3%, and 77.7  ±  3.1% for homogeneous and heterogeneous-normoxic, and heterogeneous hypoxic GBMs, respectively. Monte-Carlo model was developed to quantitatively evaluate SF for genetically heterogeneous and hypoxic GBM with two CTV margins and three MEP distributions. The results suggest that photon therapy may not provide cure for hypoxic and genetically heterogeneous GBM. However, the extension of the CTV margin by 0.5 cm could be beneficial to delay the recurrence time for this tumour type due to significant increase in tumour cell irradiation.

Mathematical Modelling of a Brain Tumour Initiation and Early Development: A Coupled Model of Glioblastoma Growth, Pre-Existing Vessel Co-Option, Angiogenesis and Blood Perfusion

We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic changes in chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels including vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment on the early phase of glioblastoma growth.

A Glycolysis-Based In Silico Model for the Solid Tumor Growth

Cancer-tumor growth is a complex process depending on several biological factors, such as the chemical microenvironment of the tumor, the cellular metabolic profile, and its proliferation rate. Several mathematical models have been developed for identifying the interactions between tumor cells and tissue microenvironment, since they play an important role in tumor formation and progression. Toward this direction we propose a new continuum model of avascular glioma-tumor growth, which incorporates a new factor, namely, the glycolytic potential of cancer cells, to express the interactions of three different tumor-cell populations (proliferative, hypoxic, and necrotic) with their tissue microenvironment. The glycolytic potential engages three vital nutrients, i.e., oxygen, glucose, and lactate, which provide cells with the necessary energy for their survival and proliferation. Extensive simulations are performed for different evolution times and various proliferation rates, in order to investigate how the tumor growth is affected. According to medical experts, the experimental observations indicate that the model predicts quite satisfactorily the overall tumor growth as well as the expansion of each region separately. Following extensive evaluation, the proposed model may provide an essential tool for patient-specific tumor simulation and reliable prediction of glioma spatiotemporal expansion.

Investigating the Influence of HUVECs in the Formation of Glioblastoma Spheroids in High-Throughput Three-Dimensional Microwells

Glioblastoma (GBM) is the most common form of primary brain tumor with a high infiltrative capacity, increased vascularity, and largely elusive tumor progression mechanism. The current GBM treatment methods do not increase the patient survival rate and studies using two-dimensional (2D) cell cultures and in vivo animal models to investigate GBM behavior and mechanism have limitations. Therefore, there is an increasing need for in vitro three-dimensional (3D) models that closely mimic in vivo microenvironment of the GBM tumors to understand the underlying mechanisms of the tumor progression. In this study we propose to use a 3D in vitro model to overcome these limitations, using poly (ethylene glycol) dimethyl acrylate (PEGDA) hydrogel-based microwells and co-culture GBM (U87) cells and endothelial cells (HUVEC) in the 3D microwells to provide a 3D in vitro simulation of the tumor microenvironment. Furthermore, we investigated the gene expression differences of co-cultures by quantitative real-time PCR. Our results suggested that the relative expression profiles of tumor angiogenesis markers, PECAM1/CD31, and VEGFR2, in co-cultures are consistent with in vivo GBM studies. Furthermore, we suggest that our microwell platform could provide robust and useful 3D co-culture models for high-throughput drug screening and treatment of the GBM.

An Emerging Allee Effect Is Critical for Tumor Initiation and Persistence

Tumor cells develop different strategies to cope with changing microenvironmental conditions. A prominent example is the adaptive phenotypic switching between cell migration and proliferation. While it has been shown that the migration-proliferation plasticity influences tumor spread, it remains unclear how this particular phenotypic plasticity affects overall tumor growth, in particular initiation and persistence. To address this problem, we formulate and study a mathematical model of spatio-temporal tumor dynamics which incorporates the microenvironmental influence through a local cell density dependence. Our analysis reveals that two dynamic regimes can be distinguished. If cell motility is allowed to increase with local cell density, any tumor cell population will persist in time, irrespective of its initial size. On the contrary, if cell motility is assumed to decrease with respect to local cell density, any tumor population below a certain size threshold will eventually extinguish, a fact usually termed as Allee effect in ecology. These results suggest that strategies aimed at modulating migration are worth to be explored as alternatives to those mainly focused at keeping tumor proliferation under control.

Controlling tumor growth remains a major medical challenge. Current clinical therapies focus on strategies to reduce tumor cell proliferation. However, during tumor progression, tumor cells may switch between proliferative and migratory behaviors, thereby allowing adaptation to microenvironmental changes that result in variations in local tumor cell density. We herein explore by means of a mathematical model the impact of migration-proliferation plasticity on tumor initiation and persistence. Our work suggests that small tumors can become extinct solely by their intrinsic cell population dynamics if cell motility decreases along with local cell density. In contrast, if cell motility increases with cell density, the tumor inevitably grows. Our model suggests that the regulation of cell migration plays a key role in tumor growth as a whole, making this feature a potential target for clinical studies.

Mathematically modeling the biological properties of gliomas: A review

Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be difficult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the infiltrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their influence on the surrounding anatomical structures in the brain.