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

Mathematical modeling of multicellular tumor spheroids quantifies inter-patient and intra-tumor heterogeneity

In the study of brain tumors, patient-derived three-dimensional sphere cultures provide an important tool for studying emerging treatments. The growth of such spheroids depends on the combined effects of proliferation and migration of cells, but it is challenging to make accurate distinctions between increase in cell number versus the radial movement of cells. To address this, we formulate a novel model in the form of a system of two partial differential equations (PDEs) incorporating both migration and growth terms, and show that it more accurately fits our data compared to simpler PDE models. We show that traveling-wave speeds are strongly associated with population heterogeneity. Having fitted the model to our dataset we show that a subset of the cell lines are best described by a "Go-or-Grow"-type model, which constitutes a special case of our model. Finally, we investigate whether our fitted model parameters are correlated with patient age and survival.

Biopsy location and tumor-associated macrophages in predicting malignant glioma recurrence using an in-silico model

Predicting the biological behavior and time to recurrence (TTR) of high-grade diffuse gliomas (HGG) after maximum safe neurosurgical resection and combined radiation and chemotherapy plays a pivotal role in planning clinical follow-up, selecting potentially necessary second-line treatment and improving the quality of life for patients diagnosed with a malignant brain tumor. The current standard-of-care (SoC) for HGG includes follow-up neuroradiological imaging to detect recurrence as early as possible and relies on several clinical, neuropathological, and radiological prognostic factors, which have limited accuracy in predicting TTR. In this study, using an in-silico analysis, we aim to improve predictive power for TTR by considering the role of (i) prognostically relevant information available through diagnostics used in the current SoC, (ii) advanced image-based information not currently part of the standard diagnostic workup, such as tumor-normal tissue interface (edge) features and quantitative data specific to biopsy positions within the tumor, and (iii) information on tumor-associated macrophages. In particular, we introduced a state-of-the-art spatio-temporal model of tumor-immune interactions, emphasizing the interplay between macrophages and glioma cells. This model serves as a synthetic reality for assessing the predictive value of various features. We generated a cohort of virtual patients based on our mathematical model. Each patient's dataset includes simulated T1Gd and Fluid-attenuated inversion recovery (FLAIR) MRI volumes. T1-weighted imaging highlights anatomical structures with high contrast, providing clear detail on brain morphology, whereas FLAIR suppresses fluid signals, improving the visualization of lesions near fluid-filled spaces, which is particularly helpful for identifying peritumoral edema. Additionally, we simulated results on macrophage density and proliferative activity, either in a specified part of the tumor, namely the tumor core or edge ("localized"), or unspecified ("non-localized"). To enhance the realism of our synthetic data, we imposed different levels of noise. Our findings reveal that macrophage density at the tumor edge contributed to a high predictive value of feature importance for the selected regression model. Moreover, there are lower MSE values for the "localized" biopsy in prediction accuracy toward recurrence post-resection compared with "non-localized" specimens in the noisy data. In conclusion, the results show that localized biopsies provided more information about tumor behavior, especially at the interface of tumor and normal tissue (Edge).

Microenvironmental entropy dynamics analysis reveals novel insights into Notch-Delta-Jagged decision-making mechanism

Notch-Delta-Jagged (NDJ) signaling among neighboring cells contributes crucially to spatiotemporal pattern formation and developmental decision-making. Despite numerous detailed mathematical models, their high-dimensionality parametric space limits analytical treatment, especially regarding local microenvironmental fluctuations. Using the low-dimensional dynamics of the recently postulated least microenvironmental uncertainty principle (LEUP) framework, we showcase how the LEUP formalism recapitulates a noisy NDJ spatial patterning. Our LEUP simulations show that local phenotypic entropy increases for lateral inhibition but decreases for lateral induction. This distinction allows us to identify a critical parameter that captures the transition from a Notch-Delta-driven lateral inhibition to a Notch-Jagged-driven lateral induction phenomenon and suggests random phenotypic patterning in the case of lack of dominance of either Notch-Delta or Notch-Jagged signaling. Our results enable an analytical treatment to map the high-dimensional dynamics of NDJ signaling on tissue-level patterning and can possibly be generalized to decode operating principles of collective cellular decision-making.

New insights into targeted therapy of glioblastoma using smart nanoparticles

In recent times, the intersection of nanotechnology and biomedical research has given rise to nanobiomedicine, a captivating realm that holds immense promise for revolutionizing diagnostic and therapeutic approaches in the field of cancer. This innovative fusion of biology, medicine, and nanotechnology aims to create diagnostic and therapeutic agents with enhanced safety and efficacy, particularly in the realm of theranostics for various malignancies. Diverse inorganic, organic, and hybrid organic-inorganic nanoparticles, each possessing unique properties, have been introduced into this domain. This review seeks to highlight the latest strides in targeted glioblastoma therapy by focusing on the application of inorganic smart nanoparticles. Beyond exploring the general role of nanotechnology in medical applications, this review delves into groundbreaking strategies for glioblastoma treatment, showcasing the potential of smart nanoparticles through in vitro studies, in vivo investigations, and ongoing clinical trials.

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.

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.

A combined experimental-computational approach uncovers a role for the Golgi matrix protein Giantin in breast cancer progression

Our understanding of how speed and persistence of cell migration affects the growth rate and size of tumors remains incomplete. To address this, we developed a mathematical model wherein cells migrate in two-dimensional space, divide, die or intravasate into the vasculature. Exploring a wide range of speed and persistence combinations, we find that tumor growth positively correlates with increasing speed and higher persistence. As a biologically relevant example, we focused on Golgi fragmentation, a phenomenon often linked to alterations of cell migration. Golgi fragmentation was induced by depletion of Giantin, a Golgi matrix protein, the downregulation of which correlates with poor patient survival. Applying the experimentally obtained migration and invasion traits of Giantin depleted breast cancer cells to our mathematical model, we predict that loss of Giantin increases the number of intravasating cells. This prediction was validated, by showing that circulating tumor cells express significantly less Giantin than primary tumor cells. Altogether, our computational model identifies cell migration traits that regulate tumor progression and uncovers a role of Giantin in breast cancer progression.

Nanomedicine for Glioblastoma: Progress and Future Prospects

Glioblastoma is the most aggressive form of brain tumor, accounting for the highest mortality and morbidity rates. Current treatment for patients with glioblastoma includes maximal safe tumor resection followed by radiation therapy with concomitant temozolomide (TMZ) chemotherapy. The addition of TMZ to the conformal radiation therapy has improved the median survival time only from 12 months to 16 months in patients with glioblastoma. Despite these aggressive treatment strategies, patients' prognosis remains poor. This therapeutic failure is primarily attributed to the blood-brain barrier (BBB) that restricts the transport of TMZ from reaching the tumor site. In recent years, nanomedicine has gained considerable attention among researchers and shown promising developments in clinical applications, including the diagnosis, prognosis, and treatment of glioblastoma tumors. This review sheds light on the morphological and physiological complexity of the BBB. It also explains the development of nanomedicine strategies to enhance the permeability of drug molecules across the BBB.

Roadmap on plasticity and epigenetics in cancer

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

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.

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

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

BACKGROUND

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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 .

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.

Glucose transporter Glut1 controls diffuse invasion phenotype with perineuronal satellitosis in diffuse glioma microenvironment

Background

Gliomas typically escape surgical resection and recur due to their “diffuse invasion” phenotype, enabling them to infiltrate diffusely into the normal brain parenchyma. Over the past 80 years, studies have revealed 2 key features of the “diffuse invasion” phenotype, designated the Scherer’s secondary structure, and include perineuronal satellitosis (PS) and perivascular satellitosis (PVS). However, the mechanisms are still unknown.

Methods

We established a mouse glioma cell line (IG27) by manipulating the histone H3K27M mutation, frequently harboring in diffuse intrinsic pontine gliomas, that reproduced the diffuse invasion phenotype, PS and PVS, following intracranial transplantation in the mouse brain. Further, to broadly apply the results in this mouse model to human gliomas, we analyzed data from 66 glioma patients.

Results

Increased H3K27 acetylation in IG27 cells activated glucose transporter 1 (Glut1) expression and induced aerobic glycolysis and TCA cycle activation, leading to lactate, acetyl-CoA, and oncometabolite production irrespective of oxygen and glucose levels. Gain- and loss-of-function in vivo experiments demonstrated that Glut1 controls the PS of glioma cells, that is, attachment to and contact with neurons. GLUT1 is also associated with early progression in glioma patients.

Conclusions

Targeting the transporter Glut1 suppresses the unique phenotype, “diffuse invasion” in the diffuse glioma mouse model. This work leads to promising therapeutic and potential useful imaging targets for anti-invasion in human gliomas widely.

Tumor Volume Dynamics as an Early Biomarker for Patient-Specific Evolution of Resistance and Progression in Recurrent High-Grade Glioma

Recurrent high-grade glioma (HGG) remains incurable with inevitable evolution of resistance and high inter-patient heterogeneity in time to progression (TTP). Here, we evaluate if early tumor volume response dynamics can calibrate a mathematical model to predict patient-specific resistance to develop opportunities for treatment adaptation for patients with a high risk of progression. A total of 95 T1-weighted contrast-enhanced (T1post) MRIs from 14 patients treated in a phase I clinical trial with hypo-fractionated stereotactic radiation (HFSRT; 6 Gy × 5) plus pembrolizumab (100 or 200 mg, every 3 weeks) and bevacizumab (10 mg/kg, every 2 weeks; NCT02313272) were delineated to derive longitudinal tumor volumes. We developed, calibrated, and validated a mathematical model that simulates and forecasts tumor volume dynamics with rate of resistance evolution as the single patient-specific parameter. Model prediction performance is evaluated based on how early progression is predicted and the number of false-negative predictions. The model with one patient-specific parameter describing the rate of evolution of resistance to therapy fits untrained data ( R 2 = 0.70 ). In a leave-one-out study, for the nine patients that had T1post tumor volumes ≥1 cm3, the model was able to predict progression on average two imaging cycles early, with a median of 9.3 (range: 3-39.3) weeks early (median progression-free survival was 27.4 weeks). Our results demonstrate that early tumor volume dynamics measured on T1post MRI has the potential to predict progression following the protocol therapy in select patients with recurrent HGG. Future work will include testing on an independent patient dataset and evaluation of the developed framework on T2/FLAIR-derived data.

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.

Mathematical Modeling Shows That the Response of a Solid Tumor to Antiangiogenic Therapy Depends on the Type of Growth

It has been hypothesized that solid tumors with invasive type of growth should possess intrinsic resistance to antiangiogenic therapy, which is aimed at cessation of the formation of new blood vessels and subsequent shortage of nutrient inflow to the tumor. In order to investigate this effect, a continuous mathematical model of tumor growth is developed, which considers variables of tumor cells, necrotic tissue, capillaries, and glucose as the crucial nutrient. The model accounts for the intrinsic motility of tumor cells and for the convective motion, arising due to their proliferation, thus allowing considering two types of tumor growth—invasive and compact—as well as their combination. Analytical estimations of tumor growth speed are obtained for compact and invasive tumors. They suggest that antiangiogenic therapy may provide a several times decrease of compact tumor growth speed, but the decrease of growth speed for invasive tumors should be only modest. These estimations are confirmed by numerical simulations, which further allow evaluating the effect of antiangiogenic therapy on tumors with mixed growth type and highlight the non-additive character of the two types of growth.

Investigation of solid tumor progression with account of proliferation/migration dichotomy via Darwinian mathematical model

A new continuous spatially-distributed model of solid tumor growth and progression is presented. The model explicitly accounts for mutations/epimutations of tumor cells which take place upon their division. The tumor grows in normal tissue and its progression is driven only by competition between populations of malignant cells for limited nutrient supply. Two reasons for the motion of tumor cells in space are taken into consideration, i.e., their intrinsic motility and convective fluxes, which arise due to proliferation of tumor cells. The model is applied to investigation of solid tumor progression under phenotypic alterations that inversely affect cell proliferation rate and cell motility by increasing the value of one of the parameters at the expense of another.It is demonstrated that the crucial feature that gives evolutionary advantage to a cell population is the speed of its intergrowth into surrounding normal tissue. Of note, increase in tumor intergrowth speed in not always associated with increase in motility of tumor cells. Depending on the parameters of functions, that describe phenotypic alterations, tumor cellular composition may evolve towards: (1) maximization of cell proliferation rate, (2) maximization of cell motility, (3) non-extremum values of cell proliferation rate and motility. Scenarios are found, where after initial tendency for maximization of cell proliferation rate, the direction of tumor progression sharply switches to maximization of cell motility, which is accompanied by decrease in total speed of tumor growth.

Toward Personalized Computer Simulation of Breast Cancer Treatment: A Multiscale Pharmacokinetic and Pharmacodynamic Model Informed by Multitype Patient Data

The usefulness of mechanistic models to disentangle complex multiscale cancer processes, such as treatment response, has been widely acknowledged. However, a major barrier for multiscale models to predict treatment outcomes in individual patients lies in their initialization and parametrization, which needs to reflect individual cancer characteristics accurately. In this study, we use multitype measurements acquired routinely on a single breast tumor, including histopathology, MRI, and molecular profiling, to personalize parts of a complex multiscale model of breast cancer treated with chemotherapeutic and antiangiogenic agents. The model accounts for drug pharmacokinetics and pharmacodynamics. We developed an open-source computer program that simulates cross-sections of tumors under 12-week therapy regimens and used it to individually reproduce and elucidate treatment outcomes of 4 patients. Two of the tumors did not respond to therapy, and model simulations were used to suggest alternative regimens with improved outcomes dependent on the tumor's individual characteristics. It was determined that more frequent and lower doses of chemotherapy reduce tumor burden in a low proliferative tumor while lower doses of antiangiogenic agents improve drug penetration in a poorly perfused tumor. Furthermore, using this model, we were able to correctly predict the outcome in another patient after 12 weeks of treatment. In summary, our model bridges multitype clinical data to shed light on individual treatment outcomes. SIGNIFICANCE: Mathematical modeling is used to validate possible mechanisms of tumor growth, resistance, and treatment outcome.

Treatment Strategies Based on Histological Targets against Invasive and Resistant Glioblastoma

Glioblastoma (GBM) is the most common and the most malignant primary brain tumor and is characterized by rapid proliferation, invasion into surrounding normal brain tissues, and consequent aberrant vascularization. In these characteristics of GBM, invasive properties are responsible for its recurrence after various therapies. The histomorphological patterns of glioma cell invasion have often been referred to as the “secondary structures of Scherer.” The “secondary structures of Scherer” can be classified mainly into four histological types as (i) perineuronal satellitosis, (ii) perivascular satellitosis, (iii) subpial spread, and (iv) invasion along the white matter tracts. In order to develop therapeutic interventions to mitigate glioma cell migration, it is important to understand the biological mechanism underlying the formation of these secondary structures. The main focus of this review is to examine new molecular pathways based on the histopathological evidence of GBM invasion as major prognostic factors for the high recurrence rate for GBMs. The histopathology-based pharmacological and biological targets for treatment strategies may improve the management of invasive and resistant GBMs.

On the Impact of Chemo-Mechanically Induced Phenotypic Transitions in Gliomas

Tumor microenvironment is a critical player in glioma progression, and novel therapies for its targeting have been recently proposed. In particular, stress-alleviation strategies act on the tumor by reducing its stiffness, decreasing solid stresses and improving blood perfusion. However, these microenvironmental changes trigger chemo-mechanically induced cellular phenotypic transitions whose impact on therapy outcomes is not completely understood. In this work we analyze the effects of mechanical compression on migration and proliferation of glioma cells. We derive a mathematical model of glioma progression focusing on cellular phenotypic plasticity. Our results reveal a trade-off between tumor infiltration and cellular content as a consequence of stress-alleviation approaches. We discuss how these novel findings increase the current understanding of glioma/microenvironment interactions and can contribute to new strategies for improved therapeutic outcomes.

Evaluation of Three Morphologically Distinct Virus-Like Particles as Nanocarriers for Convection-Enhanced Drug Delivery to Glioblastoma

Glioblastoma is a particularly challenging cancer, as there are currently limited options for treatment. New delivery routes are being explored, including direct intratumoral injection via convection-enhanced delivery (CED). While promising, convection-enhanced delivery of traditional chemotherapeutics such as doxorubicin (DOX) has seen limited success. Several studies have demonstrated that attaching a drug to polymeric nanoscale materials can improve drug delivery efficacy via CED. We therefore set out to evaluate a panel of morphologically distinct protein nanoparticles for their potential as CED drug delivery vehicles for glioblastoma treatment. The panel consisted of three different virus-like particles (VLPs), MS2 spheres, tobacco mosaic virus (TMV) disks and nanophage filamentous rods modified with DOX. While all three VLPs displayed adequate drug delivery and cell uptake in vitro, increased survival rates were only observed for glioma-bearing mice that were treated via CED with TMV disks and MS2 spheres conjugated to doxorubicin, with TMV-treated mice showing the best response. Importantly, these improved survival rates were observed after only a single VLP–DOX CED injection several orders of magnitude smaller than traditional IV doses. Overall, this study underscores the potential of nanoscale chemotherapeutic CED using virus-like particles and illustrates the need for further studies into how the overall morphology of VLPs influences their drug delivery properties.

Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical cues in the microenvironment. Recent studies have shown that miR-451 regulates downstream molecules including AMPK/CAB39/MARK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of the main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this complex process of cell proliferation and invasion and its response to conventional treatment, we propose a mathematical model that analyzes the intracellular dynamics of the miR-451-AMPK- mTOR-cell cycle signaling pathway within a cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress in response to fluctuating glucose levels. We show how up- or down-regulation of components in these pathways affects the key cellular decision to infiltrate or proliferate in a complex microenvironment in the absence and presence of time delays and stochastic noise. Glycosylated chondroitin sulfate proteoglycans (CSPGs), a major component of the extracellular matrix (ECM) in the brain, contribute to the physical structure of the local brain microenvironment but also induce or inhibit glioma invasion by regulating the dynamics of the CSPG receptor LAR as well as the spatiotemporal activation status of resident astrocytes and tumor-associated microglia. Using a multi-scale mathematical model, we investigate a CSPG-induced switch between invasive and non-invasive tumors through the coordination of ECM-cell adhesion and dynamic changes in stromal cells. We show that the CSPG-rich microenvironment is associated with non-invasive tumor lesions through LAR-CSGAG binding while the absence of glycosylated CSPGs induce the critical glioma invasion. We illustrate how high molecular weight CSPGs can regulate the exodus of local reactive astrocytes from the main tumor lesion, leading to encapsulation of non-invasive tumor and inhibition of tumor invasion. These different CSPG conditions also change the spatial profiles of ramified and activated microglia. The complex distribution of CSPGs in the tumor microenvironment can determine the nonlinear invasion behaviors of glioma cells, which suggests the need for careful therapeutic strategies.

Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83–90 days) of cancer cell distant invasion as well as the number (0–2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

Transient alleviation of tumor hypoxia during first days of antiangiogenic therapy as a result of therapy-induced alterations in nutrient supply and tumor metabolism - Analysis by mathematical modeling

A number of experiments on mouse tumor models, as well as certain clinical data, have demonstrated, that antiangiogenic therapy can lead to transient improvement in tumor oxygenation, that allows to increase efficiency of following radiotherapy. In the majority of works, this phenomenon has been explained by enhanced tumor perfusion due to normalization of capillaries' structure, that results in elevated oxygen inflow in tumor. However, changes in tumor perfusion often haven't been directly measured in relevant works, moreover, antiangiogenic therapy has been proven to have ambiguous effect on tumor perfusion both in mouse tumor models and in clinics. Herein, we suggest that elevation of blood perfusion may be not the only reason for transient alleviation of tumor hypoxia, and that it may manifest itself even under unchanged tumor blood flow. We propose that it may be as well caused by the decrease in tumor oxygen consumption rate (OCR) due to the reduction of tumor proliferation level, caused by nutrient shortage in result of antiangiogenic treatment. We provide detailed explanation of this hypothesis and visualize it using a specially developed mathematical model, which takes into account basic features of tumor growth and antiangiogenic therapy. We investigate the influence of the model parameters on oxygen dynamics; demonstrate, that transient alleviation of tumor hypoxia occurs in a fairly wide range of physiologically justified values of parameters; and point out the major factors, that determine oxygen dynamics during antiangiogenic therapy.

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.

Temporally feathered intensity-modulated radiation therapy: A planning technique to reduce normal tissue toxicity

PURPOSE

Intensity-modulated radiation therapy (IMRT) has allowed optimization of three-dimensional spatial radiation dose distributions permitting target coverage while reducing normal tissue toxicity. However, radiation-induced normal tissue toxicity is a major contributor to patients' quality of life and often a dose-limiting factor in the definitive treatment of cancer with radiation therapy. We propose the next logical step in the evolution of IMRT using canonical radiobiological principles, optimizing the temporal dimension through which radiation therapy is delivered to further reduce radiation-induced toxicity by increased time for normal tissue recovery. We term this novel treatment planning strategy "temporally feathered radiation therapy" (TFRT).

METHODS

Temporally feathered radiotherapy plans were generated as a composite of five simulated treatment plans each with altered constraints on particular hypothetical organs at risk (OARs) to be delivered sequentially. For each of these TFRT plans, OARs chosen for feathering receive higher doses while the remaining OARs receive lower doses than the standard fractional dose delivered in a conventional fractionated IMRT plan. Each TFRT plan is delivered a specific weekday, which in effect leads to a higher dose once weekly followed by four lower fractional doses to each temporally feathered OAR. We compared normal tissue toxicity between TFRT and conventional fractionated IMRT plans by using a dynamical mathematical model to describe radiation-induced tissue damage and repair over time.

RESULTS

Model-based simulations of TFRT demonstrated potential for reduced normal tissue toxicity compared to conventionally planned IMRT. The sequencing of high and low fractional doses delivered to OARs by TFRT plans suggested increased normal tissue recovery, and hence less overall radiation-induced toxicity, despite higher total doses delivered to OARs compared to conventional fractionated IMRT plans. The magnitude of toxicity reduction by TFRT planning was found to depend on the corresponding standard fractional dose of IMRT and organ-specific recovery rate of sublethal radiation-induced damage.

CONCLUSIONS

TFRT is a novel technique for treatment planning and optimization of therapeutic radiotherapy that considers the nonlinear aspects of normal tissue repair to optimize toxicity profiles. Model-based simulations of TFRT to carefully conceptualized clinical cases have demonstrated potential for radiation-induced toxicity reduction in a previously described dynamical model of normal tissue complication probability (NTCP).

Advances in Glioblastoma Multiforme Treatment: New Models for Nanoparticle Therapy

The most lethal form of brain cancer, glioblastoma multiforme, is characterized by rapid growth and invasion facilitated by cell migration and degradation of the extracellular matrix. Despite technological advances in surgery and radio-chemotherapy, glioblastoma remains largely resistant to treatment. New approaches to study glioblastoma and to design optimized therapies are greatly needed. One such approach harnesses computational modeling to support the design and delivery of glioblastoma treatment. In this paper, we critically summarize current glioblastoma therapy, with a focus on emerging nanomedicine and therapies that capitalize on cell-specific signaling in glioblastoma. We follow this summary by discussing computational modeling approaches focused on optimizing these emerging nanotherapeutics for brain cancer. We conclude by illustrating how mathematical analysis can be used to compare the delivery of a high potential anticancer molecule, delphinidin, in both free and nanoparticle loaded forms across the blood-brain barrier for glioblastoma.

Developmentally regulated signaling pathways in glioma invasion

Malignant gliomas are the most common, infiltrative, and lethal primary brain tumors affecting the adult population. The grim prognosis for this disease is due to a combination of the presence of highly invasive tumor cells that escape surgical resection and the presence of a population of therapy-resistant cancer stem cells found within these tumors. Several studies suggest that glioma cells have cleverly hijacked the normal developmental program of neural progenitor cells, including their transcriptional programs, to enhance gliomagenesis. In this review, we summarize the role of developmentally regulated signaling pathways that have been found to facilitate glioma growth and invasion. Furthermore, we discuss how the microenvironment and treatment-induced perturbations of these highly interconnected signaling networks can trigger a shift in cellular phenotype and tumor subtype.

Involvement of P2X7 Receptor in Proliferation and Migration of Human Glioma Cells

Previous studies have demonstrated that activation of P2X₇ receptors (P2X₇R) results in the proliferation and migration of some types of tumor. Here, we asked whether and how the activated P2X₇R contribute to proliferation and migration of human glioma cells. Results showed that the number of P2X₇R positive cells was increasing with grade of tumor. In U87 and U251 human glioma cell lines, both expressed P2X₇R and the expression was enhanced by 3′-O-(4-benzoylbenzoyl) ATP (BzATP), the agonist of P2X₇R, and siRNA. Our results also showed that 10 μM BzATP was sufficient to induce the proliferation of glioma cell significantly, while the cell proliferation reached the peak with 100 μM BzATP. Also, the migration of U87 and U251 cells was significantly increased upon BzATP treatment. However, the number of apoptotic cells of U87 and U251 was not significantly changed by BzATP. In addition, the expression of ERK, p-ERK, and proliferating cell nuclear antigen (PCNA) protein was increased in BzATP-treated U87 and U251 glioma cells. PD98059, an inhibitor of the MEK/ERK pathway, blocked the increased proliferation and migration of glioma cells activated by BzATP. These results suggest that ERK pathway is involved in the proliferation and migration of glioma cells induced by P2X₇R activation.

Mathematical modeling identifies optimum lapatinib dosing schedules for the treatment of glioblastoma patients

Human primary glioblastomas (GBM) often harbor mutations within the epidermal growth factor receptor (EGFR). Treatment of EGFR-mutant GBM cell lines with the EGFR/HER2 tyrosine kinase inhibitor lapatinib can effectively induce cell death in these models. However, EGFR inhibitors have shown little efficacy in the clinic, partly because of inappropriate dosing. Here, we developed a computational approach to model the in vitro cellular dynamics of the EGFR-mutant cell line SF268 in response to different lapatinib concentrations and dosing schedules. We then used this approach to identify an effective treatment strategy within the clinical toxicity limits of lapatinib, and developed a partial differential equation modeling approach to study the in vivo GBM treatment response by taking into account the heterogeneous and diffusive nature of the disease. Despite the inability of lapatinib to induce tumor regressions with a continuous daily schedule, our modeling approach consistently predicts that continuous dosing remains the best clinically feasible strategy for slowing down tumor growth and lowering overall tumor burden, compared to pulsatile schedules currently known to be tolerated, even when considering drug resistance, reduced lapatinib tumor concentrations due to the blood brain barrier, and the phenotypic switch from proliferative to migratory cell phenotypes that occurs in hypoxic microenvironments. Our mathematical modeling and statistical analysis platform provides a rational method for comparing treatment schedules in search for optimal dosing strategies for glioblastoma and other cancer types.