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

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.

Current Advances in the Use of Tissue Engineering for Cancer Metastasis Therapeutics

Cancer is a leading cause of death worldwide and results in nearly 10 million deaths each year. The global economic burden of cancer from 2020 to 2050 is estimated to be USD 25.2 trillion. The spread of cancer to distant organs through metastasis is the leading cause of death due to cancer. However, as of today, there is no cure for metastasis. Tissue engineering is a promising field for regenerative medicine that is likely to be able to provide rehabilitation procedures to patients who have undergone surgeries, such as mastectomy and other reconstructive procedures. Another important use of tissue engineering has emerged recently that involves the development of realistic and robust in vitro models of cancer metastasis, to aid in drug discovery and new metastasis therapeutics, as well as evaluate cancer biology at metastasis. This review covers the current studies in developing tissue-engineered metastasis structures. This article reports recent developments in in vitro models for breast, prostate, colon, and pancreatic cancer. The review also identifies challenges and opportunities in the use of tissue engineering toward new, clinically relevant therapies that aim to reduce the cancer burden.

Understanding Glioblastoma Signaling, Heterogeneity, Invasiveness, and Drug Delivery Barriers

The most prevalent and aggressive type of brain cancer, namely, glioblastoma (GBM), is characterized by intra- and inter-tumor heterogeneity and strong spreading capacity, which makes treatment ineffective. A true therapeutic answer is still in its infancy despite various studies that have made significant progress toward understanding the mechanisms behind GBM recurrence and its resistance. The primary causes of GBM recurrence are attributed to the heterogeneity and diffusive nature; therefore, monitoring the tumor's heterogeneity and spreading may offer a set of therapeutic targets that could improve the clinical management of GBM and prevent tumor relapse. Additionally, the blood-brain barrier (BBB)-related poor drug delivery that prevents effective drug concentrations within the tumor is discussed. With a primary emphasis on signaling heterogeneity, tumor infiltration, and computational modeling of GBM, this review covers typical therapeutic difficulties and factors contributing to drug resistance development and discusses potential therapeutic approaches.

Morphological instability of solid tumors in a nutrient-deficient environment

A phenomenological reaction-diffusion model that includes a nutrient-regulated growth rate of tumor cells is proposed to investigate the morphological instability of solid tumors during the avascular growth. We find that the surface instability could be induced more easily when tumor cells are placed in a harsher nutrient-deficient environment, while the instability is suppressed for tumor cells in a nutrient-rich environment due to the nutrient-regulated proliferation. In addition, the surface instability is shown to be influenced by the growth moving speed of tumor rims. Our analysis reveals that a larger growth movement of the tumor front results in a closer proximity of tumor cells to a nutrient-rich region, which tends to inhibit the surface instability. A nourished length that represents the proximity is defined to illustrate its close relation to the surface instability.

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.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

Towards an Established Intraoperative Oncological Favorable Tool: Results of Fluorescein-Guided Resection from a Monocentric, Prospective Series of 93 Primary Glioblastoma Patients

It is commonly reported that maximizing surgical resection of contrast-enhancing regions in patients with glioblastoma improves overall survival. Efforts to achieve an improved rate of resection have included several tools: among those, the recent widespread of fluorophores. Sodium fluorescein is an unspecific, vascular dye which tends to accumulate in areas with an altered blood-brain barrier. In this retrospective analysis of patients prospectively enrolled in the FLUOCERTUM study, we aimed to assess the role of fluorescein-guided surgery on surgical radicality, survival, and morbidity. A retrospective review based on 93 consecutively and prospectively enrolled IDH wild-type glioblastoma patients (2016-2022) was performed; fluorescence characteristics, rate of resection, clinical outcome, and survival were analyzed. No side effect related to fluorescein occurred; all of the tumors presented a strong yellow-green enhancement and fluorescein was judged fundamental in distinguishing tumors from viable tissue in all cases. Gross total resection was achieved in 77 cases out of 93 patients (82.8%). After a mean follow-up time of 17.4 months (3-78 months), the median progression-free survival was 12 months, with a PFS-6 and PFS-12 of 94.2% and 50%, respectively, whereas median overall survival was estimated to be 16 months; survival at 6, 12, and 24 months was 91.8%, 72.3%, and 30.1%, respectively. Based on these results, we can assert that the fluorescein-guided technique is a safe and valuable method for patients harboring a newly diagnosed, untreated glioblastoma.

Earlier Detection of Brain Tumor by Pre-Processing Based on Histogram Equalization with Neural Network

MRI is an influential diagnostic imaging technology specifically worn to detect pathological changes in tissues with organs early. It is also a non-invasive imaging method. Medical image segmentation is a complex and challenging process due to the intrinsic nature of images. The most consequential imaging analytical approach is MRI, which has been in use to detect abnormalities in tissues and human organs. The portrait was actualized for CAD (computer-assisted diagnosis) utilizing image processing techniques with deep learning, initially to perceive a brain tumor in a person with early signs of brain tumor. Using AHCN-LNQ (adaptive histogram contrast normalization with learning-based neural quantization), the first image is preprocessed. When compared to extant techniques, the simulation outcome shows that this proposed method achieves an accuracy of 93%, precision of 92%, and 94% of specificity.

Agent-based computational modeling of glioblastoma predicts that stromal density is central to oncolytic virus efficacy

Oncolytic viruses (OVs) are emerging cancer immunotherapy. Despite notable successes in the treatment of some tumors, OV therapy for central nervous system cancers has failed to show efficacy. We used an ex vivo tumor model developed from human glioblastoma tissue to evaluate the infiltration of herpes simplex OV rQNestin (oHSV-1) into glioblastoma tumors. We next leveraged our data to develop a computational, model of glioblastoma dynamics that accounts for cellular interactions within the tumor. Using our computational model, we found that low stromal density was highly predictive of oHSV-1 therapeutic success, suggesting that the efficacy of oHSV-1 in glioblastoma may be determined by stromal-to-tumor cell regional density. We validated these findings in heterogenous patient samples from brain metastatic adenocarcinoma. Our integrated modeling strategy can be applied to suggest mechanisms of therapeutic responses for central nervous system cancers and to facilitate the successful translation of OVs into the clinic.

Traveling waves of an FKPP-type model for self-organized growth

We consider a reaction–diffusion system of densities of two types of particles, introduced by Hannezo et al. (Cell 171(1):242–255.e27, 2017). It is a simple model for a growth process: active, branching particles form the growing boundary layer of an otherwise static tissue, represented by inactive particles. The active particles diffuse, branch and become irreversibly inactive upon collision with a particle of arbitrary type. In absence of active particles, this system is in a steady state, without any a priori restriction on the amount of remaining inactive particles. Thus, while related to the well-studied FKPP-equation, this system features a game-changing continuum of steady state solutions, where each corresponds to a possible outcome of the growth process. However, simulations indicate that this system self-organizes: traveling fronts with fixed shape arise under a wide range of initial data. In the present work, we describe all positive and bounded traveling wave solutions, and obtain necessary and sufficient conditions for their existence. We find a surprisingly simple symmetry in the pairs of steady states which are joined via heteroclinic wave orbits. Our approach is constructive: we first prove the existence of almost constant solutions and then extend our results via a continuity argument along the continuum of limiting points.

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.