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

Systematic simulation of tumor cell invasion and migration in response to time-varying rotating magnetic field

Cancer invasion and migration play a pivotal role in tumor malignancy, which is a major cause of most cancer deaths. Rotating magnetic field (RMF), one of the typical dynamic magnetic fields, can exert substantial mechanical influence on cells. However, studying the effects of RMF on cell is challenging due to its complex parameters, such as variation of magnetic field intensity and direction. Here, we developed a systematic simulation method to explore the influence of RMF on tumor invasion and migration, including a finite element method (FEM) model and a cell-based hybrid numerical model. Coupling with the data of magnetic field from FEM, the cell-based hybrid numerical model was established to simulate the tumor cell invasion and migration. This model employed partial differential equations (PDEs) and finite difference method to depict cellular activities and solve these equations in a discrete system. PDEs were used to depict cell activities, and finite difference method was used to solve the equations in discrete system. As a result, this study provides valuable insights into the potential applications of RMF in tumor treatment, and a series of in vitro experiments were performed to verify the simulation results, demonstrating the model's reliability and its capacity to predict experimental outcomes and identify pertinent factors. Furthermore, these findings shed new light on the mechanical and chemical interplay between cells and the ECM, offering new insights and providing a novel foundation for both experimental and theoretical advancements in tumor treatment by using RMF.

Heterogeneous biomechanical/mathematical modeling of spatial prediction of glioblastoma progression using magnetic resonance imaging-based finite element method

BACKGROUND AND OBJECTIVE

Brain tumors are one of the most common diseases and causes of death in humans. Since the growth of brain tumors has irreparable risks for the patient, predicting the growth of the tumor and knowing its effect on the brain tissue will increase the efficiency of treatment strategies.

METHODS

This study examines brain tumor growth using mathematical modeling based on the Reaction-Diffusion equation and the biomechanical model based on continuum mechanics principles. With the help of the image threshold technique of magnetic resonance images, a heterogeneous and close-to-reality environment of the brain has been modeled and experimental data validated the results to achieve maximum accuracy in predicting growth.

RESULTS

The obtained results have been compared with the reported conventional models to evaluate the presented model. In addition to incorporating the chemotherapy effects in governing equations, the real-time finite element analysis of the stress tensors of the surrounding tissue of tumor cells and considering its role in changing the shape and growth of the tumor has added to the importance and accuracy of the current model.

CONCLUSIONS

The comparison of the obtained results with conventional models shows that the heterogeneous model has higher reliability due to the consideration of the appropriate properties for the different regions of the brain. The presented model can contribute to personalized medicine, aid in understanding the dynamics of tumor growth, optimize treatment regimens, and develop adaptive therapy strategies.

Pre-Clinical Models for CAR T-Cell Therapy for Glioma

Immunotherapy represents a transformative shift in cancer treatment. Among myriad immune-based approaches, chimeric antigen receptor (CAR) T-cell therapy has shown promising results in treating hematological malignancies. Despite aggressive treatment options, the prognosis for patients with malignant brain tumors remains poor. Research leveraging CAR T-cell therapy for brain tumors has surged in recent years. Pre-clinical models are crucial in evaluating the safety and efficacy of these therapies before they advance to clinical trials. However, current models recapitulate the human tumor environment to varying degrees. Novel in vitro and in vivo techniques offer the opportunity to validate CAR T-cell therapies but also have limitations. By evaluating the strengths and weaknesses of various pre-clinical glioma models, this review aims to provide a roadmap for the development and pre-clinical testing of CAR T-cell therapies for brain tumors.

Modelling glioblastoma resistance to temozolomide. A mathematical model to simulate cellular adaptation in vitro

Drug resistance is one of the biggest challenges in the fight against cancer. In particular, in the case of glioblastoma, the most lethal brain tumour, resistance to temozolomide (the standard of care drug for chemotherapy in this tumour) is one of the main reasons behind treatment failure and hence responsible for the poor prognosis of patients diagnosed with this disease. In this work, we combine the power of three-dimensional in vitro experiments of treated glioblastoma spheroids with mathematical models of tumour evolution and adaptation. We use a novel approach based on internal variables for modelling the acquisition of resistance to temozolomide that was observed in experiments for a group of treated spheroids. These internal variables describe the cell's phenotypic state, which depends on the history of drug exposure and affects cell behaviour. We use model selection to determine the most parsimonious model and calibrate it to reproduce the experimental data, obtaining a high level of agreement between the in vitro and in silico outcomes. A sensitivity analysis is carried out to investigate the impact of each model parameter in the predictions. More importantly, we show how the model is useful for answering biological questions, such as what is the intrinsic adaptation mechanism, or for separating the sensitive and resistant populations. We conclude that the proposed in silico framework, in combination with experiments, can be useful to improve our understanding of the mechanisms behind drug resistance in glioblastoma and to eventually set some guidelines for the design of new treatment schemes.

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

Tumor proliferation and invasion are intrinsically coupled and unraveled through tunable spheroid and physics-based models

Proliferation and invasion are two key drivers of tumor growth that are traditionally considered independent multicellular processes. However, these processes are intrinsically coupled through a maximum carrying capacity, i.e., the maximum spatial cell concentration supported by the tumor volume, total cell count, nutrient access, and mechanical properties of the tissue stroma. We explored this coupling of proliferation and invasion through in vitro and in silico methods where we modulated the mechanical properties of the tumor and the surrounding extracellular matrix. E-cadherin expression and stromal collagen concentration were manipulated in a tunable breast cancer spheroid to determine the overall impacts of these tumor variables on net tumor proliferation and continuum invasion. We integrated these results into a mixed-constitutive formulation to computationally delineate the influences of cellular and extracellular adhesion, stiffness, and mechanical properties of the extracellular matrix on net proliferation and continuum invasion. This framework integrates biological in vitro data into concise computational models of invasion and proliferation to provide more detailed physical insights into the coupling of these key tumor processes and tumor growth. STATEMENT OF SIGNIFICANCE: Tumor growth involves expansion into the collagen-rich stroma through intrinsic coupling of proliferation and invasion within the tumor continuum. These processes are regulated by a maximum carrying capacity that is determined by the total cell count, tumor volume, nutrient access, and mechanical properties of the surrounding stroma. The influences of biomechanical parameters (i.e., stiffness, cell elongation, net proliferation rate and cell-ECM friction) on tumor proliferation or invasion cannot be unraveled using experimental methods alone. By pairing a tunable spheroid system with computational modeling, we delineated the interdependencies of each system parameter on tumor proliferation and continuum invasion, and established a concise computational framework for studying tumor mechanobiology.