Meitham Amereh

Topic

In-vitro In-silico Modeling of Glioblastoma Tumor Growth and Invasion

Department of Mechanical Engineering

Date & location

• Monday, March 18, 2024

• 9:00 A.M.

• Engineering Office Wing, Room 430 and

• Virtual Defence

Reviewers

Supervisory Committee

• Dr. Mohsen Akbari, Department of Mechanical Engineering, University of Victoria (Co-Supervisor)

• Dr. Ben Nadler, Department of Mechanical Engineering, Uvic (Co-Supervisor)

• Dr. Patrick Walter, Department of Biology, UVic (Outside Member)

• Dr. Roderick Edwards, Department of Mathematics and Statistics, UVic (Outside Member) 

External Examiner

• Dr. Matt Kinsella, Department of Bioengineering, McGill University 

Chair of Oral Examination

• Dr. Falk Herwig, Department of Physics and Astronomy, UVic

Abstract

In this thesis, we investigate various aspects of tumor progression through formation, growth, and invasion, by a multidisciplinary approach involving mathematical modeling and experimental validation. We begin this study by modeling the transient formation of tumors by a system of reaction-diffusion partial differential equations (PDEs) that considers adhesion forces, cell proliferation, and pressure-induced growth. Provide analytical and numerical solutions, the model’s reliability is confirmed through experiments with tumor-cultured human glioblastoma (hGB) cancer cell lines. We expand the model to analyze the instability of radially symmetric growth in response to asymmetric perturbations. By improving the model to incorporate additional variables such as nutrient concentration, consumption rates, and surface tension, we focus on the asymmetric modes of growth, which grow in time and change the spherical configuration of the tumor. This analysis, indicating the natural instability of the spherical configuration of tumor was confirmed by a comparison between the shapes of in-vitro hGB tumoroids and the configuration of the first few asymmetric modes predicted by the model.

 To further understand the effect of tumor microenvironment (TME) on tumor con figuration, we study biomechanical stimuli-induced remodeling of tumors in respond to gradient of external biochemical stimuli, considering the tumor as an evolving material. We develop an evolution law for the remodeling-associated deformation which correlates the remodeling to a characteristic tensor of external biochemical stimuli. The asymmetric remodeling and the induced mechanical stresses are analyzed for different types of biochemical distributions. Using a tumoroid-on-a-chip platform, the degree of remodeling is estimated for the ellipsoidal tumors over time. Additionally, we explore invasion as one of the key hallmarks of tumors by introducing a continuum model that integrates various factors to predict a distinctive shell-type invasion pattern in which cells at the outer layer of the tumor collectively move away from the core and form a shell-type shape. We adopt a non-convex free energy that allows for phase separation to model the motion of the invasive shell.

 To develop a more realistic model, we extend our mathematical framework to include heterogeneities within a tumor as they play a crucial role in cancer diagnosis, treatment, and prognosis. We present a hybrid discrete-continuum (HDC) model incorporating experimental measurements and in-vitro tumor-on-a-chip platforms to study tumor growth, invasion, and their dependency on matrix stiffness. The model integrates the continuum field of variables with a discrete approach and incorporates the random walk method for individual cell migration. The presented framework is capable of distinguishing the growth and invasion of non-resistant versus chemo resistant tumors, as well as the inhibitory effect of a chemotherapeutic drug. This hybrid model, validated against an in-vitro co-culturing of hGB tumors with healthy neurons all embedded within a hydrogel matrix, shows promise in quantitative predictions on volumetric growth, invasion length, and invasion patterns of tumors. 

Our study concludes by highlighting the comprehensive understanding achieved through analytical modeling, experimental validation, and hybrid modeling techniques. The findings lay the groundwork for future investigations into therapeutic interventions, considering the intricate interplay between biological and mechanical factors in the tumor TME.