Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Abstract

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2–3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Cancer as a Model System for Testing Metabolic Scaling Theory

“…The biological processes of tumor growth and angiogenesis represent a unique opportunity to study metabolic scaling theory beyond the vascular regime. Many conventional tumor growth and angiogenesis models are cast as reaction-diffusion processes that highlight different phenomena operating at different scales (Hormuth et al, 2021). Cellular-scale models incorporate any number of terms specific to cellular growth, death, interactions, and importantly include cellular motion due to diffusion, advection and chemical attraction (Frieboes et al, 2010).…”

An image-informed Cahn-Hilliard Keller-Segel multiphase field model for tumor growth with angiogenesis

“…Tumor-associated microvasculature, being responsible for the delivery of cell substrates (e.g. oxygen and nutrients), metabolite removal and drug delivery, influences in a complex way the response of solid tumors to both systemic and radiation therapy [30,23,28]. Indeed, the highly disorganized structure of tumor-induced vasculature yields an heterogeneous distribution of therapeutics throughout the tumor tissues.…”

“…To this end, it seems of crucial importance to study mathematical and computational models, designed on a patient-specific basis, for tumor progression and tumor-induced angiogenesis [28], especially for what concerns those cases that are particularly difficult to be treated with standard therapeutic protocols, such as Glioblastoma Multiforme (GBM). GBM is the most common malignant primary brain tumor in adults.…”

“…In light of these observations, biomathematical theories that accurately describe the multiscale dynamic relationships between tumor growth, vasculature and therapy are needed to design optimized therapies and improve the patients outcome. Despite the numerous theoretical and numerical studies in literature which characterize tumor growth and tumor angiogenesis from the cell to the tissue scale, only a small amount of them relate the models with in-vivo imaging data, especially for what concerns the coupling between tumor growth with angiogenesis [28].…”

“…Mathematical models of tumor angiogenesis can be divided into discrete (with endothelial cells represented as individual objects), continuous (with endothelial cells represented as concentrations), or hybrid (combining both the discrete and the continuum pictures) models [28]. In discrete models, the evolution in time of the vasculature is dictated by a set of rules governing the individual cells behavior.…”