Angiogenic Networks in Tumors—Insights via Mathematical Modeling

Mohsen Dorraki,Anahita Fouladzadeh,Andrew Allison,Claudine S Bonder,Derek Abbott

doi:10.1109/access.2020.2977062

Abstract

Angiogenesis, the formation of a network of blood vessels, is a vital process in the growth of solid tumors as it delivers required nutrients and oxygen. Prior medical studies assert that angiogenesis is influenced by a number of parameters such as endothelial cell migration and proliferation, existence of tumor angiogenesis factors, oxygen, extracellular matrix components, etc. Along with the early developments and findings in the area of tumor angiogenesis, a field of research that has emerged uses mathematical models to interpret and predict the time-course of the crucial factors, as well as new capillary vessel formation, loop formation, and vessel branching. However, most of these early mathematical approaches rely on a small number of parameters; and the characteristics of blood flow, which are significant factors in tumor vessel formation, are neglected. Relatively new integrated models based on the impact of multiple crucial factors and blood flow have seen some success in elucidating the behavior of angiogenesis. Here we review the contributions, opportunities, progress, and challenges of mathematical and computational models for understanding of the tumor-induced angiogenesis, and also consider studies that apply mathematical models to represent blood flow and opportunities for the investigation of therapies and treatments. At the same time, we identify a need for the inclusion of endothelial cell shape and dynamics in models of tumor-induced angiogenesis. Particularly, cell-matrix, cell shape, and cell-cell interaction is necessary for the explanation of blood vessel formation.

Highlights

Within the human body, tissue requires access to a blood supply for the provision of both oxygen and nutrients. This occurs via a connected network of blood vessels, which spans over 100,000 kilometers in each human adult
CRUCIAL AGENTS IN ANGIOGENESIS More than a dozen different proteins have been identified as pro-angiogenic, including vascular endothelial growth factor (VEGF), basic fibroblast growth factor, angiogenin, transforming growth factor (TGF)-α, TGF-β, tumor necrosis factor (TNF)-α, platelet-derived endothelial growth factor, granulocyte colony-stimulating factor, placental growth factor, interleukin-8, hepatocyte growth factor, and epidermal growth factor [13]
Building upon a simple 1D model [77], a two-dimensional model tracks motion of an endothelial cells (ECs) population n, at or near a capillary sprout tip [87]. In this 2D model, the tumor angiogenesis factors’ (TAF) gradient is considered as the chemotactic flux, and the fibronectin gradients are used as the haptotaxis term in Equation 2

Summary

INTRODUCTION

Tissue requires access to a blood supply for the provision of both oxygen and nutrients. Dorraki et al.: Angiogenic Networks in Tumors—Insights via Mathematical Modeling inducible factor (HIF1α) in ECs, which in turn stimulates the transcription and production of angiogenic factors such as vascular endothelial growth factor (VEGF)-A as well as the expression of the cognate receptor VEGFR2 [14] These pro-angiogenic factors activate ECs to form filapodia expressing tip cells that become the leading edge of a new sprouting vessel. These important biological interactions have inspired studies on the angiogenic process via mathematical and computational models to provide new insight on how ECs form vessels and thereby promising improved understanding of how tumors grow and cancer progresses. We discuss the association of tumor vascular structures and therapies

CRUCIAL AGENTS IN ANGIOGENESIS

HOW CAN A CONTINUUM APPROACH CONSTRUCT A PRIMARY MODEL OF TUMOR ANGIOGENESIS?

MODELING BLOOD FLOW

CELL DYNAMICS MODELS

VIII. DISCUSSION AND CONCLUSION