Influence of Tissue Mechanics in Blood Vessel Growth

Abstract

Sprouting angiogenesis, the process of creating new blood vessels from pre-existing vasculature, is a fundamental routine in the animal body, being responsible for growth and development, wound healing and, in some cases, pathologies.

Conditions such as cancer and diabetic retinopathy can be treated with the aid of drugs or strategies developed using new knowledge of how blood vessel growth occurs. Some of the results of pre-existing knowledge are already applicable in healthcare, such as antiangiogenic drugs.

Over the last 30 years, researchers have come up with some mathematical models to simulate vascular growth, focusing in specific aspects or a simplified overview of the process. However, almost none of the proposed models account for the mechanical environment experienced by the cells of the capillary network.

This work's goal is to rectify this gap by incorporating mechanical features in a continuum model of angiogenesis. This model is a phase-field approach to the problem that bridges the macroscopic and microscopic descriptions of the process.

The successive steps that were taken from beginning with a standard phase-field model, deriving and integrating the mechanical equations and experimenting with several control parameters are documented and discussed in each appropriate section.

For each step, several possibilities on how to control the system in a way that remained closely tied to the biology perspective were considered. Emulating the tension that the tip cells exert on the extracellular medium by incorporating its analytical description in the equations was chosen.

The results gave enough information that corroborated the success of incorporating mechanical tension in the model, as the vessels that were simulated responded in the way it was expected.

In some cases regression of vessels was observed. This is an important result as, despite being very present in the Biological literature, it had not been successfully modelled within this type of approach.