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2.5D Model for Ex Vivo Mechanical Characterization of Sprouting Angiogenesis in Living Tissue

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Mathematical modelling of tissue-engineered angiogenesis.

Greg Lemon¹, Daniel Howard, Matthew J Tomlinson

¹School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.

Mathematical Biosciences

|July 22, 2009

Summary

A mathematical model simulates porous scaffold vascularization in vivo. Prevascularization strategies, like seeding with vascular cells, can overcome cell loss and improve tissue integration.

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Area of Science:

Biomedical Engineering
Mathematical Biology
Tissue Engineering

Background:

Vascularization is crucial for porous scaffold integration after implantation.
Mathematical modeling offers insights into complex biological processes like tissue ingrowth.

Purpose of the Study:

To develop a mathematical model for in vivo porous scaffold vascularization.
To analyze the influence of various parameters on scaffold vascularization extent.
To investigate strategies for enhancing scaffold vascularization.

Main Methods:

A system of coupled non-linear ordinary differential equations (ODEs) was formulated.
Bifurcation analysis was employed to study parameter dependencies.
Model predictions were compared with experimental data from the chick chorioallantoic membrane (CAM) assay.

Main Results:

The model predicts how scaffold vascularization evolves over time.
Bifurcation analysis identified key parameters influencing vascularization.
A prevascularization strategy using seeded vascular cells can mitigate cell loss due to slow infiltration.

Conclusions:

The mathematical model provides a framework for understanding scaffold vascularization dynamics.
Prevascularization is a viable strategy to improve cell survival and tissue integration.
The model offers a basis for optimizing scaffold design and implantation protocols.