Computational study of growth and remodelling in the aortic arch

Abstract

Opening angles (OAs) are associated with growth and remodelling in arteries. One curiosity has been the relatively large OAs found in the aortic arch of some animals. Here, we use computational models to explore the reasons behind this phenomenon. The artery is assumed to contain a smooth muscle/collagen phase and an elastin phase. In the models, growth and remodelling of smooth muscle/collagen depends on wall stress and fluid shear stress. Remodelling of elastin, which normally turns over very slowly, is neglected. The results indicate that OAs generally increase with longitudinal curvature (torus model), earlier elastin production during development, and decreased wall stiffness. Correlating these results with available experimental data suggests that all of these effects may contribute to the large OAs in the aortic arch. The models also suggest that the slow turnover rate of elastin limits longitudinal growth. These results should promote increased understanding of the causes of residual stress in arteries.

Keywords:

• artery
• vascular mechanics
• vascular development
• wall stress
• torus
• tissue mechanics

Acknowledgements

This work was supported by NIH grants R01 GM075200 (LAT) and R01 HL64372 (PI: Jay Humphrey). We thank Guy Genin for suggesting the diffusion control of lumen size and shape used in the analysis.

Notes

^1. This simplification was used because including collagen remodelling in the torus models increased computation time by more than an order of magnitude. To test the accuracy of this approximation, we ran some simulations with the cylinder models with and without separate collagen remodelling and found only minor differences for the problems in this paper.

^2. The bulk modulus κ used in this study is several orders of magnitude greater than the material modulus. So in the compressible model, J ^* ≈ 1, and the pressure–radius curves for the cylinder models are nearly identical for the incompressible and slightly compressible cases (results not shown).

^3. Cauchy stress is computed relative to convected base vectors. Thus, circumferential stress in the torus may not correspond to the circumferential direction in the reference configuration.