A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

Coccarelli, A., Carson, J. M., Aggarwal, A. and Pant, S. (2021) A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations. Biomechanics and Modeling in Mechanobiology, 20(4), pp. 1231-1249. (doi: 10.1007/s10237-021-01437-5) (PMID:33683514)

Abstract

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

• Item Type: Articles
• Additional Information: A.C. gratefully acknowledges the support provided by the College of Engineering, Swansea University. J.M.C gratefully acknowledges the support of Health Data Research UK [MR/ S004076/1], which is funded by the UK Medical Research Council, Engineering and Physical Sciences Research Council, Economic and Social Research Council, Department of Health and Social Care (England), Chief Scientist Office of the Scottish Government Health and Social Care Directorates, Health and Social Care Research and Development Division (Welsh Government), Public Health Agency (Northern Ireland), British Heart Foundation and the Wellcome Trust. A.A. gratefully acknowledges the support from Engineering and Physical Sciences Research Council of the UK (Grant Nos. EP/P018912/1 and EP/P018912/2). S.P. gratefully acknowledges the support from Engineering and Physical Sciences Research Council of the UK (Grant Nos. EP/R010811/1).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Aggarwal, Dr Ankush
• Authors: Coccarelli, A., Carson, J. M., Aggarwal, A., and Pant, S.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Biomechanics and Modeling in Mechanobiology
• Publisher: Springer
• ISSN: 1617-7959
• ISSN (Online): 1617-7940
• Published Online: 08 March 2021
• Copyright Holders: Copyright © 2021 The Authors
• First Published: First published in Biomechanics and Modeling in Mechanobiology 20(4): 1231-1249
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
306966		Predicting cardiovascular biomechanical stiffening due to the interplay of tissue layers with focus on calcific aortic valve disease	Ankush Aggarwal	Engineering and Physical Sciences Research Council (EPSRC)	EP/P018912/2	ENG - Infrastructure & Environment