Modelling the viscoelastic behaviour of arteries using constituent-based quasi-linear viscoelasticity

Preface It is a pleasure to welcome all participants of the 7 th International Conference on Computational & Mathematical Biomedical Engineering to Milan. This seventh edition is hosted by one of the most prestigious universities in Italy, Politecnico di Milano. CMBE is an important forum for sharing progress and knowledge within the community interested in engineering mathematics, computational and experimental methods applied to biomedical problems. This year's conference has received a large number of abstracts, each of which was peer-reviewed by members of the programme committee and mini-symposia organisers. We would like to thank all the authors and session organisers, committee members and external reviewers for their efforts. The CMBE22 proceedings in electronic format is available to download from the conference web-site. All authors are invited to submit an extended version of their paper to the 'International Journal for Numerical Methods in Biomedical Engineering'. The conference consist of an opening, 2 plenary and 5 keynote lectures, 17 tracks or mini-symposia divided into multiple sessions and 7 standard sessions. CMBE also awards the 'Interna-tional Journal for Numerical Methods in Biomedical Engineering (IJNMBE) Best PhD Award in Biomedical Engineering', in recognition of important contributions to the advancement of computational and/or mathematical biomedical engineering. Finally, we would like to thank all delegates who attended CMBE22 and made its success. iii SUMMARY Arteries are known to exhibit viscoelastic mechanical properties. Given the assumption that a tissue's viscous relaxation rate is independent of the instantaneous local strain, quasi-linear viscoelasticity (QLV) is a convenient mathematical formulation to model viscoelasticity in biological soft tissues. Recent experimental work, however, suggests that the QLV assumption at tissue level may be inadequate to describe arterial viscoelasticity. A possible explanation is that arteries are heterogeneous tissues and viscoelastic properties likely differ between different arterial constituents. Hence, we propose a revised version of QLV in which the QLV assumption is made on a constituent (i.e., elastin and collagen) rather than on a tissue level to attain a deformation-dependent viscoelastic response.