Math. Model. Nat. Phenom.
Volume 17, 2022
|Number of page(s)||20|
|Published online||11 July 2022|
Rational choice of modelling assumptions for simulation of blood vessel end-to-side anastomosis
Lavrentyev Institute of Hydrodynamics, Pr. Lavrentyeva 15, 630090, Novosibirsk, Russia
2 Novosibirsk State University, Ul. Pirogova 1, 630090 Novosibirsk, Russia
* Corresponding author: email@example.com
Accepted: 6 June 2022
Blood vessels exhibit highly nonlinear, anisotropic behaviour with numerous mechanical interactions. Since exact modelling of all involved effects would yield a computationally prohibitive procedure, a practical clinical simulation tool needs to account for a minimum threshold of relevant factors. In this study, we analyse needed modelling assumptions for a reliable simulation of the end-to-side anastomosis. The artery wall is modelled in a geometrically exact setting as a pre-stressed fibre-reinforced composite. The study focuses on the sensitivity analysis of post-anastomosis stress fields concerning the modelling assumptions. Toward that end, a set of full-scale finite element simulations is carried out for three sensitivity cases: (i) The post-operational stresses are estimated with and without taking the residual stresses into account, (ii) Different geometries of the cut in the recipient vessel are examined, (iii) The influence of errors in material stiffness identification on the post-operational stress field is estimated. The studied cases (i)–(iii) have shown a substantial impact of the considered modelling assumptions on the predictive capabilities of the simulation. Approaches to more accurate predictions of post-operational stress distribution are outlined, and a quest for more accurate experimental procedures is made. As a by-product, the occurrence of the pseudo-aneurysm is explained.
Mathematics Subject Classification: 74L15 / 74B20 / 74S05
Key words: Residual stress / anisotropic hyperelasticity / anastomosis / cut geometry / experimental errors
© The authors. Published by EDP Sciences, 2022
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