Simulation of balloon angioplasty in residually stressed blood vessels—Application of a gradient-enhanced fibre damage model

Polindara, César; Waffenschmidt, Tobias; Menzel, Andreas

doi:10.1016/j.jbiomech.2016.01.037

Cited by 21 publications

(8 citation statements)

References 20 publications

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“…However, three‐field formulations similar to the ones investigated here have been proposed in the literature not only in the context of gradient elasticity at small strains . Also for gradient damage at large strains similar mixed formulations have been proposed, where any mathematical analysis (also of the continuous problem) is still missing. Therefore, a comprehensive numerical study on all elements has been conducted at finite strains in order to show potential problems resulting from the expected instabilities at large strains, which were indeed numerically verified.…”

Section: Resultsmentioning

confidence: 94%

Three‐field mixed finite element formulations for gradient elasticity at finite strains

et al. 2019

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Gradient elasticity formulations have the advantage of avoiding geometry‐induced singularities and corresponding mesh dependent finite element solution as apparent in classical elasticity formulations. Moreover, through the gradient enrichment the modeling of a scale‐dependent constitutive behavior becomes possible. In order to remain C0 continuity, three‐field mixed formulations can be used. Since so far in the literature these only appear in the small strain framework, in this contribution formulations within the general finite strain hyperelastic setting are investigated. In addition to that, an investigation of the inf sup condition is conducted and unveils a lack of existence of a stable solution with respect to the L2‐H1‐setting of the continuous formulation independent of the constitutive model. To investigate this further, various discretizations are analyzed and tested in numerical experiments. For several approximation spaces, which at first glance seem to be natural choices, further stability issues are uncovered. For some discretizations however, numerical experiments in the finite strain setting show convergence to the correct solution despite the stability issues of the continuous formulation. This gives motivation for further investigation of this circumstance in future research. Supplementary numerical results unveil the ability to avoid singularities, which would appear with classical elasticity formulations.

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Section: Resultsmentioning

confidence: 94%

Three‐field mixed finite element formulations for gradient elasticity at finite strains

et al. 2019

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“…It is possible that these factors contributed to the changes observed in the C and L groups during the biomechanical tests, since the mechanical tension in the artery wall is dependent on the load applied and the deformed vascular geometry. [31][32][33] Since the biomechanical parameters of the artery wall are to a great extent due to its collagen and elastic fibers, stains specific to these components of the wall were included, but even so, no marked and significant changes were observed in these slides under light microscopy. Borges et al 7 demonstrated that Picrosirius Red analyzed under polarized light, together with conventional light microscopy would be the best method for evaluating the structure of collagen, since it allows the arrangement and grouping of collagen fibers to be studied, because of its normal birefringence.…”

Section: Discussionmentioning

confidence: 99%

Lesão aguda da parede arterial provocada pelo método de interrupção temporária de fluxo em diferentes vias de cirurgia aórtica: estudo morfológico e biomecânico da aorta de porcos

et al. 2020

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Resumo Contexto O clampeamento aórtico e a oclusão da aorta com balão poderiam levar a lesões na parede aórtica. Objetivo O objetivo deste estudo foi verificar as alterações da parede aórtica relacionadas ao método de interrupção de fluxo (cample ou balão) em diferentes técnicas disponíveis para cirurgia de aorta. Métodos Os experimentos foram realizados em 40 porcos fêmeas pesando de 25-30 kg, alocados para quatro grupos: S (n = 10), nenhuma intervenção (sham); C (n = 10), laparotomia mediana transperitoneal para acesso à aorta abdominal infrarrenal com tempo de clampeamento de 60 minutos; L (n = 10), cirurgia laparoscópica da aorta abdominal infrarrenal com tempo de clampeamento de 60 minutos; EV (n = 10), controle aórtico proximal com inserção de cateter-balão para oclusão aórtica por acesso femoral, inflado a fim de promover oclusão aórtica contínua por 60 minutos. Após a eutanásia, as aortas foram removidas e seccionadas para obtenção de espécimes histológicos destinados a análises morfométricas e por microscopia de luz. Os fragmentos longitudinais restantes foram estirados até a ruptura, e determinaram-se padrões mecânicos. Resultados Observou-se redução do limite de proporcionalidade da aorta abdominal, diminuição da rigidez e da carga de ruptura nos grupos submetidos a campleamento aórtico (C e L) em comparação ao grupo EV. Conclusões O campleamento aórtico durante cirurgia aberta ou laparoscópica pode afetar as propriedades mecânicas da aorta, ocasionando redução de resistência da parede aórtica sem desencadear alterações na estrutura histológica da parede aórtica.

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“…The additional boundary conditions require that the displacements of the wedge walls are only allowed to deform in the radial direction (its out‐of‐plane deformations are blocked). Similar approach was, for instance, described in the paper of Polindara et al, where the wedge cross section of 1.125° was used to model a balloon angioplasty.…”

Section: Methodsmentioning

confidence: 99%

The influence of the nylon balloon stiffness on the efficiency of the intra‐aortic balloon occlusion

Gajewski

Szajek

Stępak³

et al. 2019

Numer Methods Biomed Eng

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In interventional procedures, the balloon inflation is used to occlude the artery and thus reduce bleeding. There is no practically accepted measure of the procedure efficiency. A finite element method model with state‐of‐the‐art modelling techniques was built in order to predict the occlusion levels under the influence of different balloon inflation and its material stiffness. The geometries of a healthy human thoracic aorta and an occlusion balloon were idealized. The non‐linear constitutive material of Gasser‐Ogden‐Holzapfel model was employed for the thoracic aorta; the balloon was model as the hyperelastic model. The realistic physiological blood pressure and the balloon inflation pressures were applied to simulate the different occlusion levels. The final outcome shows an important influence of the material stiffness on the balloon deformation and thus the occlusion efficiency.

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Simulation of balloon angioplasty in residually stressed blood vessels—Application of a gradient-enhanced fibre damage model

Cited by 21 publications

References 20 publications

Three‐field mixed finite element formulations for gradient elasticity at finite strains

Three‐field mixed finite element formulations for gradient elasticity at finite strains

Lesão aguda da parede arterial provocada pelo método de interrupção temporária de fluxo em diferentes vias de cirurgia aórtica: estudo morfológico e biomecânico da aorta de porcos

The influence of the nylon balloon stiffness on the efficiency of the intra‐aortic balloon occlusion

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