Multi-sector approximation method for arteries: the residual stresses of circumferential rings with non-trivial openings

Sigaeva, Taisiya; Destrade, Michel; Martino, Elena S. Di

doi:10.1098/rsif.2019.0023

Cited by 10 publications

(7 citation statements)

References 29 publications

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“…Needless to say, this is not always true, particularly in opening angle studies of arteries, where a single cut of an arterial ring can have a non-uniform curvature. 25 In addition, with the cylindrical assumption, we cannot model the experimental observation that opening angles are location-dependent, with higher values at heart apex. 21 Indeed, the ''true'' residual stress can only be achieved through infinite cuts using the opening angle method, which is not practical.…”

Section: Discussionmentioning

confidence: 99%

Residual Stress Estimates from Multi-cut Opening Angles of the Left Ventricle

Zhuan

Luo

2020

Cardiovasc Eng Tech

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Purpose-Residual stress tensor has an essential influence on the mechanical behaviour of soft tissues and can be particularly useful in evaluating growth and remodelling of the heart and arteries. It is currently unclear if one single radial cut using the opening angle method can accurately estimate the residual stress. In many previous models, it has been assumed that a single radial cut can release the residual stress in a ring of the artery or left ventricle. However, experiments by Omens et al. (Biomech Model Mechanobiol 1:267-277, 2003) on mouse hearts, have shown that this is not the case. The aim of this paper is to answer this question using a multiple-cut mathematical model. Methods-In this work, we have developed models of multiple cuts to estimate the residual stress in the left ventricle and compared with the one-cut model. Both two and four-cut models are considered. Given that the collagen fibres are normally coiled in the absence of loading, we use the isotropic part of the Holzapfel-Ogden strain energy function to model the unloaded myocardium. Results-The estimated residual hoop stress from our multiple-cut model is around 8 to 9 times greater than that of a single-cut model. Although in principle infinite cuts are required to release the residual stress, we find four cuts seem to be sufficient as the model agrees well with experimental measurements of the myocardial thickness. Indeed, even the two-cut model already gives a reasonable estimate of the maximum residual hoop stress. We show that the results are not significantly different using homogeneous or heterogeneous material models. Finally, we explain that the multiple cuts approach also applies to arteries. Conclusion-We conclude that both radial and circumferential cuts are required to release the residual stress in the left ventricle; using multiple radial cuts alone is not sufficient. A multiple-cut model gives a marked increase of residual stress in a left ventricle ring compared to that of the commonly used single-cut model.

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Section: Discussionmentioning

confidence: 99%

Residual Stress Estimates from Multi-cut Opening Angles of the Left Ventricle

Zhuan

Luo

2020

Cardiovasc Eng Tech

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“…This work takes as reference the study by Rivera et al (2020) , which consists of the passive mechanical characterization of the aortic artery of lambs born and raised under conditions of chronic hypoxia (3,600 m above sea level) with and without melatonin application. As the subject of analysis, emphasis is placed on a specific sample of the abdominal zone of a control group lamb (33 days old and 9.1 kg weight at the time of euthanasia with injection of sodium thiopental, 100 mg kg −1 ), whose stress-free configuration (after the ring-opening test) presented a highly variable curvature, so that the geometric assumptions of the most widely used methodologies ( Chuong and Fung, 1986 ; Sigaeva et al, 2019 ) lose representativeness of the physical phenomenon.…”

Section: Methodsmentioning

confidence: 99%

“…Although the hypothesis was successfully verified, the geometry changes exhibited within each segment, such as curvature differences, were not analyzed. Sigaeva et al (2019) has proposed a method that consists of assessing the non-uniform geometries with a multi-sector approximation, in which the entire ring shape is mathematically discretized into different arc sectors, calculating the stretches and stresses in each one of them, with both theoretical and numerical approaches. Ohayon et al (2007) have investigated the effects of residual strains and stresses in tissues with vulnerable plaque, using patient-specific geometries produced by the opened shape of the diseased tissues to evaluate the stress field using a finite element analysis.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the geometrical influence of ring-opening samples on arterial circumferential residual stress reconstruction

Inostroza,

Utrera,

García-Herrera

et al. 2023

Front. Bioeng. Biotechnol.

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This work consists of analyzing the impact of geometrical features (thickness and curvature) on the estimation of circumferential residual stresses in arteries. For this purpose, a specific sample of lamb abdominal artery is chosen for analysis and, through computational tools based on Python libraries, the stress-free geometry is captured after the ring opening test. Numerical simulations are then used to reconstruct the sample in order to estimate the circumferential residual stresses. Then, four stress-free geometry models are analyzed: an ideal geometry, i.e., constant curvature and thickness; a constant curvature and variable thickness geometry; a variable curvature and constant thickness geometry; and a variable curvature and thickness geometry. The numerical results show that models perform well from a geometric point of view, where the most different feature was the closed outer perimeter that differs about 14% from the closed real sample. As far as residual stress is concerned, differences up to 198% were found in more realistic models taking a constant curvature and thickness model as reference. Thus, the analysis of a realistic geometry with highly variable curvature and thickness can introduce, compared to an idealized geometry, significant differences in the estimation of residual stresses. This could indicate that the characterization of arterial residual stresses is not sufficient when considering only the opening angle and, therefore, it is also necessary to incorporate more geometrical variables.

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“…Recently, in 2019 and 2021, respectively, Sigaeva et al. ( 2019 ) and Lefloch et al. ( 2021 ) developed novel ways of assessing residual strains without this perfect circle assumption to make the measurement of tissue rings more accurate, particularly when the tissue being investigated is diseased (as these specimens are often more irregular compared to healthy tissue).…”

Section: Experimental Techniquesmentioning

confidence: 99%

Mechanical experimentation of the gastrointestinal tract: a systematic review

Durcan,

Hossain,

Chagnon

et al. 2023

Biomech Model Mechanobiol

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The gastrointestinal (GI) organs of the human body are responsible for transporting and extracting nutrients from food and drink, as well as excreting solid waste. Biomechanical experimentation of the GI organs provides insight into the mechanisms involved in their normal physiological functions, as well as understanding of how diseases can cause disruption to these. Additionally, experimental findings form the basis of all finite element (FE) modelling of these organs, which have a wide array of applications within medicine and engineering. This systematic review summarises the experimental studies that are currently in the literature (n = 247) and outlines the areas in which experimentation is lacking, highlighting what is still required in order to more fully understand the mechanical behaviour of the GI organs. These include (i) more human data, allowing for more accurate modelling for applications within medicine, (ii) an increase in time-dependent studies, and (iii) more sophisticated in vivo testing methods which allow for both the layer- and direction-dependent characterisation of the GI organs. The findings of this review can also be used to identify experimental data for the readers’ own constitutive or FE modelling as the experimental studies have been grouped in terms of organ (oesophagus, stomach, small intestine, large intestine or rectum), test condition (ex vivo or in vivo), number of directions studied (isotropic or anisotropic), species family (human, porcine, feline etc.), tissue condition (intact wall or layer-dependent) and the type of test performed (biaxial tension, inflation–extension, distension (pressure-diameter), etc.). Furthermore, the studies that investigated the time-dependent (viscoelastic) behaviour of the tissues have been presented.

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Multi-sector approximation method for arteries: the residual stresses of circumferential rings with non-trivial openings

Cited by 10 publications

References 29 publications

Residual Stress Estimates from Multi-cut Opening Angles of the Left Ventricle

Residual Stress Estimates from Multi-cut Opening Angles of the Left Ventricle

Analysis of the geometrical influence of ring-opening samples on arterial circumferential residual stress reconstruction

Mechanical experimentation of the gastrointestinal tract: a systematic review

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