Direct and inverse identification of constitutive parameters from the structure of soft tissues. Part 1: micro- and nanostructure of collagen fibers

Marino, Michele; Hoegen, Markus von; Schröder, Jörg; Wriggers, Peter

doi:10.1007/s10237-018-1009-8

Cited by 16 publications

(4 citation statements)

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“…We focus on the mechanical properties of two general families of fibres under tension in the current study; however, in a more complex setting, various generalisations of (2.4) are available, e.g. those accounting for fibre dispersion [15], slackness [40], and buckling under compression [61].…”

Section: Fibre Behaviourmentioning

confidence: 99%

Rational choice of modelling assumptions for simulation of blood vessel end-to-side anastomosis

Tagiltsev¹,

Parshin²,

Shutov³

2022

Math. Model. Nat. Phenom.

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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.

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Section: Fibre Behaviourmentioning

confidence: 99%

Rational choice of modelling assumptions for simulation of blood vessel end-to-side anastomosis

Tagiltsev¹,

Parshin²,

Shutov³

2022

Math. Model. Nat. Phenom.

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“…An appropriate calibration of these coefficients is necessary to ensure that the numerical model mimics the actual physical behavior [5]. Numerical parametric studies, consisting of analyzing the influence of the parameter values on the solutions, are typically used to perform the identification.…”

Section: Introductionmentioning

confidence: 99%

Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

Olivier

Ryckelynck

Cortial

2019

MCA

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This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients. Math. Comput. Appl. 2019, 24, 17 2 of 17 the conducting of parametric studies. In particular, the robustness of the calibration process can be dramatically improved using surrogate model approaches.The idea of representing the set of all possible parameter-dependent solutions of ODEs and PDEs as a multiway tensor was pioneered with the introduction of the Proper Generalized Decomposition (PGD) [6][7][8]. In this representation, each dimension corresponds to a spatial/temporal coordinate or a parameter coefficient. The resulting tensor is never assembled explicitly, but instead remains an abstract object for which a low-rank approximation based on a canonical polyadic decomposition [9] is computed. The PGD method further alleviates the curse of dimensionality by introducing a multidimensional weak formulation over the entire parameter space, and the solutions are sought in a particular form where all variables are separated. When differential operators admit a tensor decomposition, the PGD method is very efficient because the multiple integrals involved in the multidimensional weak form of the equations can be rewritten as a sum of products of simple integrals.Unfortunately, realistic constitutive equations or even less sophisticated elasto-viscoplastic models admit no tensor decomposition with respect to the material coefficients and the time variables. An extension of the PGD to highly nonlinear laws is therefore non-trivial. However, many other tensor decomposition approaches have been successfully proposed to approximate functions or solutions of differential equations defined over high-dimensional spaces. We refer the reader to [10-12] for detailed reviews on tensor decomposition techniques and their applications.Among the existing formats-CP decomposition [9,13,14], Tucker decomposition [11,15], hierarchical Tucker decomposition [11,16]-this work investigates the Tensor-Train (TT) decomposition [17,18]. The TT-cross algorithm, introduced in [17] and further developed in [19,20], is a sampling procedure to build an approximation of a given tensor under the tensor-train format. Sampling procedures in parameter space have proven their ability to reduce nonlinear and non-separable DAEs by using the Proper Orthogonal Decomposition (POD) [21], the gappy...

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“…This investigation technique allows defining the principal features of a tissue's mechanical behavior, with particular regard to isotropic or anisotropic configuration, linear or non-linear elastic phenomena, time-dependent effects, etc. [17,18] On the other hand, a morphometric investigation by means of anatomical sections, ultrasonography, CT, and MRI data, leads to 3D CAD models of the anatomical district [19][20][21], which are mandatory for developing computational models. Mechanical tests are performed at tissue and structure levels [22,23].…”

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confidence: 99%

“…Experimental activities provide data for the development of computational models. In detail, results from mechanical tests at the tissue level, together with preliminary hypotheses from the histological analysis, determine the constitutive formulation that actually interprets tissue mechanics [17,18]. Regarding constitutive modeling, it is necessary to report the complexity of hollow organ tissue mechanics.…”

mentioning

confidence: 99%

Biomechanics of Hollow Organs: Experimental Testing and Computational Modeling

Fontanella

Carniel

2023

Bioengineering

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Direct and inverse identification of constitutive parameters from the structure of soft tissues. Part 1: micro- and nanostructure of collagen fibers

Cited by 16 publications

References 50 publications

Rational choice of modelling assumptions for simulation of blood vessel end-to-side anastomosis

Rational choice of modelling assumptions for simulation of blood vessel end-to-side anastomosis

Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

Biomechanics of Hollow Organs: Experimental Testing and Computational Modeling

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