Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution

Ezquerro, Francisco; Vacas, Francisco García; Postigo, Sergio; Prado, María; Simón, A.

doi:10.1016/j.medengphy.2010.09.010

Cited by 24 publications

(14 citation statements)

References 33 publications

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“…This method allows the individual contributions of the fibers and the matrix of the AF to be determined. On the other hand, a model developed by Ezquerro et al [11] represented the NP as incompressible and hyperelastic using the Mooney-Rivlin energy function with two constants, and the AF was modeled as a fiber setup embedded into a matrix. They used a polynomial hyperelastic function for the matrix and stress-strain curves for the fibers.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus

Jaramillo

2018

Mathematical Problems in Engineering

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Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the intervertebral disc is nonlinear, heterogeneous, and anisotropic and, due to the low permeability, is usually represented as a hyperelastic model. The intervertebral disc is composed of the nucleus pulposus, the endplates, and the annulus fibrosus. The annulus fibrosus is modeled as a hyperelastic matrix reinforced with several fiber families, and researchers have used different strain energy density functions to represent it. This paper presents a comparative study between the strain energy density functions most frequently used to represent the mechanical behavior of the annulus fibrosus: the Yeoh and Mooney-Rivlin functions. A finite element model of the annulus fibrosus of the L4-L5 segment under the action of three independent and orthogonal moments of 8 N-m was used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction of annulus fibrosus and tetrahedron elements for the endplates were used, and an exponential energy function was employed to represent the mechanical behavior of the fibers. A total of 16 families were used; the fiber orientation varied with the radial coordinate from 25° on the outer boundary to 46° on the inner boundary, measuring it with respect to the transverse plane. The mechanical constants were taken from the reported literature. The range of motion was obtained by finite element analysis using different values of the mechanical constants and these results were compared with the reported experimental data. It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear region.

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Section: Introductionmentioning

confidence: 99%

Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus

Jaramillo

2018

Mathematical Problems in Engineering

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“…However, Naserkhaki et al (2018) did not take the consequently arising step: to follow the instruction at the end of the abstract from Heuer et al (2007) and generate own ligament characteristics by modeling the experiment backward. In fact, to our knowledge, only one FE group accepted this challenge so far (Ezquerro et al 2011). They obtained purely exponential, even more pliable ligament characteristics than we did in our Fig.…”

Section: Commendations and Critics Of The Stepwise Reduction Experimentsmentioning

confidence: 49%

Lumbar spinal ligament characteristics extracted from stepwise reduction experiments allow for preciser modeling than literature data

Damm

Rockenfeller

Gruber

2019

Biomech Model Mechanobiol

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Lumbar ligaments play a key role in stabilizing the spine, particularly assisting muscles at wide-range movements. Hence, valid ligament force-strain data are required to generate physiological model predictions. These data have been obtained by experiments on single ligaments or functional units throughout the literature. However, contrary to detailed spine geometries, gained, for instance, from CT data, ligament characteristics are often inattentively transferred to multi-body system (MBS) or finite element models. In this paper, we use an elaborated MBS model of the lumbar spine to demonstrate how individualized ligament characteristics can be obtained by reversely reenacting stepwise reduction experiments, where the range of motion (ROM) was measured. We additionally validated the extracted characteristics with physiological experiments on intradiscal pressure (IDP). Our results on a total of in each case 160 ROM and 49 IDP simulations indicated superiority of our procedure (seven and eight outliers) toward the incorporation of classical literature data (on average 71 and 31 outliers).Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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“…In this work we have selected DE, which has already been used in the parameter calibration of several simulation models [81,82]. It is an efficient continuous optimization technique that is able to work with a relative small population size.…”

Section: Differential Evolution and Model Calibrationmentioning

confidence: 99%

Model calibration using a parallel differential evolution algorithm in computational neuroscience: Simulation of stretch induced nerve deficit

LaTorre¹,

Kwong²,

García-Grajales³

et al. 2020

Journal of Computational Science

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Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution

Cited by 24 publications

References 33 publications

Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus

Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus

Lumbar spinal ligament characteristics extracted from stepwise reduction experiments allow for preciser modeling than literature data

Model calibration using a parallel differential evolution algorithm in computational neuroscience: Simulation of stretch induced nerve deficit

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