A non-linear viscoelastic model for the tympanic membrane

Motallebzadeh, Hamid; Charlebois, Mathieu; Funnell, W. Robert J.

doi:10.1121/1.4828831

Cited by 20 publications

(11 citation statements)

References 32 publications

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“…As key examples in the transversely isotropic (TI) scalar relaxation function QLV context, Huyghe et al [16] considered such an implementation for heart muscle tissue, Puso and Weiss [17] studied ligaments, Sahoo et al [18] and Chatelin et al [19] studied the brain, Motallebzadeh et al [20], the eardrum and Jennesar et al [21] focused on the spinal cord under tension. Vena et al implemented incompressible QLV with a scalar relaxation function but with separate relaxation contributions from fibres and matrix [22].…”

Section: Introductionmentioning

confidence: 99%

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

2018

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The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

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Section: Introductionmentioning

confidence: 99%

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

2018

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“…(4) Biological tissues can be expected to have frequency-dependent behaviour (e.g. Cheng et al 2007;Luo et al 2009a, b;Motallebzadeh et al 2013aMotallebzadeh et al , 2015, but in the models here, all material properties are assumed to be constant across frequencies. Such potential frequency dependence should be taken into account when the models are refined.…”

Section: Displacement Patternsmentioning

confidence: 99%

“…Since then, this method has been widely used to investigate different aspects of both human and animal ears (e.g. Wada et al 1992;Ladak and Funnell 1996;Koike et al 2002;Gan et al 2004; Motallebzadeh et al 2013a). Qi et al (2006Qi et al ( , 2008 developed nonlinear finite-element models of the newborn ear canal and middle ear.…”

Section: Introductionmentioning

confidence: 99%

Finite-Element Modelling of the Acoustic Input Admittance of the Newborn Ear Canal and Middle Ear

Motallebzadeh

Maftoon

Pitaro

et al. 2016

JARO

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Admittance measurement is a promising tool for evaluating the status of the middle ear in newborns. However, the newborn ear is anatomically very different from the adult one, and the acoustic input admittance is different than in adults. To aid in understanding the differences, a finite-element model of the newborn ear canal and middle ear was developed and its behaviour was studied for frequencies up to 2000 Hz. Material properties were taken from previous measurements and estimates. The simulation results were within the range of clinical admittance measurements made in newborns. Sensitivity analyses of the material properties show that in the canal model, the maximum admittance and the frequency at which that maximum admittance occurs are affected mainly by the stiffness parameter; in the middle-ear model, the damping is as important as the stiffness in influencing the maximum admittance magnitude but its effect on the corresponding frequency is negligible. Scaling up the geometries increases the admittance magnitude and shifts the resonances to lower frequencies. The results suggest that admittance measurements can provide more information about the condition of the middle ear when made at multiple frequencies around its resonance.

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“…Some studies have used hyperelastic (e.g., Aernouts et al 2010) or visco-hyperelastic (Motallebzadeh et al 2013) constitutive equations for the pars tensa.…”

Section: Baseline Materials Propertiesmentioning

confidence: 99%

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound

Maftoon

Funnell

Daniel

et al. 2015

JARO

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We present a finite-element model of the gerbil middle ear that, using a set of baseline parameters based primarily on a priori estimates from the literature, generates responses that are comparable with responses we measured in vivo using multi-point vibrometry and with those measured by other groups. We investigated the similarity of numerous features (umbo, pars-flaccida and pars-tensa displacement magnitudes, the resonance frequency and break-up frequency, etc.) in the experimental responses with corresponding ones in the model responses, as opposed to simply computing frequency-by-frequency differences between experimental and model responses. The umbo response of the model is within the range of variability seen in the experimental data in terms of the low-frequency (i.e., well below the middle-ear resonance) magnitude and phase, the main resonance frequency and magnitude, and the roll-off slope and irregularities in the response above the resonance frequency, but is somewhat high for frequencies above the resonance frequency. At low frequencies, the ossicular axis of rotation of the model appears to correspond to the anatomical axis but the behaviour is more complex at high frequencies (i.e., above the pars-tensa break-up). The behaviour of the pars tensa in the model is similar to what is observed experimentally in terms of magnitudes, phases, the break-up frequency of the spatial vibration pattern, and the bandwidths of the high-frequency response features. A sensitivity analysis showed that the parameters that have the strongest effects on the model results are the Young's modulus, thickness and density of the pars tensa; the Young's modulus of the stapedial annular ligament; and the Young's modulus and density of the malleus. Displacements of the tympanic membrane and manubrium and the lowfrequency displacement of the stapes did not show large changes when the material properties of the incus, stapes, incudomallear joint, incudostapedial joint, and posterior incudal ligament were changed by ±10 % from their values in the baseline parameter set.

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A non-linear viscoelastic model for the tympanic membrane

Cited by 20 publications

References 32 publications

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

Finite-Element Modelling of the Acoustic Input Admittance of the Newborn Ear Canal and Middle Ear

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound

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