Modelling of muscle behaviour by the finite element method using Hill's three‐element model

Kojic, M.; Mijailovic, Srboljub; Zdravković, Nebojša

doi:10.1002/(sici)1097-0207(19981115)43:5<941::aid-nme435>3.3.co;2-v

Cited by 16 publications

(16 citation statements)

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“…However, none of these models mimics genioglossal activation during the development of negative airway pressure as occurs during respiration. In addition, the existing contractile models for skeletal muscle generally require the shortening velocities of muscle fibers as the model input when calculating the contractile force (14,30,33), which are difficult if not impossible to determine for the genioglossal muscle under complex pharyngeal conditions. A common way to evaluate the activation of a pharyngeal muscle in clinical studies is to measure its electromyogram (EMG) under a variety of conditions.…”

mentioning

confidence: 99%

Computational simulation of human upper airway collapse using a pressure-/state-dependent model of genioglossal muscle contraction under laminar flow conditions

Huang¹,

Malhotra²,

White³

2005

Journal of Applied Physiology

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A three-element, pressure- and state (sleep and wake) -dependent contraction model of the genioglossal muscle was developed based on the microstructure of skeletal muscle and the cross-bridge theory. This model establishes a direct connection between the contractile forces generated in muscle fibers and the measured electromyogram signals during various upper airway conditions. This effectively avoids the difficulty of determining muscle shortening velocity during complex pharyngeal conditions when modeling the muscle's contractile behaviors. The activation of the genioglossal muscle under different conditions was then simulated. A sensitivity analysis was performed to determine the effects of varying each modeled parameter on the muscle's contractile behaviors. This muscle contraction model was then incorporated into our anatomically correct, two-dimensional computational model of the pharyngeal airway to perform a finite-element analysis of air flow, tissue deformation, and airway collapse. The model-predicted muscle deformations are consistent with previous observations regarding upper airway behavior in normal subjects.

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confidence: 99%

Computational simulation of human upper airway collapse using a pressure-/state-dependent model of genioglossal muscle contraction under laminar flow conditions

Huang¹,

Malhotra²,

White³

2005

Journal of Applied Physiology

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“…Note that the calculated stress from the cyclic − relation corresponds to a fibre direction in the last known equilibrium configuration 'i − 1', therefore, we have to transform the calculated stress to the global co-ordinate system in order to evaluate the nodal forces in (4) (as in, for example, Reference [13]). We follow experimental curve in the loading part and reach the amplitude…”

Section: Uniaxial Tissue Model With Hysteresismentioning

confidence: 99%

“…where t+ t E is the slope on the current cyclic curve. This tangent stiffness can be superimposed to the stiffness of the surrounding material (as in Reference [13]).…”

Section: Convergence Check For Cycle Lmentioning

confidence: 99%

Stress integration procedures for a biaxial isotropic material model of biological membranes and for hysteretic models of muscle fibres and surfactant

Kojić

Vlastelica

Stojanović

et al. 2006

Int. J. Numer. Meth. Engng

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SUMMARYStress calculation for a biaxial isotropic material model of a biological membrane and for hysteretic models of muscle fibres and surfactant is presented in the paper. The non-linear elastic membrane model is defined by uniaxial and biaxial stress-stretch relations, while the hysteretic models of tissue fibres and surfactant are described by the stress-stretch and surface tension-surfactant area ratio constitutive relationships, respectively. The conditions when tissue is or is not covered by surfactant are considered. It is assumed that the material is subjected to cyclic loading. Quasi-static and steady conditions are considered.The models are implemented in large strain finite element incremented-iterative analysis of shell deformations. Numerical examples demonstrate characteristics of the computational procedures and structural response of biological membranes when subjected to cyclic loading.Hysteretic response of biological membranes subjected to cyclic loading is caused by hysteresis of fibres and hysteresis of surfactant. The hysteretic effects may play an important role in the physiology of human body.

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“…The muscle model is based on the Hill three‐element model that represents the constituent parts of muscle fibres and is a linearised version of a recent model due to Martins et al . A complex model of the soft palate and uvula, making use of the Hill muscle model, was developed by Kojic et al . In this case, two‐dimensional and three‐dimensional models of the geometry are constructed, and the effects of passive and active muscle fibres are taken into account.…”

Section: Introductionmentioning

confidence: 99%

The biomechanics of the human tongue

Kajee

Pelteret

Reddy

2013

Numer Methods Biomed Eng

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AcknowledgementsI would like express my gratitude to the following people for their assistance, leading to the successful completion of this work:The invaluable guidance provided by Prof. B. D. Reddy was integral to completing this project.It was an honour and a privilege to have worked with someone with such vast experience, knowledge and wisdom. Throughout my time at Cerecam, he has shown great patience and understanding.Dr. Andrew T. McBride assisted in times of difficulty, even during the most demanding times of his own PhD studies. His generosity, kindness, and outstanding work ethics have been an inspiration.Jean-Paul Pelteret is the person I worked with the most during this project. Without his invaluable assistance, this project could be likened to a Sisyphean task.It was an honour to have worked amongst such an esteemed group of academics at Cerecam. Many lunch hours and tea-breaks discussing everyday issues in a friendly atmosphere has proven fruitful. The geometry of the tongue, and each muscle group of the tongue, are visually identified, and its geometry captured using Mimics [100]. Various image processing tools available in Mimics, such as image segmentation, region-growing and volume generation were used to form the three-dimensional model of the tongue geometry. Muscle fibre orientations were extracted from the same dataset, also using Mimics.The muscle model presented here is based on Hill's three-element model for representation of the constituent parts of muscle fibres. This Hill-type muscle model also draws from recent work in muscle modelling, by Martins [88]. The model is implemented in an Abaqus user element (UEL) subroutine [24]. The transversely isotropic behaviour of the muscle tissue is accounted for, as well as the influence of muscle activation.The mechanics of the model is limited to static, small-strain, anisotropic, linear-elastic behaviour, and the governing equations are suitably linearized. The body position of the patient during an apneic episode is accounted for in the simulations, as well as the effect of gravity. The focus of this study is on tongue muscle behaviour under gravitational loading, simulating a simplified OSA event.Future models will incorporate airway pressure as well. The behaviour of the model is illustrated in a number of benchmark tests, and computational examples.iii

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Modelling of muscle behaviour by the finite element method using Hill's three‐element model

Cited by 16 publications

References 0 publications

Computational simulation of human upper airway collapse using a pressure-/state-dependent model of genioglossal muscle contraction under laminar flow conditions

Computational simulation of human upper airway collapse using a pressure-/state-dependent model of genioglossal muscle contraction under laminar flow conditions

Stress integration procedures for a biaxial isotropic material model of biological membranes and for hysteretic models of muscle fibres and surfactant

The biomechanics of the human tongue

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