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On the h-adaptive PUM and the hp-adaptive FEM approaches applied to PDEs in quantum mechanics

by jppelteret

Authors: D. Davydov, T. Gerasimov, J-P. V. Pelteret, and P. Steinmann

In this paper the h-adaptive partition-of-unity method and the h- and hp-adaptive finite element method are applied to partial differential equations arising in quantum mechanics, namely, the Schrodinger equation with Coulomb and harmonic potentials, and the Poisson problem. Implementational details of the partition-of-unity method related to enforcing continuity with hanging nodes and the degeneracy of the basis are discussed. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling implementation of error-controlled adaptive mesh refinement strategies. To that end, local interpolation error estimates are derived for the partition-of-unity method enriched with a class of exponential functions. The results are the same as for the finite element method and thereby admit the usage of standard residual error indicators. The efficiency of the h -adaptive partition-of- unity method is compared to the h – and h p -adaptive finite element method. The latter is implemented by adopting the analyticity estimate from Legendre coefficients. An extension of this approach to multiple solution vectors is proposed. Numerical results confirm the remarkable accuracy of the h -adaptive partition-of-unity approach. In case of the Hydrogen atom, the h -adaptive linear partition-of-unity method was found to be comparable to the hp -adaptive finite element method for the target eigenvalue accuracy of 10-3. [1]

[1] D. Davydov, T. Gerasimov, J-P. Pelteret, and P. Steinmann, “On the h-adaptive PUM and the hp-adaptive FEM approaches applied to PDEs in quantum mechanics,” Journal of Scientific Computing, 2017.
[Bibtex]
@Article{davydov2016a-preprint,
author = {Davydov, D. and Gerasimov, T. and Pelteret, J-P. and Steinmann, P.},
title = {On the h-adaptive PUM and the hp-adaptive FEM approaches applied to PDEs in quantum mechanics},
journal = {Journal of Scientific Computing},
year = {2017},
note = {Submitted},
abstract = {In this paper the h-adaptive partition-of-unity method and the h- and hp-adaptive finite element method are applied to partial differential equations arising in quantum mechanics, namely, the Schrodinger equation with Coulomb and harmonic potentials, and the Poisson problem. Implementational details of the partition-of-unity method related to enforcing continuity with hanging nodes and the degeneracy of the basis are discussed. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling implementation of error-controlled adaptive mesh refinement strategies. To that end, local interpolation error estimates are derived for the partition-of-unity method enriched with a class of exponential functions. The results are the same as for the finite element method and thereby admit the usage of standard residual error indicators. The efficiency of the h -adaptive partition-of- unity method is compared to the h - and h p -adaptive finite element method. The latter is implemented by adopting the analyticity estimate from Legendre coefficients. An extension of this approach to multiple solution vectors is proposed. Numerical results confirm the remarkable accuracy of the h -adaptive partition-of-unity approach. In case of the Hydrogen atom, the h -adaptive linear partition-of-unity method was found to be comparable to the hp -adaptive finite element method for the target eigenvalue accuracy of 10-3.},
comment = {Submitted},
file = {davydov2016a-preprint.pdf:Users/jp/Documents/Academic/My_articles/Website/davydov2016a-preprint.pdf:PDF},
keywords = {Adaptive finite element method, partition-of-unity method, error estimators, hp-adaptive finite element method, Schrodinger equation, local interpolation error estimates},
owner = {Jean-Paul Pelteret},
timestamp = {2016.05.19},
url = {https://arxiv.org/abs/1612.02305},
}

Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space

by jppelteret

Authors: J-P. V. Pelteret, D. Davydov, A. McBride, D. K. Vu, and P. Steinmann

In this work a mixed variational formulation to simulate quasi-incompressible electro- or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media. [1]

[1] [doi] J-P. V. Pelteret, D. Davydov, A. McBride, D. K. Vu, and P. Steinmann, “Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space,” International Journal for Numerical Methods in Engineering, vol. 108, iss. 11, pp. 1307-1342, 2016.
[Bibtex]
@Article{pelteret2016a-preprint,
author = {Pelteret, J-P. V. and Davydov, D. and McBride, A. and Vu, D. K. and Steinmann, P.},
title = {Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space},
journal = {International Journal for Numerical Methods in Engineering},
year = {2016},
volume = {108},
number = {11},
pages = {1307--1342},
abstract = {In this work a mixed variational formulation to simulate quasi-incompressible electro- or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media.},
comment = {PREPRINT},
doi = {10.1002/nme.5254},
file = {pelteret2016a-preprint.pdf:PDF/pelteret2016a-preprint.pdf:PDF},
keywords = {Nonlinear electro-/magneto-elasticity; quasi-incompressible media; free space; finite strain},
owner = {Jean-Paul Pelteret},
timestamp = {2016.03.21},
}

Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure

by jppelteret

Authors: P. Saxena, J-P. V. Pelteret, and P. Steinmann

Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a ‘chain deformation gradient’ and a ‘chain magnetic field’. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading. [1]

[1] [pdf] [doi] P. Saxena, J-P. V. Pelteret, and P. Steinmann, “Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure,” European Journal of Mechanics A/Solids, vol. 50, pp. 132-151, 2015.
[Bibtex]
@Article{saxena2015a-preprint,
author = {Saxena, P. and Pelteret, J-P. V. and Steinmann, P.},
title = {Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure},
journal = {European Journal of Mechanics A/Solids},
year = {2015},
volume = {50},
pages = {132--151},
month = {March--April},
abstract = {Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a 'chain deformation gradient' and a 'chain magnetic field'. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading.},
doi = {10.1016/j.euromechsol.2014.10.005},
file = {saxena2015a-preprint.pdf:PDF/saxena2015a-preprint.pdf:PDF},
keywords = {Nonlinear magnetoelasticity; Anisotropy; Chain dispersion},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

Magnetic force and torque on particles subject to a magnetic field

by jppelteret

Authors: F. Vogel, J-P. V. Pelteret, S. Kaessmair, and P. Steinmann

Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier. [1]

[1] [pdf] [doi] F. Vogel, J-P. V. Pelteret, S. Kaessmair, and P. Steinmann, “Magnetic force and torque on particles subject to a magnetic field,” European Journal of Mechanics A/Solids, vol. 48, pp. 23-31, 2014.
[Bibtex]
@Article{vogel2014a-preprint,
author = {Vogel, F. and Pelteret, J-P. V. and Kaessmair, S. and Steinmann, P.},
title = {Magnetic force and torque on particles subject to a magnetic field},
journal = {European Journal of Mechanics A/Solids},
year = {2014},
volume = {48},
pages = {23--31},
month = {November--December},
abstract = {Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier.},
doi = {10.1016/j.euromechsol.2014.03.007},
file = {vogel2014a-preprint.pdf:PDF/vogel2014a-preprint.pdf:PDF},
keywords = {Magnetoactive materials; Magnetoelasticity; Finite-element method},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

Comparison of several staggered atomistic-to-continuum concurrent coupling strategies

by jppelteret

Authors: D. Davydov, J-P. V. Pelteret, and P. Steinmann

In this contribution several staggered schemes used to couple continuum mechanics (CM) and molecular mechanics (MM) are proposed. The described approaches are based on the atomistic-to-continuum correspondence, obtained by spatial averaging in the spirit of Irving and Kirkwood, and Noll. Similarities between this and other concurrent coupling schemes are indicated, thus providing a broad overview of different approaches in the field. The schemes considered here are decomposed into the surface-type (displacement or traction boundary conditions) and the volume-type. The latter restricts the continuum displacement field (and possibly its gradient) in some sense to the atomistic (discrete) displacements using Lagrange multipliers. A large-strain CM formulation incorporating Lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented. Finally, the described coupling methods are numerically examined using two examples: uniaxial deformation and a plate with a hole relaxed under surface tension. Accuracy and convergence rates of each method are reported. It was found that the displacement (surface) coupling scheme and the Lagrangian (volume) scheme based on either discrete displacements or the H1 norm derived from continuous displacement fields provide the best performance. [1]

[1] [pdf] [doi] D. Davydov, J-P. Pelteret, and P. Steinmann, “Comparison of several staggered atomistic-to-continuum concurrent coupling strategies,” Computer Methods in Applied Mechanics and Engineering, vol. 277, pp. 260-280, 2014.
[Bibtex]
@Article{davydov2014a-preprint,
author = {Davydov, D. and Pelteret, J-P. and Steinmann, P.},
title = {Comparison of several staggered atomistic-to-continuum concurrent coupling strategies},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2014},
volume = {277},
pages = {260--280},
month = {August},
abstract = {In this contribution several staggered schemes used to couple continuum mechanics (CM) and molecular mechanics (MM) are proposed. The described approaches are based on the atomistic-to-continuum correspondence, obtained by spatial averaging in the spirit of Irving and Kirkwood, and Noll. Similarities between this and other concurrent coupling schemes are indicated, thus providing a broad overview of different approaches in the field. The schemes considered here are decomposed into the surface-type (displacement or traction boundary conditions) and the volume-type. The latter restricts the continuum displacement field (and possibly its gradient) in some sense to the atomistic (discrete) displacements using Lagrange multipliers. A large-strain CM formulation incorporating Lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented.
Finally, the described coupling methods are numerically examined using two examples: uniaxial deformation and a plate with a hole relaxed under surface tension. Accuracy and convergence rates of each method are reported. It was found that the displacement (surface) coupling scheme and the Lagrangian (volume) scheme based on either discrete displacements or the H1 norm derived from continuous displacement fields provide the best performance.},
doi = {10.1016/j.cma.2014.04.013},
file = {davydov2014a-preprint.pdf:PDF/davydov2014a-preprint.pdf:PDF},
keywords = {Concurrent multiscale methods; Atomic-to-continuum coupling methods; Molecular mechanics; Irving-Kirkwood-Noll procedure; Finite elements; Large strain},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea

by jppelteret

Author: J-P. V. Pelteret

Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnoea. The anatomy of the tongue and other upper airway tissues, and the ability to model their behaviour, is central to such investigations.

In this thesis, details of the construction and development of a three-dimensional finite element model of soft tissues of the human upper airway, as well as a simplified fluid model of the airway, are provided. The anatomical data was obtained from the Visible Human Project, and its underlying micro-histological data describing tongue musculature were also extracted from the same source and incorporated into the model. An overview of the mathematical models used to describe tissue behaviour, both at a macro- and microscopic level, is given. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group to a priori unknown external forces was determined through the use of a genetic algorithm-based neural control model.

The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. The response of the various muscles of the tongue to the complex loading developed during breathing is determined, with a particular focus being placed to that of the genioglossus. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. A comparison is then made to the response determined under quasi-static conditions using the pressure distribution extracted from computational fluid-dynamics results. An analytical model describing the time-dependent response of the components of the tongue musculature most active during oral breathing is developed and validated. It is then modified to simulate the activity of the tongue during sleep and under conditions relating to various possible neural and physiological pathologies. The retroglossal movement of the tongue resulting from the pathologies is quantified and their role in the potential to induce airway collapse is discussed. [1]

[1] [pdf] J-P. V. Pelteret, “A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea,” Engineering PhD Thesis, Rondebosch, Western Cape, South Africa, 2013.
[Bibtex]
@PhdThesis{pelteret2013b-phd_thesis,
author = {Pelteret, J-P. V.},
title = {A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea},
school = {University of Cape Town},
year = {2013},
type = {Engineering},
address = {Rondebosch, Western Cape, South Africa},
month = {November},
abstract = {Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnoea. The anatomy of the tongue and other upper airway tissues, and the ability to model their behaviour, is central to such investigations.
In this thesis, details of the construction and development of a three-dimensional finite element model of soft tissues of the human upper airway, as well as a simplified fluid model of the airway, are provided. The anatomical data was obtained from the Visible Human Project, and its underlying micro-histological data describing tongue musculature were also extracted from the same source and incorporated into the model. An overview of the mathematical models used to describe tissue behaviour, both at a macro- and microscopic level, is given. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group to a priori unknown external forces was determined through the use of a genetic algorithm-based neural control model.
The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. The response of the various muscles of the tongue to the complex loading developed during breathing is determined, with a particular focus being placed to that of the genioglossus. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. A comparison is then made to the response determined under quasi-static conditions using the pressure distribution extracted from computational fluid-dynamics results. An analytical model describing the time-dependent response of the components of the tongue musculature most active during oral breathing is developed and validated. It is then modified to simulate the activity of the tongue during sleep and under conditions relating to various possible neural and physiological pathologies. The retroglossal movement of the tongue resulting from the pathologies is quantified and their role in the potential to induce airway collapse is discussed.},
file = {pelteret2013b-phd_thesis.pdf:PDF/pelteret2013b-phd_thesis.pdf:PDF},
keywords = {sleep-disordered breathing; obstructive sleep apnoea; tongue; human upper airway; computational model; skeletal muscle model; Hill three-element model; neural control model; genetic algorithm; finite element method},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
url = {http://hdl.handle.net/11427/9519},
}

Development of a computational biomechanical model of the human upper-airway soft-tissues towards simulating obstructive sleep apnea

by jppelteret

Authors: J-P. V. Pelteret, and B. D. Reddy

Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnea (OSA). The anatomy of the tongue and other upper-airway tissues, and the ability to model their behavior, are central to such investigations. We present details of the construction and development of a soft-tissue model of the human upper airway, with the ultimate goal of simulating obstructive sleep apnea. The steps taken to produce a representative anatomical geometry, of which the associated muscle histology is also captured, are documented. An overview of the mathematical models used to describe tissue behavior, both at a macro- and microscopic level, is given. A neurological model, which mimics the proprioceptive capabilities of the body, is described as it is applies to control of the active dynamics of the tongue. A simplified scenario, which allows for the manipulation of several environmental influences, is presented. It is demonstrated that the response of the genioglossus is qualitatively similar to that determined through experimental techniques. Furthermore, insights into the stress distribution developed within the tongue are discussed. It is shown that changes in almost any aspect of the breathing or physiological conditions invoke a significant change in the response of the airway dilators. The results of this study provide further evidence of the importance of modeling and simulation techniques as an aid in understanding the complex behavior of the human body. [1]

[1] [pdf] [doi] J-P. V. Pelteret and B. D. Reddy, “Development of a computational biomechanical model of the human upper–airway soft–tissues towards simulating obstructive sleep apnea,” Clinical Anatomy, vol. 27, iss. 2, pp. 182-200, 2013.
[Bibtex]
@Article{pelteret2013a-preprint,
author = {Pelteret, J-P. V. and Reddy, B. D.},
title = {Development of a computational biomechanical model of the human upper--airway soft--tissues towards simulating obstructive sleep apnea},
journal = {Clinical Anatomy},
year = {2013},
volume = {27},
number = {2},
pages = {182--200},
abstract = {Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnea (OSA). The anatomy of the tongue and other upper-airway tissues, and the ability to model their behavior, are central to such investigations. We present details of the construction and development of a soft-tissue model of the human upper airway, with the ultimate goal of simulating obstructive sleep apnea. The steps taken to produce a representative anatomical geometry, of which the associated muscle histology is also captured, are documented. An overview of the mathematical models used to describe tissue behavior, both at a macro- and microscopic level, is given. A neurological model, which mimics the proprioceptive capabilities of the body, is described as it is applies to control of the active dynamics of the tongue. A simplified scenario, which allows for the manipulation of several environmental influences, is presented. It is demonstrated that the response of the genioglossus is qualitatively similar to that determined through experimental techniques. Furthermore, insights into the stress distribution developed within the tongue are discussed. It is shown that changes in almost any aspect of the breathing or physiological conditions invoke a significant change in the response of the airway dilators. The results of this study provide further evidence of the importance of modeling and simulation techniques as an aid in understanding the complex behavior of the human body.},
doi = {10.1002/ca.22313},
file = {pelteret2013a-preprint.pdf:PDF/pelteret2013a-preprint.pdf:PDF},
keywords = {obstructive sleep apnea; tongue; human upper-airway; computational model; skeletal muscle model; neural model; finite-element method},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

The biomechanics of the human tongue

by jppelteret

Authors: Y. Kajee, J-P. V. Pelteret, and B. D. Reddy

The human tongue is composed mainly of skeletal muscle tissue and has a complex architecture. Its anatomy is characterised by interweaving yet distinct muscle groups. It is a significant contributor to the phenomenon of obstructive sleep apnoea syndrome. A realistic model of the tongue and computational simulations are important in areas such as linguistics and speech therapy. The aim of this work is to report on the construction of a geometric and constitutive model of the human tongue and to demonstrate its use in computational simulations for obstructive sleep apnoea syndrome research. The geometry of the tongue and each muscle group of the tongue, including muscle fibre orientations, are captured from the Visible Human Project dataset. The fully linear muscle model is based on the Hill three-element model that represents the constituent parts of muscle fibres. The mechanics of the model are limited to quasi-static, small-strain, linear-elastic behaviour. The main focus of this work is on the material directionality and muscle activation. The transversely isotropic behaviour of the muscle tissue is accounted for, as well as the influence of muscle activation. The behaviour of the model is illustrated in a number of benchmark tests and for the case of a subject in the supine position. [1]

[1] [pdf] [doi] Y. Kajee, J-P. V. Pelteret, and B. D. Reddy, “The biomechanics of the human tongue,” International Journal for Numerical Methods in Biomedical Engineering, vol. 29, iss. 4, pp. 492-514, 2013.
[Bibtex]
@Article{kajee2013a-preprint,
author = {Kajee, Y. and Pelteret, J-P. V. and Reddy, B. D.},
title = {The biomechanics of the human tongue},
journal = {International Journal for Numerical Methods in Biomedical Engineering},
year = {2013},
volume = {29},
number = {4},
pages = {492--514},
month = {April},
abstract = {The human tongue is composed mainly of skeletal muscle tissue and has a complex architecture. Its anatomy is characterised by interweaving yet distinct muscle groups. It is a significant contributor to the phenomenon of obstructive sleep apnoea syndrome. A realistic model of the tongue and computational simulations are important in areas such as linguistics and speech therapy. The aim of this work is to report on the construction of a geometric and constitutive model of the human tongue and to demonstrate its use in computational simulations for obstructive sleep apnoea syndrome research. The geometry of the tongue and each muscle group of the tongue, including muscle fibre orientations, are captured from the Visible Human Project dataset. The fully linear muscle model is based on the Hill three-element model that represents the constituent parts of muscle fibres. The mechanics of the model are limited to quasi-static, small-strain, linear-elastic behaviour. The main focus of this work is on the material directionality and muscle activation. The transversely isotropic behaviour of the muscle tissue is accounted for, as well as the influence of muscle activation. The behaviour of the model is illustrated in a number of benchmark tests and for the case of a subject in the supine position.},
doi = {10.1002/cnm.2531},
file = {kajee2013a-preprint.pdf:PDF/kajee2013a-preprint.pdf:PDF},
keywords = {obstructive sleep apnoea ; human tongue ; hill model ; FEM},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

Computational model of soft tissues in the human upper airway

by jppelteret

Authors: J-P. V. Pelteret, and B. D. Reddy

This paper presents a three-dimensional finite element model of the tongue and surrounding soft tissues with potential application to the study of sleep apnoea and of linguistics and speech therapy. The anatomical data was obtained from the Visible Human Project, and the underlying histological data was also extracted and incorporated into the model. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. [1]

[1] [pdf] [doi] J-P. V. Pelteret and B. D. Reddy, “Computational model of soft tissues in the human upper airway,” International Journal for Numerical Methods in Biomedical Engineering, vol. 28, iss. 1, pp. 111-132, 2012.
[Bibtex]
@Article{pelteret2012a-preprint,
author = {Pelteret, J-P. V. and Reddy, B. D.},
title = {Computational model of soft tissues in the human upper airway},
journal = {International Journal for Numerical Methods in Biomedical Engineering},
year = {2012},
volume = {28},
number = {1},
pages = {111--132},
month = {January},
abstract = {This paper presents a three-dimensional finite element model of the tongue and surrounding soft tissues with potential application to the study of sleep apnoea and of linguistics and speech therapy. The anatomical data was obtained from the Visible Human Project, and the underlying histological data was also extracted and incorporated into the model. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus.},
doi = {10.1002/cnm.1487},
file = {pelteret2012a-preprint.pdf:PDF/pelteret2012a-preprint.pdf:PDF},
keywords = {human upper airway; tongue; muscle model; neural control model; genetic algorithm; finite element method},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}