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W. Beerepoot, S. Schutte, F. C. T. van der Helm, G. Asmussen, F. van Keulen, H. Simonsz; Implementation of Force-Length-Activation Muscle Characteristics in a Finite-Element Model of Orbital Biomechanics. Invest. Ophthalmol. Vis. Sci. 2007;48(13):5284.
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© ARVO (1962-2015); The Authors (2016-present)
To gain more insight in mechanical behavior of tissues within the human orbit, we enhanced our Finite-Element-Analysis (FEA) model of orbital biomechanics with active muscle behavior and sliding between fat and sclera. This study focused on implementation and validation of active muscle behavior (i.e. Force-Length-activation (FLα) relation) into our FEA model, based on in vivo data.
Geometries of our original FEA model of the orbit were used, obtained from MRI data (Vision Res. 2006 May;46(11):1724-31). In our original model we distinguished the eye, four rectus muscles and orbital fat in- and outside the muscle cone. The rectus muscles were meshed with cubic elements. The muscles were assigned an incompressible transverse isotropic hyperelastic material model based on three standard invariants of the Green Lagrange strain tensor that was extended with two invariants that represented muscle fiber direction. Incompressibility was accounted for by Herrmann based formulation. Large rotations of the eye were made possible with a remeshing technique and sliding surfaces. Force-length-activation characteristics were obtained from in vivo data. Passive muscle properties were represented by an exponential relation and active properties by a Gaussian function.
The experimental data could well be described by a Gaussian and exponential function, resulting in FLα-characteristics dependent on two parameters. With activation as only input between zero and one, angles of gaze between zero and forty degrees were obtained respectively. Stresses and strains in the muscle were in the physiological range, fat movement was comparable to what we found in MRI studies (Invest Ophthalmol Vis Sci. 2006 Nov;47(11):4819-26).
Implementation of active muscle behavior within the FEA model has been possible. Together with the implemented passive muscle properties it offers unique possibilities to further investigate complex disorders of eye motility and enables a full understanding of the suspension of the eye in the orbit.
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