Viscoelastic properties of bovine orbital connective tissue and fat: constitutive models
Lawrence Yoo
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Vijay Gupta
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Choongyeop Lee
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Pirouz Kavehpore
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Joseph L. Demer
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Support: Supported by US Public Health Service, National Eye Institute: grants EY08313 and EY00331, and Research to Prevent Blindness. J. Demer is Leonard Apt Professor of Ophthalmology
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J. L. Demer Department of Neurology, University of California
,
Los Angeles, USA
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J. L. Demer Neuroscience Interdepartmental Program, University of California
,
Los Angeles, USA
Reported mechanical properties of orbital connective tissue and fat have been too sparse to model strainstress relationships underlying biomechanical interactions in strabismus. We performed rheological tests to develop a multi-mode upper convected Maxwell (UCM) model of these tissues under shear loading. From 20 fresh bovine orbits, 30 samples of connective tissue were taken from rectus pulley regions and 30 samples of fatty tissues from the posterior orbit. Additional samples were defatted to determine connective tissue weight proportion, which was verified histologically. Mechanical testing in shear employed a triborheometer to perform: strain sweeps at 0.5-2.0 Hz; shear stress relaxation with 1% strain; viscometry at 0.01 0.5 s1 strain rate; and shear oscillation at 1% strain. Average connective tissue weight proportion was 98% for predominantly connective tissue and 76% for fatty tissue. Connective tissue specimens reached a long-term relaxation modulus of 668 Pa after 1,500 s, while corresponding values for fatty tissue specimens were 290 Pa and 1,100 s. Shear stress magnitude for connective tissue exceeded that of fatty tissue by five-fold. Based on these data, we developed a multimode UCM model with variable viscosities and time constants, and a damped hyperelastic response that accurately described measured properties of both connective and fatty tissues. Model parameters differed significantly between the two tissues. Viscoelastic properties of predominantly connective orbital tissues under shear loading differ markedly from properties of orbital fat, but both are accurately reflected using UCM models. These viscoelastic models will facilitate realistic global modeling of EOM behavior in binocular alignment and strabismus.
1 Introduction
The mechanical properties of extraocular tissues are
attracting increasing experimental interest of investigators
interested in ocular motility. Detailed mechanical characterization
of these tissues is crucial to quantitative understanding of
strabismus, the pathological misalignment of the eyes.
However, approaches to characterize biosolids have varied among
investigators, with some treating soft tissues as discrete
systems composed of simplified springs and dampers (Bilston
et al. 1998; Bilston and Thibault 1996; Lanir 1979; Liu and
Bilston 2000; Shoemaker et al. 1986), while others treat them
as time dependent continuous elastic systems(De Hoff 1978;
Fung 1967; Pinto and Fung 1973; Yoo et al. 2009). Prior
studies, including those of Robinson et al. (1969), Collins
et al. (1981), Simonsz 1994 and Yoo et al. (2009), have
appreciated some active and passive behavior of
extraocular muscles (EOMs), but biomechanical characterization of
orbital connective tissue and fat has been largely neglected
in the field of ocular motility. A rare exception has been
the study of bovine retrobulbar tissue by Schoemaker et al.
(2006), which nonetheless did not differentiate orbital fat
from connective tissue. Biomechanical properties of
orbital connective tissue have been typically neglected or
arbitrarily assumed in simulation studies of extraocular
mechanics.
Discovery of the orbital pulley system motivated efforts to
clarify the mechanical properties of the orbital connective
tissues. Imaging studies in monkeys (Miller and Robins 1987)
and humans (Simonsz et al. 1985) demonstrated that
rectus EOM bellies, rather than taking shortest distance paths,
instead have paths that are largely stable in the orbit over
the full range of gaze directions (Miller 1989). In secondary
and tertiary gazes, rectus and inferior oblique EOM paths
are sharply inflected at locations coinciding with
connective tissue rings encircling the EOMs into which the
orbital layer EOM fibers insert (Demer et al. 2003). These
connective tissue rings, consisting of densely woven collagen
reinforced by elastin, are termed the pulleys. Rectus pulleys
are located posterior to the globe equator in Tenons fascia
(Demer et al. 1995) and mechanically coupled to the
orbital walls and adjacent pulleys via connective tissue bands or
ligaments. These connective structures are uniform among
most individuals and are composed of collagen, elastin, and
sometimes also smooth muscle (Kono et al. 2002). While
there is fat distributed among the EOMs posterior to the
globe and pulley system, the relative contributions of
pulley tissues versus fat to orbital biomechanics remain poorly
delineated.
From the point of view of biomechanics and solid
mechanics, a materia (...truncated)