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A. Vijayaraghavan, J.L. Demer; A Ring–sling Computational Model of Active Rectus Muscle Pulleys Supports Active Pulley Hypothesis (APH) . Invest. Ophthalmol. Vis. Sci. 2005;46(13):4675.
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Purpose: The APH proposes that rectus pulleys receive insertions from orbital layers (OLs) of rectus extraocular muscles (EOMs) to shift pulleys anteroposteriorly during EOM activity so as to maintain a constant distance from pulleys to scleral insertions. This coordination of pulley position is proposed to underlie Listing’s Law (LL) of ocular torsion. We developed a computational simulation of the rectus EOMs and pulleys to determine if mechanical behavior postulated by the APH is quantitatively consistent with known orbital anatomy and reasonable force distributions. Methods: To account for its greater resistance to transverse than axial displacement, we modeled each rectus pulley as an encircling ring sliding anteroposteriorly within an elastic sling coupled via multiple discrete bands to the orbital walls and to adjacent pulleys. EOM paths and anatomic relationships were determined from magnetic resonance imaging in living humans. EOMs were modeled as two parallel strings comprising global layers (GLs) and orbital layers (OLs) capable of independent tensions. The OL terminated on the pulley, while the GL traversed the pulley to insert on the globe. Connective tissue bands suspending pulleys from bony entheses and adjacent pulleys were modeled as discrete elastic elements whose stiffnesses were scaled based on human connective tissue distribution data of Kono et al. (IOVS 43:2923,2002). The globe was free to translate horizontally and vertically, but posterior displacement was assumed canceled by forces representing fat and connective tissues. Results: Reasonable parameterization of tissue stiffnesses and total EOM forces yielded translational globe stability, as well as coordinated anteroposterior movements of rectus pulleys and realistic EOM paths during horizontal and vertical gaze shifts of >30°. Consistent with metabolic and structural properties, forces were higher in the OL than GL of each EOM over the gaze range. Due to the effect of the OL on EOM path geometry, OL forces influence GL forces without direct insertion or frictional coupling, but GL forces have little effect on OL forces. Conclusions: Rectus pulleys can be realistically modeled as rings within sleeves. This approach might be extended to the inferior oblique pulley. Quantitative biomechanical modeling supports the APH proposition that rectus pulleys are actively translated by OL forces. The model is consistent with the experimental finding of Dimitrova et al. (JNP 90:3809,2003) that acute pulley ablation decreases GL tension in monkey. Even without oblique EOMs, the ring–sleeve pulley model mechanically accounts for LL.
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