Long Time-Constant Behavior of the Oculomotor Plant in Barbiturate-Anesthetized Primate

Abstract

The mechanics of the extraocular muscles and orbital tissue ("oculomotor plant") can be approximated by a small number of viscoelastic (Voigt) elements in series. Recent analysis of the eye's return from displacement in lightly anesthetized rhesus monkeys has suggested a four-element plant model with time constants (TCs) of approximately 0.01, 0.1, 1, and 10 s. To demonstrate directly the presence of long (1,10 s) TC elements and to assess their contribution quantitatively, horizontal eye displacement was induced in Cynomolgus monkeys under deep barbiturate anesthesia that prevented interference from spontaneous eye movements. The displacement was maintained for either a prolonged (30 s) or brief (0.2 s) period before release. Return to resting position took 20-30 s after prolonged displacement but only 1-2 s after brief displacement, consistent with the presence of long TC elements that would only be substantially stretched in the former condition. Quantitative fitting of the release curves after prolonged displacement indicated that the two long TC elements contribute a substantial proportion (approximately 30%) of the total plant compliance. A model based on the estimated compliance values is shown to account quantitatively both for our release data and for Goldstein and Robinson's data on hysteresis of ocular motoneuron firing rates measured after centripetal saccades following prolonged eccentric fixation. Long time-constant elements in the plant thus make a substantial contribution to some types of eye movement, and their inclusion in plant models can help interpret the firing patterns of single units in the oculomotor system.

Alexander's Law and the Oculomotor Neural Integrator: Three-Dimensional Eye Velocity in Patients With an Acute Vestibular Asymmetry

“…Thus changing the reference position causes the gaze-dependent drift patterns for horizontal and vertical to become more similar, suggesting the horizontal and vertical NIs react similarly to altered vestibular input. Although there have been a few studies of the viscoelastic properties of the orbit in the horizontal (Robinson 1964;Sklavos et al 2005Sklavos et al , 2006 and torsional (Seidman et al 1995) directions, little is known for vertical movements, and the actual location of equilibrium point is unknown. Shifting the null point, however, does not account for why the shape of the fitted velocity function was concave down, whereas the surface for horizontal was concave up.…”

Mechanics of mouse ocular motor plant quantified by optogenetic techniques

“…These individual viscoelastic assemblies are termed "Voigt" elements. The response speeds of the Voigt elements (i.e., their time constants) are spread over a broad range of values (Sklavos et al 2005(Sklavos et al , 2006. Whereas a model exactly replicating the eye and orbit would require an essentially infinite set of viscoelastic elements with continuously distributed time constants (Quaia et al 2009;Tschoegl 1989), in practice much of the experimental data can be accommodated by models consisting of a small number of discrete elements (about 4) with time constants spanning 0.01-10 s.…”

Viscoelastic and failure properties of spine ligament collagen fascicles

“…The time constants, τ n , were constrained to decade values (τ 1 = 1 s, τ 2 = 100 ms, τ 3 = 10 ms, τ 4 = 1 ms) (c.f. Goh et al 2003;Kauer et al 2002;Sklavos et al 2006;Van Dommelen et al 2005b). The range of time constants (1 ms to 1 s) was chosen to encompass all rates exhibited in the test methodology, including an order of magnitude faster than the strain ramp onset to the end of the force relaxation data that were included in the model.…”