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1.  Independent Active Contraction of Extraocular Muscle Compartments 
Intramuscular innervation of horizontal rectus extraocular muscle (EOMs) is segregated into superior and inferior (transverse) compartments, whereas all EOMs are also divided into global (GL) and orbital (OL) layers with scleral and pulley insertions, respectively. Mechanical independence between both types of compartments has been demonstrated during passive tensile loading. We examined coupling between EOM compartments during active, ex vivo contraction.
Fresh bovine EOMs were removed, and one compartment of each was coated with hydrophobic petrolatum. Contraction of the uncoated compartment was induced by immersion in a solution of 50 mM CaCl2 at 38°C labeled with sodium fluorescein dye, whereas tensions in both compartments were monitored by strain gauges. Control experiments omitted petrolatum so that the entire EOM contracted. After physiological experiments, EOMs were sectioned transversely to demonstrate specificity of CaCl2 permeation by yellow fluorescence dye excited by blue light.
In control experiments without petrolatum, both transverse and GL and OL compartments contracted similarly. Selective compartmental omission of petrolatum caused markedly independent compartmental contraction whether measured at the GL or the OL insertions or for transverse compartments at the scleral insertion. Although some CaCl2 spread occurred, mean (±SD) tension in the coated compartments averaged only 10.5 ± 3.3% and 6.0 ± 1.5% in GL/OL and transverse compartments, respectively relative to uncoated compartments. Fluorescein penetration confirmed selective CaCl2 permeation.
These data confirm passive tensile findings of mechanical independence of EOM compartments and extend results to active contraction. EOMs behave actively as if composed of mechanically independent parallel fiber bundles having different insertional targets, consistent with the active pulley and transverse compartmental hypotheses.
The orbital, global, and transverse compartments of individual bovine extraocular muscles generate tension independently of one another during ex vivo calcium activation. This finding, the result of parallel fibers in extraocular muscle, supports a postulate essential to the active pulley and compartmental hypotheses.
PMCID: PMC4290554  PMID: 25503460
active pulley hypothesis; compartmental hypothesis; extraocular muscle
2.  Viscoelastic Characterization of Extraocular Z-Myotomy 
Z-myotomy is an extraocular muscle (EOM) weakening procedure in which two incisions are made from longitudinally-separated, opposite EOM margins for treatment of strabismus. We examined the in vitro biomechanics of Z-myotomy using tensile loading.
Fresh bovine rectus EOMs were reduced to 20 × 10 × 2–mm dimensions, and clamped in a microtensile load cell under physiological conditions. Extraocular muscles were elongated until failure following scissors incisions made from opposite sides, spaced 8 mm apart and each encompassing 0%, 40%, 50%, 60%, or 80% EOM width. Initial strain to 30% elongation was imposed at 100 mm/s, after which elongation was maintained for greater than 100 seconds during force recording at maintained deformation. Stress relaxation tests with nonincised specimens having widths ranging from 1 to 9 mm were conducted for viscoelastic characterization of corresponding equivalence to 20% to 80% Z-myotomy. Data were modeled using the Wiechert viscoelastic formulation.
There was progressively reduced EOM failure force to an asymptotic minimum at 60% or greater Z-myotomy. Each Z-myotomy specimen could be matched for equivalent failure force to a non–Z-myotomy specimen with a different width. Both tensile and stress relaxation data could be modeled accurately using the Wiechert viscoelastic formulation.
The parallel fiber structure results in low shear force transfer across EOM width, explaining the biomechanics of Z-myotomy. Z-myotomy progressively reduces force transmission to an asymptotic minimum for less than 60% surgical dose, with no further reduction for greater amounts of surgery. Equivalence to EOM specimens having regular cross-sections permits viscoelastic biomechanical characterization of Z-myotomy specimens with irregular cross-sections.
Z-myotomy comprises longitudinally spaced transverse incisions tolengthen and weaken extraocular muscle (EOM) for strabismus treatment. Because of generally parallel structure and scant transverse coupling among EOM fibers, 60percnt; or more Z-myotomy mechanically equates to completely dividing all fibers.
PMCID: PMC4309311  PMID: 25477318
biomechanics; strabismus surgery; extraocular muscle
3.  Atomic Force Microscopy Determination of Young’s Modulus of Bovine Extra-ocular Tendon Fiber Bundles 
Journal of biomechanics  2014;47(8):1899-1903.
Extra-ocular tendons (EOTs) transmit the oculorotary force of the muscles to the eyeball to generate dynamic eye movements and align the eyes, yet the mechanical properties of the EOTs remain undefined. The EOTs are known to be composed of parallel bundles of small fibers whose mechanical properties must be determined in order to characterize the overall behavior of EOTs. The current study aimed to investigate the transverse Young’s modulus of EOT fiber bundles using atomic force microscopy (AFM).
Fresh bovine EOT fiber bundle specimens were maintained under temperature and humidity control, and indented 100 nm by the inverted pyramid tip of an AFM (Veeco Digital Instruments, NY). Ten indentations were conducted for each of 3 different locations of 10 different specimens from each of 6 EOTs, comprising a total of 1,800 indentations. Young’s modulus for each EOT was determined using a Hertzian contact model.
Young’s moduli for fiber bundles from all six EOTs were determined. Mean Young’s moduli for fiber bundles were similar for the six anatomical EOTs: lateral rectus 60.12 ± 2.69 (±SD) MPa, inferior rectus 59.69 ± 5.34 MPa, medial rectus 56.92 ±1.91 MPa, superior rectus 59.66 ±2.64 MPa, inferior oblique 57.7± 1.36 MPa, and superior oblique 59.15± 2.03. Variation in Young’s moduli among the six EOTs was not significant (P > 0.25).
The Young’s modulus of bovine EOT fibers is highly uniform among the six extraocular muscles, suggesting that each EOT is assembled from fiber bundles representing the same biomechanical elements. This uniformity will simplify overall modeling.
PMCID: PMC4028417  PMID: 24767704
biomechanics; extra-ocular tendon; orbital mechanics; strabismus
4.  Biomechanics of superior oblique Z-tenotomy 
A recent report suggests that 70%-80% Z-tenotomy of the superior oblique tendon is necessary to effectively treat A-pattern strabismus associated with over depression in adduction. To clarify the clinical effect, we compared the biomechanics of Z-tenotomy on the superior oblique tendon, superior rectus tendon, and isotropic latex material.
Fresh bovine superior oblique tendons were trimmed to 20 mm × 10 mm dimensions similar to human superior oblique tendon and clamped in a microtensile load cell under physiological conditions of temperature and humidity. Minimal preload was applied to avoid slackness. Tendons were elongated until failure following Z-tenotomies, made from opposite tendon sides, spaced 8 mm apart and each encompassing 0%, 20%, 40%, 50%, 60%, or 80% tendon width. Digitally sampled failure force was monitored using a precision strain gauge. Control experiments were performed in similar-sized specimens of bovine superior rectus tendon and isotropic latex.
Progressively increasing Z-tenotomy of latex caused a linearly graded reduction in force. In contrast, Z-tenotomy of up to 50% in superior oblique and superior rectus tendons caused nonlinear reduction in force transmission that reached a negligible value at 50% tenotomy and greater.
Z-tenotomy up to 50% progressively reduces extraocular tendon force transmission, but Z-tenotomy of ≥50% is biomechanically equivalent in vitro to complete tenotomy.
PMCID: PMC3858822  PMID: 24321425
5.  Independent Passive Mechanical Behavior of Bovine Extraocular Muscle Compartments 
Intramuscular innervation of horizontal rectus extraocular muscles (EOMs) is segregated into superior and inferior (transverse) compartments, while all EOMs are also divided into global (GL) and orbital (OL) layers with scleral and pulley insertions, respectively. We sought evidence of potential independent action by examining passive mechanical coupling between EOM compartments.
Putative compartments of each of the six whole bovine anatomical EOMs were separately clamped to a physiologically controlled, dual channel microtensile load cell (5-mN force resolution) driven by independent, high-speed, linear motors having 20-nm position resolution. One channel at a time was extended or retracted by 3 to 5 mm, with the other channel stationary. Fiducials distributed on the EOM global surface enabled optical tracking of local deformation. Loading rates of 5 to 100 mm/sec were applied to explore speeds from slow vergence to saccades. Control loadings employed transversely loaded EOM and isotropic latex.
All EOM bellies and tendons exhibited substantial compartmental independence when loaded in the physiologic direction, both between OL and GL, and for arbitrary transverse parsings of EOM width ranging from 60%:40% to 80%:20%. Intercompartmental force coupling in the physiologic direction was less than or equal to 10% in all six EOMS even for saccadic loading rates. Coupling was much higher for nonphysiologic transverse EOM loading and isotropic latex. Optical tracking demonstrated independent strain distribution between EOM compartments.
Substantial mechanical independence exists among physiologically loaded fiber bundles in bovine EOMs and tendons, providing biomechanical support for the proposal that differential compartmental function in horizontal rectus EOMs contributes to novel torsional and vertical actions.
Dual-channel tensile loading demonstrates that adjacent extraocular muscle (EOMs) regions have marked mechanical independence. This finding supports the active pulley hypothesis and the proposal that topographic innervation within horizontal rectus EOMs could command torsional and vertical actions.
PMCID: PMC4113332  PMID: 23188730
6.  Determination of Poisson Ratio of Bovine Extraocular Muscle by Computed X-Ray Tomography 
BioMed Research International  2012;2013:197479.
The Poisson ratio (PR) is a fundamental mechanical parameter that approximates the ratio of relative change in cross sectional area to tensile elongation. However, the PR of extraocular muscle (EOM) is almost never measured because of experimental constraints. The problem was overcome by determining changes in EOM dimensions using computed X-ray tomography (CT) at microscopic resolution during tensile elongation to determine transverse strain indicated by the change in cross-section. Fresh bovine EOM specimens were prepared. Specimens were clamped in a tensile fixture within a CT scanner (SkyScan, Belgium) with temperature and humidity control and stretched up to 35% of initial length. Sets of 500–800 contiguous CT images were obtained at 10-micron resolution before and after tensile loading. Digital 3D models were then built and discretized into 6–8-micron-thick elements. Changes in longitudinal thickness of each microscopic element were determined to calculate strain. Green's theorem was used to calculate areal strain in transverse directions orthogonal to the stretching direction. The mean PR from discretized 3D models for every microscopic element in 14 EOM specimens averaged 0.457 ± 0.004 (SD). The measured PR of bovine EOM is thus near the limit of incompressibility.
PMCID: PMC3591112  PMID: 23484091
7.  Viscoelastic properties of bovine orbital connective tissue and fat: constitutive models 
Reported mechanical properties of orbital connective tissue and fat have been too sparse to model strain–stress 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 s−1 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.
PMCID: PMC3286436  PMID: 21207094
Biomechanics; Cow; Extra-ocular muscle; Oculomotor mechanics; Pulley; Strabismus
8.  Expanding Repertoire In The Oculomotor Periphery: Selective Compartmental Function In Rectus Extraocular Muscles 
Since connective tissue pulleys implement Listing's law by systematically changing rectus extraocular muscle (EOM) pulling directions, non-Listing's law gaze-dependence of the vestibulo-ocular reflex is currently inexplicable. Differential activation of compartments within rectus EOMs may endow the ocular motor system with more behavioral diversity than previously supposed. Innervation to horizontal, but not vertical, rectus EOMs of mammals is segregated into superior and inferior compartments. Magnetic resonance imaging in normal subjects demonstrates contractile changes in the lateral rectus (LR) inferior, but not superior, compartment during ocular counter-rolling (OCR) induced by head tilt. In human orbits ipsilesional to unilateral superior oblique palsy, neither LR compartment exhibits contractile change during head tilt, although the inferior compartment contracts normally in contralesional orbits. This suggests that differential compartmental LR contraction assists normal OCR. Computational simulation suggests that differential compartmental action in horizontal rectus EOMs could achieve more force than required by vertical fusional vergence.
PMCID: PMC3286355  PMID: 21950970
extraocular muscles; magnetic resonance imaging; motor nerve; pulleys; vestibulo-ocular reflex
9.  Mechanical Interferometry Imaging for Creep Modeling of the Cornea 
Nanoindentation by magnetic microspheres imaged by optical interferometry permits determination of the viscoelastic properties of fine local regions of each layer of the cornea. This approach provides robust biomechanical data on corneal creep behavior that scales reliably with the magnitude of applied force throughout the tissue.
A novel nanoindentation technique was used to biomechanically characterize each of three main layers of the cornea by using Hertzian viscoelastic formulation of creep, the deformation resulting from sustained-force application.
The nanoindentation method known as mechanical interferometry imaging (MII) with <1-nm displacement precision was used to observe indentation of bovine corneal epithelium, endothelium, and stroma by a spherical ferrous probe in a calibrated magnetic field. For each specimen, creep testing was performed using two different forces for 200 seconds. Measurements for single force were used to build a quantitative Hertzian model that was then used to predict creep behavior for another imposed force.
For all three layers, displacement measurements were highly repeatable and were well predicted by Hertzian models. Although short- and long-term stiffnesses of the endothelium were highest of the three layers at 339.2 and 20.2 kPa, respectively, both stromal stiffnesses were lowest at 100.4 and 3.6 kPa, respectively. Stiffnesses for the epithelium were intermediate at 264.6 and 12.2 kPa, respectively.
Precise, repeatable measurements of corneal creep behavior can be conveniently obtained using MII at mechanical scale as small as one cell thickness. When interpreted in analytical context of Hertzian viscoelasticity, MII technique proved to be a powerful tool for biomechanical characterization of time-dependent biomechanics of corneal regions.
PMCID: PMC3388749  PMID: 21969299
10.  Creep Behavior of Passive Bovine Extraocular Muscle 
This paper characterized bovine extraocular muscles (EOMs) using creep, which represents long-term stretching induced by a constant force. After preliminary optimization of testing conditions, 20 fresh EOM samples were subjected to four different loading rates of 1.67, 3.33, 8.33, and 16.67%/s, after which creep was observed for 1,500 s. A published quasilinear viscoelastic (QLV) relaxation function was transformed to a creep function that was compared with data. Repeatable creep was observed for each loading rate and was similar among all six anatomical EOMs. The mean creep coefficient after 1,500 seconds for a wide range of initial loading rates was at 1.37 ± 0.03 (standard deviation, SD). The creep function derived from the relaxation-based QLV model agreed with observed creep to within 2.7% following 16.67%/s ramp loading. Measured creep agrees closely with a derived QLV model of EOM relaxation, validating a previous QLV model for characterization of EOM biomechanics.
PMCID: PMC3216464  PMID: 22131809
11.  Characterization of Ocular Tissues Using Microindentation and Hertzian Viscoelastic Models 
Microindentation permits biomechanical characterization of small specimens of ocular tissues and demonstrates that although properties of periocular fatty tissues vary markedly by location, comparable bovine and human tissues behave similarly.
The authors applied a novel microindentation technique to characterize biomechanical properties of small ocular and orbital tissue specimens using the Hertzian viscoelastic formulation, which defines material viscoelasticity in terms of the contact pressure required to maintain deformation by a harder body.
They used a hard spherical indenter having 100 nm displacement and 100 μg force precision to impose small deformations on fresh bovine sclera, iris, crystalline lens, kidney fat, orbital pulley tissue, and orbital fatty tissue; normal human orbital fat, eyelid fat, and dermal fat; and orbital fat associated with thyroid eye disease. For each tissue, stress relaxation testing was performed using a range of ramp displacements. Results for single displacements were used to build quantitative Hertzian models that were, in turn, compared with behavior for other displacements. Findings in orbital tissues were correlated with quantitative histology.
Viscoelastic properties of small specimens of orbital and ocular tissues were reliably characterized over a wide range of rates and displacements by microindentation using the Hertzian formulation. Bovine and human orbital fatty tissues exhibited highly similar elastic and viscous behaviors, but all other orbital tissues exhibited a wide range of biomechanical properties. Stiffness of fatty tissues tissue depended strongly on the connective tissue content.
Relaxation testing by microindentation is a powerful method for characterization of time-dependent behaviors of a wide range of ocular and orbital tissues using small specimens, and provides data suitable to define finite element models of a wide range of tissue interactions.
PMCID: PMC3109037  PMID: 21310907
12.  Intramuscular Innervation of Primate Extraocular Muscles: Unique Compartmentalization in Horizontal Recti 
Segregation of intramuscular motor nerves indicates distinct superior and inferior zones within the horizontal but not vertical rectus extraocular muscles in humans and monkeys, supporting a potential functional role for differential innervation that might mediate oculorotary actions.
It has been proposed that the lateral rectus (LR), like many skeletal and craniofacial muscles, comprises multiple neuromuscular compartments subserving different physiological functions. To explore the anatomic potential of compartmentalization in all four rectus extraocular muscles (EOMs), evidence was sought of possible regional selectivity in intramuscular innervation of all rectus EOMs.
Whole orbits of two humans and one macaque monkey were serially sectioned at 10 μm thickness and stained with Masson's trichrome. Three-dimensional reconstruction was performed of the intramuscular courses of motor nerves from the deep orbit to the anterior extents of their arborizations within all four rectus EOMs in each orbit.
Findings concorded in monkey and human orbits. Externally to the global surface of the lateral (LR) and medial rectus (MR) EOMs, motor nerve trunks bifurcated into approximately equal-sized branches before entering the global layer and observing a segregation of subsequent arborization into superior zones that exhibited minimal overlap along the length of the LR and only modest overlap for MR. In contrast, intramuscular branches of the superior and the nasal portion of the inferior rectus were highly mixed.
Consistent segregation of intramuscular motor nerve arborization suggests functionally distinct superior and inferior zones within the horizontal rectus EOMs in both humans and monkeys. Reduced or absent compartmentalization in vertical rectus EOMs supports a potential functional role for differential innervation in horizontal rectus zones that could mediate previously unrecognized vertical oculorotary actions.
PMCID: PMC3088565  PMID: 21220556
13.  Compartmentalized Innervation of Primate Lateral Rectus Muscle 
Innervation to monkey and human lateral rectus muscles is segregated into well-defined superior and inferior zones, so that the lateral rectus may function as two parallel muscles under separate control. Differential activation of the two lateral rectus zones could impart previously unrecognized torsional and vertical actions to this nominally “horizontal” rectus muscle, potentially resolving an important paradox in ocular kinematics.
Skeletal and craniofacial muscles are frequently composed of multiple neuromuscular compartments that serve different physiological functions. Evidence of possible regional selectivity in LR intramuscular innervation was sought in a study of the anatomic potential of lateral rectus (LR) muscle compartmentalization.
Whole orbits of two humans and five macaque monkeys were serially sectioned at 10-μm thickness and stained with Masson trichrome. The abducens nerve (CN6) was traced anteriorly from the deep orbit as it branched to enter the LR and arborized among extraocular muscle (EOM) fibers. Three-dimensional reconstruction was performed in human and monkey orbits.
Findings were in concordance in the monkey and human orbits. External to the LR global surface, CN6 bifurcated into approximately equal-sized trunks before entering the global layer. Subsequent arborization showed a systematic topography, entering a well-defined inferior zone 0.4 to 2.5 mm more posteriorly than branches entering the largely nonoverlapping superior zone. Zonal innervation remained segregated anteriorly and laterally within the LR.
Consistent segregation of intramuscular CN6 arborization in humans and monkeys suggests functionally distinct superior and inferior zones for the LR. Since the LR is shaped as a broad vertical strap, segregated control of the two zones could activate them separately, potentially mediating previously unappreciated but substantial torsional and vertical oculorotary LR actions.
PMCID: PMC2941164  PMID: 20435590
14.  Quasilinear Viscoelastic Behavior of Bovine Extraocular Muscle Tissue 
Until now, there has been no comprehensive mathematical model of the nonlinear viscoelastic stress-strain behavior of extraocular muscles (EOMs). The present study describes, with the use of a quasilinear viscoelastic (QLV) model, the nonlinear, history-dependent viscoelastic properties and elastic stress-strain relationship of EOMs.
Six oculorotary EOMs were obtained fresh from a local abattoir. Longitudinally oriented specimens were taken from different regions of the EOMs and subjected to uniaxial tensile, relaxation, and cyclic loading testing with the use of an automated load cell under temperature and humidity control. Twelve samples were subjected to uniaxial tensile loading with 1.7%/s strain rate until failure. Sixteen specimens were subjected to relaxation studies over 1500 seconds. Cyclic loading was performed to validate predictions of the QLV model characterized from uniaxial tensile loading and relaxation data.
Uniform and highly repeatable stress-strain behavior was observed for 12 specimens extracted from various regions of all EOMs. Results from 16 different relaxation trials illustrated that most stress relaxation occurred during the first 30 to 60 seconds for 30% extension. Elastic and reduced relaxation functions were fit to the data, from which a QLV model was assembled and compared with cyclic loading data. Predictions of the QLV model agreed with observed peak cyclic loading stress values to within 8% for all specimens and conditions.
Close agreement between the QLV model and the relaxation and cyclic loading data validates model quantification of EOM mechanical properties and will permit the development of accurate overall models of mechanics of ocular motility and strabismus.
PMCID: PMC2742171  PMID: 19357357

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