Andrew Shin

Characterization of Ocular Tissues Using Microindentation and Hertzian Viscoelastic Models

PURPOSEnThe 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.nnnMETHODSnThey 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.nnnRESULTSnViscoelastic 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.nnnCONCLUSIONSnRelaxation 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.

Independent passive mechanical behavior of bovine extraocular muscle compartments.

PURPOSEnIntramuscular 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.nnnMETHODSnPutative 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.nnnRESULTSnAll 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.nnnCONCLUSIONSnSubstantial 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.

Deformation of Optic Nerve Head and Peripapillary Tissues by Horizontal Duction

PURPOSEnTo ascertain deformation of the optic nerve head (ONH) and peripapillary tissues caused by horizontal duction.nnnDESIGNnProspective, experimental study.nnnMETHODSnOptical coherence tomography of the ONH region was performed in 23 eyes of 12 normal volunteers in central gaze and increasing (10, 20, and 30 degrees) adduction and abduction. Main outcome measures were changes from central gaze in the configuration of the ONH and peripapillary tissues in eccentric gazes.nnnRESULTSnAdduction but not abduction was associated with significant, progressive relative posterior displacement of the temporal peripapillary retinal pigment epithelium (tRPE) from its position in central gaze reaching 49 ± 10xa0μm in 30-degree adduction (standard error of mean, P < .0001). Absolute (anterior or posterior) optic cup displacement (OCD) averaged 41 ± 7xa0μm in 30-degree adduction. Linear regression showed significant effect of adduction on absolute OCD (slope 1.09 ± 0.36 μm/degree, Pxa0= .0037). In 20-degree and 30-degree adduction, all eyes exhibited significant progressive temporal ONH tilting reaching 3.1 ± 0.4 degrees in 30-degree adduction (P < .0001). Abduction was not associated with significant peripapillary RPE displacement, OCD, or ONH tilt. Both nasal and temporal peripapillary choroid averaged 9-19xa0μm thinner in adduction and abduction than in central gaze (P < .02).nnnCONCLUSIONSnAdduction temporally tilts and displaces the prelaminar ONH and peripapillary tissues. Both adduction and abduction compress the peripapillary choroid. These effects support magnetic resonance imaging and biomechanical evidence that adduction imposes strain on the ONH and peripapillary tissues. Repetitive strain from eye movements over decades might in susceptible individuals lead to optic neuropathies such as normal tension glaucoma.

Independent Active Contraction of Extraocular Muscle Compartments

PURPOSEnIntramuscular 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.nnnMETHODSnFresh 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.nnnRESULTSnIn 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.nnnCONCLUSIONSnThese 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.

Biomechanics of superior oblique Z-tenotomy.

BACKGROUNDnA 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.nnnMETHODSnFresh 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 margins, 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.nnnRESULTSnProgressively 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.nnnCONCLUSIONSnZ-tenotomy up to 50% progressively reduces extraocular tendon force transmission, butxa0Z-tenotomy of ≥50% is biomechanically equivalent inxa0vitro to complete tenotomy.

Atomic force microscopy determination of Young׳s modulus of bovine extra-ocular tendon fiber bundles

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 100nm 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 1800 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±5.34MPa, medial rectus 56.92±1.91MPa, superior rectus 59.66±2.64MPa, inferior oblique 57.7±1.36MPa, 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.

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 1,500u2009s. 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.

Determination of Poisson Ratio of Bovine Extraocular Muscle by Computed X-Ray Tomography

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. Greens 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.

Finite Element Biomechanics of Optic Nerve Sheath Traction in Adduction

Historical emphasis on increased intraocular pressure (IOP) in the pathogenesis of glaucoma has been challenged by the recognition that many patients lack abnormally elevated IOP. We employed finite element analysis (FEA) to infer contribution to optic neuropathy from tractional deformation of the optic nerve head (ONH) and lamina cribrosa (LC) by extraocular muscle (EOM) counterforce exerted when optic nerve (ON) redundancy becomes exhausted in adduction. We characterized assumed isotropic Youngs modulus of fresh adult bovine ON, ON sheath, and peripapillary and peripheral sclera by tensile elongation in arbitrary orientations of five specimens of each tissue to failure under physiological temperature and humidity. Physical dimensions of the FEA were scaled to human histological and magnetic resonance imaging (MRI) data and used to predict stress and strain during adduction 6u2009deg beyond ON straightening at multiple levels of IOP. Youngs modulus of ON sheath of 44.6u2009±u20095.6u2009MPa (standard error of mean) greatly exceeded that of ON at 5.2u2009±u20090.4u2009MPa, peripapillary sclera at 5.5u2009±u20090.8u2009MPa, and peripheral sclera at 14.0u2009±u20092.3u2009MPa. FEA indicated that adduction induced maximum stress and strain in the temporal ONH. In the temporal LC, the maximum stress was 180u2009kPa, and the maximum strain was ninefold larger than produced by IOP elevation to 45u2009mm Hg. The simulation suggests that ON sheath traction by adduction concentrates far greater mechanical stress and strain in the ONH region than does elevated IOP, supporting the novel concept that glaucomatous optic neuropathy may result at least partly from external traction on the ON, rather than exclusively on pressure on the ON exerted from within the eye.

Viscoelastic characterization of extraocular Z-myotomy.

PURPOSEnZ-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.nnnMETHODSnFresh 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.nnnRESULTSnThere 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.nnnCONCLUSIONSnThe 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.