Creep behavior of passive bovine extraocular muscle

Tensile properties of glaucomatous human sclera, optic nerve, and optic nerve sheath

We characterized the tensile behavior of sclera, optic nerve (ON), and ON sheath in eyes from donors with glaucoma, for comparison with published data without glaucoma. Twelve freshly harvested eyes were obtained from donors with history of glaucoma, of average age 86 ± 7 (standard deviation) years. Rectangular samples were taken from anterior, equatorial, posterior, and peripapillary sclera, and ON sheath, while ON was in native form and measured using calipers. Under physiological temperature and humidity, tissues were preconditioned at 5% strain before loading at 0.1 mm/s. Force-displacement data were converted into engineering stress-strain curves fit by reduced polynomial hyperelastic models and analyzed by tangent moduli at 3% and 7% strain. Data were compared with an age-matched sample of 7 published control eyes. Optic atrophy was supported by significant reduction in ON cross section to 73% of normal in glaucomatous eyes. Glaucomatous was significantly stiffer than control in equatorial and peripapillary regions (P < 0.001). However, glaucomatous ON and sheath were significantly less stiff than control, particularly at low strain (P < 0.001). Hyperelastic models were well fit to stress-strain data (R2 > 0.997). Tangent moduli had variability similar to control in most regions, but was abnormally large in peripapillary sclera. Tensile properties were varied independently among various regions of the same eyes. Glaucomatous sclera is abnormally stiff, but the ON and sheath are abnormally compliant. These abnormalities correspond to properties predicted by finite element analysis to transfer potentially pathologic stress to the vulnerable disk and lamina cribrosa region during adduction eye movement.

Interaction between eye movements and adhesion of extraocular muscles

The contact and pull-off tests and finite element simulations were used to study the extraocular muscle-sclera adhesion and its variation with eye movement in this research. The effect of the adhesion on the eye movements was also determined using equilibrium equations of eye motion. The contact and pull-off tests were performed using quasi-static and non-quasi-static unloading velocities. Finite element models were developed to simulate these tests in cases with high unloading velocity which could not be achieved experimentally. These velocities range from the eye's fixation to saccade movement. The tests confirmed that the pull-off force is related to the unloading velocity. As the unloading velocity increases, the pull-off force increases, with an insignificant increase at the high ocular saccade velocities. The adhesion moment between the extraocular muscles and the sclera exhibited the same trend, increasing with higher eye movement velocities and higher separation angles between the two interfaces. The adhesion moment ratio to the total moment was calculated by the traditional model and the active pulley model of eye movements to assess the effect of adhesion behavior on eye movements. At the high ocular saccade velocities (about 461 deg/s), the adhesion moment was found to be 0.53% and 0.50% of the total moment based on the traditional and active pulley models, respectively. The results suggest that the adhesion behavior between the extraocular muscles and the sclera has a negligible effect on eye movements. At the same time, this adhesion behavior can be ignored in eye modeling, which simplifies the model reasonably well. STATEMENT OF SIGNIFICANCE: 1. Adhesion behavior between the extraocular muscles and the sclera at different indenter unloading velocities determined by contact and pull-off tests. 2. A finite element model was developed to simulate the adhesive contact between the extraocular muscles and the sclera at different indenter unloading velocities. The bilinear cohesive zone model was used for adhesive interactions. 3. The elastic modulus and viscoelastic parameters of the extraocular muscle along the thickness direction were obtained by using compressive stress-relaxation tests. 4. The influence of the adhesion moment between the extraocular muscles and the sclera on eye movement was obtained according to the equation of oculomotor balance. The adhesion moment between the extraocular muscles and the sclera was found to increase with increased eye movement velocity and increased separation angle between the two interfaces.

Linear viscoelasticity of human sclera and posterior ocular tissues during tensile creep

PURPOSE

Despite presumed relevance to ocular diseases, the viscoelastic properties of the posterior human eye have not been evaluated in detail. We performed creep testing to characterize the viscoelastic properties of ocular regions, including the sclera, optic nerve (ON) and ON sheath.

METHODS

We tested 10 pairs of postmortem human eyes of average age 77 ± 17 years, consisting of 5 males and 5 females. Except for the ON that was tested in native shape, tissues were trimmed into rectangles. With physiologic temperature and constant wetting, tissues were rapidly loaded to tensile stress that was maintained by servo feedback as length was monitored for 1,500 sec. Relaxation modulus was computed using Prony series, and Deborah numbers estimated for times scales of physiological eye movements.

RESULTS

Correlation between creep rate and applied stress level was negligible for all tissues, permitting description as linear viscoelastic materials characterized by lumped parameter compliance equations for limiting behaviors. The ON was the most compliant, and anterior sclera least compliant, with similar intermediate values for posterior sclera and ON sheath. Sensitivity analysis demonstrated that linear behavior eventually become dominant after long time. For the range of typical pursuit tracking, all tissues exhibit Debora numbers less than 75, and should be regarded as viscoelastic. With a 6.7 Deborah number, this is especially so for the ON during pursuit and convergence.

CONCLUSIONS

Posterior ocular tissues exhibit creep consistent with linear viscoelasticity necessary for describing biomechanical behavior of the ON, its sheath, and sclera during physiological eye movements and eccentric ocular fixations. Running Head: Tensile Creep of Human Ocular Tissues.

Viscoelastic characterization of extraocular Z-myotomy

PURPOSE

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.

METHODS

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.

RESULTS

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.

CONCLUSIONS

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.

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.

Biomechanics of superior oblique Z-tenotomy

BACKGROUND

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.

METHODS

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 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.

RESULTS

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.

CONCLUSIONS

Z-tenotomy up to 50% progressively reduces extraocular tendon force transmission, but Z-tenotomy of ≥50% is biomechanically equivalent in vitro to complete tenotomy.

Towards a viscoelastic model for the unfused midpalatal suture: development and validation using the midsagittal suture in New Zealand white rabbits

Maxillary expansion treatment is a commonly used procedure by orthodontists to widen a patient's upper jaw. As this is typically performed in adolescent patients, the midpalatal suture, connective tissue adjoining the two maxilla halves, remains unfused. Studies that have investigated patient response to expansion treatment, generally through finite element analysis, have considered this suture to behave in a linear elastic manner or it was left vacant. The purpose of the study presented here was to develop a model that could represent the midpalatal suture's viscoelastic behavior. Quasilinear viscoelastic, modified superposition, Schapery's, and Burgers modeling approaches were all considered. Raw data from a previously published study using New Zealand White Rabbits was utilized for model parameter estimation and validation. In this study, Sentalloy(®) coil springs at load levels of 0.49N (50g), 0.98N (100g), and 1.96N (200g) were used to widen the midsagittal suture of live rabbits over a period of 6 weeks. Evaluation was based on a models ability to represent experimental data well over all three load sets. Ideally, a single set of model constants could be used to represent data over all loads tested. Upon completion of the analysis it was found that the modified superposition method was able to replicate experimental data within one standard deviation of the means using a single set of constants for all loads. Future work should focus on model improvement as well as prediction of treatment outcomes.

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. 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.