Viscoelastic characterization of extraocular Z-myotomy

Biomechanics Explains Variability of Response of Small Hypertropia to Graded Vertical Rectus Tenotomy

PURPOSE

Small angle hypertropia in sagging eye syndrome is conveniently treated by graded vertical rectus tenotomy, yet an adjustable technique under topical anesthesia has been recommended because of variability of effect. We performed graded tenotomy in an experimental model to elucidate the reason for variability of response to this surgical procedure.

DESIGN

Experimental study.

METHODS

Thirty-two fresh bovine rectus musculotendon specimens were prepared including continuity with insertional sclera, and extending for a total 40 mm length to the proximal muscle bellies, and trimmed to 16 mm width. Specimens were anchored by the clamps at the scleral insertion and muscle belly ends within a physiological chamber. After preconditioning and elongation to 10% strain was imposed by a linear motor, tensile force was allowed to stabilize at a plateau state. Then 25%, 50%, 75%, 90%, and 100% marginal tenotomies were performed progressively as remnant forces were measured.

RESULTS

Tendon thickness averaged 0.29 ± 0.05 mm and width 19.71 ± 2.25 mm. On average, remnant force decreased linearly (R2 = 0.985) from 4.23 ± 1.34, 2.76 ± 0.88, 1.70 ± 0.73, 1.01 ± 0.49, 0.39 ± 0.10, and 0 N, at 0%, 25%, 50%, 75%, 90%, and 100% tenotomy. However, there was marked individual variability in effect among specimens, with coefficients of variation of 32%, 32%, 43%, 49%, and 27%, respectively.

CONCLUSION

On average, there is a linear relationship between graded rectus tenotomy and percentage force reduction, but the effect among individual tendons is large, paralleling the reported variation in surgical effect. This explains and implies continued advisability of adjustable technique in this procedure.

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.

Functional anatomy of human extraocular muscles during fusional divergence

We employed magnetic resonance imaging to quantify human extraocular muscle contractility during centered target fusion and fusional divergence repeated with each eye viewing monocularly at 20 cm through 8Δ and at 400 cm through 4Δ base in prism. Contractility, indicated by posterior partial volume (PPV) change, was analyzed in transverse rectus and in medial and lateral superior oblique (SO) muscle compartments and by cross-sectional area change in the inferior oblique (IO). At 20 cm, 3.1 ± 0.5° (SE) diverging eye abduction in 10 subjects was associated with 4.2 ± 1.5% whole lateral rectus (LR) PPV increase ( P < 0.05) and 1.7 ± 1.1% overall medial rectus (MR) PPV decrease attributable to 3.1 ± 1.8% reduction in the superior compartment ( P < 0.025), without change in its inferior compartment or in muscles of the aligned eye. At 400 cm, 2.2 ± 0.5° diverging eye abduction in nine subjects was associated with 6.1 ± 1.3% whole LR PPV increase ( P < 10^-5) but no change in MR, with compartmentally similar relaxation in the LR and MR of the aligned eye. Unlike convergence, there were no IO or SO contractile changes for divergence to either target nor any change in rectus pulley positions. Results confirm and extend to proximal divergence the unique role of the superior MR compartment, yet no MR role for far divergence. Corelaxation of aligned eye LR and MR combined with failure of MR relaxation during divergence is consistent with the limited behavioral range of divergence. NEW & NOTEWORTHY Magnetic resonance imaging shows that the lateral rectus muscle must overcome continued contraction by its opponent the medial rectus when humans diverge their visual axes to achieve single, binocular vision. While the upper but not lower compartment of the medial rectus assists by relaxing for near targets, it does not do so when targets are far away. This behavior violates Sherrington's law of reciprocal action of antagonists and conventional assumptions about the ocular motor system.

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 Young's 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 6 deg beyond ON straightening at multiple levels of IOP. Young's modulus of ON sheath of 44.6 ± 5.6 MPa (standard error of mean) greatly exceeded that of ON at 5.2 ± 0.4 MPa, peripapillary sclera at 5.5 ± 0.8 MPa, and peripheral sclera at 14.0 ± 2.3 MPa. FEA indicated that adduction induced maximum stress and strain in the temporal ONH. In the temporal LC, the maximum stress was 180 kPa, and the maximum strain was ninefold larger than produced by IOP elevation to 45 mm 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.

Quantitative characterization of viscoelastic behavior in tissue-mimicking phantoms and ex vivo animal tissues

Viscoelasticity of soft tissue is often related to pathology, and therefore, has become an important diagnostic indicator in the clinical assessment of suspect tissue. Surgeons, particularly within head and neck subsites, typically use palpation techniques for intra-operative tumor detection. This detection method, however, is highly subjective and often fails to detect small or deep abnormalities. Vibroacoustography (VA) and similar methods have previously been used to distinguish tissue with high-contrast, but a firm understanding of the main contrast mechanism has yet to be verified. The contributions of tissue mechanical properties in VA images have been difficult to verify given the limited literature on viscoelastic properties of various normal and diseased tissue. This paper aims to investigate viscoelasticity theory and present a detailed description of viscoelastic experimental results obtained in tissue-mimicking phantoms (TMPs) and ex vivo tissues to verify the main contrast mechanism in VA and similar imaging modalities. A spherical-tip micro-indentation technique was employed with the Hertzian model to acquire absolute, quantitative, point measurements of the elastic modulus (E), long term shear modulus (η), and time constant (τ) in homogeneous TMPs and ex vivo tissue in rat liver and porcine liver and gallbladder. Viscoelastic differences observed between porcine liver and gallbladder tissue suggest that imaging modalities which utilize the mechanical properties of tissue as a primary contrast mechanism can potentially be used to quantitatively differentiate between proximate organs in a clinical setting. These results may facilitate more accurate tissue modeling and add information not currently available to the field of systems characterization and biomedical research.

Compartmental Innervation of the Superior Oblique Muscle in Mammals

PURPOSE

Intramuscular innervation of mammalian horizontal rectus extraocular muscles (EOMs) is compartmental. We sought evidence of similar compartmental innervation of the superior oblique (SO) muscle.

METHODS

Three fresh bovine orbits and one human orbit were dissected to trace continuity of SO muscle and tendon fibers to the scleral insertions. Whole orbits were also obtained from four humans (two adults, a 17-month-old child, and a 33-week stillborn fetus), two rhesus monkeys, one rabbit, and one cow. Orbits were formalin fixed, embedded whole in paraffin, serially sectioned in the coronal plane at 10-μm thickness, and stained with Masson trichrome. Extraocular muscle fibers and branches of the trochlear nerve (CN4) were traced in serial sections and reconstructed in three dimensions.

RESULTS

In the human, the lateral SO belly is in continuity with tendon fibers inserting more posteriorly on the sclera for infraducting mechanical advantage, while the medial belly is continuous with anteriorly inserting fibers having mechanical advantage for incycloduction. Fibers in the monkey superior SO insert more posteriorly on the sclera to favor infraduction, while the inferior portion inserts more anteriorly to favor incycloduction. In all species, CN4 bifurcates prior to penetrating the SO belly. Each branch innervates a nonoverlapping compartment of EOM fibers, consisting of medial and lateral compartments in humans and monkeys, and superior and inferior compartments in cows and rabbits.

CONCLUSIONS

The SO muscle of humans and other mammals is compartmentally innervated in a manner that could permit separate CN4 branches to selectively influence vertical versus torsional action.

Superior oblique extraocular muscle shape in superior oblique palsy

PURPOSE

To investigate the superior oblique (SO) extraocular muscle cross section in normal controls and in SO palsy using high-resolution magnetic resonance imaging (MRI).

DESIGN

Prospective observational study.

METHODS

At a single academic medical center, high-resolution MRI was obtained at 312 μm in-plane resolution using surface coils in multiple, contiguous, quasi-coronal planes perpendicular to the orbital axis in 12 controls and 62 subjects with SO palsy. Previous strabismus surgery was excluded. Imaging was repeated in central gaze and infraduction. In each image plane along the SO, its cross section was outlined to compute cross-sectional area and the major and minor axes of the best-fitting ellipse. Main outcome measures were SO morphology and ocular motility.

RESULTS

The major and minor axes, cross-sectional area distributions, and volume of the SO belly were subnormal in orbits with SO palsy at most anteroposterior locations (P = .001), but discriminant analysis showed that palsied SO cross sections segregated distinctly into round and elongate shapes representing isotropic vs anisotropic atrophy, respectively. The major axis was relatively preserved in anisotropic atrophy (P = .0146). Cases with isotropic atrophy exhibited greater hypertropia in infraversion than central gaze, as well as greater excyclotorsion, than cases with anisotropic atrophy (P < .05 for all).

CONCLUSIONS

Characteristic differences in shape of the palsied SO belly correlate with different clinical features, and may reflect both the degree of differential pathology in the medial vs lateral neuromuscular SO compartments and the basis for diversity in patterns of resulting hypertropia.