Finite Element Model of Ocular Adduction by Active Extraocular Muscle Contraction

Postmortem Digital Image Correlation and Finite Element Modeling Demonstrate Posterior Scleral Deformations during Optic Nerve Adduction Tethering

Postmortem human eyes were subjected to optic nerve (ON) traction in adduction and elevated intraocular pressure (IOP) to investigate scleral surface deformations. We incrementally adducted 11 eyes (age 74.1 ± 9.3 years, standard deviation) from 26° to 32° under normal IOP, during imaging of the posterior globe, for analysis by three-dimensional digital image correlation (3D-DIC). In the same eyes, we performed uniaxial tensile testing in multiple regions of the sclera, ON, and ON sheath. Based on individual measurements, we analyzed eye-specific finite element models (FEMs) simulating adduction and IOP loading. Analysis of 3D-DIC showed that the nasal sclera up to 1 mm from the sheath border was significantly compressed during adduction. IOP elevation from 15 to 30 mmHg induced strains less than did adduction. Tensile testing demonstrated ON sheath stiffening above 3.4% strain, which was incorporated in FEMs of adduction tethering that was quantitatively consistent with changes in scleral deformation from 3D-DIC. Simulated IOP elevation to 30 mmHg did not induce scleral surface strains outside the ON sheath. ON tethering in incremental adduction from 26° to 32° compressed the nasal and stretched the temporal sclera adjacent to the ON sheath, more so than IOP elevation. The effect of ON tethering is influenced by strain stiffening of the ON sheath.

Ciliary muscles contraction leads to axial length extension--The possible initiating factor for myopia

PURPOSE

This study aimed to investigate the underlying factors driving the onset of myopia, specifically the role of the ciliary muscle's contraction in the elongation of the axial length of the eye.

METHODS

The retrospective study was conducted utilizing data from three ophthalmic centers in Shanghai and Beijing. Both Chinese and Caucasian children were involved. The axial length of the subjects' eyes was measured in both relaxed and contracted state of the ciliary muscle. A comprehensive mechanical model was also developed to observe the influence of ciliary muscle contraction on the axial length.

RESULTS

This study included a sample of 198 right eyes of 198 myopic children. Of these, 97 were male and 101 were female, 126 were of Chinese ethnicity and 72 were Caucasian. The age of onset for myopia ranged from 5.9 to 16.9 years old. The axial length of the eye decreased 0.028 ± 0.007mm following dilation, indicating relaxation of the ciliary muscle (t paired student = 15.16, p = 6.72 x 10-35). In contrast, ciliary muscle contraction resulted in an increase in axial length. Considering proportionality, a significant 90.4% (179 eyes) exhibited a reduced axial length, while a minor 9.6% (19 eyes) demonstrated an increase post-mydriasis. Finite element modeling demonstrated that muscle contraction caused a tension force that transmits towards the posterior pole of the eye, causing it to extend posteriorly.

CONCLUSION

The contraction of the ciliary muscle leads to an extension of the axial length. This could potentially be the initiating factor for myopia.

Finite element model of ocular adduction with unconstrained globe translation

Details of the anatomy and behavior of the structures responsible for human eye movements have been extensively elaborated since the first modern biomechanical models were introduced. Based on these findings, a finite element model of human ocular adduction is developed based on connective anatomy and measured optic nerve (ON) properties, as well as active contractility of bilaminar extraocular muscles (EOMs), but incorporating the novel feature that globe translation is not otherwise constrained so that realistic kinematics can be simulated. Anatomy of the hemisymmetric model is defined by magnetic resonance imaging. The globe is modeled as suspended by anatomically realistic connective tissues, orbital fat, and contiguous ON. The model incorporates a material subroutine that implements active EOM contraction based on fiber twitch characteristics. Starting from the initial condition of 26° adduction, the medial rectus (MR) muscle was commanded to contract as the lateral rectus (LR) relaxed. We alternatively modeled absence or presence of orbital fat. During pursuit-like adduction from 26 to 32°, the globe translated 0.52 mm posteriorly and 0.1 mm medially with orbital fat present, but 1.2 mm posteriorly and 0.1 mm medially without fat. Maximum principal strains in the optic disk and peripapillary reached 0.05-0.06, and von-Mises stress 96 kPa. Tension in the MR orbital layer was ~ 24 g-force after 6° adduction, but only ~ 3 gm-f in the whole LR. This physiologically plausible simulation of EOM activation in an anatomically realistic globe suspensory system demonstrates that orbital connective tissues and fat are integral to the biomechanics of adduction, including loading by the ON.

Scanning Laser Ophthalmoscopy Demonstrates Pediatric Optic Disc and Peripapillary Strain During Horizontal Eye Rotation

Purpose: We employed automated analysis of scanning laser ophthalmoscopy (SLO) to determine if mechanical strains imposed on disc, and retinal and choroidal vessels during horizontal duction in children differ from those of adults.Methods: Thirty-one children aged 11.3 ± 2.7 (standard deviation) years underwent SLO in central gaze, and 35° ab- and adduction. Automated registration with deep learning-based optical flow analysis quantified vessel deformations as horizontal, vertical, shear, and equivalent strains. Choroidal vessel displacements in lightly pigmented fundi, and central disc vessel displacements, were also observed.Results: As in adults, strain in vessels during horizontal duction was greatest at the disc and decreased with distance from it. Strain in the pediatric disc was similar to published values in young adults,1 but in the peripapillary region was greater and propagated significantly more peripherally to at least three disc radii from it. During adduction in children, the nasal disc was compressed and disc vessels distorted, but the temporal half experienced tensile strain, while peripapillary tissues were compressed. The pattern was similar but strains were less in abduction (p < .001). Choroidal vessels were visualized in 24 of the 62 eyes and shifted directionally opposite overlying retinal vessels.Conclusions: Horizontal duction deforms the normal pediatric optic disc, central retinal vessels, peripapillary retina, and choroid, shearing the inner retina over the choroid. These mechanical effects occur at the sites of remodeling of the disc, sclera, and choroid associated with typical adult features that later emerge later, including optic cup enlargement, temporal disc tilting, and peripapillary atrophy.

Development of a three-dimensional muscle-driven lower limb model developed using an improved CFD-FE method

Analysis of the musculoskeletal movements (gait analysis) is needed in many scenarios. The in vivo method has some difficulties. For example, recruiting human subjects for the gait analysis is challenging due to many issues. In addition, when plenty of subjects are required, the follow-up experiments take a long period and the dropout of subjects always occurs. An efficient and reliable in silico simulation platform for gait analysis has been desired for a long time. Therefore, a technique using three-dimensional (3D) muscle modeling to drive the 3D musculoskeletal model was developed and the application of the technique in the simulation of lower limb movements was demonstrated. A finite element model of the lower limb with anatomically high fidelity was developed from the MRI data, where the main muscles, the bones, the subcutaneous tissues, and the skin were reconstructed. To simulate the active behavior of 3D muscles, an active, fiber-reinforced hyperelastic muscle model was developed using the user-defined material (VUMAT) model. Two typical movements, that is, hip abduction and knee lifting, were simulated by activating the responsible muscles. The results show that it is reasonable to use the improved CFD-FE method proposed in the present study to simulate the active contraction of the muscle, and it is feasible to simulate the movements by activating the relevant muscles. The results from the present technique closely match the physiological scenario and thus the technique developed has a great potential to be used in the in silico human simulation platform for many purposes.

Scanning Laser Ophthalmoscopy Demonstrates Disc and Peripapillary Strain During Horizontal Eye Rotation in Adults

PURPOSE

We used automated image analysis of scanning laser ophthalmoscopy (SLO) to investigate mechanical strains imposed on disc, and retinal and choroidal vessels during horizontal duction in adults.

DESIGN

Deep learning analysis of optical images.

METHODS

The peripapillary region was imaged by SLO in central gaze, and 35° abduction and adduction, in younger and older healthy adults. Automated image registration was followed by deep learning-based optical flow analysis to track determine local tissue deformations quantified as horizontal, vertical, and shear strain maps relative to central gaze. Choroidal vessel displacements were observed when fundus pigment was light.

RESULTS

Strains in the retina and disc could be quantified in 22 younger (mean ± SEM, 26 ± 5 years) and 19 older (64 ± 10 years) healthy volunteers. Strains were predominantly horizontal and greater for adduction than for abduction. During adduction, maximum horizontal strain was tensile in the nasal hemi-disc, and declined progressively with distance from it. Strain in the temporal hemi-retina during adduction was minimal, except for compressive strain on the disc of older subjects. In abduction, horizontal strains were less and largely confined to the disc, greater in older subjects, and generally tensile. Vertical and shear strains were small. Nasal to the disc, choroidal vessels shifted nasally relative to overlying peripapillary retinal vessels.

CONCLUSIONS

Strain analysis during horizontal duction suggests that the optic nerve displaces the optic canal, choroid, and peripapillary sclera relative to the overlying disc and retina. This peripapillary shearing of the optic nerve relative to the choroid and sclera may be a driver of disc tilting and peripapillary atrophy.

Empirical Quantification of Optic Nerve Strain Due to Horizontal Duction

Magnetic resonance imaging (MRI) was used to measure in vivo local strains in the optic nerve (ON) associated with horizontal duction in humans. Axial and coronal MRI were collected in target-controlled gazes in 24 eyes of 12 normal adults (six males and six females, 59 ± 16 years) during large (~28°) and moderate (~24°) ductions. The ON, globe, and extraocular muscles were manually identified, and the pixels were converted to point-sets that were registered across different imaging planes and eye positions. Shape of the ON was parameterized based on point-sets. Displacements and strains were computed by comparing deformed with initial ON configurations. Displacements were the largest in the most anterior region. However, strains from adduction were uniform along the length of the ON, while those during abduction increased with distance from the globe and were maximal near the orbital apex. For large gaze angles, ON strain during abduction was primarily due to bending near the orbital apex that is less transmitted to the eye, but during adduction the ON undergoes uniform stretching that transmits much greater loading to the posterior eye, implied by greater strain on the ON.

Who bears the load? IOP-induced collagen fiber recruitment over the corneoscleral shell

Collagen is the main load-bearing component of cornea and sclera. When stretched, both of these tissues exhibit a behavior known as collagen fiber recruitment. In recruitment, as the tissues stretch the constitutive collagen fibers lose their natural waviness, progressively straightening. Recruited, straight, fibers bear substantially more mechanical load than non-recruited, wavy, fibers. As such, the process of recruitment underlies the well-established nonlinear macroscopic behavior of the corneoscleral shell. Recruitment has an interesting implication: when recruitment is incomplete, only a fraction of the collagen fibers is actually contributing to bear the loads, with the rest remaining "in reserve". In other words, at a given intraocular pressure (IOP), it is possible that not all the collagen fibers of the cornea and sclera are actually contributing to bear the loads. To the best of our knowledge, the fraction of corneoscleral shell fibers recruited and contributing to bear the load of IOP has not been reported. Our goal was to obtain regionally-resolved estimates of the fraction of corneoscleral collagen fibers recruited and in reserve. We developed a fiber-based microstructural constitutive model that could account for collagen fiber undulations or crimp via their tortuosity. We used experimentally-measured collagen fiber crimp tortuosity distributions in human eyes to derive region-specific nonlinear hyperelastic mechanical properties. We then built a three-dimensional axisymmetric model of the globe, assigning region-specific mechanical properties and regional anisotropy. The model was used to simulate the IOP-induced shell deformation. The model-predicted tissue stretch was then used to quantify collagen recruitment within each shell region. The calculations showed that, at low IOPs, collagen fibers in the posterior equator were recruited the fastest, such that at a physiologic IOP of 15 mmHg, over 90% of fibers were recruited, compared with only a third in the cornea and the peripapillary sclera. The differences in recruitment between regions, in turn, mean that at a physiologic IOP the posterior equator had a fiber reserve of only 10%, whereas the cornea and peripapillary sclera had two thirds. At an elevated IOP of 50 mmHg, collagen fibers in the limbus and the anterior/posterior equator were almost fully recruited, compared with 90% in the cornea and the posterior sclera, and 70% in the peripapillary sclera and the equator. That even at such an elevated IOP not all the fibers were recruited suggests that there are likely other conditions that challenge the corneoscleral tissues even more than IOP. The fraction of fibers recruited may have other potential implications. For example, fibers that are not bearing loads may be more susceptible to enzymatic digestion or remodeling. Similarly, it may be possible to control tissue stiffness through the fraction of recruited fibers without the need to add or remove collagen.

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.

The impact of horizontal eye movements versus intraocular pressure on optic nerve head biomechanics: A tridimensional finite element analysis study

It has been proposed that eye movements could be related to glaucoma development. This research aimed to compare the impact of intraocular pressure (IOP) versus horizontal duction on optic nerve head (ONH) strains. Thus, a tridimensional finite element model of the eye including the three tunics of the eye, all of the meninges, and the subarachnoid space (SAS) was developed using a series of medical tests and anatomical data. The ONH was divided into 22 subregions, and the model was subjected to 21 different eye pressures, as well as 24 different degrees of adduction and abduction ranging from 0.5° to 12°. Mean deformations were documented along anatomical axes and in principal directions. Additionally, the impact of tissue stiffness was assessed. The results show no statistically significant differences between the lamina cribrosa (LC) strains due to eye rotation and IOP variation. However, when assessing LC regions some experienced a reduction in principal strains following a 12° duction, while after the IOP reached 12 mmHg, all LC subzones showed an increase in strains. From an anatomical perspective, the effect on the ONH following 12° duction was opposite to that observed after a rise in IOP. Moreover, high strain dispersion inside the ONH subregions was obtained with lateral eye movements, which was not observed with increased IOP and variation. Finally, SAS and orbital fat stiffness strongly influenced ONH strains during eye movements, while SAS stiffness was also influential under ocular hypertension. Even if horizontal eye movements cause large ONH deformations, their biomechanical effect would be markedly distinct from that induced by IOP. It could be predicted that, at least in physiological conditions, their potential to cause axonal injury would not be so relevant. Thus, a causative role in glaucoma does not appear likely. By contrast, an important role of SAS would be expectable.

Finite element modeling of effects of tissue property variation on human optic nerve tethering during adduction

Tractional tethering by the optic nerve (ON) on the eye as it rotates towards the midline in adduction is a significant ocular mechanical load and has been suggested as a cause of ON damage induced by repetitive eye movements. We designed an ocular finite element model (FEM) simulating 6° incremental adduction beyond the initial configuration of 26° adduction that is the observed threshold for ON tethering. This FEM permitted sensitivity analysis of ON tethering using observed material property variations in measured hyperelasticity of the anterior, equatorial, posterior, and peripapillary sclera; and the ON and its sheath. The FEM predicted that adduction beyond the initiation of ON tethering concentrates stress and strain on the temporal side of the optic disc and peripapillary sclera, the ON sheath junction with the sclera, and retrolaminar ON neural tissue. However, some unfavorable combinations of tissue properties within the published ranges imposed higher stresses in these regions. With the least favorable combinations of tissue properties, adduction tethering was predicted to stress the ON junction and peripapillary sclera more than extreme conditions of intraocular and intracranial pressure. These simulations support the concept that ON tethering in adduction could induce mechanical stresses that might contribute to ON damage.

Computational Modeling of Ophthalmic Procedures: Computational Modeling of Ophthalmic Procedures

PURPOSE

To explore how finite-element calculations can continue to contribute to diverse problems in ophthalmology and vision science, we describe our recent work on modeling the force on the peripheral retina in intravitreal injections and how that force increases with shorter, smaller gauge needles. We also present a calculation that determines the location and stress on a retinal pigment epithelial detachment during an intravitreal injection, the possibility that stress induced by the injection can lead to a tear of the retinal pigment epithelium.

BACKGROUND

Advanced computational models can provide a critical insight into the underlying physics in many surgical procedures, which may not be intuitive.

METHODS

The simulations were implemented using COMSOL Multiphysics. We compared the monkey retinal adhesive force of 18 Pa with the results of this study to quantify the maximum retinal stress that occurs during intravitreal injections.

CONCLUSIONS

Currently used 30-gauge needles produce stress on the retina during intravitreal injections that is only slightly below the limit that can create retinal tears. As retina specialists attempt to use smaller needles, the risk of complications may increase. In addition, we find that during an intravitreal injection, the stress on the retina in a pigment epithelial detachment occurs at the edge of the detachment (found clinically), and the stress is sufficient to tear the retina. These findings may guide physicians in future clinical research. NOTE: Publication of this article is sponsored by the American Ophthalmological Society.

Dynamics of plant mechanics

Muscle and plant dynamics are most important during the high acceleration of saccades. Models have been developed to characterize muscle and plant dynamics. Building these models require an understanding of the length-tension (elastic) and force-velocity (viscous) relationships. Much work has been done to characterize these nonlinear functions, as they are influenced by innervation. However, the active force generator (active-state tension) in the muscle is still poorly understood. Thus, these models serve more to reveal where new studies of muscle behavior are needed than to explain what happens during a saccade.