The viscoelastic properties of passive eye muscle in primates. I: static forces and step responses

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.

Structure-Function relationships in the skeletal muscle extracellular matrix

The vast majority of skeletal muscle biomechanical studies have rightly focused on its active contractile properties. However, skeletal muscle passive biomechanical properties have significant clinical impact in aging and disease and are yet incompletely understood. This review focuses on the passive biomechanical properties of the skeletal muscle extracellular matrix (ECM) and suggests aspects of its structural basis. Structural features of the muscle ECM such as perimysial cables, collagen cross-links and endomysial structures have been described, but the way in which these structures combine to create passive biomechanical properties is not completely known. We highlight the presence and organization of perimysial cables. We also demonstrate that the analytical approaches that define passive biomechanical properties are not necessarily straight forward. For example, multiple equations, such as linear, exponential, and polynomial are commonly used to fit raw stress-strain data. Similarly, multiple definitions of zero strain exist that affect muscle biomechanical property calculations. Finally, the appropriate length range over which to measure the mechanical properties is not clear. Overall, this review summarizes our current state of knowledge in these areas and suggests experimental approaches to measuring the structural and functional properties of skeletal muscle.

Oculomotor plant and neural dynamics suggest gaze control requires integration on distributed timescales

A fundamental principle of biological motor control is that the neural commands driving movement must conform to the response properties of the motor plants they control. In the oculomotor system, characterizations of oculomotor plant dynamics traditionally supported models in which the plant responds to neural drive to extraocular muscles on exclusively short, subsecond timescales. These models predict that the stabilization of gaze during fixations between saccades requires neural drive that approximates eye position on longer timescales and is generated through the temporal integration of brief eye velocity-encoding signals that cause saccades. However, recent measurements of oculomotor plant behaviour have revealed responses on longer timescales. Furthermore, measurements of firing patterns in the oculomotor integrator have revealed a more complex encoding of eye movement dynamics. Yet, the link between these observations has remained unclear. Here we use measurements from the larval zebrafish to link dynamics in the oculomotor plant to dynamics in the neural integrator. The oculomotor plant in both anaesthetized and awake larval zebrafish was characterized by a broad distribution of response timescales, including those much longer than 1 s. Analysis of the firing patterns of oculomotor integrator neurons, which exhibited a broadly distributed range of decay time constants, demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with distributed response timescales. This work suggests that leaky integration on multiple, distributed timescales by the oculomotor integrator reflects an inverse model for generating oculomotor commands, and that multi-timescale dynamics may be a general feature of motor circuitry. KEY POINTS: Recent observations of oculomotor plant response properties and neural activity across the oculomotor system have called into question classical formulations of both the oculomotor plant and the oculomotor integrator. Here we use measurements from new and published experiments in the larval zebrafish together with modelling to reconcile recent oculomotor plant observations with oculomotor integrator function. We developed computational techniques to characterize oculomotor plant responses over several seconds in awake animals, demonstrating that long timescale responses seen in anaesthetized animals extend to the awake state. Analysis of firing patterns of oculomotor integrator neurons demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with multiple, distributed response timescales. Our results support a formulation of gaze stabilization by the oculomotor system in which commands for stabilizing gaze are generated through integration on multiple, distributed timescales.

A parameter reduced adaptive quasi-linear viscoelastic model for soft biological tissue in uniaxial tension

Mechanical characterisation of soft viscous materials is essential for many applications including aerospace industries, material models for surgical simulation, and tissue mimicking materials for anatomical models. Constitutive material models are, therefore, necessary to describe soft biological tissues in physiologically relevant strain ranges. Hereby, the adaptive quasi-linear viscoelastic (AQLV) model enables accurate modelling of the strain-dependent non-linear viscoelastic behaviour of soft tissues with a high flexibility. However, the higher flexibility produces a large number of model parameters. In this study, porcine muscle and liver tissue samples were modelled in the framework of the originally published AQLV (3-layers of Maxwell elements) model using four incremental ramp-hold experiments in uniaxial tension. AQLV model parameters were reduced by decreasing model layers (M) as well as the number of experimental ramp-hold steps (N). Leave One out cross validation tests show that the original AQLV model (3M4N) with 19 parameters, accurately describes porcine muscle tissue with an average R² of 0.90 and porcine liver tissue, R² of 0.86. Reducing the number of layers (N) in the model produced acceptable model fits for 1-layer (R² of 0.83) and 2-layer models (R² of 0.89) for porcine muscle tissue and 1-layer (R² of 0.84) and 2-layer model (R² of 0.85) for porcine liver tissue. Additionally, a 2 step (2N) ramp-hold experiment was performed on additional samples of porcine muscle tissue only to further reduce model parameters. Calibrated spring constant values for 2N ramp-hold tests parameters k₁ and k₂ had a 16.8% and 38.0% deviation from those calibrated for a 4 step (4N) ramp hold experiment. This enables further reduction of material parameters by means of step reduction, effectively reducing the number of parameters required to calibrate the AQLV model from 19 for a 3M4N model to 8 for a 2M2N model, with the added advantage of reducing the time per experiment by 50%. This study proposes a 'reduced-parameter' AQLV model (2M2N) for the modelling of soft biological tissues at finite strain ranges. Sequentially, the comparison of model parameters of soft tissues is easier and the experimental burden is reduced.

Mathematical models and human disease

Mathematical models of brain function are built from data covering anatomy, physiology, biophysics and behavior. In almost all cases, many possible models could fit the available data. Theoreticians make assumptions that allow them to constrain the number of possible model structures. However, a model that was more useful clinically would result if the constraints came from lesion studies in animals or clinical disorders. Here, we show a few examples of how clinical disorders have led to improvements in models. We also show a few examples of how models could lead to neural prostheses for patients. The best outcomes result when clinicians, basic scientists and theoreticians work together to understand brain function.

Altered Protein Composition and Gene Expression in Strabismic Human Extraocular Muscles and Tendons

Purpose

To determine whether structural protein composition and expression of key regulatory genes are altered in strabismic human extraocular muscles.

Methods

Samples from strabismic horizontal extraocular muscles were obtained during strabismus surgery and compared with normal muscles from organ donors. We used proteomics, standard and customized PCR arrays, and microarrays to identify changes in major structural proteins and changes in gene expression. We focused on muscle and connective tissue and its control by enzymes, growth factors, and cytokines.

Results

Strabismic muscles showed downregulation of myosins, tropomyosins, troponins, and titin. Expression of collagens and regulators of collagen synthesis and degradation, the collagenase matrix metalloproteinase (MMP)2 and its inhibitors, tissue inhibitor of metalloproteinase (TIMP)1 and TIMP2, was upregulated, along with tumor necrosis factor (TNF), TNF receptors, and connective tissue growth factor (CTGF), as well as proteoglycans. Growth factors controlling extracellular matrix (ECM) were also upregulated. Among 410 signaling genes examined by PCR arrays, molecules with downregulation in the strabismic phenotype included GDNF, NRG1, and PAX7; CTGF, CXCR4, NPY1R, TNF, NTRK1, and NTRK2 were upregulated. Signaling molecules known to control extraocular muscle plasticity were predominantly expressed in the tendon rather than the muscle component. The two horizontal muscles, medial and lateral rectus, displayed similar changes in protein and gene expression, and no obvious effect of age.

Conclusions

Quantification of proteins and gene expression showed significant differences in the composition of extraocular muscles of strabismic patients with respect to important motor proteins, elements of the ECM, and connective tissue. Therefore, our study supports the emerging view that the molecular composition of strabismic muscles is substantially altered.

The biomechanical significance of pulley on binocular vision

Background

Pulleys have been reported as the functional origins of the rectus extraocular muscles (EOMs). However, biomechanical significance of pulleys on binocular vision has not been reported.

Methods

Three eye movement models, i.e., non-pulley model, passive-pulley model, and active-pulley model, are used to simulate the horizontal movement of the eyes from the primary position to the left direction in the range of 1°–30°. The resultant forces of six EOMs along both orthogonal directions (i.e., the x-axis and y-axis defined in this paper) in the horizontal plane are calculated using the three models.

Results

The resultant force along the y-axis of the left eye for non-pulley model are significantly larger than that of the other two pulley models. The difference of the force, between the left eye and the right eye in non-pulley model, is larger than those in the other two pulley models along x-axis and y-axis.

Conclusion

The pulley models present more biomechanical advantage on the horizontally binocular vision than the non-pulley model. Combining with the previous imaging evidences of pulleys, the results show that pulley model coincides well with the real physiological conditions.

Contractile Force of Human Extraocular Muscle: A Theoretical Analysis

Aim. The length-contractile force relationships of six human extraocular muscles (EOMs) in primary innervations should be determined during eye movement modeling and surgery of clinical EOMs. This study aims to investigate these relationships. Method. The proposal is based on the assumption that six EOMs have similar constitutive relationships, with the eye suspended in the primary position. The constitutive relationships of EOMs are obtained by optimizing from previous experimental data and the theory of mechanical equilibrium using traditional model. Further, simulate the existing experiment of resistance force, and then compare the simulated results with the existing experimental results. Finally, the mechanical constitutive relationships of EOMs are obtained. Results. The results show that the simulated resistance forces from the other four EOMs except for the horizontal recti well agree with previous experimental results. Conclusion. The mechanical constitutive relationships of six EOMs in primary innervations are obtained, and the rationality of the constitutive relationships is verified. Whereafter, the active stress-strain relationships of the six EOMs in the primary innervations are obtained. The research results can improve the eye movement model to predict the surgical amounts of EOMs before EOM surgery more precisely.

A noninvasive electromagnetic perturbation approach to probe extraocular proprioception

BACKGROUND

Extraocular proprioception has been shown to participate in spatial perception and binocular alignment. Yet the physiological approaches used to study this sensory signal are limited because proprioceptive signaling takes place at the same time as visuomotor signaling. It is critical to dissociate this sensory signal from other visuomotor events that accompany eye movements.

METHODS

We present a novel noninvasive and quantifiable method for probing extraocular proprioception independent of other visuomotor processing by attaching a rare-earth magnet to a real-time model eye and placing an electromagnet <20 mm from the eye. An electromagnet can increase or decrease angular displacements and velocities of the model eye.

RESULTS

Electromagnetic activation rapidly affected (<2 ms) the rotation kinematics of the eye, which were correlated linearly with both the current supply and the distance of the electromagnet relative to the eye.

CONCLUSIONS

This method circumvented the constraints of conventional physiological manipulation of extraocular proprioception, such as manually or mechanically tugging on the eye ball. It can be applied to produce the discrepancy between the intended and the executed eye movements, so that proprioceptive reafference signals are dissociated from corollary motor discharges and other visuomotor events.

Mechanics of mouse ocular motor plant quantified by optogenetic techniques

Rigorous descriptions of ocular motor mechanics are often needed for models of ocular motor circuits. The mouse has become an important tool for ocular motor studies, yet most mechanical data come from larger species. Recordings of mouse abducens neurons indicate the mouse mechanics share basic viscoelastic properties with larger species but have considerably longer time constants. Time constants can also be extracted from the rate at which the eye re-centers when released from an eccentric position. The displacement can be accomplished by electrically stimulating ocular motor nuclei, but electrical stimulation may also activate nearby ocular motor circuitry. We achieved specific activation of abducens motoneurons through photostimulation in transgenic mice expressing channelrhodopsin in cholinergic neurons. Histology confirmed strong channelrhodopsin expression in the abducens nucleus with relatively little expression in nearby ocular motor structures. Stimulation was delivered as 20- to 1,000-ms pulses and 40-Hz trains. Relaxations were modeled best by a two-element viscoelastic system. Time constants were sensitive to stimulus duration. Analysis of isometric relaxation of isolated mouse extraocular muscles suggest the dependence is attributable to noninstantaneous decay of active forces in non-twitch fibers following stimulus offset. Time constants were several times longer than those obtained in primates, confirming that the mouse ocular motor mechanics are relatively sluggish. Finally, we explored the effects of 0.1- to 20-Hz sinusoidal photostimuli and demonstrated their potential usefulness in characterizing ocular motor mechanics, although this application will require further data on the temporal relationship between photostimulation and neuronal firing in extraocular motoneurons.

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.

Tests of linearity in the responses of eye-movement-sensitive vestibular neurons to sinusoidal yaw rotation

The rotational vestibulo-ocular reflex in primates is linear and stabilizes gaze in space over a large range of head movements. Best evidence suggests that position-vestibular-pause (PVP) and eye-head velocity (EHV) neurons in the vestibular nuclei are the primary mediators of vestibulo-ocular reflexes for rotational head movements, yet the linearity of these neurons has not been extensively tested. The current study was undertaken to understand how varying magnitudes of yaw rotation are coded in these neurons. Sixty-six PVP and 41 EHV neurons in the rostral vestibular nuclei of 7 awake rhesus macaques were recorded over a range of frequencies (0.1 to 2 Hz) and peak velocities (7.5 to 210°/s at 0.5 Hz). The sensitivity (gain) of the neurons decreased with increasing peak velocity of rotation for all PVP neurons and EHV neurons sensitive to ipsilateral rotation (type I). The sensitivity of contralateral rotation-sensitive (type II) EHV neurons did not significantly decrease with increasing peak velocity. These data show that, like non-eye-movement-related vestibular nuclear neurons that are believed to mediate nonlinear vestibular functions, PVP neurons involved in the linear vestibulo-ocular reflex also behave in a nonlinear fashion. Similar to other sensory nuclei, the magnitude of the vestibular stimulus is not linearly coded by the responses of vestibular neurons; rather, amplitude compression extends the dynamic range of PVP and type I EHV vestibular neurons.

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.

Dynamics of abducens nucleus neurons in the awake mouse

The mechanics of the eyeball and orbital tissues (the "ocular motor plant") are a fundamental determinant of ocular motor signal processing. The mouse is used increasingly in ocular motor physiology, but little is known about its plant mechanics. One way to characterize the mechanics is to determine relationships between extraocular motoneuron firing and eye movement. We recorded abducens nucleus neurons in mice executing compensatory eye movements during 0.1- to 1.6-Hz oscillation in the light. We analyzed firing rates to extract eye position and eye velocity sensitivities, from which we determined time constants of a viscoelastic model of the plant. The majority of abducens neurons were already active with the eye in its central rest position, with only 6% recruited at more abducted positions. Firing rates exhibited largely linear relationships to eye movement, although there was a nonlinearity consisting of increasing modulation in proportion to eye movement as eye amplitudes became small (due to reduced stimulus amplitude or reduced alertness). Eye position and velocity sensitivities changed with stimulus frequency as expected for an ocular motor plant dominated by cascaded viscoelasticities. Transfer function poles lay at approximately 0.1 and 0.9 s. Compared with previously studied animal species, the mouse plant is stiffer than the rabbit but laxer than cat and rhesus. Differences between mouse and rabbit can be explained by scaling for eye size (allometry). Differences between the mouse and cat or rhesus can be explained by differing ocular motor repertoires of animals with and without a fovea or area centralis.

Components of the neural signal underlying congenital nystagmus

Congenital nystagmus is an involuntary bilateral horizontal oscillation of the eyes that develops soon after birth. In this study, the time constants of each of the components of the neural signal underlying congenital nystagmus were obtained by time series analysis and interpreted by comparison with those of the normal oculomotor system. In the neighbourhood of the fixation position, the system generating the neural signal is approximately linear with 3 degrees of freedom. The shortest time constant was in the range of 7-9 ms and corresponds to a normal saccadic burst signal. The other stable time constant was in the range of 22-70 ms and corresponds to the slide signal. The final time constant characterises the unidentified neural mechanism underlying the unstable drift component of the oscillation cycle and ranges between 31 and 32 ms across waveforms. The characterisation of this unstable time constant poses a challenge for the modelling of both the normal and abnormal oculomotor control system. We tentatively identify the unstable component with the eye position signal supplied to the superior colliculus in the normal eye movement system and explore some of the implications of this hypothesis.

A nonlinear model of passive muscle viscosity

The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.

Extraocular muscle motor units characterized by spike-triggered averaging in alert monkey

Single-unit recording in macaque monkeys has been widely used to study extraocular motoneuron behavior during eye movements. However, primate extraocular motor units have only been studied using electrical stimulation in anesthetized animals. To study motor units in alert, behaving macaques, we combined chronic muscle force transducer (MFT) and single-unit extracellular motoneuron recordings. During steady fixation with low motoneuron firing rates, we used motoneuron spike-triggered averaging of MFT signals (STA-MFT) to extract individual motor unit twitches, thereby characterizing each motor unit in terms of twitch force and dynamics. It is then possible, as in conventional studies, to determine motoneuron activity during eye movements, but now with knowledge of underlying motor unit characteristics. We demonstrate the STA-MFT technique for medial rectus motor units. Recordings from 33 medial rectus motoneurons in three animals identified 20 motor units, which had peak twitch tensions of 0.5-5.25mg, initial twitch delays averaging 2.4 ms, and time to peak contraction averaging 9.3 ms. These twitch tensions are consistent with those reported in unanesthetized rabbits, and with estimates of the total number of medial rectus motoneurons and twitch tension generated by whole-nerve stimulation in monkey, but are substantially lower than those reported for lateral rectus motor units in anesthetized squirrel monkey. Motor units were recruited in order of twitch tension magnitude with stronger motor units reaching threshold further in the muscle's ON-direction, showing that, as in other skeletal muscles, medial rectus motor units are recruited according to the "size principle".

The nonlinearity of passive extraocular muscles

Passive extraocular muscles (EOMs), like most biological tissues, are hyperelastic, that is, their stiffness increases as they are stretched. It has always been assumed, and in a few occasions argued, that this is their only nonlinearity and that it can be ignored in central gaze. However, using novel measurement techniques in anesthetized paralyzed monkeys, we have recently demonstrated that EOMs are characterized by another prominent nonlinearity: the forces induced by sequences of stretches do not sum. Thus, superposition, a central tenet of linear and quasi-linear models, does not hold in passive EOMs. Here, we outline the implications of this finding, especially in light of the common assumption that it is easier for the brain to control a linear than a nonlinear plant. We argue against this common belief: the specific nonlinearity of passive EOMs may actually make it easier for the brain to control the plant than if muscles were linear.

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.

Characterization of ocular tissues using microindentation and hertzian viscoelastic models

PURPOSE

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.

METHODS

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.

RESULTS

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.

CONCLUSIONS

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.

Disorders of vergence eye movements

PURPOSE OF REVIEW

The aim is to re-interpret disorders of vergence in the light of recent studies that view disjunctive eye movements as but one component of three-dimensional gaze control.

RECENT FINDINGS

Most natural eye movements combine vergence with saccades, pursuit and vestibular eye movements. Electrophysiological studies in epileptic patients, as well as evidence from monkeys, indicate that frontal and parietal cortex govern vergence as a component of three-dimensional gaze. Clinicians apply Hering's law of equal innervation to interpret disjunctive movements as the superposition of conjugate and vergence commands. However, electrophysiological studies indicate that disjunctive saccades are achieved by programming each eye's movement independently. Patients with internuclear ophthalmoplegia (INO) may have preserved vergence, which can be recruited to compensate for loss of conjugacy. Vergence may also enable gaze shifts in saccadic palsy. Some forms of nystagmus suppress or change with convergence; co-contraction of the horizontal rectus muscles does not appear to be the explanation. Rather, effects of near viewing on central vestibular mechanisms or differential activation of specific types of extra-ocular muscle fiber may be responsible.

SUMMARY

Interpretation of disorders of vergence is aided by applying a scheme in which their contributions to three-dimensional gaze control is considered.

The viscoelastic properties of passive eye muscle in primates. III: force elicited by natural elongations

We have recently shown that in monkey passive extraocular muscles the force induced by a stretch does not depend on the entire length history, but to a great extent is only a function of the last elongation applied. This led us to conclude that Fung's quasi-linear viscoelastic (QLV) model, and more general nonlinear models based on a single convolution integral, cannot faithfully mimic passive eye muscles. Here we present additional data about the mechanical properties of passive eye muscles in deeply anesthetized monkeys. We show that, in addition to the aforementioned failures, previous models also grossly overestimate the force exerted by passive eye muscles during smooth elongations similar to those experienced during normal eye movements. Importantly, we also show that the force exerted by a muscle following an elongation is largely independent of the elongation itself, and it is mostly determined by the final muscle length. These additional findings conclusively rule out the use of classical viscoelastic models to mimic the mechanical properties of passive eye muscles. We describe here a new model that extends previous ones using principles derived from research on thixotropic materials. This model is able to account reasonably well for our data, and could thus be incorporated into models of the eye plant.

The viscoelastic properties of passive eye muscle in primates. II: testing the quasi-linear theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory.We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fung's model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition.While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.