Dynamic response of intraocular pressure and biomechanical effects of the eye considering fluid-structure interaction

The vibration characteristics of shell structures such as eyes have been shown to vary with intraocular pressure (IOP). Therefore, vibration characteristics of the eye have the potential to provide improved correlation to IOP over traditional IOP measurements. As background to examine an improved IOP correlation, this paper develops a finite element model of an eye subject to vibration. The eye is modeled as a shell structure filled with inviscid pressurized fluid in which there is no mean flow. This model solves a problem of a fluid with coupled structural interactions of a generally spherically shaped shell system. The model is verified by comparing its vibrational characteristics with an experimental modal analysis of an elastic spherical shell filled with water. The structural dynamic effects due to change in pressure of the fluid are examined. It is shown that the frequency response of this fluid-solid coupled system has a clear increase in natural frequency as the fluid pressure rises. The fluid and structure interaction is important for accurate prediction of system dynamics. This model is then extended to improve its accuracy in modeling the eye by including the effect of the lens to study corneal vibration. The effect of biomechanical parameters such as the thicknesses of different parts of the eye and eye dimensions in altering measured natural frequencies is investigated and compared to the influence of biomechanical parameters in Goldmann applanation tonometry models. The dynamic response of the eye is found to be less sensitive to biomechanical parameters than the applanation tonometry model.     

A model for the human cornea: constitutive formulation and numerical analysis

The human cornea (the external lens of the eye) has the macroscopic structure of a thin shell, originated by the organization of collagen lamellae parallel to the middle surface of the shell. The lamellae, composed of bundles of collagen fibrils, are responsible for the experimentally observed anisotropy of the cornea. Anomalies in the fibril structure may explain the changes in the mechanical behavior of the tissue observed in pathologies such as keratoconus. We employ a fiber-matrix constitutive model and propose a numerical model for the human cornea that is able to account for its mechanical behavior in healthy conditions or in the presence of keratoconus under increasing values of the intraocular pressure. The ability of our model to reproduce the behavior of the human cornea opens a promising perspective for the numerical simulation of refractive surgery.     

Development of a novel compact sonicator for cell disruption

Ultrasound microbial cell disrupters operating at around 20 kHz are often physically large and, due to significant heating, can be unsuitable for small sample volumes where biochemical integrity of the extracted product is required. Development of a compact device based on a 63.5-mm diameter, 6.5-mm thick tubular transducer for rapid cell disruption in small-volume samples in a high-intensity acoustic cavitation field with minimal temperature rises is described here. Suspensions of Saccharomyces cerevisiae were exposed to cavitation for various times in the compact device and a 20-kHz probe sonicator. Cell disruption was assessed by protein release and by staining. Yeast cell disruption was greater in the novel 267-kHz sonicator than in the 20-kHz probe sonicator for the same exposure time. A 1-dimensional (1-D) transfer matrix model analysis for piezoelectric resonators was applied to an axial cross-section of the tubular sonicator to predict frequencies of mechanical resonance in the sample volume associated with maximum acoustic pressure. Admittance measurements identified frequencies of electrical resonance. Ultrasonic cavitation noise peaks were detected by a hydrophone at both the mechanical and electrical resonances. Cell breakage efficiency was twice as great in terms of protein released per dissipated watt at the mechanical resonance predicted by the model, compared to those at the electrical resonance frequencies. The results form a basis for rational design of an ultrasound cell disruption technique for small-volume samples.     

Resonance Raman studies of the flavin and iron-sulfur centers of milk xanthine oxidase

Resonance Raman spectroscopy has been used to study milk xanthine oxidase, an enzyme containing molybdenum, binuclear iron-sulfur clusters, and FAD as cofactors. The contribution of FAD dominates the resonance Raman spectrum at frequencies above 500 cm-1. As expected, no bands assignable to FAD are observed in deflavo xanthine oxidase. The resonance Raman spectrum below 500 cm-1 reveals the contribution of the Fe2S2(Cys)4 groups with frequencies similar to those of adrenodoxin and putidaredoxin. Resonance enhancement profiles of the Fe2S2(Cys)4 clusters indicate intensity variations among the Fe2S2(Cys)4 peaks that are attributed to different excitation wavelength maxima of their bridging and terminal iron-sulfur vibrations. No evidence for Mo-ligand vibrations could be obtained by using excitation wavelengths between 363.8 and 514.5 nm.     

Metal-ligand vibrations of cyanoferric myeloperoxidase and cyanoferric horseradish peroxidase: evidence for a constrained heme pocket in myeloperoxidase

The low-frequency FeCN vibrations of cyanoferric myeloperoxidase (MPO) and horseradish peroxidase (HRP) have been measured by resonance Raman spectroscopy. The ordering of the frequencies of the predominantly FeC stretching and FeCN bending normal vibrational modes in the two peroxidases differs. These normal mode vibrations are identified by their wavenumber shifts upon isotopic substitution of the cyanide ligand. For MPO, the stretching mode nu 1 (361 cm-1) occurs at a lower frequency than the bending mode delta 2 (454 cm-1). For HRP, the order is reversed as nu 1 (456 cm-1) is at a higher frequency than delta 2 (404 cm-1). Normal coordinate analyses and model complexes have been used to address the origin of this behavior. The nu 1 stretching frequencies in cyanide complexes of iron porphyrin and iron chlorin model compounds are similar to one another and to that of HRP. Thus, the inverted order and altered frequencies of the nu 1 and delta 2 vibrations in MPO, relative to those in HRP and the model compounds, are not inherent to the proposed iron chlorin prosthetic group in MPO but, rather, are attributed to distinct distal environmental effects in the MPO active site. The normal coordinate analyses for MPO and HRP showed that the nu 1 and delta 2 vibrational frequencies are not pure; the potential energy distributions for these modes respond not only to the geometry but also to the force constants of the nu(FeC) and delta(FeCN) internal coordinates.(ABSTRACT TRUNCATED AT 250 WORDS)     

A computational remodeling approach to predict the physiological architecture of the collagen fibril network in corneo-scleral shells

Organized collagen fibrils form complex networks that introduce strong anisotropic and highly nonlinear attributes into the constitutive response of human eye tissues. Physiological adaptation of the collagen network and the mechanical condition within biological tissues are complex and mutually dependent phenomena. In this contribution, a computational model is presented to investigate the interaction between the collagen fibril architecture and mechanical loading conditions in the corneo-scleral shell. The biomechanical properties of eye tissues are derived from the single crimped fibril at the micro-scale via the collagen network of distributed fibrils at the meso-scale to the incompressible and anisotropic soft tissue at the macro-scale. Biomechanically induced remodeling of the collagen network is captured on the meso-scale by allowing for a continuous re-orientation of preferred fibril orientations and a continuous adaptation of the fibril dispersion. The presented approach is applied to a numerical human eye model considering the cornea and sclera. The predicted fibril morphology correlates well with experimental observations from X-ray scattering data.     

Effect of cornea material stiffness on measured intraocular pressure

Intraocular pressure (IOP) in the human eye as measured by a Goldmann applanation tonometer (GAT) is known to be affected by individual differences in central corneal thickness (CCT). However, data from clinical studies also show considerable scatter in the correlation between measured IOP and CCT. One possible implication of the large observed scatter is that the true IOP (IOPT) also depends significantly on individual variations in the material stiffness properties of the cornea. This hypothesis is explored and evaluated herein using computational simulation of applanation tonometry. A simplified 2D finite element model of the eye, which employs a calibrated nonlinear transversely isotropic material model for the cornea, is developed, and a series of GAT simulations is carried out to study the effect of geometry and material properties of the cornea on the IOP readings obtained via GAT. The results of this parametric study provide a simple correction equation, which quantifies the effect on measured IOP of variations in CCT and corneal material stiffness. In addition, several previously proposed IOP correction equations are compared with the one proposed here.     

Selective laser trabeculoplasty in the treatment of pseudoexfoliation glaucoma in patients allergic to all anti-glaucoma drops

Secondary chronic open-angle glaucoma associated with pseudoexfoliation (PEX) syndrome accounts for approximately 25% of all glaucomas and represents the most common identifiable cause of glaucoma overall. Selective laser trabeculoplasty (SLT) is effective in reducing intraocular pressure (IOP) in glaucomatous patients and has the advantage of preserving surrounding structures. We report here SLT treatment of a 82 year old female with a secondary developed open-angle pseudoexfoliation glaucoma allergic to all anti glaucoma eye drops especially those which contain bensalconium chloridum as preservative. Since patient was allergic also to methyl-cellulose, we performed SLT with water as a mediator. Patient had PEX syndrome for 10 years, immature cataracts on both eyes, and best corrected visual acuity (BCVA) 0.7 on the right and 0.2 on the left eye. We have monitored intraocular pressure (IOP), the changes in the visual field and optic nerve. Preoperative IOP was 28 mmHg on the right and 30 mmHg on the left eye. The follow up period was 24 months with time points for measured parameters every 3 months. After 18 months IOP remained in the normal values (average 17 mmHg) on the right eye, but on the left eye it increased up to 28 mmHg. SLT re-treatment was carried out on the left eye and the IOP stabilized again on the values between 16-18mmHg. There were no significant change in the visual field and optic nerve configuration before and after SLT (C/D value for right eye: 0.3-0.4; C/D left eye: 0.5). Based on this case report, SLT seems to be very effective treatment for maintaining regular IOP in patient with PEX who is allergic to all types of medications.     

Texture coding in the rat whisker system: slip-stick versus differential resonance

Rats discriminate surface textures using their whiskers (vibrissae), but how whiskers extract texture information, and how this information is encoded by the brain, are not known. In the resonance model, whisker motion across different textures excites mechanical resonance in distinct subsets of whiskers, due to variation across whiskers in resonance frequency, which varies with whisker length. Texture information is therefore encoded by the spatial pattern of activated whiskers. In the competing kinetic signature model, different textures excite resonance equally across whiskers, and instead, texture is encoded by characteristic, nonuniform temporal patterns of whisker motion. We tested these models by measuring whisker motion in awake, behaving rats whisking in air and onto sandpaper surfaces. Resonant motion was prominent during whisking in air, with fundamental frequencies ranging from approximately 35 Hz for the long Delta whisker to approximately 110 Hz for the shorter D3 whisker. Resonant vibrations also occurred while whisking against textures, but the amplitude of resonance within single whiskers was independent of texture, contradicting the resonance model. Rather, whiskers resonated transiently during discrete, high-velocity, and high-acceleration slip-stick events, which occurred prominently during whisking on surfaces. The rate and magnitude of slip-stick events varied systematically with texture. These results suggest that texture is encoded not by differential resonant motion across whiskers, but by the magnitude and temporal pattern of slip-stick motion. These findings predict a temporal code for texture in neural spike trains.     

Directional characteristics of the auditory system of cicadas: is the sound producing tymbal an integral part of directional hearing?

Abstract. Directional hearing is investigated in males of two species of cicadas, Tympanistalna gastrica (Stål) and Tettigetta josei Boulard, that are similar in size but show different calling song spectra. The vibrational response of the ears is measured with laser vibrometry and compared with thresholds determined from auditory nerve recordings. The data are used to investigate to what extent the directional characteristic of the tympanal vibrations is encoded by the activity of auditory receptors. Laser measurements show complex vibrations of the tympanum, and reveal that directional differences are rather high (>15 dB) in characteristic but limited frequency ranges. At low frequencies, both species show a large directional difference at the same frequency (3–5 kHz) whereas, above 10 kHz, the directional differences correspond to the different resonant frequencies of the respective tymbals. Consequently, due to the mechanical resonance of the tymbal, the frequency range at which directional differences are high differs between the two species that otherwise show similar dimensions of the acoustic system. The directional differences observed in the tympanal vibrations are also observed in the auditory nerve activity. These recordings confirm that the biophysically determined directional differences are available within the nervous system for further processing. Despite considerable intra as well as interindividual variability, the ears of the cicadas investigated here exhibit profound directional characteristics, because the thresholds determined from recordings of the auditory nerve at 30° to the right and left of the longitudinal axis differ by more than 5 dB.     

Interpretation of the resonance Raman spectra of hemoproteins

The interpretation of the resonance Raman spectra of hemoproteins is given based on the normal coordinate analysis of model compounds (Cu octamethylporphin and Cu octaethylporphin). The correlation between the form of normal vibrations and the sensitivity of vibrational frequencies to the valence and spin state of the Fe atom is discussed.     

Vibrational characteristics of bone fracture and fracture repair: application to excised rat femur

BACKGROUND: The vibrational characteristics of any object are directly dependent on the physical properties of that object. Therefore, changing the physical properties of an object will cause the object to adopt changed natural frequencies. A fracture in a bone results in the loss of mechanical stability of the bone. This change in mechanical properties of a bone should result in a change of the resonant frequencies of that bone. A vibrational method for bone evaluation has been introduced. METHOD OF APPROACH: This method uses the radiation force of focused amplitude-modulated ultrasound to exert a vibrating force directly, and remotely, on a bone. The vibration frequency is varied in the range of interest to induce resonances in the bone. The resulting bone motion is recorded and the resonance frequencies are determined. Experiments are conducted on excised rat femurs and resonance frequencies of intact, fractured, and bonded (simulating healed) bones are measured. RESULTS: The experiments demonstrate that changes in the resonance frequency are indicative of bone fracture and healing, i.e., the fractured bone exhibits a lower resonance frequency than the intact bone, and the resonance frequency of the bonded bone approaches that of the intact bone. CONCLUSION: It is concluded that the proposed radiation force method may be used as a remote and noninvasive tool for monitoring bone fracture and healing process, and the use of focused ultrasound enables one to selectively evaluate individual bones.     

A passive pressure sensor for continuously measuring the intraocular pressure in glaucomatous patients

ObjectiveThe main risk factor for the development of glaucoma, a retinal disease leading to blindness, is an increase in the intraocular pressure (IOP). Reducing this IOP can be obtained by eye drops but unfortunately the disease can still progress because IOP increases are painless, can fluctuate and, thus remain undetected during a visit to an ophthalmologist. The “MATEO” ANR project aims to develop sensors embedded in a contact lens for continuously IOP monitoring.Materials and methodsPressure sensors were produced by MEMS technology and tested with pig eyes obtained at a local slaughterhouse. Solution was injected by 50 μL steps in the eye with a Hamilton syringe while IOP was monitored in parallel with a TonoVET system and an industrial pressure transducer inserted in the injection tubing system.ResultsOur first pressure sensor prototypes were generated and inserted in a lens compatible with eye application. A wireless system was developed to excite the sensor. At same time, it was recorded the data in components inserted into spectacles and a pocket recorder. In parallel, we showed that injecting a solution in the eye anterior chamber triggered an IOP increase smaller and more stable than injections in the posterior chamber. Finally, a direct correlation was observed between IOP measured on the corneal surface with the TonoVET and the pressure transducer placed close to eye injection point.DiscussionOur results indicate that our in vitro model on pig eyes is adequate to test our new lens sensor. Finally, the pressure sensor was successfully inserted in contact lens opening the way for their in vitro and in vivo preclinical validation.     

Resonance in the mouse tibia as a predictor of frequencies and locations of loading-induced bone formation

To enhance new bone formation for the treating of patients with osteopenia and osteoporosis, various mechanical loading regimens have been developed. Although a wide spectrum of loading frequencies is proposed in those regimens, a potential linkage between loading frequencies and locations of loading-induced bone formation is not well understood. In this study, we addressed a question: Does mechanical resonance play a role in frequency-dependent bone formation? If so, can the locations of enhanced bone formation be predicted through the modes of vibration? Our hypothesis is that mechanical loads applied at a frequency near the resonant frequencies enhance bone formation, specifically in areas that experience high principal strains. To test the hypothesis, we conducted axial tibia loading using low, medium, or high frequency to the mouse tibia, as well as finite element analysis. The experimental data demonstrated dependence of the maximum bone formation on location and frequency of loading. Samples loaded with the low-frequency waveform exhibited peak enhancement of bone formation in the proximal tibia, while the high-frequency waveform offered the greatest enhancement in the midshaft and distal sections. Furthermore, the observed dependence on loading frequencies was correlated to the principal strains in the first five resonance modes at 8.0–42.9 Hz. Collectively, the results suggest that resonance is a contributor to the frequencies and locations of maximum bone formation. Further investigation of the observed effects of resonance may lead to the prescribing of personalized mechanical loading treatments.     

Coupled Biomechanical Response of the Cornea Assessed by Non-Contact Tonometry. A Simulation Study

The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a linear variation with IOP for all materials examined. On the contrary, the maximum apex displacement followed a cubic relation with corneal thickness. In addition, a significant sensitivity of the apical displacement to the corneal stiffness was also obtained. Explanation to this behavior was found in the fact that the cornea experiences bending when subjected to an air-puff loading, causing the anterior surface to work in compression whereas the posterior surface works in tension. Hence, collagen fibers located at the anterior surface do not contribute to load bearing. Non-contact tonometry devices give useful information that could be misleading since the corneal deformation is the result of the interaction between the mechanical properties, IOP, and geometry. Therefore, a non-contact tonometry test is not sufficient to evaluate their individual contribution and a complete in-vivo characterization would require more than one test to independently determine the membrane and bending corneal behavior.     

The feasibility of modal testing for measurement of the dynamic characteristics of goat vertebral motion segments

Structural vibration testing might be a promising method to study the mechanical properties of spinal motion segments as an alternative to imaging and spinal manipulation techniques. Structural vibration testing is a non-destructive measurement technique that measures the response of a system to an applied vibration as a function of frequency, and allows determination of modal parameters such as resonance frequencies (ratio between stiffness and mass), vibration modes (pattern of motion) and damping. The objective of this study was to determine if structural vibration testing can reveal the resonance frequencies that correspond to the mode shapes flexion-extension, lateroflexion and axial rotation of lumbar motion segments, and to establish whether resonance frequencies can discriminate specific structural alterations of the motion segment. Therefore, a shaker was used to vibrate the upper vertebra of 16 goat lumbar motion segments, while the response was obtained from accelerometers on the transverse and spinous processes and the anterior side of the upper vertebra. Measurements were performed in three conditions: intact, after dissection of the ligaments and after puncturing the annulus fibrosus. The results showed clear resonance peaks for flexion-extension, lateral bending and axial rotation for all segments. Dissection of the ligaments did not affect the resonance frequencies, but puncturing the annulus reduced the resonance frequency of axial rotation. These results indicate that vibration testing can be utilised to assess the modal parameters of lumbar motion segments, and might eventually be used to study the mechanical properties of spinal motion segments in vivo.     

An evaluation of different methods for assessing eggshell pigmentation and pigment concentration using great tit eggs

The striking variation in colour and maculation of bird eggs has fascinated biologists since centuries, and many hypotheses based on mechanical, physiological or signalling functions have been proposed for its evolution by natural and sexual selection. Protoporphyrin is the main eggshell pigment found in brown maculated eggs, and is assumed to function as a mediator of these selection processes. It is a precursor of heme with pro‐oxidant properties, and hence a link between brown maculation and female condition has been proposed and tested in a number of studies, albeit with contrasting results. A variety of different visual methods have been used to quantify outer eggshell pigmentation, which has been assumed to correspond to overall quantity of protoporphyrin in the shell. Yet, this relationship has rarely been tested. The aim of this study was to apply four commonly used methods to assess pigmentation in great tit eggs with protoporphyrin as the predominant eggshell pigment, and to compare the results of these methods. Specifically, we 1) ranked eggshell pigmentation by human naked eye, 2) applied a granularity approach and 3) measured spectrophotometric reflectance of eggshell pigments. Second, we estimated the relationship between outer eggshell pigmentation (i.e. estimated by three different methods above) and true protoporphyrin concentration deposited in the entire shell measured by HPLC. Among‐method estimates were significantly correlated for the traits describing pigment ‘darkness’ only. While the model including scores based on human naked eyes explained 16% of the variance of pigment concentration in the entire shell, spectrometry explained 27%, and the granularity approach explained 40%. Thus, the estimation of true pigment concentration in the entire shell from the visible outer side of the shell is most reliable with the granularity approach. It is relevant for studies where the maintenance of the integrity of the eggs is essential.     

A forward incremental prestressing method with application to inverse parameter estimations and eye-specific simulations of posterior scleral shells

Numerical simulations or inverse numerical analyses of individual eyes or eye segments are often based on an eye-specific geometry obtained from in vivo medical images such as computed tomography (CT) scans or from in vitro 3D digitiser scans. These eye-specific geometries are usually measured while the eye is subjected to internal pressure. Due to the nonlinear stiffening of the collagen fibril network in the eye, numerical incorporation of the pre-existing stress/strain state may be essential for realistic eye-specific computational simulations. Existing prestressing methods either compute accurate predictions of the prestressed state or guarantee a unique solution. In this contribution, a forward incremental prestressing method is presented which unifies the advantages of the existing approaches by providing accurate and unique predictions of the pre-existing stress/strain state at the true measured geometry. The impact of prestressing is investigated on (i) the inverse constitutive parameter identification of a synthetic sclera inflation test and (ii) an eye-specific simulation that estimates the realistic mechanical response of a pre-loaded posterior monkey scleral shell. Evaluation of the pre-existing stress/strain state in the inverse analysis had a significant impact on the reproducibility of the constitutive parameters but may be estimated based on an approximative approach. The eye-specific simulation of one monkey eye shows that prestressing is required for accurate displacement and stress/strain predictions. The numerical results revealed an increasing error in displacement, strain and stress predictions with increasing pre-existing pressure load when the pre-stress/strain state is disregarded. Disregarding the prestress may lead to a significant underestimation of the strain/stress environment in the sclera and overestimation in the lamina cribrosa.     

Analysis of the Viscoelastic Properties of the Human Cornea Using Scheimpflug Imaging in Inflation Experiment of Eye Globes

Purpose

To demonstrate a Scheimpflug-based imaging procedure for investigating the depth- and time-dependent strain response of the human cornea to inflation testing of whole eye globes.

Methods

Six specimens, three of which with intact corneal epithelium, were mounted in a customized apparatus within a humidity and temperature-monitored wet chamber. Each specimen was subjected to two mechanical tests in order to measure corneal strain resulting from application of cyclic (cyclic regimen) and constant (creep regimen) stress by changing the intra-ocular pressure (IOP) within physiological ranges (18–42 mmHg). Corneal shape changes were analyzed as a function of IOP and both corneal stress-strain curves and creep curves were generated.

Results

The procedure was highly accurate and repeatable. Upon cyclic stress application, a biomechanical corneal elasticity gradient was found in the front-back direction. The average Young''s modulus of the anterior cornea ranged between 2.28±0.87 MPa and 3.30±0.90 MPa in specimens with and without intact epithelium (P = 0.05) respectively. The Young''s modulus of the posterior cornea was on average 0.21±0.09 MPa and 0.17±0.06 MPa (P>0.05) respectively. The time-dependent strain response of the cornea to creep testing was quantified by fitting data to a modified Zener model for extracting both the relaxation time and compliance function.

Conclusion

Cyclic and creep mechanical tests are valuable for investigating the strain response of the intact human cornea within physiological IOP ranges, providing meaningful results that can be translated to clinic. The presence of epithelium influences the results of anterior corneal shape changes when monitoring deformation via Scheimpflug imaging in inflation experiments of whole eye globes.