No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Biomechanical modelling of the accommodation problem of human eye
Abstract
This paper deals with the biomechanical analyse of the human eye with a complex numerical model. We present our three dimensional finite element model including the built-up parts, applied material and geometric properties. Hereupon we describe the subjects which we want to investigate with this 3D model, such as accommodation, presbyopia and so on. We high-light the accommodation problem of the crystalline lens and its surrounding parts. We discuss and explain the connection between the age-related material properties, geometric and refractive parameters and amplitude of accommodation. The results have shown that beside the geometry and material properties, the refractive attributes might be important too.
... Both the vitreous body and the aqueous humour were modeled as viscoelastic fluids. Table 1 presents the values of mechanical constants of different structures of the eye that can be found in the literature [17][18][19][20][21][22][23][24][25]. In case of zonules, a significant spread between the data can be noticed [21,22,26,27]. ...
... Table 1 presents the values of mechanical constants of different structures of the eye that can be found in the literature [17][18][19][20][21][22][23][24][25]. In case of zonules, a significant spread between the data can be noticed [21,22,26,27]. We adapted the 2 extreme values in order to test the respondability of the simulation and analysis approach to the biomechanical variability of ocular structures. ...
... But it needs to be emphasized that development of such an opto-mechanical model was not in the scope of the present study. We decided to adapt the optical model [14] based on ocular biometry and use it together with the mechanical data found in the literature [15][16][17][18][19][20][21][22][23]. It was meant to be used simply as an utensil for presentation of the computation methodology. ...
Crystalline lens wobbling is a phenomenon when the lens oscillates briefly from its normal position immediately after stopping the rotational movement of the eye globe. It can be observed by means of Purkinje imaging. The aim of this research is to present the data and computation workflow that involve both biomechanical and optical simulations that can mimic this effect, aimed to better understanding of lens wobbling. The methodology described in the study allows to visualize both the dynamic changes of the lens conformation within the eye and its optical effect in terms of Purkinje performance.
... The incompressibility of the orbital fat and the rigidity of the orbital walls can effectively restrict the excessive distortion of the eye and the optic nerve. Subsequently, several finite element models were developed with more accurate anatomy structures to fit different purposes such as the effects of impact, blast, and shaking, as well as eye mechanics and accommodation, respectively (19)(20)(21)(22). ...
... The impact analysis was performed using a dynamic module in Abaqus FE software, employing an explicit numerical timestepping procedure. We referred to earlier investigations for a variety of impactors employed during studies of head trauma (20,45,46). It is commonly accepted that the mass and momentum (product of mass and velocity) of impactors play an important role in defining the energies of the impactor. ...
Indirect traumatic optic neuropathy (ITON) is an injury to the optic nerve due to head trauma and usually results in partial or complete loss of vision. In order to advance a mechanistic understanding of the injury to the optic nerve, we developed a head model with a biofidelic orbit. Head impacts were simulated under controlled conditions of impactor velocity. The locations of impact were varied to include frontal, lateral, and posterior parts of the head. Impact studies were conducted using two types of impactors that differed in their rigidity relative to the skull. The simulated results from both the impactors suggest that forehead impacts are those to which the optic nerve is most vulnerable. The mode and location of optic nerve injury is significantly different between the impacting conditions. Simulated results using a relatively rigid impactor (metal cylinder) suggest optic nerve injury initiates at the location of the intracranial end of the optic canal and spreads to the regions of the optic nerve in the vicinity of the optic canal. In this case, the deformation of the skull at the optic canal, resulting in deformation of the optic nerve, was the primary mode of injury. On the other hand, simulated results using a relatively compliant impactor (soccer ball) suggest that primary mode of injury comes from the brain tugging upon the optic nerve (from where it is affixed to the intracranial end of the optic canal) during coup countercoup motion of the brain. This study represents the first published effort to employ a biofidelic simulation of the full length of the optic nerve in which the orbit is integrated within the whole head.
... The most critical stage of the modeling and simulation procedure is the selection of mechanical and geometric parameters of ocular tissues. Since some earlier studies demonstrated that material features may significantly influence the results of simulations (Bocskai and Bojtár, 2013), the behavior of the zonular fibers, vitreous body, and aqueous humor may be of particular importance in biomechanical simulations. Furthermore, the position of the lens during saccades, acceleration, and velocity should be monitored. ...
Introduction: Crystalline lens overshooting refers to a situation in which the lens momentarily shifts too much from its typical location immediately after stopping the rotational movement of the eye globe. This movement can be observed using an optical technique called Purkinje imaging.
Methods: In this work, an experimental setup was designed to reproduce this effect ex vivo using a fresh porcine eye. The sample was rotated 90° around its centroid using a high-velocity rotation stage, and the Purkinje image sequences were recorded, allowing us to quantify the overshooting effect. The numerical part of the study consisted of developing a computational model of the eye, based on the finite element method, that allowed us to understand the biomechanical behavior of the different tissues in this dynamic scenario. A 2D fluid–structure interaction model of the porcine eye globe, considering both the solid parts and humors, was created to reproduce the experimental outcomes.
Results: Outputs of the simulation were analyzed using an optical simulation software package to assess whether the mechanical model behaves optically like the real ex vivo eye. The simulation predicted the experimental results by carefully adjusting the mechanical properties of the zonular fibers and the damping factor.
Conclusion: This study effectively demonstrates the importance of characterizing the dynamic mechanical properties of the eye tissues to properly comprehend and predict the overshooting effect.
... The models developed are represented in Table 2, where models Band3 and Band7 have a band width correspondence with literature values [24,33], and the remaining models evaluate the intermediary values between the forementioned band widths. The gravitational force impact in the lens complex was assessed, where the density values of cortex, nucleus, and capsule were equivalent (δC = δN = δCB = 1099 kg/m 3 ) [34], and the density of the zonules was determined as δZ = 1000 kg/m 3 [35]. ...
Pseudoexfoliation, one of the most frequent crystalline lens complex disorders, is prevalent in up to 30% of individuals older than 60 years old. This disease can lead to severe conditions, such as subluxation or dislocation of the lens, due to the weakening of the zonules. The goal for the present study was to understand the relevant biomechanical features that can lead to the worsening of an individual's visual capacity under pseudoexfoliation. To this end, finite element models based on a 62-year-old lens complex were developed, composed by the capsular bag, cortex, nucleus, anterior, equatorial, and posterior zonular fibers. Healthy and pseudoexfoliative conditions were simulated, varying the location of the zonulopathy (inferior/superior) and the degenerated layer. The accommodative capacity of the models with inferior dialysis of the zonular fibers was, on average, 4.7% greater than for the cases with superior dialysis. If the three sets of zonules were disrupted, this discrepancy increased to 14.9%. The present work provides relevant data to be further analyzed in clinical scenarios, as these models (and their future extension to a wider age range) can help in identifying the most influential regions for the reduction of the visual capacity of the lens.
... Although numerical simulation studies can be found on the literature related to the eye, ranging from the study of the eye temperature to the study of specific eye components [9][10][11][12][13][14][15], to the authors' knowledge no study exists concerning the numerical simulations of the ERM contraction. In the existing literature related to numerical studies of the eye [16][17][18][19][20][21], the most used method in these types of works is the Finite Element Method (FEM), being the method chosen in the present study. ...
The epiretinal membrane is a thin sheet of fibrous tissue that can form over the macular area of the retina, and may result in the loss of visual acuity or metamorphopsia, due to superficial retinal folds. A vitrectomy surgery, the current treatment procedure for this pathology, is only performed after symptoms are present. However, sometimes the patients do not present any vision improvements after the surgery. The use of computational methods for a patient-specific biomechanical analysis can contribute to better understanding the mechanisms behind the success or failure of a vitrectomy. Using medical data from two patients who underwent a vitrectomy, one with substantial improvements and another with no improvements, an analysis of the retinal displacement due to the contraction of the epiretinal membrane was performed. Our results suggest a causal effect between the magnitude of the retinal displacements caused by the epiretinal membrane contraction and the outcome of the vitrectomy procedure.
... The finite-element method is a powerful mathematical tool more and more used to understand the biomechanics of the human body. Several eye finite element models (FEM) can be found in the literature, designed for different purposes such as impact, blast, SBS, eye mechanics and accommodation (Al-Sukhun et al. 2006;Gray et al. 2011;Rossi et al. 2012;Esposito et al. 2015;Bhardwaj et al. 2014;Ng and Ooi 2006;Schutte et al. 2006;Bocskai and Bojtár 2013;Sigal et al. 2004). This paper focuses on those dealing with impact and SBS only and proposes a step towards numerical injury prediction tools. ...
Retinal hemorrhages (RH) are among injuries sustained by a large number of shaken baby syndrome victims, but also by a small proportion of road accident victims. In order to have a better understanding of the underlying of RH mechanisms, we aimed to develop a complete human eye and orbit finite element model. Five occipital head impacts, at different heights and on different surfaces, and three shaking experiments were conducted with a 6-week-old dummy (Q0 dummy). This allowed obtaining a precise description of the motion in those two specific situations, which was then used as input for the eye model simulation. Results showed that four parameters (pressure, Von Mises stress and strain, 1st principal stress) are relevant for shaking–fall comparison. Indeed, in the retina, the softest shaking leads to pressure that is 4 times higher than the most severe impact (1.43 vs. 0.34 kPa). For the Von Mises stress, strain and 1st principal stress, this ratio rises to 4.27, 6.53 and 14.74, respectively. Moreover, regions of high stress and strain in the retina and the choroid were identified and compared to what is seen on fundoscopy. The comparison between linear and rotational acceleration in fall and shaking events demonstrated the important role of the rotational acceleration in inducing such injuries. Even though the eye model was not validated, the conclusion of this study is that compared to falls, shaking an infant leads to extreme eye loading as demonstrated by the values taken by the four mentioned mechanical parameters in the retina and the choroid.
... In this study, the commercial FEM package Comsol Multiphysics (COMSOL, UK) was used for numerical simulations. A three-dimensional continuum model of the material properties and geometry of corneas, consisting of the six layers of the cornea, namely the epithelium, basement membrane, Bowman's membrane, stroma, Descemet's membrane, and endothelium, has been described previously 28,51,52 . Based on these studies, the Young's modulus of each layer, the hyperelastic and anisotropic material 23,25 , and the N-T and the I-S fibres 12,13,25,30 were subjected to global analyses (Tables 1 and 2). ...
Recent advances in the analysis of corneal biomechanical properties remain difficult to predict the structural stability before and after refractive surgery. In this regard, we applied the finite element method (FEM) to determine the roles of the Bowman’s membrane, stroma, and Descemet’s membrane in the hoop stresses of cornea, under tension (physiological) and bending (nonphysiological), for patients who undergo radial keratotomy (RK), photorefractive keratectomy (PRK), laser-assisted in situ keratomileusis (LASIK), or small incision lenticule extraction (SMILE). The stress concentration maps, potential creak zones, and potential errors in intraocular pressure (IOP) measurements were further determined. Our results confirmed that the Bowman’s membrane and Descemet’s membrane accounted for 20% of the bending rigidity of the cornea, and became the force pair dominating the bending behaviour of the cornea, the high stress in the distribution map, and a stretch to avoid structural failure. In addition, PRK broke the central linking of hoop stresses and concentrated stress on the edge of the Bowman’s membrane around ablation, which posed considerable risk of potential creaks. Compared with SMILE, LASIK had a higher risk of developing creaks around the ablation in the stroma layer. Our FEM models also predicted the postoperative IOPs precisely in a conditional manner.
... Young's modulus, viscoelastic parameters) are better metrics for diagnostics and treatment planning and monitoring. In particular, finite element (FE) analysis is a standard numerical tool to study mechanical behavior of structures, even soft materials [25], including ocular tissues [26][27][28]. Using temporal and spatial corneal deformation data as input, optimization algorithms allows in principle retrieving corneal biomechanical parameters. ...
Objective
To validate a new method for reconstructing corneal biomechanical properties from air puff corneal deformation images using hydrogel polymer model corneas and porcine corneas.
Methods
Air puff deformation imaging was performed on model eyes with artificial corneas made out of three different hydrogel materials with three different thicknesses and on porcine eyes, at constant intraocular pressure of 15 mmHg. The cornea air puff deformation was modeled using finite elements, and hyperelastic material parameters were determined through inverse modeling, minimizing the difference between the simulated and the measured central deformation amplitude and central-peripheral deformation ratio parameters. Uniaxial tensile tests were performed on the model cornea materials as well as on corneal strips, and the results were compared to stress-strain simulations assuming the reconstructed material parameters.
Results
The measured and simulated spatial and temporal profiles of the air puff deformation tests were in good agreement (< 7% average discrepancy). The simulated stress-strain curves of the studied hydrogel corneal materials fitted well the experimental stress-strain curves from uniaxial extensiometry, particularly in the 0–0.4 range. Equivalent Young´s moduli of the reconstructed material properties from air-puff were 0.31, 0.58 and 0.48 MPa for the three polymer materials respectively which differed < 1% from those obtained from extensiometry. The simulations of the same material but different thickness resulted in similar reconstructed material properties. The air-puff reconstructed average equivalent Young´s modulus of the porcine corneas was 1.3 MPa, within 18% of that obtained from extensiometry.
Conclusions
Air puff corneal deformation imaging with inverse finite element modeling can retrieve material properties of model hydrogel polymer corneas and real corneas, which are in good correspondence with those obtained from uniaxial extensiometry, suggesting that this is a promising technique to retrieve quantitative corneal biomechanical properties.
... The finite-element method is a powerful and widely used tool in different fields, in particular in biomechanics. Few eye finite-element models (FEM) have been developed in the literature for specific purposes: blunt impact studies, effects of blast, eye accommodation studies [5][6][7]. ...
Retinal haemorrhages appear both in case of traffic accidents, fall cases and in case of child abuse.
Their mechanisms are poorly investigated. Existing eye finite‐element models are used for very specific
purposes and there is a lack of detailed modelling. The aim of this study was to develop a complete infant eye
finite‐element model to investigate eye injuries after falls. The finite‐element model of the eye and surrounding
components were generated from dimensions available in the literature and from infant MRI data. A set of five
occipital impact experiments on a six weeks old baby dummy was performed on different surfaces and heights.The recorded accelerations were used as inputs for the eye finite‐element model to replicate occipital, lateral
and frontal impacts. Results from experiments showed that the maximum linear acceleration ranged from 110‐
687 g (HIC15 values from 150 to 6000). From the simulations, five parameters (Pressure, Von‐Mises stress/strain, Principal stress/strain) were computed or all eye components and compared. Focus was put on the retina and results demonstrated that parameter values increase along acceleration and HIC15 values. Moreover in frontal impacts, intra‐ocular parameters are higher than in occipital or temporal ones. More documented infant falls will help to establish an injury threshold for retinal haemorrhages to be applied in automotive crash environment.
... The force from the ciliary body is transferring to the lens through the zonular fi bre system. 1 Based on the Helmholtz theory 1 the geometry of the apparatus of the zonules is very important at the accommodation process of the eye. For measuring of the mechanical properties of these fibres -for example with tension tests -we need the geometry e.g. ...
Purpose
The porcine eye serves as a valuable surrogate for studying human ocular anatomy and physiology because of its close resemblance. This study focuses on the influence of material properties, specifically Young’s modulus and Poisson’s ratio, on the crystalline lens overshooting amplitude during rapid eye rotation.
Methods
The Finite Element Method (FEM) is employed to explore various material property scenarios, and sensitivity analysis is conducted to assess their impact on the mechanical displacement of the crystalline lens apex. The measurements were made of three output parameters: maximum displacement, time of maximum displacement appearance , and stabilization time.
Results
The results highlight the significance of fine-tuning of the zonule’s material properties, particularly Young’s modulus, in achieving a reliable model. They suggest that fine-tuning of these parameters can lead to a highly reliable model, enabling in-depth research in the opto-dynamic simulations.
Conclusions
Having a complete examination of crystalline lens displacement in ex vivo porcine eye models and detailing crucial factors for accurate modeling will open the path for future studies especially in conditions affected by dynamic aspects of the crystalline lens or in in vivo research.
Purpose
To find out the effect on the biomechanical response of the eye in the setting of diabetes combined with glaucoma.
Method
Five finite element models of the human eyes with various iris-lens channel (ILC) distances (2 μm–20 μm) were constructed, respectively. The human eye model used for finite element analysis contain all the ocular contents and the optic nerve head. All these models with different ILC distances were used to simulate the effect of pupillary block and abnormal aqueous flow induced by diabetes. And those models were also used for the biomechanical properties study of ocular tissues under the elevated intraocular pressure (IOP), using unidirectional fluid-solid coupling numerical simulation method.
Results
For the most severe cases of pupil block (2 μm), a significant difference in chamber pressure caused the iris to move forward and had posterior adhesion to the lens. And the strain, stress, and displacement of the whole eyeball were significantly higher than those of the other four cases, while the Optic Nerve Head (ONH) region was the opposite. The promotion of IOP to biomechanical response at both global eye and ONH region was close to the normal eye conditions, or even ease for ILC = 2 μm. But in the cases of glaucoma with pupil block and high aqueous flow, the biomechanical properties of the whole eyeball were remarkably enhanced for all IOP conditions. Less influence was observed in the ONH region.
Conclusion
The promotion of diabetes for glaucoma is not directly on the optic nerve, instead, it indirectly affects the optic nerve by affecting the global eye. Glaucoma combined with diabetes complications may increase the biomechanical damage of IOP to the whole eye.
In this study, the biomechanics of the human lens geometry were numerically analyzed to quantitate micro-fluidic movement of lens fiber cells. Literature values were collected to develop a lens geometry paradigm related to optical output for both distant and near vision. We show that our numerical methods can successfully quantitate the micro-fluidic flow of lens fiber cells. Small changes in the lens fluidic movement responsible for optics are confined to a cortical volume element that appears compromised by lens modulus changes. The result imply that aging of the lens is accompanied by an almost constant inward equatorial movement at 21.2 ± 0.002 microns/∂D. This creates a corresponding fluid volume of 1.74 ± 0.17 μL/∂D that is displaced per diopter of accommodation. A possible presbyopia lens treatment that achieves an acceptable accommodative end-point requires an estimate of the active pharmacological dose level. A therapeutic delivery requirementi nvolving the entire lens mass may therefore be substituted by a treatment that targets the outer cortical region (or <2% ofthe total lens protein).
Elevated intraocular pressure (IOP) may be the primary risk factor to the development of glaucoma. Finite element (FE) modeling is commonly considered as an effective method to quantitatively analyze pathogenesis of glaucoma. Recent researches focus on establishing partial human eye models. A refined global human eye model was developed using ANSYS software to investigate the correlation between IOP elevation and biomechanical responses. First, the pressure transferring process according to IOP elevation in the whole eye was analyzed to simulate the effects of IOP elevation on glaucoma. Then, the biomechanical responses of the anterior eye segment under various pressure differences between the anterior and posterior chambers (AC and PC) were analyzed to simulate posterior nonadhesion of iris and posterior synechia. This global eye model not only simulated the responses of elevated IOP on ocular structures, but also revealed the process of pressure transferring among each tissue from the anterior eye segment to the optic nerve head (ONH) region. The local mechanical characteristics of the ocular structures obtained from the global model agreed with previous findings. This global model may shed light on the studies of multifactorial glaucoma.
Purpose
For the development of new intraocular pressure (IOP) measurement devices, as well as for comparison with existing devices it is important to consider the various biomechanical properties of the eye in test setups. Therefore, a controllable physical phantom with flexibility in the adjustment of biomechanical parameters and geometries is being proposed and analyzed.
Methods
Different configurations of a mechanical eye model are simulated together with the applanation process, based on the finite element method (FEM). Forming tools are designed to produce artificial corneas with variable thicknesses and stiffness’s using injection molding. An apparatus is assembled for controlling and evaluating the phantom eye in connection with a piezoelectric IOP test sensor. Measurements are also performed using the commercially available non-contact tonometer NCT-800.
Results
Simulation results for surface pressure and stress distribution at the cornea together with the pressure in the central part of the applanation body show that the pressure reaches a maximum when the local stress is centrally concentrated and decreases to a stable level afterwards. More rigid corneas result in higher maximum values for the pressure. The measurements with the piezoelectric IOP test sensor are in good agreement with the simulation results. The NCT-800 measurements show a significant influence of the biomechanical properties of the cornea on measured IOPs.
Conclusions
Our phantom is suitable for describing the effect of biomechanical characteristics of the human eye on tonometric measurements and will facilitate the evaluation of new tonometry systems.
The mechanical behaviour of zonular fibres greatly affects the accommodation process in mammalian eyes. This paper introduces a detailed measurement procedure for the purpose of obtaining the force-displacement diagram necessary to evaluate the mechanical properties of porcine zonular fibres in situ. It is a complex technique, keeping the integrity of the zonular bundles between the crystalline lens and the ciliary muscle cells. We present a brief description of the measurement procedure both in theory and in practice, along with the force-displacement diagrams acquired from a porcine sample group. The strengths of this newly developed method are the unequivocal force transmission between the sample and the transducer, and the intact connection between the ciliary body and the crystalline lens via zonular fibres. With the aid of these measurements, we define an estimated material model for the zonular apparatus both analytically and using the finite element method. The two different evaluation methods show close agreement in the calculated Young׳s modulus for the zonular fibres. The range of the calculated elastic modulus is 200-250kPa. This new measuring method is adaptable to human specimens. Despite its complexity, the entire procedure and the evaluation part are reproducible. The constitutive model aims to shed light on the mechanics of the accommodation process.
The purpose of the study was to investigate the influence of age on the biomechanical properties of the human anterior lens capsule.
The material comprised 67 lens capsules obtained from human donors ranging in age from 7 months to 98 years. Test specimens were prepared from the anterior lens capsule as tissue rings by means of excimer laser technique using a metal ring (mask) to shape the laser output (outer diameter = 3.2 mm, width = 100 microns). Capsular thickness was measured under microscope as the difference in focus between microspherules placed on the outer and inner surfaces of the capsule. The rings were slipped over two pins connected to a motorized micropositioner and a force transducer, respectively, and stretched at constant speed until rupture, with continuous recording of load and elongation.
Capsular thickness was associated significantly with age of the donors and increased gradually (1.2% per year) until age 75, after which a slight decrease was observed. The elastic response curves showed a high degree of nonlinearity and were influenced markedly by age. Ultimate strain decreased 0.5% per year (range, 108% to 40%). Ultimate tensile strength decreased 1% per year (range, 17.5 N/mm2 to 1.5 N/mm2), and ultimate elastic stiffness (tangent modulus) decreased 0.9% per year (range, 44.8 N/mm2 to 4.4 N/mm2), whereas elastic stiffness corresponding to a specific strain level (30%) increased until age 35, after which a slight decrease was observed.
Aging of the human anterior lens capsule is associated with a progressive loss of mechanical strength. The young capsule is strong, tough, and highly extensible, whereas the older, thicker capsule is less extensible and much more brittle, and it has a markedly reduced breaking strength.
To use high-resolution magnetic resonance (MR) images of the eye to directly measure the relationship between ciliary muscle contraction and lens response with advancing age.
A General Electric, 1.5-Tesla MR imager and a custom-designed eye imaging coil were used to collect high-resolution MR images from 25 subjects, 22 through 83 years of age. A nonmagnetic binocular stimulus apparatus was used to induce both relaxed accommodation (0.1 diopter [D]) and strong accommodative effort (8.0 D). Measurements of the ciliary muscle ring diameter (based on the inner apex), lens equatorial diameter, and lens thickness were derived from the MR images.
Muscle contraction is present in all subjects and reduces only slightly with advancing age. A decrease in the diameter of the unaccommodated ciliary muscle ring was highly correlated with advancing age. Lens equatorial diameter does not correlate with age for either accommodative state. Although unaccommodated lens thickness (i.e., lens minor axis length) increases with age, the thickness of the lens under accommodative effort is only modestly age-dependent.
Ciliary muscle contractile activity remains active in all subjects. A decrease in the unaccommodated ciliary muscle diameter, along with the previously noted increase in lens thickness (the "lens paradox"), demonstrates the greatest correlation with advancing age. These results support the theory that presbyopia is actually the loss in ability to disaccommodate due to increases in lens thickness, the inward movement of the ciliary ring, or both.
A simulation model of the human eye was developed. It was applied to the determination of the physical and mechanical conditions of impacting foreign bodies causing intraocular foreign body (IOFB) injuries.
Modules of the Hypermesh (Altair Engineering, Tokyo, Japan) were used for solid modelling, geometric construction, and finite element mesh creation based on information obtained from cadaver eyes. The simulations were solved by a supercomputer using the finite element analysis (FEA) program PAM-CRASH (Nihon ESI, Tokyo, Japan). It was assumed that rupture occurs at a strain of 18.0% in the cornea and 6.8% in the sclera and at a stress of 9.4 MPa for both cornea and sclera. Blunt-shaped missiles were shot and set to impact on the surface of the cornea or sclera at velocities of 30 and 60 m/s, respectively.
According to the simulation, the sizes of missile above which corneal rupture occurred at velocities of 30 and 60 m/s were 1.95 and 0.82 mm. The missile sizes causing scleral rupture were 0.95 and 0.75 mm at velocities of 30 and 60 m/s.
These results suggest that this FEA model has potential usefulness as a simulation tool for ocular injury and it may provide useful information for developing protective measures against industrial and traffic ocular injuries.
To characterize the age dependence of isolated human crystalline lens power and quantify the contributions of the lens surfaces and refractive index gradient.
Experiments were performed on 100 eyes of 73 donors (average 2.8 +/- 1.6 days postmortem) with an age range of 6 to 94 years. Lens power was measured with a modified commercial lensmeter or with an optical system based on the Scheiner principle. The radius of curvature and asphericity of the isolated lens surfaces were measured by shadow photography. For each lens, the contributions of the surfaces and the refractive index gradient to the measured lens power were calculated by using optical ray-tracing software. The age dependency of these refractive powers was assessed.
The total refractive power and surface refractive power both showed a biphasic age dependency. The total power decreased at a rate of -0.41 D/y between ages 6 and 58.1, and increased at a rate of 0.33D/y between ages 58.1 and 82. The surface contribution decreased at a rate of -0.13 D/y between ages 6 and 55.2 and increased at a rate of 0.04 D/y between ages 55.2 and 94. The relative contribution of the surfaces increased by 0.17% per year. The equivalent refractive index also showed a biphasic age dependency with a decrease at a rate of -3.9 x 10(-4) per year from ages 6 to 60.4 followed by a plateau.
The lens power decreases with age, due mainly to a decrease in the contribution of the gradient. The use of a constant equivalent refractive index value to calculate lens power with the lens maker formula will underestimate the power of young lenses and overestimate the power of older lenses.
The values of the biomechanical human eyeball model parameters reported in the literature are still being disputed. The primary motivation behind this work was to predict the material parameters of the cornea through numerical simulations and to assess the applicability of the ubiquitously accepted law of applanation tonometry - the Imbert-Fick equation.
Numerical simulations of a few states of eyeball loading were run to determine the stroma material parameters. In the computations, the elasticity moduli of the material were related to the stress sign, instead of the orientation in space.
Stroma elasticity secant modulus E was predicted to be close to 0.3 MPa. The numerically simulated applanation tonometer readings for the cornea with the calibration dimensions were found to be lower by 11 mmHg then IOP = 48 mmHg.
This discrepancy is the result of a strictly mechanical phenomenon taking place in the tensioned and simultaneously flattened corneal shell and is not related to the tonometer measuring accuracy. The observed deviation has not been amenable to any GAT corrections, contradicting the Imbert-Fick law. This means a new approach to the calculation of corrections for GAT readings is needed.
Airbags have been saving lives in automobile crashes for many years and are now being used in helicopters. The purpose of this study was to investigate the potential for ocular injuries to helicopter pilots wearing night vision goggles when the airbag is deployed. A nonlinear finite element model of the human eye was constructed. Ocular structures never before included in finite element models of the eye, such as the fatty tissue, extraocular muscles, and bony orbit were included in this model. In addition, this model includes material properties up to rupture making the eye suitable for large deformation applications. The model was imported into Madymo and used to determine the worst-case position of a helicopter pilot wearing night vision goggles. This was evaluated as the greatest Von Mises stress in the eye when the airbag is deployed. The worst-case position was achieved by minimizing the distance between the eyes and goggles, having the occupant look directly into the airbag, and making initial contact with the airbag halfway through its full deployment. By removing the extraocular muscles, the stress sustained by the eye decreased. Simulations with both the goggles remaining fastened and breaking away from the aviator helmet were performed. Finally, placing a protective lens in front of the eyes was found to reduce the stress to the eye but increase the force experienced by the surrounding orbital bones. The finite element model of the eye proved effective at evaluating the experimental boundary conditions, and could be used in the future to evaluate impact loading on eyes that have been surgically corrected and to model the geometry of the orbital bones. System requirements: PC, World Wide Web browser and PDF reader. Available electronically via Internet. Title from electronic submission form. Thesis (M.S.)--Virginia Polytechnic Institute and State University, 2001. Vita. Abstract. Includes bibliographical references.
1. Apparatus has been designed to alter the shape of the human lens by tensile forces applied to the zonular fibres indirectly through the ciliary body. The changes in dioptric power of the lens for monochromatic sodium light were measured at the same time. Simultaneous serial photography, and direct measurement enabled one to relate a change in shape of the lens to the change in dioptric power. Subsequently, the same lens was isolated and spun around its antero‐posterior polar axis and high speed photography recorded its changing profile.
2. By comparing the changes in lens profile due to zonular tension and centrifugal force respectively, the force developed in the zonule for a given change in the shape of the lens could be calculated. Changes in dioptric power associated with those of shape can thus be related directly to the force of contraction of the ciliary muscle necessary to reduce the initial tension of the zonule in the unaccommodated state.
3. The force of contraction of the ciliary muscle as measured by radial force exerted through the zonule and the change in dioptric power of the lens were not linearly related. The relationship is more exactly expressed by the equation [Formula: see text] where D = amplitude of accommodation in dioptres (m ⁻¹ ), F CB = force of contraction of the ciliary muscle as measured by changes in tension of the zonule (N), K df = dioptric force coefficient and is constant for a given age ( m ⁻¹ N −½ × 10 2·5 ). This coefficient is 0·41 at 15 yr and 0·07 at 45 yr of age.
4. In youth for maximum accommodation (10‐12 D) the force is approximately 1·0 × 10 ⁻² N while to produce sufficient accommodation for near vision (3·5 D) the force is less than 0·05 × 10 ⁻² N.
5. After the age of 30 yr the force of contraction of the ciliary muscle necessary to produce maximum accommodation rises steadily to about 50 yr of age and thereafter probably falls slightly. At about 50 yr of age the ciliary muscle is some 50% more powerful than in youth.
6. Even if hypertrophy of the muscle did not occur the amplitude of accommodation would be reduced at the most by only 0·8 D of that observed at the onset of presbyopia.
Specimens of bovine, rabbit, and human corneas were systematically tested in uniaxial tension to experimentally determine their effective nonlinear stress-strain relations, and hysteresis. Cyclic tensile tests were performed over the physiologic load range of the cornea, up to a maximum of 10 percent strain beyond slack strain. Dimensional changes to corneal test specimens, due to varying laboratory environmental conditions, were also assessed. The measured stress-strain data was found to closely fit exponential power function relations typical of collagenous tissues when appropriate account was taken of specimen slack strain. These constitutive relations are very similar for rabbit, human and bovine corneas; there was no significant difference between the species after preconditioning by one cycle. The uniaxial stress strain curves for all species behave similarly in that their tangent moduli increase at high loads and decrease at low loads as a function of cycling. In the bovine and rabbit data, there is a general trend towards more elastic behavior from the first to second cycles, but there is little variation in these parameters from the second to third cycles. In comparison, the human data demonstrates relatively little change between cycles. Increases in width of corneal test specimens, up to a maximum of 2 percent were found to occur under 95 percent relative humidity test conditions over 10 minutes elapsed time test periods, while specimens which were exposed to normal laboratory conditions (45 percent RH) were found to shrink in width up to a maximum of 9.5 percent over the same elapsed time period. The thickness of the test specimens were observed to decrease by 3 percent in 95 percent relative humidity and by 12 percent in 45 percent relative humidity over the same elapsed time period.
1. When the lens is spun around its antero‐posterior polar axis in an apparatus designed for the purpose, high speed photography can be used to record its changing profile. By this method a variable radial centrifugal force can be applied to the lens which mimics the pull of the zonule.
2. If the lens is not stressed at its centre beyond 100 Nm ⁻² it behaves as a truly elastic body. When stressed beyond this limit visco‐elastic strain is produced at its poles.
3. The human lens has isotropic elastic properties at the extremes of life, but at the other times Young's Modulus of Elasticity varies with the direction in which it is measured.
4. Young's Modulus of Elasticity of the lens varies with age, polar elasticity and equatorial elasticity, at birth being 0·75 × 10 ³ and 0·85 × 10 ³ Nm ⁻² respectively, while at 63 years of age both are equal to 3 × 10 ³ Nm ⁻² .
5. A comparison of Young's Modulus of the young human lens with that of the rabbit and cat shows that the polar elasticity of the lenses of these animals was 5 times greater in the young rabbit, and 21 times greater in the adult cat. Equatorial elasticities of the rabbit and human lens were equal, while in the cat the equatorial elasticity was four times greater.
6. A mathematical model showing the lens substance possessing a nucleus of lower isotropic elasticity than that of the isotropic elastic cortex surrounding it, accounts for the difference between polar and equatorial elasticity of the intact adult lens.
7. The implications of these findings are discussed in relation to:
(i) accommodation and the rheological properties of the lens;
(ii) possible differences in the physical state of the lenticular proteins in the cortex and nucleus which may account for the senile variations in Young's Modulus of Elasticity in these regions of the lens;
(iii) the loss of accommodation due solely to an increase in Young's Modulus of Elasticity of the lens between the ages of 15 and 60. This would amount to 44% of the total observed in vivo .
1. A technique is described whereby the elasticity of the human lens capsule has been determined at birth and throughout life. This technique requires three separate determinations: ( a ) thickness; ( b ) stress and strain; ( c ) Poisson's ratio; ( a ) the capsule was clamped between accurately perforated ground glass plates and its thickness determined by noting the change in depth of focus between Latex spherules adhering to its upper and lower surfaces; ( b ) the undisturbed capsule was then placed in a specially designed glass distension apparatus and the relationship between volume and pressure recorded when it was distended with isotonic saline. The permeability of the capsule was also measured; ( c ) in some cases Poisson's ratio was determined by measuring the change of thickness of the capsule and the height to which it rose when distended with isotonic saline at different pressures. An apparatus was designed for this purpose.
2. The average thickness of the anterior capsule increases from birth until about the 60th year but thereafter it decreases slightly.
3. Poisson's ratio was about 0·47 for both cat and human capsule, and no significant variations with age in human capsule could be detected.
4. Corrected volume pressure curves obeyed Hook's law almost to the point of capsule rupture.
5. In childhood Young's Modulus of elasticity is about 6 × 10 ⁷ dyn/cm ² and decreases to 3 × 10 ⁷ dyn/cm ² at 60 and 1·5 × 10 ⁷ dyn/cm ² in extreme old age.
6. The ultimate tensile stress was 2·3 × 10 ⁷ dyn/cm ² in young capsules and 0·7 × 10 ⁷ dyn/cm ² in old ones. The maximum percentage elongation was 29 per cent and independent of age.
7. The implications of these findings are discussed in relation to
( a ) the mechanical properties of the lens capsule;
( b ) the ageing of the lens capsule and basement membranes; and
( c ) the decrease in elasticity of the lens capsule as a cause of presbyopia.
The uniaxial tensile strength was determined for six keratoconus and seven normal corneas. Strip specimens were stretched at a constant speed in a materials testing machine while recording load and deformation. Load-deformation curves were transformed into load-strain and stress-strain curves. The following parameters were derived from the load-strain and stress-strain curves: the maximum load and stress values and the corresponding strain value, the values for maximum stiffness, and the relative energy absorption of the specimens during testing. With the exception of the strain value at maximum load or stress, these parameters were smaller in the keratoconus group than in the normal group. The load and stress values at corresponding strain values were less in keratoconus corneas than in normal corneas both for the initial and for the linear parts of the curves.Biochemically, no difference was found in the concentration of uronic acid in the two groups. Similarly no difference was found in the concentration of hydroxyproline in the two groups. The solubility of pepsin treated collagen in the keratoconus corneas was greater than that in the normal corneas, however, the solubility was less than that in tendons.
To investigate the susceptibility to rupture of a human donor cornea with fully healed radial keratotomy (RK) incisions using biomechanical measurement methods and finite element analysis.
A human cornea 8 years after RK was cut into four strips and subjected to tensile testing until rupture occurred. The fellow cornea was pressurized on an artificial anterior chamber beyond the initiation of wound gape. The tensile strengths of nine strips from unincised corneas were measured as controls. To investigate the effect of epithelial plugs on the RK strip test results, a finite element model of a strip containing an epithelial plug was analyzed.
Rupture occurred along the wound site with wide variability in the measured tensile strengths. There was no significant difference in tensile strength between the RK corneal strips (16.6 +/- 4.43 N/mm2) and the control strips (19.1 +/- 3.50 N/mm2). Four of the eight incisions of the fellow RK cornea gaped, but the cornea did not rupture up to a pressure of 2740 mm Hg. An epithelial plug of 10% of the corneal thickness was found in one of the incisions. The finite element results demonstrated higher stresses at the wound site that increased with the size of the epithelial plug.
The presence of an epithelial plug in a fully healed radial keratotomy incision will create a stress concentration at the incision site that may predispose the cornea to rupture. The variability in the strength measurements indicates that the increase in rupture susceptibility due to RK may be hard to predict and may depend on factors such as the size of the plug and the strength of the wound collagen.
Data on geometric and material properties of the human lens derived from various published sources are used to construct axisymmetric, large displacement, finite element models of the accommodating lens of subjects aged 11, 29 and 45 years. The nucleus, cortex, capsule and zonule are modelled as linearly elastic materials. The numerical model of the 45-year lens is found to be significantly less effective in accommodating than the 29-year lens, suggesting that the modelling procedure is capable of capturing at least some of the features of presbyopia. The model of the 11-year lens shows some anomalous behaviour, and reasons for this are explored.
To investigate mechanical properties of the human posterior lens capsule.
Twenty-five human donor eyes were obtained from an eye bank. The age of the donors ranged from 1 to 94 years. Test specimens were prepared as tissue rings from posterior lens capsules by means of excimer laser. Capsular thickness was measured microscopically as the difference in focus between microspherules placed on the outer and inner surfaces of the capsule. The capsular rings were slipped over two pins connected to a motorized micropositioner and a force transducer and stretched at a constant rate with continuous recording of load and deformation. Data for the posterior lens capsule were compared with previously published data for the anterior lens capsule.
The thickness of the posterior lens capsule ranged from 4 to 9 micro m and showed no significant changes with age. Ultimate mechanical strength of the posterior lens capsule decreased significantly with age. Ultimate strain ranged from 101% to 34%, ultimate load ranged from 15.9 to 1.1 mN, ultimate stress ranged from 16.1 to 1.1 N/mm(2), ultimate elastic stiffness ranged from 52.1 to 5.7 mN, and ultimate elastic modulus ranged from 27.4 to 3.3 N/mm(2). The load-strain and the stress-strain relationships in the posterior lens capsule were nonlinear, and therefore elastic stiffness and elastic modulus varied as a function of strain. In the low-strain region (0%-10% strain), elastic stiffness and elastic modulus ranged between 0.3 to 2.4 mN and 0.3 to 2.3 N/mm(2), respectively, and seemed to increase during the first part of life until middle age.
Mechanical strength of the posterior lens capsule was found to decrease markedly with age. The age-related loss of mechanical strength seemed to begin earlier in the posterior lens capsule than in the anterior lens capsule. In accommodative function range (low strains), the mechanical quality of the posterior lens capsule was similar to the anterior lens capsule, which indicates that the mechanical effectiveness of the lens capsule in situ varies proportionally with capsular thickness.
To determine the changes in corneal curvature in accommodation.
Department of Ophthalmology, St. Luke's International Hospital, Tokyo, Japan.
Twenty-eight eyes of 14 healthy volunteers with a mean age of 38.9 years (range 28 to 65 years) were enrolled in this prospective study. Corneal topographies were taken before and during accommodation. Subjects achieved maximal accommodation by gazing at a target letter "A" in front of the eye. Keratometric values (K-values) obtained by topographies before and during accommodation were compared.
Steepened corneal curvatures during accommodation were observed with the difference-plot view. Maximum K-values for the central 3.0 mm, 5.0 mm, and 7.0 mm corneal diameters significantly increased by a mean of 0.62 diopters (D) +/- 0.83 (SD) (P =.0005, paired t test), 0.60 +/- 0.90 D (P =.0015), and 0.72 +/- 0.65 D (P<.0001), respectively. Respective minimum K-values significantly increased by a mean of 0.62 +/- 0.83 D (P=.0005), 0.67 +/- 0.68 D (P<.0001), and 0.64 +/- 0.62 D (P<.0001). No statistically significant relationship was found between age and change in K-values.
The results suggest that changes in corneal curvature in accommodation participate in the mechanism of accommodation.
A nonlinear axisymmetric finite element method (FEM) analysis was employed to determine the critical geometric and material properties that affect human accommodation. In this model, commencing at zero, zonular traction on all lens profiles resulted in central lenticular surface steepening and peripheral surface flattening, with a simultaneous increase in central lens thickness and central optical power. An age-related decline in maximum zonular tension appears to be the most likely etiology for the decrease in accommodative amplitude with age.
This paper constructs two finite element models of human crystalline lens and zonules based on published clinical data. Displacement and pressure were applied to study the mechanism of vision accommodation. The simulation results show that, in Model A, under the pull of the zonules, the thickness of the lens decreased linearly, and the lens diameter increased linearly. The optical power of the lens increased as the zonules displacement increased. Furthermore, the pressure had a remarkable influence on the shape of the lens and the optical power. The lens also became thinner and flatter as the pressure increased. The optical power increased when the pressure increased. In Model B, the lens became thicker and optical power increased as the equatorial zonules stretched. It is basically consistent with Schachar's hypothesis. The outcome of this paper proved that the analytical model presented in this paper can be used in the theoretical study of the accommodation mechanism of the lens.
To evaluate anterior segment alterations with age and during accommodation in different age groups.
Department of Ophthalmology, Medical and Health Science Center, University of Debrecen, Debrecen, Hungary.
Fifty-three subjects (101 normal eyes) were enrolled in this study and divided into 3 age groups: younger than 30 years (Group 1), between 31 years and 44 years (Group 2), and older than 45 years (Group 3). The total amplitude of accommodation was determined with a defocusing technique, and anterior segment measurements were performed by partial coherence interferometry.
Group 1 comprised 32 eyes; Group 2, 37 eyes; and Group 3, 32 eyes. The total amplitude of accommodation decreased with age (P<.0001). With the target position at infinity, the lens thickness (LT) and anterior segment length (ASL) increased and the anterior chamber depth (ACD) decreased significantly with age (P<.0001). During accommodation in the youngest group, the mean change in LT was 36.3 mum/diopter (D) and in ACD, -26.7 mum/D. The mean accommodation-induced ACD change was -0.08 mm +/- 0.06 (SD) in Group 1, -0.064 +/- 0.087 mm in Group 2, and -0.03 +/- 0.06 mm in Group 3 (P = .0004). The mean LT change during near fixation was 0.109 +/- 0.063 mm in Group 1, 0.103 +/- 0.136 mm in Group 2, and 0.006 +/- 0.05 mm in Group 3 (P<.0001). The mean ASL change during accommodation was 0.029 +/- 0.037 mm, 0.039 +/- 0.114 mm, and -0.023 +/- 0.051, respectively (P<.0001).
In addition to forward movement of the anterior lens surface with age, the posterior surface moved backward. Alterations in LT and ACD sufficient for a unit of refractive power change during accommodation might be smaller than previously thought. Anterior shifting of the lens may also participate in the accommodative response.
finite element model of the human eye to investigate ocular injuries from night vision goggles, Master thesis, Virginia Polytechnic Institute Evaluating the material parameters of the human cornea in a numerical model
- Ed Power
Power ED, A nonlinear finite element model of the human eye to investigate
ocular injuries from night vision goggles, Master thesis, Virginia Polytechnic
Institute; Blacksburg, Virginia, 2001.
19´Sródka19´ 19´Sródka W, Evaluating the material parameters of the human cornea in a
numerical model, Acta of Bioengineering and Biomechanics, 13(3), (2011),
77–85.
Biomechanical analyses of the human eye
- Z Bocskai
- I Bojtár
Bocskai Z, Bojtár I, Biomechanical analyses of the human eye, In: Kiss
R (ed.), Biomechanikai modellezés: Monográfia, TERC; Budapest, 2012,
pp. 187-202. in Hungarian.
Biomechanical properties of keratoconus and normal corneas
- T T Andreassen
- A H Simonsen
- H Oxlund
Andreassen TT, Simonsen AH, Oxlund H, Biomechanical properties of
keratoconus and normal corneas, Experimental Eye Research, 31, (1980),
435-441, DOI 10.1016/S0014-4835(80)80027-3.
Optical power of the isolated human crystalline lens
- D Borja
- F Manns
- A Ho
- N Ziebarth
- A M Rosen
- R Jain
- A Amelinckx
- E Arrieta
- R C Augusteyn
- J M Parel
Borja D, Manns F, Ho A, Ziebarth N, Rosen AM, Jain R, Amelinckx
A, Arrieta E, Augusteyn RC, Parel JM, Optical power of the isolated human crystalline lens, Investigative Ophthalmology and Visual Science, 49(6),
(2008), 2541-2548, DOI 10.1167/iovs.07-1385.
Biomechanical characteristic of human anterior lens capsule in relation to age, Investigative Opthalmology and Visual Science
- S Krag
- T T Andreassen
- T Olsen
Krag S, Andreassen TT, Olsen T, Biomechanical characteristic of human
anterior lens capsule in relation to age, Investigative Opthalmology and Visual Science, 38, (1997), 357-363.
A study for accommodating the human crystalline lens by finite element simulation, Computerized Medical Imaging and Graphics
- Z Liu
- B Wang
- X Z Xu
- C Wang
Liu Z, Wang B, Xu XZ, Wang C, A study for accommodating the human crystalline lens by finite element simulation, Computerized Medical Imaging and Graphics, 30, (2006), 371-376, DOI
10.1016/j.compmedimag.2006.09.008.
Anterior segment changes with age and during accommodation measured with partial coherence interferometry
- A Tsorbatzoglou
- G Németh
- N Széll
- Z Biró
- A Berta
Tsorbatzoglou A, Németh G, Széll N, Biró Z, Berta A, Anterior segment
changes with age and during accommodation measured with partial coherence interferometry, Journal of Cataract and Refractive Surgery, 33, (2007),
1597-1601, DOI 10.1016/j.jcrs.2007.05.021.
Simulation model of eyeball based on finite element analysis on a supercomputer
- E Uchio
- S Ohno
- J Kudoh
- K Aoki
- L T Kisielewicz
Uchio E, Ohno S, Kudoh J, Aoki K, Kisielewicz LT, Simulation model of
eyeball based on finite element analysis on a supercomputer, British Journal
of Ophthalmology, 83, (1999), 1106-1111, DOI 10.1136/bjo.83.10.1106.