R.I. Park

A porohyperelastic finite element model of the eye: the influence of stiffness and permeability on intraocular pressure and optic nerve head biomechanics.

Progressively deteriorating visual field is a characteristic feature of primary open-angle glaucoma (POAG), and the biomechanics of optic nerve head (ONH) is believed to be important in its onset. We used porohyperelasticity to model the complex porous behavior of ocular tissues to better understand the effect variations in ocular material properties can have on ONH biomechanics. An axisymmetric model of the human eye was constructed to parametrically study how changes in the permeabilities of retina–Bruchs–choroid complex , sclera , uveoscleral pathway , and trabecular meshwork as well as how changes in the stiffness of the lamina cribrosa (LC) and sclera affect IOP, LC strains, and translaminar interstitial pressure gradients (TLIPG). Decreasing from 5 × 10− 12 to 5 × 10− 13 m/s increased IOP and LC strains by 17%, and TLIPG by 21%. LC strains increased by 13% and 9% when the scleral and LC moduli were decreased by 48% and 50%, respectively. In addition to the trabecular meshwork and uveoscleral pathway, the retina–Bruchs–choroid complex had an important effect on IOP, LC strains, and TLIPG. Changes in and scleral modulus resulted in nonlinear changes in the IOP, and LC strains especially at the lowest and . This study demonstrates that porohyperelastic modeling provides a novel method for computationally studying the biomechanical environment of the ONH. Porohyperelastic simulations of ocular tissues may help provide further insight into the complex biomechanical environment of posterior ocular tissues in POAG.

Retinal oximetry using intravitreal illumination.

Purpose: To demonstrate spectroscopic retinal oximetry measurements on arteries and veins in swine using intravitreal illumination. Retinal arterial and venous saturations are measured for a range of inspired O2 levels after pars plana vitrectomy. Methods: Pars plana vitrectomy and intravitreal manipulations were performed on two female American Yorkshire domestic swine. Light from a scanning monochromator was coupled into a fiberoptic intraocular illuminator inserted into the vitreous. The retinal vessels were illuminated obliquely, minimizing vessel glints. Multispectral images of the retinal vasculature were obtained as the swines arterial blood oxygen saturation was decreased from 100% to 67% in decrements of approximately 10%. Retinal vessel spectra were used to calculate oxygen saturation in selected arteries and veins. Arterial oxygen saturations were calibrated using blood gas analysis on blood drawn from a Swan-Ganz catheter placed in the femoral artery. Results: Oblique illumination of retinal vessels using an intravitreal fiberoptic illuminator provided a substantial reduction in the central vessel glint usually seen in fundus images, thus simplifying the analysis of spectral data. The vessel shadows were displaced from the vessel image simplifying the light paths in the eye. Using a full spectral analysis simplified by the light path reductions, we calculated retinal vessel saturations. The reduction of glint allowed for increased accuracy in measuring retinal vessel spectral optical density. Abnormally low retinal venous oxygen saturations were observed shortly after pars plana vitrectomy. Conclusions: Retinal oximetry using intravitreal illumination has been demonstrated. As a research tool, intravitreal illumination addresses several difficulties encountered when performing retinal oximetry with transcorneal illumination.

Blue-green spectral minimum correlates with oxyhemoglobin saturation in vivo

An imaging multi-spectral retinal oximeter with intravitrial illumination is used to perform the first in vivo test of the blue-green minima shift oximetry method (BGO) in swine eyes [K. R. Dennighoff, R. A. Chipman, and L. W. Hillman, Opt. Lett. 31, 924-926 (2006); J. Biomed. Opt. 12, 034020 (2007).] A fiber optic intravitreal illuminator inserted through the pars plana was coupled to a monochromator and used to illuminate the retina from an angle. A camera viewing through the cornea recorded a series of images at each wavelength. This intravitreal light source moves the specular vessel glint away from the center of the vessel and directly illuminates the fundus behind most blood vessels. These two conditions combine to provide accurate measurements of vessel and perivascular reflectance. Equations describing these different light paths are solved, and BGO is used to evaluate large retinal vessels. In order to test BGO calibration in vivo, data were acquired from swine with varied retinal arterial oxyhemoglobin saturations (60-100% saturation.). The arterial saturations determined using BGO to analyze the multispectral image sets showed excellent correlation with co-oximeter data (r2=0.98, and residual error +/-3.4% saturation) and are similar to results when hemoglobin and blood were analyzed using this technique.

Diffuse spectral fundus reflectance measured using subretinally placed spectralon

The diffuse fundus reflectance and the spectral transmittance of the swine sensory retina was measured in vivo using intravitreal illumination. Pars plana vitrectomy and intravitreal manipulations were performed on a female American Yorkshire domestic swine. Light from a scanning monochromator was coupled into a fiber optic intraocular illuminator inserted into the vitreous. A 1.93-mm(2) region of the illuminated fundus was imaged from an oblique illumination angle. Multispectral retinal images were acquired for four experimental conditions: the eye (1) prior to vitrectomy, (2) after vitrectomy, (3) after insertion of a Spectralon disk super-retinally, and (4) after subretinal insertion of the disk. The absorption of melanin and hemoglobin in the red wavelengths was used to convert relative spectral reflectance to absolute reflectance. The flux scattered from the super-retinal Spectralon was used to correct for scattering in the globe. The transmittance of the sensory retina was measured in vivo using the scatter corrected subretinal Spectralon disk reflectance. The hemoglobin and melanin components of the spectrum due to scattered light were removed from the retinal transmission spectrum. The in vivo spectral transmittance of the sensory retina in this swine was essentially flat across the visible spectrum, with an average transmittance >90%.

Wavelength dependence of the apparent diameter of retinal blood vessels

Imaging of retinal blood vessels may assist in the diagnosis and monitoring of diseases such as glaucoma, diabetic retinopathy, and hypertension. However, close examination reveals that the contrast and apparent diameter of vessels are dependent on the wavelength of the illuminating light. In this study multispectral images of large arteries and veins within enucleated swine eyes are obtained with a modified fundus camera by use of intravitreal illumination. The diameters of selected vessels are measured as a function of wavelength by cross-sectional analysis. A fixed scale with spectrally independent dimension is placed above the retina to isolate the chromatic effects of the imaging system and eye. Significant apparent differences between arterial and venous diameters are found, with larger diameters observed at shorter wavelengths. These differences are due primarily to spectral absorption in the cylindrical blood column.

Porohyperelastic-Transport Finite Element Models of the Eye Using ABAQUS

Glaucoma is related to damage to nerve ganglion cells in the optic nerve head (ONH) including the lamina cribrosa, (LC). This disease is associated with elevated intraocular pressure (IOP) and possibly reduced trabecular meshwork (TM) outflow. The ABAQUS program was used to develop axisymmetric porohyperelastic (PHE) pore fluid finite element models (FEMs) to determine deformations, stresses, tissue fluid pressures (pf ), and mobile fluid flux in the eye. These FEMs simulated aqueous pressure-fluid flow fields in the anterior chamber via the TM and posterior pressure-flow fields in the vitreous body (VIT) and ONH. Constant inlet flow at the ciliary processes (CP) was applied. The anterior chamber was modeled as a highly porous material containing large amounts of fluid whereas the VIT was modeled as a gel with mobile fluid. All ocular soft tissues were considered to be linear, isotropic PHE materials. Posterior transport was regulated by varying the permeability of the LC, retina, choroid, and sclera material layers. Two FEMs, i.e. IOP=15 mm Hg (normal) and IOP=44 mm Hg (glaucoma) were developed by varying the permeability of the TM. Deformations and tissue fluid pressures, fluid flux (relative fluid velocities), and stresses were determined and agree well with experimental data and other numerical model results. The displacement of the LC was 21–62 μm; the LC pressure gradient was 25–73 mm Hg/mm; and the posterior outflow ranged from 5%–15% of the inflow at the CP. The PHE material law can be extended to include nonlinear permeability effects and mobile species transport using a porohyperelastic-transport-swelling (PHETS) theory in future FEMs.Copyright

Analytic and Computational Comparison of Poroelastic and Elastic Biomechanical Models for Soft Ocular Tissues

Current investigations into the cause of glaucoma reveal the importance and influence of biomechanical properties and response in ocular tissue [1–4]. Finite element models (FEMs) supported by experimental data are essential in quantifying stress, strain and displacement values at vulnerable locations in the eye; (e.g., the optic nerve head (ONH, lamina cribrosa (LC), etc); associated with normal and elevated intraocular pressures (IOP). In order to create such FEMs, our analysis shows the importance of extending elastic to poroelastic (PE) material models in FEMs used to describe ocular structures. The current study investigates the quantitative differences between elastic and PE representations of material behavior and compares the accuracy of analytical results with computational results from a PE FEM. Such differences may be important when investigating the pathophysiology and diagnosis of ocular diseases.Copyright

ABAQUS-Based, Coupled Porohyperelastic Transport Finite Element Models for Soft Hydrated Biological Structures

General theoretical, experimental, and finite element models (FEMs) based on porous media formulations were developed to study complex normal and pathological mechanical-transport phenomena in biological structures and soft tissues. These continuum models view soft tissues as a solid (fibrous matrix) in which mobile fluid (water) and mobile species (ions, molecules, drugs) are transported during finite deformation. Two specific models were considered, i.e. the mixed porohyperelastic transport swelling (MPHETS) or equivalent porohyperelastic transport swelling (PHETS) [1] and the “porohypereleastic mass transport (PHEXPT)” ABAQUS models [2]. The theoretical formulations are the basis for FEMs and identify necessary material property functions. A suite of experiments is described that allows measurement of material parameters (elasticity, permeability, diffusivity, etc). If the PHETS “osmotic coefficient” is relatively small, then a novel partially coupled PHEXPT model can be implemented using an extended version of ABAQUS CAE [3]. Mathematical relations were identified that relate PHETS and ABAQUS constitutive equations. A specialized FORTRAN program transfers PHE FEM (hyperelastic and pore fluid element) material parameters and transient response (deformation, pore fluid pressure, water flux, etc.) to the mass transport XPT FEM. This second XPT FEM then provides the transient diffusion-convection mass transport solution (concentration, relative species flux, etc.). The extensive capabilities of ABAQUS CAE (finite element library, anisotropic nonlinear materials, automated model generation, inputoutput display, etc.) can be used in PHEXPT simulations of complex soft tissue mechanics where finite deformations are coupled to fluid and species transport. Example applications of this new PHEXPT FEM procedure will include coupled structural-transport in large arteries, (drug eluting) stented arteries, tissue engineered vascular grafts, and the eyeball.