Modeling the biomechanics of the lamina cribrosa microstructure in the human eye

Comparative analysis of traction forces in normal and glaucomatous trabecular meshwork cells within a 3D, active fluid-structure interaction culture environment

This study presents a 3D in vitro cell culture model, meticulously 3D printed to replicate the conventional aqueous outflow pathway anatomical structure, facilitating the study of trabecular meshwork (TM) cellular responses under glaucomatous conditions. Glaucoma affects TM cell functionality, leading to extracellular matrix (ECM) stiffening, enhanced cell-ECM adhesion, and obstructed aqueous humor outflow. Our model, reconstructed from polyacrylamide gel with elastic moduli of 1.5 and 21.7 kPa, is based on serial block-face scanning electron microscopy images of the outflow pathway. It allows for quantifying 3D, depth-dependent, dynamic traction forces exerted by both normal and glaucomatous TM cells within an active fluid-structure interaction (FSI) environment. In our experimental design, we designed two scenarios: a control group with TM cells observed over 20 hours without flow (static setting), focusing on intrinsic cellular contractile forces, and a second scenario incorporating active FSI to evaluate its impact on traction forces (dynamic setting). Our observations revealed that active FSI results in higher traction forces (normal: 1.83-fold and glaucoma: 2.24-fold) and shear strains (normal: 1.81-fold and glaucoma: 2.41-fold), with stiffer substrates amplifying this effect. Glaucomatous cells consistently exhibited larger forces than normal cells. Increasing gel stiffness led to enhanced stress fiber formation in TM cells, particularly in glaucomatous cells. Exposure to active FSI dramatically altered actin organization in both normal and glaucomatous TM cells, particularly affecting cortical actin stress fiber arrangement. This model while preliminary offers a new method in understanding TM cell biomechanics and ECM stiffening in glaucoma, highlighting the importance of FSI in these processes. STATEMENT OF SIGNIFICANCE: This pioneering project presents an advanced 3D in vitro model, meticulously replicating the human trabecular meshwork's anatomy for glaucoma research. It enables precise quantification of cellular forces in a dynamic fluid-structure interaction, a leap forward from existing 2D models. This advancement promises significant insights into trabecular meshwork cell biomechanics and the stiffening of the extracellular matrix in glaucoma, offering potential pathways for innovative treatments. This research is positioned at the forefront of ocular disease study, with implications that extend to broader biomedical applications.

Fibrous finite element modeling of the optic nerve head region

The optic nerve head (ONH) region at the posterior pole of the eye is supported by a fibrous structure of collagen fiber bundles. Discerning how the fibrous structure determines the region biomechanics is crucial to understand normal physiology, and the roles of biomechanics on vision loss. The fiber bundles within the ONH structure exhibit complex three-dimensional (3D) organization and continuity across the various tissue components. Computational models of the ONH, however, usually represent collagen fibers in a homogenized fashion without accounting for their continuity across tissues, fibers interacting with each other and other fiber-specific effects in a fibrous structure. We present a fibrous finite element (FFE) model of the ONH that incorporates discrete collagen fiber bundles and their histology-based 3D organization to study ONH biomechanics as a fibrous structure. The FFE model was constructed using polarized light microscopy data of porcine ONH cryosections, representing individual fiber bundles in the sclera, dura and pia maters with beam elements and canal tissues as continuum structures. The FFE model mimics the histological in-plane orientation and width distributions of collagen bundles as well as their continuity across different tissues. Modeling the fiber bundles as linear materials, the FFE model predicts the nonlinear ONH response observed in an inflation experiment from the literature. The model also captures important microstructural mechanisms including fiber interactions and long-range strain transmission among bundles that have not been considered before. The FFE model presented here advances our understanding of the role of fibrous collagen structure in the ONH biomechanics. STATEMENT OF SIGNIFICANCE: The microstructure and mechanics of the optic nerve head (ONH) are central to ocular physiology. Histologically, the ONH region exhibits a complex continuous fibrous structure of collagen bundles. Understanding the role of the fibrous collagen structure on ONH biomechanics requires high-fidelity computational models previously unavailable. We present a computational model of the ONH that incorporates histology-based fibrous collagen structure derived from polarized light microscopy images. The model predictions agree with experiments in the literature, and provide insight into important microstructural mechanisms of fibrous tissue biomechanics, such as long-range strain transmission along fiber bundles. Our model can be used to study the microstructural basis of biomechanical damage and the effects of collagen remodeling in glaucoma.

Segmental biomechanics of the normal and glaucomatous human aqueous outflow pathway

The conventional aqueous outflow pathway, encompassing the trabecular meshwork (TM), juxtacanalicular connective tissue (JCT), and inner wall endothelium of Schlemm's canal (SC), governs intraocular pressure (IOP) regulation. This study targets the biomechanics of low-flow (LF) and high-flow (HF) regions within the aqueous humor outflow pathway in normal and glaucomatous human donor eyes, using a combined experimental and computational approach. LF and HF TM/JCT/SC complex tissues from normal and glaucomatous eyes underwent uniaxial tensile testing. Dynamic motion of the TM/JCT/SC complex was recorded using customized green-light optical coherence tomography during SC pressurization in cannulated anterior segment wedges. A hyperviscoelastic model quantified TM/JCT/SC complex properties. A fluid-structure interaction model simulated tissue-aqueous humor interaction. FluoSpheres were introduced into the pathway via negative pressure in the SC, with their motion tracked using two-photon excitation microscopy. Tensile test results revealed that the elastic moduli of the LF and HF regions in glaucomatous eyes are 3.5- and 1.5-fold stiffer than the normal eyes, respectively. The FE results also showed significantly larger shear moduli in the TM, JCT, and SC of the glaucomatous eyes compared to the normal subjects. The LF regions in normal eyes demonstrated larger elastic moduli compared to the HF regions in glaucomatous eyes. The resultant strain in the outflow tissues and velocity of the aqueous humor in the FSI models were in good agreement with the digital volume correlation and 3D particle image velocimetry data, respectively. This study uncovers stiffer biomechanical responses in glaucomatous eyes, with LF regions stiffer than HF regions in both normal and glaucomatous eyes. STATEMENT OF SIGNIFICANCE: This study delves into the biomechanics of the conventional aqueous outflow pathway, a crucial regulator of intraocular pressure and ocular health. By analyzing mechanical differences in low-flow and high-flow regions of normal and glaucomatous eyes, this research unveils the stiffer response in glaucomatous eyes. The distinction between regions' properties offers insights into aqueous humor outflow regulation, while the integration of experimental and computational methods enhances credibility. These findings have potential implications for disease management and present a vital step toward innovative ophthalmic interventions. This study advances our understanding of glaucoma's biomechanical basis and its broader impact on ocular health.

Implementing new computational methods for the study of JCT and SC inner wall basement membrane biomechanics and hydrodynamics

PURPOSE

The conventional aqueous outflow pathway, which includes the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and the inner wall endothelium of Schlemm's canal (SC), regulates intraocular pressure (IOP) by controlling the aqueous humor outflow resistance. Despite its importance, our understanding of the biomechanics and hydrodynamics within this region remains limited. Fluid-structure interaction (FSI) offers a way to estimate the biomechanical properties of the JCT and SC under various loading and boundary conditions, providing valuable insights that are beyond the reach of current imaging techniques.

METHODS

In this study, a normal human eye was fixed at a pressure of 7 mm Hg, and two radial wedges of the TM tissues, which included the SC inner wall basement membrane and JCT, were dissected, processed, and imaged using 3D serial block-face scanning electron microscopy (SBF-SEM). Four different sets of images were used to create 3D finite element (FE) models of the JCT and inner wall endothelial cells of SC with their basement membrane. The outer JCT portion was carefully removed as the outflow resistance is not in that region, leaving only the SCE inner wall and a few µm of the tissue, which does contain the resistance. An inverse iterative FE algorithm was then utilized to calculate the unloaded geometry of the JCT/SC complex at an aqueous humor pressure of 0 mm Hg. Then in the model, the intertrabecular spaces, pores, and giant vacuole contents were replaced by aqueous humor, and FSI was employed to pressurize the JCT/SC complex from 0 to 15 mm Hg.

RESULTS

In the JCT/SC complex, the shear stress of the aqueous humor is not evenly distributed. Areas proximal to the inner wall of SC experience larger stresses, reaching up to 10 Pa, while those closer to the JCT undergo lower stresses, approximately 4 Pa. Within this complex, giant vacuoles with or without I-pore behave differently. Those without I-pores experience a more significant strain, around 14%, compared to those with I-pores, where the strain is roughly 9%.

CONCLUSIONS

The distribution of aqueous humor wall shear stress is not uniform within the JCT/SC complex, which may contribute to our understanding of the underlying selective mechanisms in the pathway.

Computational study of the mechanical behavior of the astrocyte network and axonal compartments in the mouse optic nerve head

Glaucoma is a blinding disease characterized by the degeneration of the retinal ganglion cell (RGC) axons at the optic nerve head (ONH). A major risk factor for glaucoma is the intraocular pressure (IOP). However, it is currently impossible to measure the IOP-induced mechanical response of the axons of the ONH. The objective of this study was to develop a computational modeling method to estimate the IOP-induced strains and stresses in the axonal compartments in the mouse astrocytic lamina (AL) of the ONH, and to investigate the effect of the structural features on the mechanical behavior. We developed experimentally informed finite element (FE) models of six mouse ALs to investigate the effect of structure on the strain responses of the astrocyte network and axonal compartments to pressure elevation. The specimen-specific geometries of the FE models were reconstructed from confocal fluorescent images of cryosections of the mouse AL acquired in a previous study that measured the structural features of the astrocytic processes and axonal compartments. The displacement fields obtained from digital volume correlation in prior inflation tests of the mouse AL were used to determine the displacement boundary conditions of the FE models. We then applied Gaussian process regression to analyze the effects of the structural features on the strain outcomes simulated for the axonal compartments. The axonal compartments experienced, on average, 6 times higher maximum principal strain but 1800 times lower maximum principal stress compared to those experienced by the astrocyte processes. The strains experienced by the axonal compartments were most sensitive to variations in the area of the axonal compartments. Larger axonal compartments that were more vertically aligned, closer to the AL center, and with lower local actin area fraction had higher strains. Understanding the factors affecting the deformation in the axonal compartments will provide insights into mechanisms of glaucomatous axonal damage.

Biomechanics of the JCT and SC Inner Wall Endothelial Cells with Their Basement Membrane Using 3D Serial Block-Face Scanning Electron Microscopy

BACKGROUND

More than ~70% of the aqueous humor exits the eye through the conventional aqueous outflow pathway that is comprised of the trabecular meshwork (TM), juxtacanalicular tissue (JCT), the inner wall endothelium of Schlemm's canal (SC). The flow resistance in the JCT and SC inner wall basement membrane is thought to play an important role in the regulation of the intraocular pressure (IOP) in the eye, but current imaging techniques do not provide enough information about the mechanics of these tissues or the aqueous humor in this area.

METHODS

A normal human eye was perfusion-fixed and a radial wedge of the TM tissue from a high-flow region was dissected. The tissues were then sliced and imaged using serial block-face scanning electron microscopy. Slices from these images were selected and segmented to create a 3D finite element model of the JCT and SC cells with an inner wall basement membrane. The aqueous humor was used to replace the intertrabecular spaces, pores, and giant vacuoles, and fluid-structure interaction was employed to couple the motion of the tissues with the aqueous humor.

RESULTS

Higher tensile stresses (0.8-kPa) and strains (25%) were observed in the basement membrane beneath giant vacuoles with open pores. The volumetric average wall shear stress was higher in SC than in JCT/SC. As the aqueous humor approached the inner wall basement membrane of SC, the velocity of the flow decreased, resulting in the formation of small eddies immediately after the flow left the inner wall.

CONCLUSIONS

Improved modeling of SC and JCT can enhance our understanding of outflow resistance and funneling. Serial block-face scanning electron microscopy with fluid-structure interaction can achieve this, and the observed micro-segmental flow patterns in ex vivo perfused human eyes suggest a hypothetical mechanism.

Developing an experimental-computational workflow to study the biomechanics of the human conventional aqueous outflow pathway

The aqueous humor actively interacts with the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and Schlemm's canal (SC) through a dynamic fluid-structure interaction (FSI) coupling. Despite the fact that intraocular pressure (IOP) undergoes significant fluctuations, our understanding of the hyperviscoelastic biomechanical properties of the aqueous outflow tissues is limited. In this study, a quadrant of the anterior segment from a normal human donor eye was dynamically pressurized in the SC lumen, and imaged using a customized optical coherence tomography (OCT). The TM/JCT/SC complex finite element (FE) with embedded collagen fibrils was reconstructed based on the segmented boundary nodes in the OCT images. The hyperviscoelastic mechanical properties of the outflow tissues' extracellular matrix with embedded viscoelastic collagen fibrils were calculated using an inverse FE-optimization method. Thereafter, the 3D microstructural FE model of the TM, with adjacent JCT and SC inner wall, from the same donor eye was constructed using optical coherence microscopy and subjected to a flow load-boundary from the SC lumen. The resultant deformation/strain in the outflow tissues was calculated using the FSI method, and compared to the digital volume correlation (DVC) data. TM showed larger shear modulus (0.92 MPa) compared to the JCT (0.47 MPa) and SC inner wall (0.85 MPa). Shear modulus (viscoelastic) was larger in the SC inner wall (97.65 MPa) compared to the TM (84.38 MPa) and JCT (56.30 MPa). The conventional aqueous outflow pathway is subjected to a rate-dependent IOP load-boundary with large fluctuations. This necessitates addressing the biomechanics of the outflow tissues using hyperviscoelastic material-model. STATEMENT OF SIGNIFICANCE: While the human conventional aqueous outflow pathway is subjected to a large-deformation and time-dependent IOP load-boundary, we are not aware of any studies that have calculated the hyperviscoelastic mechanical properties of the outflow tissues with embedded viscoelastic collagen fibrils. A quadrant of the anterior segment of a normal humor donor eye was dynamically pressurized from the SC lumen with relatively large fluctuations. The TM/JCT/SC complex were OCT imaged and the mechanical properties of the tissues with embedded collagen fibrils were calculated using the inverse FE-optimization algorithm. The resultant displacement/strain in the FSI outflow model was validated versus the DVC data. The proposed experimental-computational workflow may significantly contribute to understanding of the effects of different drugs on the biomechanics of the conventional aqueous outflow pathway.

Morphological and biomechanical analyses of the human healthy and glaucomatous aqueous outflow pathway: Imaging-to-modeling

BACKGROUND AND OBJECTIVE

Intraocular pressure (IOP) is maintained via a dynamic balance between the production of aqueous humor and its drainage through the trabecular meshwork (TM), juxtacanalicular connective tissue (JCT), and Schlemm's canal (SC) endothelium of the conventional outflow pathway. Primary open angle glaucoma (POAG) is often associated with IOP elevation that occurs due to an abnormally high outflow resistance across the outflow pathway. Outflow tissues are viscoelastic and actively interact with aqueous humor dynamics through a two-way fluid-structure interaction coupling. While glaucoma affects the morphology and stiffness of the outflow tissues, their biomechanics and hydrodynamics in glaucoma eyes remain largely unknown. This research aims to develop an image-to-model method allowing the biomechanics and hydrodynamics of the conventional aqueous outflow pathway to be studied.

METHODS

We used a combination of X-ray computed tomography and scanning electron microscopy to reconstruct high-fidelity, eye-specific, 3D microstructural finite element models of the healthy and glaucoma outflow tissues in cellularized and decellularized conditions. The viscoelastic TM/JCT/SC complex finite element models with embedded viscoelastic beam elements were subjected to a physiological IOP load boundary; the stresses/strains and the flow state were calculated using fluid-structure interaction and computational fluid dynamics.

RESULTS

Based on the resultant hydrodynamics parameters across the outflow pathway, the primary site of outflow resistance in healthy eyes was in the JCT and immediate vicinity of the SC inner wall, while the majority of the outflow resistance in the glaucoma eyes occurred in the TM. The TM and JCT in the glaucoma eyes showed 1.32-fold and 1.13-fold larger beam thickness and smaller trabecular space size (2.24-fold and 1.50-fold) compared to the healthy eyes.

CONCLUSIONS

Characterizing the accurate morphology of the outflow tissues may significantly contribute to constructing more accurate, robust, and reliable models, that can eventually help to better understand the dynamic IOP regulation, hydrodynamics of the aqueous humor, and outflow resistance dynamic in the human eyes. This model demonstrates proof of concept for determining changes to outflow resistance in healthy and glaucomatous tissues and thus may be utilized in larger cohorts of donor tissues where disease specificity, race, age, and gender of the eye donors may be accounted for.

A position- and time-dependent pressure profile to model viscoelastic mechanical behavior of the brain tissue due to tumor growth

This study proposed a computational framework to calculate the resultant position- and time-dependent pressure profile on the brain tissue due to tumor growth. A finite element (FE) patch of the brain tissue was constructed and an inverse dynamic FE-optimization algorithm was used to calculate its viscoelastic mechanical properties under compressive uniaxial loading. Two patient-specific post-tumor resection FE models were input to the FE-optimization algorithm to calculate the optimized 3rd-order position-dependent and normal distribution time-dependent pressure profile parameters. The optimized viscoelastic material properties, the most suitable simulation time, and the optimized 3rd-order position- and -time-dependent pressure profiles were calculated.

Opto-mechanical self-adjustment model of the human eye

The eye has specific optical and biomechanical properties that jointly regulate the eye's quality of vision, shape, and elasticity. These two characteristics are interdependent and correlated. Contrary to most currently available computational models of the human eye that only focus on biomechanical or optical aspects, the current study explores the inter-relationships between biomechanics, structure, and optical properties. Possible combinations of mechanical properties, boundary conditions, and biometrics were specified to ensure the opto-mechanical (OM) integrity to compensate for physiological changes in intraocular pressure (IOP) without compromising image acuity. This study evaluated the quality of the vision by analyzing the minimum spot diameters formed on the retina and drew how the self-adjustment mechanism affects the eye globe shape by adopting a finite element (FE) model of the eyeball. The model was verified by a water drinking test with biometric measurement (OCT Revo NX, Optopol) and tonometry (Corvis ST, Oculus).

Longitudinal Changes of Bruch's Membrane Opening, Anterior Scleral Canal Opening, and Border Tissue in Experimental Juvenile High Myopia

Purpose

To investigate the relative positional changes between the Bruch's membrane opening (BMO) and the anterior scleral canal opening (ASCO), and border tissue configuration changes during experimental high myopia development in juvenile tree shrews.

Methods

Juvenile tree shrews were assigned randomly to two groups: binocular normal vision (n = 9) and monocular -10 D lens treatment starting at 24 days of visual experience to induce high myopia in one eye while the other eye served as control (n = 12). Refractive and biometric measurements were obtained daily, and 48 radial optical coherence tomography B-scans through the center of the optic nerve head were obtained weekly for 6 weeks. ASCO and BMO were segmented manually after nonlinear distortion correction.

Results

Lens-treated eyes developed high degree of axial myopia (-9.76 ± 1.19 D), significantly different (P < 0.001) from normal (0.34 ± 0.97 D) and control eyes (0.39 ± 0.88 D). ASCO-BMO centroid offset gradually increased and became significantly larger in the experimental high myopia group compared with normal and control eyes (P < 0.0001) with an inferonasal directional preference. The border tissue showed a significantly higher tendency of change from internally to externally oblique configuration in the experimental high myopic eyes in four sectors: nasal, inferonasal, inferior, and inferotemporal (P < 0.005).

Conclusions

During experimental high myopia development, progressive relative deformations of ASCO and BMO occur simultaneously with changes in border tissue configuration from internally to externally oblique in sectors that are close to the posterior pole (nasal in tree shrews). These asymmetric changes may contribute to pathologic optic nerve head remodeling and an increased risk of glaucoma later in life.

Histology of the optic nerve head with special reference to the layer-specific distribution of composite fibers at and near the lamina cribrosa: An immunohistochemical study using specimens from elderly donated cadavers

BACKGROUND

This study aimed to demonstrate the composite fibers of the lamina cribrosa (LC) and their layer-specific distributions. The elastic fiber-rich septa, showing a cribriform arrangement in the optic nerve, may continue into the LC.

METHODS

Orbital content, including the long course of the optic nerve, was obtained from 25 elderly cadavers. Sagittal and cross-sections were prepared from each specimen. In addition to elastica Masson staining, immunohistochemistry was performed for elastin, glial fibrillary acidic protein (GFAP), S100 protein (S100), and CD68 in microglia.

RESULTS

The LC beam usually had fewer elastic fibers than the septa, but an elastic fiber-rich zone was observed along the scleral flange. GFAP-positive fibers were rich in the prelaminar area, whereas S100-positive fibers were rich in all layers of the LC. Double-positive (GFAP+/S100+) fibers were present in the prelaminar area. In contrast, S100-single positive fibers were evident in the LC and retrolaminar areas and were likely to insert into a sclera-choroid border area. The density of macrophages and microglia was not different between the septa and LC. Individual variations were observed in the distribution and density of the nerve-associated fibrous tissues.

CONCLUSION

The LC beam was quite different from the septa in the composite fibers and architecture. Transverse fibers, dominant in the LC beam, corresponded to fibrous processes of astrocytes and other nerve-associated fibrous tissues. Many of these nerve elements suggest low mechanical properties of the LC.

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

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

Ocular Rigidity and Current Therapy

Purpose: Ocular rigidity (OR) is an important biomechanical parameter of the eye accounting for the material and geometrical properties of the corneoscleral shell.Methods: This study used a literature search to review the role of ocular rigidity and the application of potential therapies targeting this parameter in glaucoma and myopia.Conclusion: Biomechanical modeling and improved understanding of the biochemistry, and molecular arrangement of sclera and its constituents have yielded important insights. Recent developments, including that of a non-invasive and direct OR measurement method and improved ocular imaging techniques are helping to elucidate the role of OR in healthy and diseased eyes by facilitating large scale and longitudinal clinical studies. Improved understanding of OR at the initial stages of disease processes and its alterations with disease progression will undoubtedly propel research in the field. Furthermore, a better understanding of the determinants of OR is helping to refine novel therapeutic approaches which target and alter the biomechanical properties of the sclera in sight-threatening conditions such as glaucoma and myopia.

Modeling the Endothelial Glycocalyx Layer in the Human Conventional Aqueous Outflow Pathway

A layer of proteoglycans and glycoproteins known as glycocalyx covers the surface of the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and Schlemm's canal (SC) inner wall of the conventional aqueous outflow pathway in the eye. This has been shown to play a role in the mechanotransduction of fluid shear stress and in the regulation of the outflow resistance. The outflow resistance in the conventional outflow pathway is the main determinant of the intraocular pressure (IOP) through an active, two-way, fluid-structure interaction coupling between the outflow tissues and aqueous humor. A 3D microstructural finite element (FE) model of a healthy human eye TM/JCT/SC complex with interspersed aqueous humor was constructed. A very thin charged double layer that represents the endothelial glycocalyx layer covered the surface of the elastic outflow tissues. The aqueous humor was modeled as electroosmotic flow that is charged when it is in contact with the outflow tissues. The electrical-fluid-structure interaction (EFSI) method was used to couple the charged double layer (glycocalyx), fluid (aqueous humor), and solid (outflow tissues). When the IOP was elevated to 15 mmHg, the maximum aqueous humor velocity in the EFSI model was decreased by 2.35 mm/s (9%) compared to the fluid-structure interaction (FSI) model. The charge or electricity in the living human conventional outflow pathway generated by the charged endothelial glycocalyx layer plays a minor biomechanical role in the resultant stresses and strains as well as the hydrodynamics of the aqueous humor.

Biomechanical analysis of ocular diseases and its in vitro study methods

Ocular diseases are closely related to the physiological changes in the eye sphere and its contents. Using biomechanical methods to explore the relationship between the structure and function of ocular tissue is beneficial to reveal the pathological processes. Studying the pathogenesis of various ocular diseases will be helpful for the diagnosis and treatment of ocular diseases. We provide a critical review of recent biomechanical analysis of ocular diseases including glaucoma, high myopia, and diabetes. And try to summarize the research about the biomechanical changes in ocular tissues (e.g., optic nerve head, sclera, cornea, etc.) associated with those diseases. The methods of ocular biomechanics research in vitro in recent years are also reviewed, including the measurement of biomechanics by ophthalmic equipment, finite element modeling, and biomechanical analysis methods. And the preparation and application of microfluidic eye chips that emerged in recent years were summarized. It provides new inspiration and opportunity for the pathogenesis of eye diseases and personalized and precise treatment.

The Effect of Intraocular Pressure Load Boundary on the Biomechanics of the Human Conventional Aqueous Outflow Pathway

BACKGROUND

Aqueous humor outflow resistance in the trabecular meshwork (TM), juxtacanalicular connective tissue (JCT), and Schlemm's canal (SC) endothelium of the conventional outflow pathway actively contribute to intraocular pressure (IOP) regulation. Outflow resistance is actively affected by the dynamic outflow pressure gradient across the TM, JCT, and SC inner wall tissues. The resistance effect implies the presence of a fluid-structure interaction (FSI) coupling between the outflow tissues and the aqueous humor. However, the biomechanical interactions between viscoelastic outflow tissues and aqueous humor dynamics are largely unknown.

METHODS

A 3D microstructural finite element (FE) model of a healthy human eye TM/JCT/SC complex was constructed with elastic and viscoelastic material properties for the bulk extracellular matrix and embedded elastic cable elements. The FE models were subjected to both idealized and a physiologic IOP load boundary using the FSI method.

RESULTS

The elastic material model for both the idealized and physiologic IOP load boundary at equal IOPs showed similar stresses and strains in the outflow tissues as well as pressure in the aqueous humor. However, outflow tissues with viscoelastic material properties were sensitive to the IOP load rate, resulting in different mechanical and hydrodynamic responses in the tissues and aqueous humor.

CONCLUSIONS

Transient IOP fluctuations may cause a relatively large IOP difference of ~20 mmHg in a very short time frame of ~0.1 s, resulting in a rate stiffening in the outflow tissues. Rate stiffening reduces strains and causes a rate-dependent pressure gradient across the outflow tissues. Thus, the results suggest it is necessary to use a viscoelastic material model in outflow tissues that includes the important role of IOP load rate.

Viscoelastic Biomechanical Properties of the Conventional Aqueous Outflow Pathway Tissues in Healthy and Glaucoma Human Eyes

Background: Although the tissues comprising the ocular conventional outflow pathway have shown strong viscoelastic mechanical response to aqueous humor pressure dynamics, the viscoelastic mechanical properties of the trabecular meshwork (TM), juxtacanalicular connective tissue (JCT), and Schlemm’s canal (SC) inner wall are largely unknown. Methods: A quadrant of the anterior segment from two human donor eyes at low- and high-flow (LF and HF) outflow regions was pressurized and imaged using optical coherence tomography (OCT). A finite element (FE) model of the TM, the adjacent JCT, and the SC inner wall was constructed and viscoelastic beam elements were distributed in the extracellular matrix (ECM) of the TM and JCT to represent anisotropic collagen. An inverse FE-optimization algorithm was used to calculate the viscoelastic properties of the ECM/beam elements such that the TM/JCT/SC model and OCT imaging data best matched over time. Results: The ECM of the glaucoma tissues showed significantly larger time-dependent shear moduli compared to the heathy tissues. Significantly larger shear moduli were also observed in the LF regions of both the healthy and glaucoma eyes compared to the HF regions. Conclusions: The outflow tissues in both glaucoma eyes and HF regions are stiffer and less able to respond to dynamic IOP.

Relative Contributions of Intraocular and Cerebrospinal Fluid Pressures to the Biomechanics of the Lamina Cribrosa and Laminar Neural Tissues

Purpose

The laminar region of the optic nerve head (ONH), thought to be the site of damage to the retinal ganglion cell axons in glaucoma, is continuously loaded on its anterior and posterior surfaces by dynamic intraocular pressure (IOP) and orbital cerebrospinal fluid pressure (CSFP), respectively. Thus, translaminar pressure (TLP; TLP = IOP-CSFP) has been proposed as a glaucoma risk factor.

Methods

Three eye-specific finite element models of the posterior human eye were constructed, including full 3D microstructures of the load-bearing lamina cribrosa (LC) with interspersed laminar neural tissues (NTs), and heterogeneous, anisotropic, hyperelastic material formulations for the surrounding peripapillary sclera and adjacent pia. ONH biomechanical responses were simulated using three combinations of IOP and CSFP loadings consistent with posture change from sitting to supine.

Results

Results show that tensile, compressive, and shear stresses and strains in the ONH were higher in the supine position compared to the sitting position (P < 0.05). In addition, LC beams bear three to five times more TLP-driven stress than interspersed laminar NT, whereas laminar NT exhibit three to five times greater strain than supporting LC (P < 0.05). Compared with CSFP, IOP drove approximately four times greater stress and strain in the LC, NT, and peripapillary sclera, normalized per mm Hg pressure change. In addition, IOP drove approximately three-fold greater scleral canal expansion and anterior-posterior laminar deformation than CSFP per mm Hg (P < 0.05).

Conclusions

Whereas TLP has been hypothesized to play a prominent role in ONH biomechanics, the IOP and CSFP effects are not equivalent, as IOP-driven stress, strain, and deformation play a more dominant role than CSFP effects.

Electrophysiological, biomechanical, and finite element analysis study of sacral nerve injury caused by sacral fracture

Background: We aimed to study the mechanism of sacral nerve injury caused by sacral fractures and the relationship between nerve decompression and nerve function.

Methods: First, we observed the anatomical features of lumbosacral nerve root region in Sprague-Dawley rats. Next, the rats were divided into the sham, 10 g, 30 g, and 60 g groups for electrophysiological studies on nerve root constriction injury. Then we studied the biomechanical properties of rat nerve roots, lumbosacral trunk, and sacrum. Finally, we established a finite element analysis model of sacral nerve roots injury in rats and determined the correlation between sacral deformation and the degree of sacral nerve roots injury.

Result: Anatomical study showed L5 constitutes sciatic nerve, the length of the L5 nerve root is 3.67 ± 0.15 mm, which is suitable for electrophysiological research on nerve root compression injury. After a series of electrophysiological study of L5 nerve roots, our results showed that nerve root function was almost unaffected at a low degree of compression (10 g). Nerve root function loss began at 30 g compression, and was severe at 60 g compression. The degree of neurological loss was therefore positively correlated with the degree of compression. Combining biomechanical testing of the lumbosacral nerve roots, finite element analysis and neuroelectrophysiological research, we concluded when the sacral foramina deformation is &gt;22.94%, the sacral nerves lose function. When the compression exceeds 33.16%, early recovery of nerve function is difficult even after decompression.

Conclusion: In this study, we found that the neurological loss was positively correlated with the degree of compression. After early decompression, nerve root function recovery is possible after moderate compression; however, in severe compression group, the nerve function would not recover. Furthermore, FEA was used to simulate nerve compression during sacral fracture, as well as calculate force loading on nerve with different deformation rates. The relationship between sacral fractures and neurological loss can be analyzed in combination with neurophysiological test results.

Interaction of the Blood Components with Ascending Thoracic Aortic Aneurysm Wall: Biomechanical and Fluid Analyses

Background: Ascending thoracic aortic aneurysm (ATAA) is an asymptomatic localized dilation of the aorta that is prone to rupture with a high rate of mortality. While diameter is the main risk factor for rupture assessment, it has been shown that the peak wall stress from finite element (FE) simulations may contribute to refinement of clinical decisions. In FE simulations, the intraluminal boundary condition is a single-phase blood flow that interacts with the thoracic aorta (TA). However, the blood is consisted of red blood cells (RBCs), white blood cells (WBCs), and plasma that interacts with the TA wall, so it may affect the resultant stresses and strains in the TA, as well as hemodynamics of the blood. Methods: In this study, discrete elements were distributed in the TA lumen to represent the blood components and mechanically coupled using fluid–structure interaction (FSI). Healthy and aneurysmal human TA tissues were subjected to axial and circumferential tensile loadings, and the hyperelastic mechanical properties were assigned to the TA and ATAA FE models. Results: The ATAA showed larger tensile and shear stresses but smaller fluid velocity compared to the ATA. The blood components experienced smaller shear stress in interaction with the ATAA wall compared to TA. The computational fluid dynamics showed smaller blood velocity and wall shear stress compared to the FSI. Conclusions: This study is a first proof of concept, and future investigations will aim at validating the novel methodology to derive a more reliable ATAA rupture risk assessment considering the interaction of the blood components with the TA wall.

Biomechanics of human trabecular meshwork in healthy and glaucoma eyes via dynamic Schlemm's canal pressurization

BACKGROUND AND OBJECTIVE

The trabecular meshwork (TM) consists of extracellular matrix (ECM) with embedded collagen and elastin fibers providing its mechanical support. TM stiffness is considerably higher in glaucoma eyes. Emerging data indicates that the TM moves dynamically with transient intraocular pressure (IOP) fluctuations, implying the viscoelastic mechanical behavior of the TM. However, little is known about TM viscoelastic behavior. We calculated the viscoelastic mechanical properties of the TM in n = 2 healthy and n = 2 glaucoma eyes.

METHODS

A quadrant of the anterior segment was submerged in a saline bath, and a cannula connected to an adjustable saline reservoir was inserted into Schlemm's canal (SC). A spectral domain-OCT (SD-OCT) provided continuous cross-sectional B-scans of the TM/JCT/SC complex during pressure oscillation from 0 to 30 mmHg at two locations. The TM/JCT/SC complex boundaries were delineated to construct a 20-µm-thick volume finite element (FE) mesh. Pre-tensioned collagen and elastin fibrils were embedded in the model using a mesh-free penalty-based cable-in-solid algorithm. SC pressure was represented by a position- and time-dependent pressure boundary; floating boundary conditions were applied to the other cut edges of the model. An FE-optimization algorithm was used to adjust the ECM/fiber mechanical properties such that the TM/JCT/SC model and SD-OCT imaging data best matched over time.

RESULTS

Significantly larger short- and long-time ECM shear moduli (p = 0.0032), and collagen (1.82x) and elastin (2.72x) fibril elastic moduli (p = 0.0001), were found in the TM of glaucoma eyes compared to healthy controls.

CONCLUSIONS

These findings provide additional clarity on the mechanical property differences in healthy and glaucomatous outflow pathway under dynamic loading. Understanding the viscoelastic properties of the TM may serve as a new biomarker in early diagnosis of glaucoma.

Modeling the biomechanics of the conventional aqueous outflow pathway microstructure in the human eye

BACKGROUND AND OBJECTIVE

Intraocular pressure (IOP) is determined by aqueous humor outflow resistance, which is a function of the combined resistance of Schlemm's canal (SC) endothelium and the trabecular meshwork (TM) and their interactions in the juxtacanalicular connective tissue (JCT) region. Aqueous outflow in the conventional outflow pathway results in pressure gradient across the TM, JCT, and SC inner wall, and induces mechanical stresses and strains that influence the geometry and homeostasis of the outflow system. The outflow resistance is affected by alteration in tissues' geometry, so there is potential for active, two-way, fluid-structure interaction (FSI) coupling between the aqueous humor (fluid) and the TM, JCT, and SC inner wall (structure). However, our understanding of the biomechanical interactions of the aqueous humor with the outflow connective tissues and its contribution to the outflow resistance regulation is incomplete.

METHODS

In this study, a microstructural finite element (FE) model of a human eye TM, JCT, and SC inner wall was constructed from a segmented, high-resolution histologic 3D reconstruction of the human outflow system. Three different elastic moduli (0.004, 0.128, and 51.5 MPa based on prior reports) were assigned to the TM/JCT complex while the elastic modulus of the SC inner wall was kept constant at 0.00748 MPa. The hydraulic conductivity was programmed separately for the TM, JCT, and SC inner wall using a custom subroutine. Cable elements were embedded into the TM and JCT extracellular matrix to represent the directional stiffness imparted by anisotropic collagen fibril orientation. The resultant stresses and strains in the outflow system were calculated using fluid-structure interaction method.

RESULTS

The higher TM/JCT stiffness resulted in larger stresses, but smaller strains in the outflow connective tissues, and resulted in a 4- and 5-fold larger pressure drop across the SC inner wall, respectively, compared to the most compliant model. Funneling through µm-sized SC endothelial pores was evident in the models at lower tissue stiffness, but aqueous flow was more turbulent in models with higher TM/JCT stiffness.

CONCLUSIONS

The mechanical properties of the outflow tissues play a crucial role in the hydrodynamics of the aqueous humor in the conventional outflow system.

Microstructural Deformations Within the Depth of the Lamina Cribrosa in Response to Acute In Vivo Intraocular Pressure Modulation

Purpose

The lamina cribrosa (LC) is a leading target for initial glaucomatous damage. We investigated the in vivo microstructural deformation within the LC volume in response to acute IOP modulation while maintaining fixed intracranial pressure (ICP).

Methods

In vivo optic nerve head (ONH) spectral-domain optical coherence tomography (OCT) scans (Leica, Chicago, IL, USA) were obtained from eight eyes of healthy adult rhesus macaques (7 animals; ages = 7.9-14.4 years) in different IOP settings and fixed ICP (8-12 mm Hg). IOP and ICP were controlled by cannulation of the anterior chamber and the lateral ventricle of the brain, respectively, connected to a gravity-controlled reservoir. ONH images were acquired at baseline IOP, 30 mm Hg (H1-IOP), and 40 to 50 mm Hg (H2-IOP). Scans were registered in 3D, and LC microstructure measurements were obtained from shared regions and depths.

Results

Only half of the eyes exhibited LC beam-to-pore ratio (BPR) and microstructure deformations. The maximal BPR change location within the LC volume varied between eyes. BPR deformer eyes had a significantly higher baseline connective tissue volume fraction (CTVF) and lower pore aspect ratio (P = 0.03 and P = 0.04, respectively) compared to BPR non-deformer. In all eyes, the magnitude of BPR changes in the anterior surface was significantly different (either larger or smaller) from the maximal change within the LC (H1-IOP: P = 0.02 and H2-IOP: P = 0.004).

Conclusions

The LC deforms unevenly throughout its depth in response to IOP modulation at fixed ICP. Therefore, analysis of merely the anterior LC surface microstructure will not fully capture the microstructure deformations within the LC. BPR deformer eyes have higher CTVF than BPR non-deformer eyes.

Ocular biomechanics during improvised explosive device blast: A computational study using eye-specific models

BACKGROUND

Eye injuries comprise 10-13% of civilian improvised explosive device (IED) injuries. The bomb blast wave induces a normal and shear forces on the tissues, causing a large acute IOP elevation. This study calculated the biomechanical stresses and strains in the eye due to IED explosion via eye-specific fluid-structure interaction (FSI) models.

METHODS

Blast occurred at 2, 3, and 4 m from the front and side of the victim and the weights of the IED were 1 and 2 kg. The ground was covered with the deformable soil to mimic the realistic IED explosion condition and reflect the blast wave.

RESULTS

The IOP elevation of ∼6,000-48,000 mmHg was observed in the eyes while the highest IOP was occurred with the IED weight and distance of 2 kg and 2 m (front) and the lowest was occurred with the IED weight and distance of 1 kg and 4 m (side). Our findings suggest the importance of the victim location and orientation concerning the blast wave when it comes to ocular injury assessment. IOP elevation of ∼2900 and ∼2700 mmHg were observed in ∼1.6 ms after the blast for the IEDS weight of 2 kg and a victim distance of 2 m in front and side blasts, respectively, in consistence with the literature. Nonetheless, IOPs were considerably higher after ∼1.6 ms due to the merging of the bomb blast wave and its reflection off the ground.

CONCLUSIONS

The stresses and strains were highest for the frontal blast. Both side and frontal blasts caused higher stresses and strains at the rectus muscle insertions where the sclera is thinnest and prone to rupture. Blast angle has no considerable role in the resultant IOP. Front blast with a heavier IED resulted a higher stresses and deformations in the eye connective tissues compared to the side blast.

Finite element modeling of the complex anisotropic mechanical behavior of the human sclera and pia mater

BACKGROUND AND OBJECTIVE

Accurate finite element (FE) simulation of the optic nerve head (ONH) depends on accurate mechanical properties of the load-bearing tissues. The peripapillary sclera in the ONH exhibits a depth-dependent, anisotropic, heterogeneous collagen fiber distribution. This study proposes a novel cable-in-solid modeling approach that mimics heterogeneous anisotropic collagen fiber distribution, validates the approach against published experimental biaxial tensile tests of scleral patches, and demonstrates its effectiveness in a complex model of the posterior human eye and ONH.

METHODS

A computational pipeline was developed that defines control points in the sclera and pia mater, distributes the depth-dependent circumferential, radial, and isotropic cable elements in the sclera and pia in a pattern that mimics collagen fiber orientation, and couples the cable elements and solid matrix using a mesh-free penalty-based cable-in-solid algorithm. A parameter study was performed on a model of a human scleral patch subjected to biaxial deformation, and computational results were matched to published experimental data. The new approach was incorporated into a previously published eye-specific model to test the method; results were then interpreted in relation to the collagen fibers' (cable elements) role in the resultant ONH deformations, stresses, and strains.

RESULTS

Results show that the cable-in-solid approach can mimic the full range of scleral mechanical behavior measured experimentally. Disregarding the collagen fibers/cable elements in the posterior eye model resulted in ∼20-60% greater tensile and shear stresses and strains, and ∼30% larger posterior deformations in the lamina cribrosa and peripapillary sclera.

CONCLUSIONS

The cable-in-solid approach can easily be implemented into commercial FE packages to simulate the heterogeneous and anisotropic mechanical properties of collagenous biological tissues.

Inverse dynamic finite element-optimization modeling of the brain tumor mass-effect using a variable pressure boundary

BACKGROUND AND OBJECTIVE

Statistical atlases of brain structure can potentially contribute in the surgical and radiotherapeutic treatment planning for the brain tumor patients. However, the current brain image-registration methods lack of accuracy when it comes to the mass-effect caused by tumor growth. Numerical simulations, such as finite element method (FEM), allow us to calculate the resultant pressure and deformation in the brain tissue due to tumor growth, and to predict the mass-effect. To date, however, the pressure boundary in the brain tissue due to tumor growth has been simply presented as a constant profile throughout the entire tumor outer surface that resulted in discrepancy between the patient imaging data and brain atlases.

METHODS

In this study, we employed a fully-coupled inverse dynamic FE-optimization method to estimate the resultant variable pressure boundary due to tumor resection surgery. To do that, magnetic resonance imaging data of two patients' pre- and post-tumor resection surgery were registered, segmented, volume-meshed, and prepared for fully-coupled inverse dynamic FE-optimization simulations. Two different pressure boundaries were defined on the brain cavity after tumor resection including: a) a constant pressure boundary and b) a variable pressure boundary. The inverse FE-optimization algorithm was used to find the optimum constant and variable pressure boundaries that result in the least distance between the surface-nodes of the post-surgery brain cavity and pre-surgery tumor.

RESULTS

The results revealed that a variable pressure boundary causes a considerably lower mean percentage error compared to a constant pressure one; hence, it can more effectively address the realistic boundary in tumor resection surgery and predict the mass-effect.

CONCLUSIONS

The proposed variable pressure boundary can be a robust tool that allows batch processing to register the brains with tumors to statistical atlases of normal brains and construction of brain tumor atlases. This approach is also computationally inexpensive and can be coupled to any FE software to run. The findings of this study have implications for not only predicting the accurate pressure boundary and mass-effect before tumor resection surgery, but also for predicting some clinical symptoms of brain cancers and presenting useful tools for APPLICATIONs in image-guided neurosurgery.

Ocular biomechanics due to ground blast reinforcement

BACKGROUND AND OBJECTIVE

Bomb blast injuries exerts a shearing force on the air-tissue interfaces, causing devastating ocular injury from the blast wave. Improvised explosive devices (IEDs) are usually placed at different heights from the ground to induce more severe injury through ground blast reinforcement (GBR). However, there is still a lack of knowledge of the role of GBR and IED height from the ground on ocular biomechanics, and how they can affect the intraocular pressure (IOP) in the eye. This study aimed to estimate the IOP due to frontal IED explosion at different heights from the ground using a fluid-structure interaction model with and without GBR effects.

METHODS

A 2 kg IED was placed within 5 m of the victim at 5 different heights from the ground, including 0, 0.42, 0.85, 1.27, and 1.70 m. Two different blast formulations were used to simulate the IED explosion: (a) spherical airburst, with no amplification of the initial shock wave due to interaction with the ground-surface, and (b) hemispherical surface-burst, where the initial blast wave is immediately reflected and reinforced by the ground (GBR).

RESULTS

Results revealed that the blast wave due to GBR reaches to the skull prior to the IED blast itself. The GBR also reached to the skull ∼ 0.6 ms earlier when the IED was on the ground compared to the height of 1.70 m. The highest and lowest IOPs of ∼ 17,000 and ∼ 15,000 mmHg were observed at the IED heights of 1.70 and 0 m from the ground considering GBR. However, when the role of the GBR is ignored, IOP of ∼ 9,000 mmHg was observed regardless of the IED height from the ground. The deformation in the apex of the cornea was higher when considering the GBR (∼ 0.75 cm) versus no GBR (∼ 0.65 cm). Considering GBR led to higher stresses and strains in the sclera.

CONCLUSIONS

When the role of GBR was ignored, the results showed similar patterns and magnitudes of stresses and deformations in the skull and eye regardless of the height of the IED from the ground, which was not the case when GBR was considered. The findings of this study suggest the critical role of GBR in ocular blast simulations.