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.

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.

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.

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.

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.

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.

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.

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.

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.

Biomechanics of the keratoconic cornea: Theory, segmentation, pressure distribution, and coupled FE-optimization algorithm

Understanding of the corneal biomechanical properties is of high interest due to its potential application in the early diagnosis of keratoconus (KC). KC by itself is a non-inflammatory eye disorder causes corneal structural and/or compositional anomalies. The biomechanically weakened cornea is no longer able to preserve the normal shape of the cornea against the intraocular pressure (IOP) and gradually starts to bulge outward, invoking a conical shape and subsequent distorted vision. The most popular way to measure the in vivo corneal biomechanical properties is the CorVis-ST, which enables to analyze the dynamic response of the cornea under a temporary air puff pressure. However, the complications, such as the lack of knowledge on the accurate air-puff pressure distribution on the cornea's surface as a function of the distance from the apex of the cornea as well as the time, hinder us to have a reliable estimation of the cornea's mechanical parameters. This study aims to establish patient-specific geometries of the healthy and KC corneas and calculate the pressure distribution on the cornea's surface as a function of both the distance from the apex of the cornea and time, and thereafter, the viscoelastic mechanical properties of both the healthy and KC corneas using a coupled finite element (FE)-optimization algorithm. To do that, the dynamic deformation response of six healthy and six KC corneas were measured via CorVis-ST. The videos of the in vivo deformation of the corneas under the applied air puff pressure were segmented using our segmentation algorithm to determine the anterior and posterior curvatures of the corneas during the dynamic movement of the cornea. The FE model of the corneas were established using the segmented data and subjected to a negative (pre-stress), positive IOP, and air puff pressure while the floating boundary conditions were applied to the two ends of the corneas' FE models. The simulation results were imported into a loop of FE-optimization algorithm and analyzed until the deformation amplitude at the apex of the cornea reaches to its minimum difference compared to the clinical data by CorVis-ST. The results revealed that the pressure distributions found in the literature as a function of the distance from the apex of the cornea and time unable to provide satisfactory results. Therefore, the pressure distributions both as a function of the distance and time were optimized using our coupled FE-optimization algorithm and employed to estimate the viscoelastic properties of the healthy and KC corneas. The mean percentage error (MPE) of 8.45% and 10.79% were found for the healthy and KC corneas compared to the clinical data of CorVis-ST, respectively. The results also revealed a significantly higher short-time shear modulus for the KC (62.33 MPa) compared to the healthy (37.45 MPa) corneas while the long-time shear modulus of both the healthy and KC corneas were almost the same (4.01 vs. 3.91 MPa). The proposed algorithm is a noninvasive technique capable of accurately estimating the viscoelastic mechanical properties of the cornea, which can contribute to understand the mechanism of KC development and improve diagnosis and intervention in KC.

A patient-specific fluid–structure interaction model of the cerebrovascular damage in relation to traumatic brain injury

Background

There is a lack of knowledge on the magnitudes of the biomechanical stresses and deformations occurring in the cerebral arterial wall after traumatic brain injury (TBI). Experimental techniques are unable to calculate the stresses and deformations in the cerebral arterial wall after TBI; therefore, the application of numerical simulations, such as finite element modeling, is preferred.

Methods

This study was aimed to calculate the stresses and deformations as well as the alteration in the pressure and velocity of the blood in the cerebrovascular artery using a fluid–structure interaction model.

Results

The results revealed considerable increase in the pressure and velocity of the blood which might lead to cerebrovascular damage followed by hemorrhage. The arterial wall showed the highest deformation of 0.047 mm in the X direction which was higher than that in the Y (0.035–0.050 mm) and Z (0.019–0.030 mm) directions.

Conclusions

These results have implications not only for the understanding of the stresses and deformations in the cerebral artery because of TBI, but also for providing a comprehensive knowledge for biomechanical and medical experts in regard to thresholds of cerebrovascular damage for use in establishing preventive and/or treatment methods.

A patient-specific numerical modeling of the spontaneous coronary artery dissection in relation to atherosclerosis

The spontaneous coronary artery dissection (SCAD) is a clinical complication of angioplasty leading to an initiation of a tear/crack in the intima layer of the artery. The crack can propagate to the interface of the intima-media layer following by intramural hematoma. The relation between the SCAD and atherosclerosis is a controversial issue, as some studies stated no correlation between them while others showed that a crack can initiate in the intima but cannot propagate into the atrophied media layer. To investigate the relation between the intraluminal crack propagation in the atherosclerotic artery and SCAD, this study numerically investigated the initiation and propagation of a crack in the intraluminal and radial locations of the healthy and atherosclerotic human coronary arterial walls. The energy release rate, namely J-integral, is computed as a numerical derivative of the strain energy with respect to a crack extension using a user-defined virtual crack method (VCE) of extended finite element method (XFEM). Experimental measurements were carried out to calculate the elasto-plastic mechanical properties of the healthy and atherosclerotic human coronary arteries. The experimental data were then assigned to our own established patient-specific FE model of the coronary artery. Cracks were sketched in the intraluminal and radial locations of the arterial wall and allowed to propagate to the virtual interface of the intima-media to form a false lumen. The results revealed a higher stress at the crack tip of the healthy arterial wall compared to the atherosclerotic one. Lower crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) were observed in the intraluminal crack of the atherosclerotic artery. J-integral of the atherosclerotic arterial wall was also found to be higher than the healthy one at the intraluminal crack. The results revealed that although a crack can initiate in the intraluminal of an atherosclerotic artery, it cannot propagate into the media layer due to a relatively higher rate of the strain energy release in the atherosclerotic arterial wall compared to the healthy one.

Finite element modeling of the periodontal ligament under a realistic kinetic loading of the jaw system

Purpose

The stresses and deformations in the periodontal ligament (PDL) under the realistic kinetic loading of the jaw system, i.e., chewing, are difficult to be determined numerically as the mechanical properties of the PDL is variably present in different finite element (FE) models. This study was aimed to conduct a dynamic finite element (FE) simulation to investigate the role of the PDL (PDL) material models in the induced stresses and deformations using a simplified patient-specific FE model of a human jaw system.

Methods

To do that, a realistic kinetic loading of chewing was applied to the incisor point, contralateral, and ipsilateral condyles, through the experimentally proven trajectory approach. Three different material models, including the elasto-plastic, hyperelastic, and viscoelastic, were assigned to the PDL, and the resulted stresses of the tooth FE model were computed and compared.

Results

The results revealed the highest von Mises stress of 620.14 kPa and the lowest deformation of 0.16 mm in the PDL when using the hyperelastic model. The concentration of the stress in the elastoplastic and viscoelastic models was in the mid-root and apex of the PDL, while for the hyperelastic model, it was concentrated in the cervical margin. The highest deformation in the PDL regardless of the employed material model was located in the caudal direction of the tooth. The viscoelastic PDL absorbed the transmitted energy from the dentine and led to lower stress in the cancellous bone compared to the elastoplastic and hyperelastic material models.

Conclusion

These results have implications not only for understanding the stresses and deformations in the PDL under chewing but also for providing comprehensive information for the medical and biomechanical experts in regard of the role of the material models being used to address the mechanical behavior of the PDL in other components of the tooth.

Risk of rupture of the cerebral aneurysm in relation to traumatic brain injury using a patient-specific fluid-structure interaction model

BACKGROUND AND OBJECTIVE

Cerebral aneurysm, which is defined as one of the weakened area in the wall of an artery in the brain, ruptures when wall tension exceeds its mechanical strength. Traumatic brain injury (TBI) by exerting a sudden impact load to the brain can lead to mechanical failure of the cerebral blood vessels followed by an alteration in not only the structure but also the function of the cerebrovascular. TBI also alters the hemodynamics of the blood flow in the cerebrovascular, while it has been shown that hemodynamics has a key asset in the progression and rupture of the cerebral aneurysms. So far, there is a lack of knowledge on the risk of rupture of the cerebral aneurysm in relation to TBI. Therefore, this study aimed to calculate the mechanical stresses and deformations in the arterial wall as well as the pressure and velocity of the blood using a fluid-structure interaction (FSI) model of the cerebral aneurysm located in the anterior circulation region of the circle of Willis.

METHOD

A patient-specific FSI model of the human skull, brain, and cerebral aneurysm, was established using human computed tomography (CT)/ magnetic resonance imaging (MRI) data and subjected to a frontal TBI.

RESULTS

The results revealed considerable increasing of ∼ 8 kPa (60 mmHg) and 0.40 m/s in the pressure and velocity of the blood in the intraluminal of the cerebral artery after TBI. The von Mises stress, shear stress, and deformation of the cerebral aneurysm wall also showed the increasing of 56.03 kPa, 15.66 Pa, and 0.072 mm after TBI, respectively.

CONCLUSIONS

Although the injury to the aneurysm wall after TBI is lower than that of the aneurysm wall mechanical strength, it still can alter the stress pattern in the wall and disrupt the hemodynamics of the blood. These results have implications in understanding the rupture risk of the cerebral aneurysm due to TBI, which may contribute in establishing preventive and/or treatment methods.

Mechanical measurement of the human cerebellum under compressive loading

The cerebellum is responsible for controlling the posture and walking stability of the body. The cerebellum can subject to the traumatic injuries following by complicated clinical problems, i.e., the cerebellar pathologies. Application of the computational models can be helpful to figure out the injury mechanisms of the cerebellum, however, there is a lack of knowledge on the mechanical properties of the cerebellum under compressive loading. Therefore, this study aimed to perform an experimental study to measure the mechanical properties of 17 male individuals' cerebellum under the series of compressive loadings. The resulted stress-strain data of the cerebellum revealed the elastic modulus and maximum/failure stress of 13.48 ± 2.65 (Mean ± SD) and 19.65 ± 3.89 kPa, respectively. The findings of this study have implications not only for understanding the mechanical properties of the human cerebellum tissue under the compressive loading, but also for providing a raw data for the doctors and biomechanical experts as the mechanical threshold of the cerebellum as well as computational modelling of the traumatic brain injuries.

Dynamic finite element simulation of dental prostheses during chewing using muscle equivalent force and trajectory approaches

The long-term application of dental prostheses inside the bone has a narrow relation to its biomechanical performance. Chewing is the most complicated function of a dental implant as it implements different forces to the implant at various directions. Therefore, a suitable holistic modelling of the jaw bone, implant, food, muscles, and their forces would be deemed significant to figure out the durability as well as functionality of a dental implant while chewing. So far, two approaches have been proposed to employ the muscle forces into the Finite Element (FE) models, i.e. Muscle Equivalent Force (MEF) and trajectory. This study aimed at propounding a new three-dimensional dynamic FE model based on two muscle forces modelling approaches in order to investigate the stresses and deformations in the dental prosthesis as well as maxillary bone during the time of chewing a cornflakes bio. The results revealed that both contact and the maximum von Mises stress in the implant and bones for trajectory approach considerably exceed those of the MEF. The maximum stresses, moreover, are located around the neck of implant which should be both clinically and structurally strong enough to functionally maintain the bone-implant interface. In addition, a higher displacement due to compressive load is observed for the implant head in trajectory approach. The results suggest the benefits provided by trajectory approach since MEF approach would significantly underestimate the stresses and deformations in both the dental prosthesis and bones.

DYNAMIC SIMULATION AND FINITE ELEMENT ANALYSIS OF THE MAXILLARY BONE INJURY AROUND DENTAL IMPLANT DURING CHEWING DIFFERENT FOOD

Since a long term patency of the dental implant has a direct relationship with their biomechanical performance, it is of vital important to understand the stresses and deformations that happen during chewing around the dental implant and bone. However, this model so far has not been well realized and this is why in this study we aim to establish a Finite Element (FE) model to analyse the stresses and deformations. A trajectory approach has been used to implement the action of muscles into the mode. To do this, a cornflake bio is mounted between the teeth and force applied until the breakage of the food in mouth. Furthermore, an experimental study was performed using the Digital Image Correlation (DIC) method and a set of three markers used to verify the numerical observations. The results revealed that in the maxillary bones, the maximum stresses were located within the cortical bone surrounding the implant and within the neck of implant. In addition, as the elastic modulus of the food is increased the stress in cortical bone increased accordingly. The results also revealed that the highest stress in the system is 74% of the yield stress while this value has been reported as 41% in previous studies.

Computing the stresses and deformations of the human eye components due to a high explosive detonation using fluid-structure interaction model

INTRODUCTION

In spite the fact that a very small human body surface area is comprised by the eye, its wounds due to detonation have recently been dramatically amplified. Although many efforts have been devoted to measure injury of the globe, there is still a lack of knowledge on the injury mechanism due to Primary Blast Wave (PBW). The goal of this study was to determine the stresses and deformations of the human eye components, including the cornea, aqueous, iris, ciliary body, lens, vitreous, retina, sclera, optic nerve, and muscles, attributed to PBW induced by trinitrotoluene (TNT) explosion via a Lagrangian-Eulerian computational coupling model.

MATERIALS AND METHODS

Magnetic Resonance Imaging (MRI) was employed to establish a Finite Element (FE) model of the human eye according to a normal human eye. The solid components of the eye were modelled as Lagrangian mesh, while an explosive TNT, air domain, and aqueous were modelled using Arbitrary Lagrangian-Eulerian (ALE) mesh. Nonlinear dynamic FE simulations were accomplished using the explicit FE code, namely LS-DYNA. In order to simulate the blast wave generation, propagation, and interaction with the eye, the ALE formulation with Jones-Wilkins-Lee (JWL) equation defining the explosive material were employed.

RESULTS

The results revealed a peak stress of 135.70kPa brought about by detonation upsurge on the cornea at the distance of 25cm. The highest von Mises stresses were observed on the sclera (267.3kPa), whereas the lowest one was seen on the vitreous body (0.002kPa). The results also showed a relatively high resultant displacement for the macula as well as a high variation for the radius of curvature for the cornea and lens, which can result in both macular holes, optic nerve damage and, consequently, vision loss.

CONCLUSION

These results may have implications not only for understanding the value of stresses and strains in the human eye components but also giving an outlook about the process of PBW triggers damage to the eye.

Dynamic finite element simulation of the gunshot injury to the human forehead protected by polyvinyl alcohol sponge

Although there are some traditional models of the gunshot wounds, there is still a need for more modeling analyses due to the difficulties related to the gunshot wounds to the forehead region of the human skull. In this study, the degree of damage as a consequence of penetrating head injuries due to gunshot wounds was determined using a preliminary finite element (FE) model of the human skull. In addition, the role of polyvinyl alcohol (PVA) sponge, which can be used as an alternative to reinforce the kinetic energy absorption capacity of bulletproof vest and helmet materials, to minimize the amount of skull injury due to penetrating processes was investigated through the FE model. Digital computed tomography along with magnetic resonance imaging data of the human head were employed to launch a three-dimensional (3D) FE model of the skull. Two geometrical shapes of projectiles (steel ball and bullet) were simulated for penetrating with an initial impact velocity of 734 m/s using nonlinear dynamic modeling code, namely LS-DYNA. The role of the damaged/distorted elements were removed during computation when the stress or strain reached their thresholds. The stress distributions in various parts of the forehead and sponge after injury were also computed. The results revealed the same amount of stress for both the steel ball and bullet after hitting the skull. The modeling results also indicated the time that steel ball takes to penetrate into the skull is lower than that of the bullet. In addition, more than 21% of the steel ball's kinetic energy was absorbed by the PVA sponge and, subsequently, injury sternness of the forehead was considerably minimized. The findings advise the application of the PVA sponge as a substitute strengthening material to be able to diminish the energy of impact as well as the load transmitted to the object.

A COMBINATION OF EXPERIMENTAL AND NUMERICAL ANALYSES TO MEASURE THE COMPRESSIVE MECHANICAL PROPERTIES OF TENNIS BALL

Tennis is almost a newly born sport (1859) that can be played individually against a single opponent (singles) or between two teams of two players each, namely doubles. Materially, tennis balls were made of cloth strips stitched together from thread. They have also been made of hollow rubber with a felt coating appearing in different colors from traditionally white to yellow in the recent years to permit their visibility. Although the most common injuries associated with tennis have been reported to be related to rotator cuff, elbow, wrist, anterior knee pain, and ankle, the injury that a tennis ball can cause, for example, for eye is still not clear. However, as the tennis ball can reach to a speed of 260 km/h, it seems vital to understand its mechanical properties to have a deep insight into the injury that can happen during playing. Therefore, this study aimed to perform an experimental study to evaluate the linear elastic and nonlinear hyperelastic mechanical properties of the tennis ball under compressive loading. To do this, 40 numbers of approved tennis balls by international tennis federation (ITF) were prepared and subjected to a series of compressive loadings. The strain of the balls was measured via a pair of CCD cameras using digital image correlation (DIC) technique. The results revealed the mean elastic modulus, maximum stress, and strain of 336.69 kPa, 410.15 kPa, and 66%, for the tennis balls, respectively. The nonlinear mechanical behavior of the tennis balls were also computationally investigated through a hyperelastic material model, namely Ogden. Finally, a finite element (FE) model was executed to verify the hyperelastic data with that of experimental and, interestingly, the numerical data were in good agreement with experimental ones. The findings of this study may have implications not only for understanding the compressive mechanical properties of the tennis ball, but also for investigating the injury that can occur in the human body by tennis ball, especially the eye.

A computational fluid–structure interaction model of the blood flow in the healthy and varicose saphenous vein

Objective

Varicose vein has become enlarged and twisted and, consequently, has lost its mechanical strength. As a result of the varicose saphenous vein (SV) mechanical alterations, the hemodynamic parameters of the blood flow, such as blood velocity as well as vein wall stress and strain, would change accordingly. However, little is known about stress and strain and there consequences under experimental conditions on blood flow and velocity within normal and varicose veins. In this study, a three-dimensional (3D) computational fluid–structure interaction (FSI) model of a human healthy and varicose SVs was established to determine the hemodynamic characterization of the blood flow as a function of vein wall mechanical properties, i.e. elastic and hyperelastic.

Methods

The mechanical properties of the human healthy and varicose SVs were experimentally measured and implemented into the computational model. The fully coupled fluid and structure models were solved using the explicit dynamics finite element code LS-DYNA.

Results

The results revealed that, regardless of healthy and varicose, the elastic walls reach to the ultimate strength of the vein wall, whereas the hyperelastic wall can tolerate more stress. The highest von Mises stress compared to the healthy ones was seen in the elastic and hyperelastic varicose SVs with 1.412 and 1.535 MPa, respectively. In addition, analysis of the resultant displacement in the vein wall indicated that the varicose SVs experienced a higher displacement compared to the healthy ones irrespective of elastic and hyperelastic material models. The highest blood velocity was also observed for the healthy hyperelastic SV wall.

Conclusion

The findings of this study may have implications not only for determining the role of the vein wall mechanical properties in the hemodynamic alterations of the blood, but also for employing as a null information in balloon-angioplasty and bypass surgeries.

An experimental-nonlinear finite element study of a balloon expandable stent inside a realistic stenotic human coronary artery to investigate plaque and arterial wall injury

The stresses induced within plaque tissues and arterial layers during stent expansion inside an atherosclerotic artery can be exceeded from the yield stresses of those tissues and, consequently, lead to plaque or arterial wall rupture. The distribution and magnitude of the stresses in the plaque-artery-stent structure might be distinctly different for different plaque types. In this study, the mechanical properties of six healthy and atherosclerotic human coronary arteries were determined for application in plaque and arterial vulnerability assessment. A nonlinear finite element simulation based on an Ogden material model was established to investigate the effect of plaque types on the stresses induced in the arterial wall during implantation of a balloon expandable coronary stent. The atherosclerotic artery was assumed to consist of a plaque and normal arterial tissues on its outer side. The results indicated a significant influence of plaque types on the maximum stresses induced within the plaque wall and arterial wall during stenting but not when computing maximum stress on the stent. The stress on the stiffest calcified plaque wall was 3.161 MPa, whereas cellular and hypocellular plaques showed relatively less stress on their wall. The highest von Mises stresses within the arterial wall were observed on the hypocellular plaque, whereas the lowest stresses were seen to be located in the calcified and cellular plaques. Although the computed stresses on the arterial wall for the calcified and cellular plaques were not high enough to invoke a rupture, the stress on the hypocellular plaque was relatively higher than that of the strength of the arterial wall. These findings may have implications not only for understanding the stresses induced in plaque and the arterial wall, but also for developing surgeries such as balloon-angioplasty and stenting.

A nonlinear finite element simulation of balloon expandable stent for assessment of plaque vulnerability inside a stenotic artery

The stresses induced on plaque wall during stent implantation inside a stenotic artery are associated with plaque rupture. The stresses in the plaque-artery-stent structure appear to be distinctly different for different plaque types in terms of both distribution and magnitude. In this study, a nonlinear finite element simulation was executed to analyze the influence of plaque composition (calcified, cellular, and hypocellular) on plaque, artery layers (intima, media, and adventitia), and stent stresses during implantation of a balloon expandable coronary stent into a stenosed artery. The atherosclerotic artery was assumed to consist of a plaque and normal arterial tissues on its outer side. The results revealed a significant influence of plaque types on the maximum stresses induced within plaque wall and artery layers during stenting, but not when calculating maximum stress on stent. The stress on stiffer calcified plaque wall was in the fracture level (2.21 MPa), whereas cellular and hypocellular plaques play a protective role by displaying less stress on their wall. The highest von Mises stresses were observed on less stiff media layer. The findings of this study suggest a lower risk of arterial vascular injury for calcified plaque, while higher risk of plaque ruptures for cellular and hypocellular plaques.

A comparative study on the elastic modulus of polyvinyl alcohol sponge using different stress-strain definitions

There have been different stress-strain definitions to measure the elastic modulus of spongy materials, especially polyvinyl alcohol (PVA) sponge. However, there is no agreement as to which stress-strain definition should be implemented. This study was aimed to show how different results are given by the various definitions of stress-strain used, and to recommend a specific definition when testing spongy materials. A fabricated PVA sponge was subjected to a series of tensile tests in order to measure its mechanical properties. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were used to determine the elastic modulus. The results revealed that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and, as a result, may overestimate the elastic modulus at different stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress). The Green-St. Venant strain definition failed to address the non-linear stress-strain relation using different definitions of stress and invoked an underestimation of the elastic modulus values. Engineering stress and strain definitions were only valid for small strains and displacements, which make them impractical when analyzing spongy materials. The results showed that the effect of varying the stress definition on the maximum stress measurements was significant but not when calculating the elastic modulus. It is important to consider which stress-strain definition is employed when characterizing the mechanical properties of spongy materials. Although the true stress-true strain definition exhibits a non-linear relation, we favor it in spongy materials mechanics as it gives more accurate measurements of the material's response using the instantaneous values.