Collagen Architecture of the Posterior Pole: High-Resolution Wide Field of View Visualization and Analysis Using Polarized Light Microscopy

How is eyeball growth associated with optic nerve head shape and glaucoma? The Lamina cribrosa/Bruch's membrane opening offset theory

The optic nerve head (ONH) is a complex structure wherein the axons of the retinal ganglion cells extrude from the eyeball through three openings: 1) the Bruch's membrane opening (BMO) in the retinal layer, 2) the anterior scleral canal opening in the anterior scleral layer, and 3) the lamina cribrosa (LC). Eyeball expansion during growth induces an offset among openings, since the expansion affects the inner retinal and outer scleral layers differently: the posterior polar retinal structure is preserved by the preferential growth in the equatorial region, whereas no such regional difference is observed in the scleral layer. The various modes and extents of eyeball expansion result in diverse directionality and amount of offset among openings, which causes diverse ONH morphology in adults, especially in myopia. In this review, we summarize the ONH changes that occur during myopic axial elongation. These changes were observed prospectively in our previous studies, wherein LC shift and subsequent offset from the BMO center could be predicted by tracing the central retinal vascular trunk position. This offset induces the formation of γ-zone parapapillary atrophy or externally oblique border tissue. As a presumptive site of glaucomatous damage, the LC/BMO offset may render the LC pores in the opposite direction more vulnerable. To support such speculation, we also summarize the relationship between LC/BMO offset and glaucomatous damage. Indeed, LC/BMO offset is not only the cause of diverse ONH morphology in adults, but is also, potentially, an important clinical marker for assessment of glaucoma.

Lamina Cribrosa Insertions Into the Sclera Are Sparser, Narrower, and More Slanted in the Anterior Lamina

Purpose

The lamina cribrosa (LC) depends on the sclera for support. The support must be provided through the LC insertions. Although a continuous insertion over the whole LC periphery is often assumed, LC insertions are actually discrete locations where LC collagenous beams meet the sclera. We hypothesized that LC insertions vary in number, size, and shape by quadrant and depth.

Methods

Coronal cryosections through the full LCs from six healthy monkey eyes were imaged using instant polarized light microscopy. The images were registered into a stack, on which we manually marked LC insertion outlines, nothing their position in-depth and quadrant (inferior, superior, nasal, or temporal). From the marks, we determined the insertion number, width, angle to the canal wall (90 degrees = perpendicular), and insertion ratio (fraction of LC periphery represented by insertions). Using linear mixed effect models, we determined if the insertion characteristics were associated with depth or quadrant.

Results

Insertions in the anterior LC were sparser, narrower, and more slanted than those in deeper LC (P values < 0.001). There were more insertions spanning a larger ratio of the canal wall in the middle LC than in the anterior and posterior (P values < 0.001). In the nasal quadrant, the insertion angles were significantly smaller (P < 0.001).

Conclusions

LC insertions vary substantially and significantly over the canal. The sparser, narrower, and more slanted insertions of the anterior-most LC may not provide the robust support afforded by insertions of the middle and posterior LC. These variations may contribute to the progressive deepening of the LC and regional susceptibility to glaucoma.

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.

Optical Coherence Tomographic Optic Nerve Head Morphology in Myopia III: The Exposed Neural Canal Region in Healthy Eyes-Implications for High Myopia

PURPOSE

To determine the prevalence and magnitude of optical coherence tomography (OCT) exposed neural canal (ENC), externally oblique choroidal border tissue (EOCBT), and exposed scleral flange (ESF) regions in 362 non-highly myopic (spherical equivalent -6.00 to 5.75 diopters) eyes of 362 healthy subjects.

DESIGN

Cross-sectional study.

METHODS

After OCT optic nerve head (ONH) imaging, Bruch membrane opening (BMO), the anterior scleral canal opening (ASCO), and the scleral flange opening (SFO) were manually segmented. BMO, ASCO, and SFO points were projected to the BMO reference plane. The direction and magnitude of BMO/ASCO offset as well as the magnitude of ENC, EOCBT, and ESF was calculated within 30° sectors relative to the foveal-BMO axis. Hi-ESF eyes demonstrated an ESF ≥100 µm in at least 1 sector. Sectoral peri-neural canal choroidal thickness (pNC-CT) was measured and correlations between the magnitude of sectoral ESF and proportional pNC-CT were assessed.

RESULTS

Seventy-three Hi-ESF (20.2%) and 289 non-Hi-ESF eyes (79.8%) were identified. BMO/ASCO offset as well as ENC, EOCBT, and ESF prevalence and magnitude were greatest inferior temporally where the pNC-CT was thinnest. Among Hi-ESF eyes, the magnitude of each ENC region correlated with the BMO/ASCO offset magnitude, and the sectors with the longest ESF correlated with the sectors with proportionally thinnest pNC-CT.

CONCLUSIONS

ONH BMO/ASCO offset, either as a cause or result of ONH neural canal remodeling, corresponds with the sectoral location of maximum ESF and minimum pNC-CT in non-highly myopic eyes. Longitudinal studies to characterize the development and clinical implications of ENC Hi-ESF regions in non-highly myopic and highly myopic eyes are indicated.

Direct measurements of collagen fiber recruitment in the posterior pole of the eye

Collagen is the main load-bearing component of the peripapillary sclera (PPS) and lamina cribrosa (LC) in the eye. Whilst it has been shown that uncrimping and recruitment of the PPS and LC collagen fibers underlies the macro-scale nonlinear stiffening of both tissues with increased intraocular pressure (IOP), the uncrimping and recruitment as a function of local stretch have not been directly measured. This knowledge is crucial to understanding their functions in bearing loads and maintaining tissue integrity. In this project we measured local stretch-induced collagen fiber bundle uncrimping and recruitment curves of the PPS and LC. Thin coronal samples of PPS and LC of sheep eyes were mounted and stretched biaxially quasi-statically using a custom system. At each step, we imaged the PPS and LC with instant polarized light microscopy and quantified pixel-level (1.5 μm/pixel) collagen fiber orientations. We used digital image correlation to measure the local stretch and quantified collagen crimp by the circular standard deviation of fiber orientations, or waviness. Local stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers than the LC at the low levels of stretch. At 10% stretch the curves crossed with 75% bundles recruited. The PPS had higher uncrimping rate and waviness remaining after recruitment than the LC: 0.9º vs. 0.6º and 3.1º vs. 2.7º. Altogether our findings support describing fiber recruitment of both PPS and LC with sigmoid curves, with the PPS recruiting faster and at lower stretch than the LC, consistent with a stiffer tissue. STATEMENT OF SIGNIFICANCE: Peripapillary sclera (PPS) and lamina cribrosa (LC) collagen recruitment behaviors are central to the nonlinear mechanical behavior of the posterior pole of the eye. How PPS and LC collagen fibers recruit under stretch is crucial to develop constitutive models of the tissues but remains unclear. We used image-based stretch testing to characterize PPS and LC collagen fiber bundle recruitment under local stretch. We found that fiber-level stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers at a low stretch, but at 10% bundle stretch the two curves crossed with 75% bundles recruited. We also found that PPS and LC fibers had different uncrimping rates and non-zero waviness's when recruited.

2D or not 2D? Mapping the in-depth inclination of the collagen fibers of the corneoscleral shell

The collagen fibers of the corneoscleral shell play a central role in the eye mechanical behavior. Although it is well-known that these fibers form a complex three-dimensional interwoven structure, biomechanical and microstructural studies often assume that the fibers are aligned in-plane with the tissues. This is convenient as it removes the out-of-plane components and allows focusing on the 2D maps of in-plane fiber organization that are often quite complex. The simplification, however, risks missing potentially important aspects of the tissue architecture and mechanics. In the cornea, for instance, fibers with high in-depth inclination have been shown to be mechanically important. Outside the cornea, the in-depth fiber orientations have not been characterized, preventing a deeper understanding of their potential roles. Our goal was to characterize in-depth collagen fiber organization over the whole corneoscleral shell. Seven sheep whole-globe axial sections from eyes fixed at an IOP of 50 mmHg were imaged using polarized light microscopy to measure collagen fiber orientations and density. In-depth fiber orientation distributions and anisotropy (degree of fiber alignment) accounting for fiber density were quantified over the whole sclera and in 15 regions: central cornea, peripheral cornea, limbus, anterior equator, equator, posterior equator, posterior sclera and peripapillary sclera on both nasal and temporal sides. Orientation distributions were fitted using a combination of a uniform distribution and a sum of π-periodic von Mises distributions, each with three parameters: primary orientation μ, fiber concentration factor k, and weighting factor a. To study the features of fibers that are not in-plane, i.e., fiber inclination, we quantified the percentage of inclined fibers and the range of inclination angles (half width at half maximum of inclination angle distribution). Our measurements showed that the fibers were not uniformly in-plane but exhibited instead a wide range of in-depth orientations, with fibers significantly more aligned in-plane in the anterior parts of the globe. We found that fitting the orientation distributions required between one and three π-periodic von Mises distributions with different primary orientations and fiber concentration factors. Regions of the posterior globe, particularly on the temporal side, had a larger percentage of inclined fibers and a larger range of inclination angles than anterior and equatorial regions. Variations of orientation distributions and anisotropies may imply varying out-of-plane tissue mechanical properties around the eye globe. Out-of-plane fibers could indicate fiber interweaving, not necessarily long, inclined fibers. Effects of small-scale fiber undulations, or crimp, were minimized by using tissues from eyes at high IOPs. These fiber features also play a role in tissue stiffness and stability and are therefore also important experimental information.

A direct fiber approach to model sclera collagen architecture and biomechanics

Sclera collagen fiber microstructure and mechanical behavior are central to eye physiology and pathology. They are also complex, and are therefore often studied using modeling. Most models of sclera, however, have been built within a conventional continuum framework. In this framework, collagen fibers are incorporated as statistical distributions of fiber characteristics such as the orientation of a family of fibers. The conventional continuum approach, while proven successful for describing the macroscale behavior of the sclera, does not account for the sclera fibers are long, interwoven and interact with one another. Hence, by not considering these potentially crucial characteristics, the conventional approach has only a limited ability to capture and describe sclera structure and mechanics at smaller, fiber-level, scales. Recent advances in the tools for characterizing sclera microarchitecture and mechanics bring to the forefront the need to develop more advanced modeling techniques that can incorporate and take advantage of the newly available highly detailed information. Our goal was to create a new computational modeling approach that can represent the sclera fibrous microstructure more accurately than with the conventional continuum approach, while still capturing its macroscale behavior. In this manuscript we introduce the new modeling approach, that we call direct fiber modeling, in which the collagen architecture is built explicitly by long, continuous, interwoven fibers. The fibers are embedded in a continuum matrix representing the non-fibrous tissue components. We demonstrate the approach by doing direct fiber modeling of a rectangular patch of posterior sclera. The model integrated fiber orientations obtained by polarized light microscopy from coronal and sagittal cryosections of pig and sheep. The fibers were modeled using a Mooney-Rivlin model, and the matrix using a Neo-Hookean model. The fiber parameters were determined by inversely matching experimental equi-biaxial tensile data from the literature. After reconstruction, the direct fiber model orientations agreed well with the microscopy data both in the coronal plane (adjusted R2 = 0.8234) and in the sagittal plane (adjusted R2 = 0.8495) of the sclera. With the estimated fiber properties (C10 = 5746.9 MPa; C01 = -5002.6 MPa, matrix shear modulus 200 kPa), the model's stress-strain curves simultaneously fit the experimental data in radial and circumferential directions (adjusted R2's 0.9971 and 0.9508, respectively). The estimated fiber elastic modulus at 2.16% strain was 5.45 GPa, in reasonable agreement with the literature. During stretch, the model exhibited stresses and strains at sub-fiber level, with interactions among individual fibers which are not accounted for by the conventional continuum methods. Our results demonstrate that direct fiber models can simultaneously describe the macroscale mechanics and microarchitecture of the sclera, and therefore that the approach can provide unique insight into tissue behavior questions inaccessible with continuum approaches.

Instant polarized light microscopy pi (IPOLπ) for quantitative imaging of collagen architecture and dynamics in ocular tissues

Collagen architecture determines the biomechanical environment in the eye, and thus characterizing collagen fiber organization and biomechanics is essential to fully understand eye physiology and pathology. We recently introduced instant polarized light microscopy (IPOL) that encodes optically information about fiber orientation and retardance through a color snapshot. Although IPOL allows imaging collagen at the full acquisition speed of the camera, with excellent spatial and angular resolutions, a limitation is that the orientation-encoding color is cyclic every 90 degrees (π/2 radians). In consequence, two orthogonal fibers have the same color and therefore the same orientation when quantified by color-angle mapping. In this study, we demonstrate IPOLπ, a new variation of IPOL, in which the orientation-encoding color is cyclic every 180 degrees (π radians). Herein we present the fundamentals of IPOLπ, including a framework based on a Mueller-matrix formalism to characterize how fiber orientation and retardance determine the color. The improved quantitative capability of IPOLπ enables further study of essential biomechanical properties of collagen in ocular tissues, such as fiber anisotropy and crimp. We present a series of experimental calibrations and quantitative procedures to visualize and quantify ocular collagen orientation and microstructure in the optic nerve head, a region in the back of the eye. There are four important strengths of IPOLπ compared to IPOL. First, IPOLπ can distinguish the orientations of orthogonal collagen fibers via colors, whereas IPOL cannot. Second, IPOLπ requires a lower exposure time than IPOL, thus allowing faster imaging speed. Third, IPOLπ allows visualizing non-birefringent tissues and backgrounds from tissue absorption, whereas both appear dark in IPOL images. Fourth, IPOLπ is cheaper and less sensitive to imperfectly collimated light than IPOL. Altogether, the high spatial, angular, and temporal resolutions of IPOLπ enable a deeper insight into ocular biomechanics and eye physiology and pathology.

Direct measurements of collagen fiber recruitment in the posterior pole of the eye

Collagen is the main load-bearing component of the peripapillary sclera (PPS) and lamina cribrosa (LC) in the eye. Whilst it has been shown that uncrimping and recruitment of the PPS and LC collagen fibers underlies the macro-scale nonlinear stiffening of both tissues with increased intraocular pressure (IOP), the uncrimping and recruitment as a function of local stretch have not been directly measured. This knowledge is crucial for the development of constitutive models associating micro and macro scales. In this project we measured local stretch-induced collagen fiber bundle uncrimping and recruitment curves of the PPS and LC. Thin coronal samples of PPS and LC of sheep eyes were mounted and stretched biaxially quasi-statically using a custom system. At each step, we imaged the PPS and LC with instant polarized light microscopy and quantified pixel-level (1.5 μm/pixel) collagen fiber orientations. We used digital image correlation to measure the local stretch and quantified collagen crimp by the circular standard deviation of fiber orientations, or waviness. Local stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers than the LC at the low levels of stretch. At 10% stretch the curves crossed with 75% bundles recruited. The PPS had higher uncrimping rate and waviness remaining after recruitment than the LC: 0.9° vs. 0.6° and 3.1° vs. 2.7°. Altogether our findings support describing fiber recruitment of both PPS and LC with sigmoid curves, with the PPS recruiting faster and at lower stretch than the LC, consistent with a stiffer tissue.

Who bears the load? IOP-induced collagen fiber recruitment over the corneoscleral shell

Collagen is the main load-bearing component of cornea and sclera. When stretched, both of these tissues exhibit a behavior known as collagen fiber recruitment. In recruitment, as the tissues stretch the constitutive collagen fibers lose their natural waviness, progressively straightening. Recruited, straight, fibers bear substantially more mechanical load than non-recruited, wavy, fibers. As such, the process of recruitment underlies the well-established nonlinear macroscopic behavior of the corneoscleral shell. Recruitment has an interesting implication: when recruitment is incomplete, only a fraction of the collagen fibers is actually contributing to bear the loads, with the rest remaining "in reserve". In other words, at a given intraocular pressure (IOP), it is possible that not all the collagen fibers of the cornea and sclera are actually contributing to bear the loads. To the best of our knowledge, the fraction of corneoscleral shell fibers recruited and contributing to bear the load of IOP has not been reported. Our goal was to obtain regionally-resolved estimates of the fraction of corneoscleral collagen fibers recruited and in reserve. We developed a fiber-based microstructural constitutive model that could account for collagen fiber undulations or crimp via their tortuosity. We used experimentally-measured collagen fiber crimp tortuosity distributions in human eyes to derive region-specific nonlinear hyperelastic mechanical properties. We then built a three-dimensional axisymmetric model of the globe, assigning region-specific mechanical properties and regional anisotropy. The model was used to simulate the IOP-induced shell deformation. The model-predicted tissue stretch was then used to quantify collagen recruitment within each shell region. The calculations showed that, at low IOPs, collagen fibers in the posterior equator were recruited the fastest, such that at a physiologic IOP of 15 mmHg, over 90% of fibers were recruited, compared with only a third in the cornea and the peripapillary sclera. The differences in recruitment between regions, in turn, mean that at a physiologic IOP the posterior equator had a fiber reserve of only 10%, whereas the cornea and peripapillary sclera had two thirds. At an elevated IOP of 50 mmHg, collagen fibers in the limbus and the anterior/posterior equator were almost fully recruited, compared with 90% in the cornea and the posterior sclera, and 70% in the peripapillary sclera and the equator. That even at such an elevated IOP not all the fibers were recruited suggests that there are likely other conditions that challenge the corneoscleral tissues even more than IOP. The fraction of fibers recruited may have other potential implications. For example, fibers that are not bearing loads may be more susceptible to enzymatic digestion or remodeling. Similarly, it may be possible to control tissue stiffness through the fraction of recruited fibers without the need to add or remove collagen.

Stretch-Induced Uncrimping of Equatorial Sclera Collagen Bundles

Stretch-induced collagen uncrimping underlies the nonlinear mechanical behavior of the sclera according to what is often called the process of recruitment. We recently reported experimental measurements of sclera collagen crimp and pressure-induced uncrimping. Our studies, however, were cross-sectional, providing statistical descriptions of crimp with no information on the effects of stretch on specific collagen bundles. Data on bundle-specific uncrimping is necessary to better understand the effects of macroscale input on the collagen microscale and tissue failure. Our goal in this project was to measure bundle-specific stretch-induced collagen uncrimping of sclera. Three goat eyes were cryosectioned sagittally (30 μm). Samples of equatorial sclera were isolated, mounted to a custom uni-axial stretcher and imaged with polarized light microscopy at various levels of clamp-to-clamp stretch until failure. At each stretch level, local strain was measured using image tracking techniques. The level of collagen crimping was determined from the bundle waviness, defined as the circular standard deviation of fiber orientation along a bundle. Eye-specific recruitment curves were then computed using eye-specific waviness at maximum stretch before sample failure to define fibers as recruited. Nonlinear mixed effect models were used to determine the associations of waviness to local strain and recruitment to clamp-to-clamp stretch. Waviness decreased exponentially with local strain (p < 0.001), whereas bundle recruitment followed a sigmoidal curve with clamp-to-clamp stretch (p < 0.001). Individual bundle responses to stretch varied substantially, but recruitment curves were similar across sections and eyes. In conclusion, uni-axial stretch caused measurable bundle-specific uncrimping, with the sigmoidal recruitment pattern characteristic of fiber-reinforced soft tissues.

Instant polarized light microscopy pi (IPOLπ) for quantitative imaging of collagen architecture and dynamics in ocular tissues

Collagen architecture determines the biomechanical environment in the eye, and thus characterizing collagen fiber organization and biomechanics is essential to fully understand eye physiology and pathology. We recently introduced instant polarized light microscopy (IPOL) that encodes optically information about fiber orientation and retardance through a color snapshot. Although IPOL allows imaging collagen at the full acquisition speed of the camera, with excellent spatial and angular resolutions, a limitation is that the orientation-encoding color is cyclic every 90 degrees (π/2 radians). In consequence, two orthogonal fibers have the same color and therefore the same orientation when quantified by color-angle mapping. In this study, we demonstrate IPOLπ, a new variation of IPOL, in which the orientation-encoding color is cyclic every 180 degrees (π radians). Herein we present the fundamentals of IPOLπ, including a framework based on a Mueller-matrix formalism to characterize how fiber orientation and retardance determine the color. The improved quantitative capability of IPOLπ enables further study of essential biomechanical properties of collagen in ocular tissues, such as fiber anisotropy and crimp. We present a series of experimental calibrations and quantitative procedures to visualize and quantify ocular collagen orientation and microstructure in the optic nerve head, a region in the back of the eye. There are four important strengths of IPOLπ compared to IPOL. First, IPOLπ can distinguish the orientations of orthogonal collagen fibers via colors, whereas IPOL cannot. Second, IPOLπ requires a lower exposure time than IPOL, thus allowing faster imaging speed. Third, IPOLπ allows visualizing non-birefringent tissues and backgrounds from tissue absorption, whereas both appear dark in IPOL images. Fourth, IPOLπ is cheaper and less sensitive to imperfectly collimated light than IPOL. Altogether, the high spatial, angular, and temporal resolutions of IPOLπ enable a deeper insight into ocular biomechanics and eye physiology and pathology.

The Strain Response to Intraocular Pressure Decrease in the Lamina Cribrosa of Patients with Glaucoma

OBJECTIVE

To measure biomechanical strains in the lamina cribrosa (LC) of living human eyes with intraocular pressure (IOP) lowering.

DESIGN

Cohort study.

PARTICIPANTS

Patients with glaucoma underwent imaging before and after laser suturelysis after trabeculectomy surgery (29 image pairs; 26 persons).

INTERVENTION

Noninvasive imaging of the eye.

MAIN OUTCOME MEASURES

Strains in optic nerve head tissue and changes in depths of the anterior border of the LC.

RESULTS

Intraocular pressure decreases caused the LC to expand in thickness in the anterior-posterior strain (Ezz = 0.94 ± 1.2%; P = 0.00020) and contract in radius in the radial strain (Err = - 0.19 ± 0.33%; P = 0.0043). The mean LC depth did not significantly change with IOP lowering (1.33 ± 6.26 μm; P = 0.26). A larger IOP decrease produced a larger, more tensile Ezz (P < 0.0001), greater maximum principal strain (Emax; P < 0.0001), and greater maximum shear strain (Γmax; P < 0.0001). The average LC depth change was associated with the Γmax and radial-circumferential shear strain (Erθ; P < 0.02) but was not significantly related to tensile or compressive strains. An analysis by clock hour showed that in temporal clock hours 3 to 6, a more anterior LC movement was associated with a more positive Emax, and in clock hours 3, 5, and 6, it was associated with a more positive Γmax. At 10 o'clock, a more posterior LC movement was related to a more positive Emax (P < 0.004). Greater compliance (strain/ΔIOP) of Emax (P = 0.044), Γmax (P = 0.052), and Erθ (P = 0.018) was associated with a thinner retinal nerve fiber layer. Greater compliance of Emax (P = 0.041), Γmax (P = 0.021), Erθ (P = 0.024), and in-plane shear strain (Erz; P = 0.0069) was associated with more negative mean deviations. Greater compliance of Γmax (P = 0.055), Erθ (P = 0.040), and Erz (P = 0.015) was associated with lower visual field indices.

CONCLUSIONS

With IOP lowering, the LC moves either into or out of the eye but, on average, expands in thickness and contracts in radius. Shear strains are nearly as substantial as in-plane strains. Biomechanical strains are more compliant in eyes with greater glaucoma damage. This work was registered at ClinicalTrials.gov as NCT03267849.

Finite element modeling of effects of tissue property variation on human optic nerve tethering during adduction

Tractional tethering by the optic nerve (ON) on the eye as it rotates towards the midline in adduction is a significant ocular mechanical load and has been suggested as a cause of ON damage induced by repetitive eye movements. We designed an ocular finite element model (FEM) simulating 6° incremental adduction beyond the initial configuration of 26° adduction that is the observed threshold for ON tethering. This FEM permitted sensitivity analysis of ON tethering using observed material property variations in measured hyperelasticity of the anterior, equatorial, posterior, and peripapillary sclera; and the ON and its sheath. The FEM predicted that adduction beyond the initiation of ON tethering concentrates stress and strain on the temporal side of the optic disc and peripapillary sclera, the ON sheath junction with the sclera, and retrolaminar ON neural tissue. However, some unfavorable combinations of tissue properties within the published ranges imposed higher stresses in these regions. With the least favorable combinations of tissue properties, adduction tethering was predicted to stress the ON junction and peripapillary sclera more than extreme conditions of intraocular and intracranial pressure. These simulations support the concept that ON tethering in adduction could induce mechanical stresses that might contribute to ON damage.

High-resolution polarization-sensitive Fourier ptychography microscopy using a high numerical aperture dome illuminator

Polarization-sensitive Fourier-ptychography microscopy (pFPM) allows for high resolution imaging while maintaining a large field of view, and without mechanical movements of optical-setup components. In contrast to ordinary light microscopes, pFPM provides quantitative absorption and phase information, for complex and birefringent specimens, with high resolution across a wide field of view. Using a semi-spherical home-built LED illumination array, a single polarizer, and a 10x /0.28NA objective, we experimentally demonstrate high performance pFPM with a synthesized NA of 1.1. Applying the standard quantitative method, a measured half-pitch resolution of 244 nm is achieved for the 1951 USAF resolution test target. As application examples, the polarimetric properties of a herbaceous flowering plant and the metastatic carcinoma of human liver cells are analyzed and quantitatively imaged.

Quantitative Microstructural Analysis of Cellular and Tissue Remodeling in Human Glaucoma Optic Nerve Head

Purpose

To measure quantitatively changes in lamina cribrosa (LC) cell and connective tissue structure in human glaucoma eyes.

Methods

We studied 27 glaucoma and 19 age-matched non-glaucoma postmortem eyes. In 25 eyes, LC cross-sections were examined by confocal and multiphoton microscopy to quantify structures identified by anti-glial fibrillary acidic protein (GFAP), phalloidin-labeled F-actin, nuclear 4',6-diamidino-2-phenylindole (DAPI), and by second harmonic generation imaging of LC beams. Additional light and transmission electron microscopy were performed in 21 eyes to confirm features of LC remodeling, including immunolabeling by anti-SOX9 and anti-collagen IV. All glaucoma eyes had detailed clinical histories of open-angle glaucoma status, and degree of axon loss was quantified in retrolaminar optic nerve cross-sections.

Results

Within LC pores, the proportionate area of both GFAP and F-actin processes was significantly lower in glaucoma eyes than in controls (P = 0.01). Nuclei were rounder (lower median aspect ratio) in glaucoma specimens (P = 0.02). In models assessing degree of glaucoma damage, F-actin process width was significantly wider in glaucoma eyes with more damage (P = 0.024), average LC beam width decreased with worse glaucoma damage (P = 0.042), and nuclear count per square millimeter rose with worse damage (P = 0.019). The greater cell count in LC pores represented 92.3% astrocytes by SOX9 labeling. The results are consistent with replacement of axons in LC pores by basement membrane labeled by anti-collagen IV and in-migrating astrocytes.

Conclusions

Alteration in LC structure in glaucoma involves migration of astrocytes into axonal bundles, change in astrocyte orientation and processes, production of basement membrane material, and thinning of connective tissue beams.

Eye-specific 3D modeling of factors influencing oxygen concentration in the lamina cribrosa

Our goal was to identify the factors with the strongest influence on the minimum lamina cribrosa (LC) oxygen concentration as potentially indicative of conditions increasing hypoxia risk. Because direct measurement of LC hemodynamics and oxygenation is not yet possible, we developed 3D eye-specific LC vasculature models. The vasculature of a normal monkey eye was perfusion-labeled post-mortem. Serial cryosections through the optic nerve head were imaged using fluorescence and polarized light microscopy to visualize the vasculature and collagen, respectively. The vasculature within a 450 μm-thick region containing the LC - identified from the collagen, was segmented, skeletonized, and meshed for simulations. Using Monte Carlo sampling, 200 vascular network models were generated with varying vessel diameter, neural tissue oxygen consumption rate, inflow hematocrit, and blood pressures (arteriole, venule, anterior boundary, and posterior boundary). Factors were varied over ranges of baseline ±20% with uniform probability. For each model we first obtained the blood flow, and from this the neural tissue oxygen concentration. ANOVA was used to identify the factors with the strongest influence on the minimum (10th percentile) oxygen concentration in the LC. The three most influential factors were, in ranked order, vessel diameter, neural tissue oxygen consumption rate, and arteriole pressure. There was a strong interaction between vessel diameter and arteriole pressure whereby the impact of one factor was larger when the other factor was small. Our results show that, for the eye analyzed, conditions that reduce vessel diameter, such as vessel compression due to elevated intraocular pressure or gaze-induced tissue deformation, may particularly contribute to decreased LC oxygen concentration. More eyes must be analyzed before generalizing.

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.

Quantitative Jones matrix imaging using vectorial Fourier ptychography

This paper presents a microscopic imaging technique that uses variable-angle illumination to recover the complex polarimetric properties of a specimen at high resolution and over a large field-of-view. The approach extends Fourier ptychography, which is a synthetic aperture-based imaging approach to improve resolution with phaseless measurements, to additionally account for the vectorial nature of light. After images are acquired using a standard microscope outfitted with an LED illumination array and two polarizers, our vectorial Fourier ptychography (vFP) algorithm solves for the complex 2x2 Jones matrix of the anisotropic specimen of interest at each resolved spatial location. We introduce a new sequential Gauss-Newton-based solver that additionally jointly estimates and removes polarization-dependent imaging system aberrations. We demonstrate effective vFP performance by generating large-area (29 mm²), high-resolution (1.24 μm full-pitch) reconstructions of sample absorption, phase, orientation, diattenuation, and retardance for a variety of calibration samples and biological specimens.

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.

Lamina cribrosa vessel and collagen beam networks are distinct

Our goal was to analyze the spatial interrelation between vascular and collagen networks in the lamina cribrosa (LC). Specifically, we quantified the percentages of collagen beams with/without vessels and of vessels inside/outside of collagen beams. To do this, the vasculature of six normal monkey eyes was labeled by perfusion post-mortem. After enucleation, coronal cryosections through the LC were imaged using fluorescence and polarized light microscopy to visualize the blood vessels and collagen beams, respectively. The images were registered to form 3D volumes. Beams and vessels were segmented, and their spatial interrelationship was quantified in 3D. We found that 22% of the beams contained a vessel (range 14%-32%), and 21% of vessels were outside beams (13%-36%). Stated differently, 78% of beams did not contain a vessel (68%-86%), and 79% of vessels were inside a beam (64%-87%). Individual monkeys differed significantly in the fraction of vessels outside beams (p < 0.01 by linear mixed effect analysis), but not in the fraction of beams with vessels (p > 0.05). There were no significant differences between contralateral eyes in the percent of beams with vessels and of vessels outside beams (p > 0.05). Our results show that the vascular and collagenous networks of the LC in monkey are clearly distinct, and the historical notions that each LC beam contains a vessel and all vessels are within beams are inaccurate. We postulate that vessels outside beams may be relatively more vulnerable to mechanical compression by elevated IOP than are vessels shielded inside of beams.

Real-time imaging of optic nerve head collagen microstructure and biomechanics using instant polarized light microscopy

Current tools lack the temporal or spatial resolution necessary to image many important aspects of the architecture and dynamics of the optic nerve head (ONH). We evaluated the potential of instant polarized light microscopy (IPOL) to overcome these limitations by leveraging the ability to capture collagen fiber orientation and density in a single image. Coronal sections through the ONH of fresh normal sheep eyes were imaged using IPOL while they were stretched using custom uniaxial or biaxial micro-stretch devices. IPOL allows identifying ONH collagen architectural details, such as fiber interweaving and crimp, and has high temporal resolution, limited only by the frame rate of the camera. Local collagen fiber orientations and deformations were quantified using color analysis and image tracking techniques. We quantified stretch-induced collagen uncrimping of lamina cribrosa (LC) and peripapillary sclera (PPS), and changes in LC pore size (area) and shape (convexity and aspect ratio). The simultaneous high spatial and temporal resolutions of IPOL revealed complex ONH biomechanics: i) stretch-induced local deformation of the PPS was nonlinear and nonaffine. ii) under load the crimped collagen fibers in the PPS and LC straightened, without torsion and with only small rotations. iii) stretch-induced LC pore deformation was anisotropic and heterogeneous among pores. Overall, with stretch the pores were became larger, more convex, and more circular. We have demonstrated that IPOL reveals details of collagen morphology and mechanics under dynamic loading previously out of reach. IPOL can detect stretch-induced collagen uncrimping and other elements of the tissue nonlinear mechanical behavior. IPOL showed changes in pore morphology and collagen architecture that will help improve understanding of how LC tissue responds to load.

Polarization sensitive optical coherence tomography with single input for imaging depth-resolved collagen organizations

Collagen organization plays an important role in maintaining structural integrity and determining tissue function. Polarization-sensitive optical coherence tomography (PSOCT) is a promising noninvasive three-dimensional imaging tool for mapping collagen organization in vivo. While PSOCT systems with multiple polarization inputs have demonstrated the ability to visualize depth-resolved collagen organization, systems, which use a single input polarization state have not yet demonstrated sufficient reconstruction quality. Herein we describe a PSOCT based polarization state transmission model that reveals the depth-dependent polarization state evolution of light backscattered within a birefringent sample. Based on this model, we propose a polarization state tracing method that relies on a discrete differential geometric analysis of the evolution of the polarization state in depth along the Poincare sphere for depth-resolved birefringent imaging using only one single input polarization state. We demonstrate the ability of this method to visualize depth-resolved myocardial architecture in both healthy and infarcted rodent hearts (ex vivo) and collagen structures responsible for skin tension lines at various anatomical locations on the face of a healthy human volunteer (in vivo).

Interplay between intraocular and intracranial pressure effects on the optic nerve head in vivo

Intracranial pressure (ICP) has been proposed to play an important role in the sensitivity to intraocular pressure (IOP) and susceptibility to glaucoma. However, the in vivo effects of simultaneous, controlled, acute variations in ICP and IOP have not been directly measured. We quantified the deformations of the anterior lamina cribrosa (ALC) and scleral canal at Bruch's membrane opening (BMO) under acute elevation of IOP and/or ICP. Four eyes of three adult monkeys were imaged in vivo with OCT under four pressure conditions: IOP and ICP either at baseline or elevated. The BMO and ALC were reconstructed from manual delineations. From these, we determined canal area at the BMO (BMO area), BMO aspect ratio and planarity, and ALC median depth relative to the BMO plane. To better account for the pressure effects on the imaging, we also measured ALC visibility as a percent of the BMO area. Further, ALC depths were analyzed only in regions where the ALC was visible in all pressure conditions. Bootstrap sampling was used to obtain mean estimates and confidence intervals, which were then used to test for significant effects of IOP and ICP, independently and in interaction. Response to pressure manipulation was highly individualized between eyes, with significant changes detected in a majority of the parameters. Significant interactions between ICP and IOP occurred in all measures, except ALC visibility. On average, ICP elevation expanded BMO area by 0.17 mm² at baseline IOP, and contracted BMO area by 0.02 mm² at high IOP. ICP elevation decreased ALC depth by 10 μm at baseline IOP, but increased depth by 7 μm at high IOP. ALC visibility decreased as ICP increased, both at baseline (-10%) and high IOP (-17%). IOP elevation expanded BMO area by 0.04 mm² at baseline ICP, and contracted BMO area by 0.09 mm² at high ICP. On average, IOP elevation caused the ALC to displace 3.3 μm anteriorly at baseline ICP, and 22 μm posteriorly at high ICP. ALC visibility improved as IOP increased, both at baseline (5%) and high ICP (8%). In summary, changing IOP or ICP significantly deformed both the scleral canal and the lamina of the monkey ONH, regardless of the other pressure level. There were significant interactions between the effects of IOP and those of ICP on LC depth, BMO area, aspect ratio and planarity. On most eyes, elevating both pressures by the same amount did not cancel out the effects. Altogether our results show that ICP affects sensitivity to IOP, and thus that it can potentially also affect susceptibility to glaucoma.

Assessment of the viscoelastic mechanical properties of the porcine optic nerve head using micromechanical testing and finite element modeling

Optic nerve head (ONH) biomechanics is centrally involved in the pathogenesis of glaucoma, a blinding ocular condition often characterized by elevation and fluctuation of the intraocular pressure and resulting loads on the ONH. Further, tissue viscoelasticity is expected to strongly influence the mechanical response of the ONH to mechanical loading, yet the viscoelastic mechanical properties of the ONH remain unknown. To determine these properties, we conducted micromechanical testing on porcine ONH tissue samples, coupled with finite element modeling based on a mixture model consisting of a biphasic material with a viscoelastic solid matrix. Our results provide a detailed description of the viscoelastic properties of the porcine ONH at each of its four anatomical quadrants (i.e., nasal, superior, temporal, and inferior). We showed that the ONH's viscoelastic mechanical response can be explained by a dual mechanism of fluid flow and solid matrix viscoelasticity, as is common in other soft tissues. We obtained porcine ONH properties as follows: matrix Young's modulus E=1.895[1.056,2.391] kPa (median [min., max.]), Poisson's ratio ν=0.142[0.060,0.312], kinetic time-constant τ=214[89,921] sec, and hydraulic permeability k=3.854×10^-1[3.457×10^-2,9.994×10^-1] mm⁴/(N.sec). These values can be used to design and fabricate physiologically appropriate ex vivo test environments (e.g., 3D cell culture) to further understand glaucoma pathophysiology. STATEMENT OF SIGNIFICANCE: Optic nerve head (ONH) biomechanics is an important aspect of the pathogenesis of glaucoma, the leading cause of irreversible blindness. The ONH experiences time-varying loads, yet the viscoelastic behavior of this tissue has not been characterized. Here, we measure the time-dependent response of the ONH in porcine eyes and use mechanical modeling to provide time-dependent mechanical properties of the ONH. This information allows us to identify time-varying stimuli in vivo which have timescales matching the characteristic response times of the ONH, and can also be used to design and fabricate ex vivo 3D cultures to study glaucoma pathophysiology in a physiologically relevant environment, enabling the discovery of new generations of glaucoma medications focusing on neuroprotection.

So-Called Lamina Cribrosa Defects May Mitigate IOP-Induced Neural Tissue Insult

Purpose

The prevailing theory about the function of lamina cribrosa (LC) connective tissues is that they provide structural support to adjacent neural tissues. Missing connective tissues would compromise this support and therefore are regarded as “LC defects”, despite scarce actual evidence of their role. We examined how so-called LC defects alter IOP-related mechanical insult to the LC neural tissues.

Methods

We built numerical models incorporating LC microstructure from polarized light microscopy images. To simulate LC defects of varying sizes, individual beams were progressively removed. We then compared intraocular pressure (IOP)-induced neural tissue deformations between models with and without defects. To better understand the consequences of defect development, we also compared neural tissue deformations between models with partial and complete loss of a beam.

Results

The maximum stretch of neural tissues decreased non-monotonically with defect size. Maximum stretch in the model with the largest defect decreased by 40% in comparison to the model with no defects. Partial loss of a beam increased the maximum stretch of neural tissues in its adjacent pores by 162%, compared with 63% in the model with complete loss of a beam.

Conclusions

Missing LC connective tissues can mitigate IOP-induced neural tissue insult, suggesting that the role of the LC connective tissues is more complex than simply fortifying against IOP. The numerical models further predict that partial loss of a beam is biomechanically considerably worse than complete loss of a beam, perhaps explaining why defects have been reported clinically but partial beams have not.

Material properties and effect of preconditioning of human sclera, optic nerve, and optic nerve sheath

The optic nerve (ON) is a recently recognized tractional load on the eye during larger horizontal eye rotations. In order to understand the mechanical behavior of the eye during adduction, it is necessary to characterize material properties of the sclera, ON, and in particular its sheath. We performed tensile loading of specimens taken from fresh postmortem human eyes to characterize the range of variation in their biomechanical properties and determine the effect of preconditioning. We fitted reduced polynomial hyperelastic models to represent the nonlinear tensile behavior of the anterior, equatorial, posterior, and peripapillary sclera, as well as the ON and its sheath. For comparison, we analyzed tangent moduli in low and high strain regions to represent stiffness. Scleral stiffness generally decreased from anterior to posterior ocular regions. The ON had the lowest tangent modulus, but was surrounded by a much stiffer sheath. The low-strain hyperelastic behaviors of adjacent anatomical regions of the ON, ON sheath, and posterior sclera were similar as appropriate to avoid discontinuities at their boundaries. Regional stiffnesses within individual eyes were moderately correlated, implying that mechanical properties in one region of an eye do not reliably reflect properties of another region of that eye, and that potentially pathological combinations could occur in an eye if regional properties are discrepant. Preconditioning modestly stiffened ocular tissues, except peripapillary sclera that softened. The nonlinear mechanical behavior of posterior ocular tissues permits their stresses to match closely at low strains, although progressively increasing strain causes particularly great stress in the peripapillary region.

Ultrasonic elastography to assess biomechanical properties of the optic nerve head and peripapillary sclera of the eye

PURPOSE

To quantitatively investigate both optic nerve head (ONH) and peripapillary sclera (PPS) biomechanical properties of porcine eyes through an ultrasonic elastography imaging system in response to both increasing and decreasing intraocular pressure (IOP).

METHODS

The Young's modulus of the ONH and PPS were assessed using our high resolution ultrasonic imaging system which utilized a mechanical shaker to induce shear waves and an off-axis aligned 40 MHz needle transducer to track micron-level displacement along the direction of wave propagation. In this study, imaging on a total of 8 ex vivo porcine eyes preloaded with IOPs from 6 mmHg to 30 mmHg was performed. To have a better understanding of the effect of varying IOP on biomechanics, both increasing and decreasing IOPs were investigated.

RESULTS

The increase of the Young's modulus of ONH (92.4 ± 13.9 kPa at 6 mmHg to 224.7 ± 71.1 kPa at 30 mmHg) and PPS (176.8 ± 14.3 kPa at 6 mmHg to 573.5 ± 64.4 kPa at 30 mmHg) following IOP elevation could be observed in the reconstructed Young's modulus of the shear wave elasticity (SWE) imaging while the B-mode structural images remained almost unchanged. In addition, for the same IOP level, both ONH and PPS have a tendency to be stiffer with decreasing IOP as compared to increasing IOP.

CONCLUSIONS

Our results demonstrate the feasibility of using our ultrasonic elastography system to investigate the stiffness mapping of posterior eye with high resolution in both increasing and decreasing IOPs, making this technique potentially useful for glaucoma.

Instant polarized light microscopy for imaging collagen microarchitecture and dynamics

Collagen fibers are a primary load-bearing component of connective tissues and are therefore central to tissue biomechanics and pathophysiology. Understanding collagen architecture and behavior under dynamic loading requires a quantitative imaging technique with simultaneously high spatial and temporal resolutions. Suitable techniques are thus rare and often inaccessible. In this study, we present instant polarized light microscopy (IPOL), in which a single snapshot image encodes information on fiber orientation and retardance, thus fulfilling the requirement. We utilized both simulation and experimental data from collagenous tissues of chicken tendon, sheep eye, and porcine heart to evaluate the effectiveness of IPOL as a quantitative imaging technique. We demonstrate that IPOL allows quantitative characterization of micron-scale collagen fiber architecture at full camera frame rates (156 frames/second herein).

Linear diattenuation imaging of biological tissues with near infrared Mueller scanning microscopy

Among the multitude of optical polarization contrasts that can be observed in complex biological specimens, linear diattenuation (LD) imaging has received little attention. It is indeed challenging to image LD with basic polarizing microscopes because it is often relatively small in comparison with linear retardance (LR). In addition, interpretation of LD images is not straightforward when experiments are conducted in the visible range because LD can be produced by both dichroism and anisotropic scattering. Mueller polarimetry is a powerful implementation of polarization sensing able to differentiate and measure the anisotropies of specimens. In this article, near infrared transmission Mueller scanning microscopy is used to image LD in thin biological specimen sections made of various proteins with unprecedented resolution and sensitivity. The near infrared spectral range makes it possible to lower the contribution of dichroism to the total linear diattenuation in order to highlight anisotropic scattering. Pixel-by-pixel comparison of LD images with LR and multiphoton images demonstrates that LD is produced by under-resolved structures that are not revealed by other means, notably within the sarcomere of skeletal muscles. LD microscopy appears as a powerful tool to provide new insights into the macro-molecular organization of biological specimens at the sub-microscopic scale without labelling.

Numerical Investigation on the Role of Mechanical Factors Contributing to Globe Flattening in States of Elevated Intracranial Pressure

Flattening of the posterior eye globe in the magnetic resonance (MR) images is a sign associated with elevated intracranial pressure (ICP), often seen in people with idiopathic intracranial hypertension (IIH). The exact underlying mechanisms of globe flattening (GF) are not fully known but mechanical factors are believed to play a role. In the present study, we investigated the effects of material properties and pressure loads on GF. For this purpose, we used a generic finite element model to investigate the deformation of the posterior eyeball. The degree of GF in numerical models and the significance of different mechanical factors on GF were characterized using an automated angle-slope technique and a statistical measure. From the numerical models, we found that ICP had the most important role in GF. We also showed that the angle-slope graphs pertaining to MR images from five people with high ICP can be represented numerically by manipulating the parameters of the finite element model. This numerical study suggests that GF observed in IIH patients can be accounted for by the forces caused by elevation of ICP from its normal level, while material properties of ocular tissues, such as sclera (SC), peripapillary sclera (PSC), and optic nerve (ON), would impact its severity.

Collagen fiber interweaving is central to sclera stiffness

The mechanical properties of the microstructural components of sclera are central to eye physiology and pathology. Because these parameters are extremely difficult to measure directly, they are often estimated using inverse-modeling matching deformations of macroscopic samples measured experimentally. Although studies of sclera microstructure show collagen fiber interweaving, current models do not account for this interweaving or the resulting fiber-fiber interactions, which might affect parameter estimates. Our goal was to test the hypothesis that constitutive parameters estimated using inverse modeling differ if models account for fiber interweaving and interactions. We developed models with non-interweaving or interweaving fibers over a wide range of volume fractions (36-91%). For each model, we estimated fiber stiffness using inverse modeling matching biaxial experimental data of human sclera. We found that interweaving increased the estimated fiber stiffness. When the collagen volume fraction was 64% or less, the stiffness of interweaving fibers was about 1.25 times that of non-interweaving fibers. For higher volume fractions, the ratio increased substantially, reaching 1.88 for a collagen volume fraction of 91%. Simulating a model (interweaving/non-interweaving) using the fiber stiffness estimated from the other model produced substantially different behavior, far from that observed experimentally. These results show that estimating microstructural component mechanical properties is highly sensitive to the assumed interwoven/non-interwoven architecture. Moreover, the results suggest that interweaving plays an important role in determining the structural stiffness of sclera, and potentially of other soft tissues in which the collagen fibers interweave. STATEMENT OF SIGNIFICANCE: The collagen fibers of sclera are interwoven, but numerical models do not account for this interweaving or the resulting fiber-fiber interactions. To determine if interweaving matters, we examined the differences in the constitutive model parameters estimated using inverse modeling between models with interweaving and non-interweaving fibers. We found that the estimated stiffness of the interweaving fibers was up to 1.88 times that of non-interweaving fibers, and that the estimate increased with collagen volume fraction. Our results suggest that fiber interweaving is a fundamental characteristic of connective tissues, additional to anisotropy, density and orientation. Better characterization of interweaving, and of its mechanical effects is likely central to understanding microstructure and biomechanics of sclera and other soft tissues.

The Effects of Glaucoma on the Pressure-Induced Strain Response of the Human Lamina Cribrosa

Purpose

To measure the ex vivo pressure-induced strain response of the human optic nerve head and analyze for variations with glaucoma diagnosis and optic nerve axon damage.

Methods

The posterior sclera of 16 eyes from 8 diagnosed glaucoma donors and 10 eyes from 6 donors with no history of glaucoma were inflation tested between 5 and 45 mm Hg. The optic nerve from each donor was examined for degree of axon loss. The posterior volume of the lamina cribrosa (LC) was imaged with second harmonic generation and analyzed using volume correlation to calculate LC strains between 5 and 10 and 5 and 45 mm Hg.

Results

Eye length and LC area were larger in eyes diagnosed with glaucoma (P≤ 0.03). Nasal-temporal E_XX and circumferential E_θθ strains were lower in the LC of diagnosed glaucoma eyes at 10 mm Hg (P≤ 0.05) and 45 mm Hg (P≤ 0.07). E_XX was smaller in the LC of glaucoma eyes with <25% axon loss compared with undamaged normal eyes (P = 0.01, 45 mm Hg). In general, the strains were larger in the peripheral than central LC. The ratio of the maximum principal strain E_max in the peripheral to central LC was larger in glaucoma eyes with >25% axon loss than in glaucoma eyes with milder damage (P = 0.004, 10 mm Hg).

Conclusions

The stiffness of the LC pressure-strain response was greater in diagnosed glaucoma eyes and varied with glaucomatous axon damage. Lower LC strains in glaucoma eyes with milder damage may represent baseline biomechanical behavior that contributes to axon loss, whereas greater LC strain and altered radial LC strain variation in glaucoma eyes with more severe damage may be caused by glaucoma-related remodeling.

Role of radially aligned scleral collagen fibers in optic nerve head biomechanics

Collagen fibers organized circumferentially around the canal in the peripapillary sclera are thought to provide biomechanical support to the sensitive tissues within the optic nerve head (ONH). Recent studies have demonstrated the existence of a family of fibers in the innermost sclera organized radially from the scleral canal. Our goal was to determine the role of these radial fibers in the sensitivity of scleral canal biomechanics to acute increases in intraocular pressure (IOP). Following the same general approach of previous parametric sensitivity studies, we created nonlinear generic finite element models of a posterior pole with various combinations of radial and circumferential fibers at an IOP of 0 mmHg. We then simulated the effects of normal and elevated IOP levels (15 and 30 mmHg). We monitored four IOP-induced geometric changes: peripapillary sclera stretch, scleral canal displacement, lamina cribrosa displacement, and scleral canal expansion. In addition, we examined the radial (maximum tension) and through-thickness (maximum compression) strains within the ONH tissues. Our models predicted that: 1) radial fibers reduced the posterior displacement of the lamina, especially at elevated IOP; 2) radial fibers reduced IOP-induced radial strain within the peripapillary sclera and retinal tissue; and 3) a combination of radial and circumferential fibers maintained strains within the ONH at a level similar to those conferred by circumferential fibers alone. In conclusion, radial fibers provide support for the posterior globe, additional to that provided by circumferential fibers. Most importantly, a combination of both fiber families can better protect ONH tissues from excessive IOP-induced deformation than either alone.

A Mesh-Free Approach to Incorporate Complex Anisotropic and Heterogeneous Material Properties into Eye-Specific Finite Element Models

Commercial finite element modeling packages do not have the tools necessary to effectively incorporate the complex anisotropic and heterogeneous material properties typical of the biological tissues of the eye. We propose a mesh-free approach to incorporate realistic material properties into finite element models of individual human eyes. The method is based on the idea that material parameters can be estimated or measured at so called control points, which are arbitrary and independent of the finite element mesh. The mesh-free approach approximates the heterogeneous material parameters at the Gauss points of each finite element while the boundary value problem is solved using the standard finite element method. The proposed method was applied to an eye-specific model a human posterior pole and optic nerve head. We demonstrate that the method can be used to effectively incorporate experimental measurements of the lamina cribrosa micro-structure into the eye-specific model. It was convenient to define characteristic material orientations at the anterior and posterior scleral surface based on the eye-specific geometry of each sclera. The mesh-free approach was effective in approximating these characteristic material directions with smooth transitions across the sclera. For the first time, the method enabled the incorporation of the complex collagen architecture of the peripapillary sclera into an eye-specific model including the recently discovered meridional fibers at the anterior surface and the depth dependent width of circumferential fibers around the scleral canal. The model results suggest that disregarding the meridional fiber region may lead to an underestimation of local strain concentrations in the retina. The proposed approach should simplify future studies that aim to investigate collagen remodeling in the sclera and optic nerve head or in other biological tissues with similar challenges.

Characterizing the Collagen Network Structure and Pressure-Induced Strains of the Human Lamina Cribrosa

Purpose

The purpose of this study was to measure the 2D collagen network structure of the human lamina cribrosa (LC), analyze for the correlations with age, region, and LC size, as well as the correlations with pressure-induced strains.

Methods

The posterior scleral cups of 10 enucleated human eyes with no known ocular disease were subjected to ex vivo inflation testing from 5 to 45 mm Hg. The optic nerve head was imaged by using second harmonic generation imaging (SHG) to identify the LC collagen structure at both pressures. Displacements and strains were calculated by using digital volume correlation of the SHG volumes. Nine structural features were measured by using a custom Matlab image analysis program, including the pore area fraction, node density, and beam connectivity, tortuosity, and anisotropy.

Results

All strain measures increased significantly with higher pore area fraction, and all but the radial-circumferential shear strain (E_rθ) decreased with higher node density. The maximum principal strain (E_max) and maximum shear strain (Γ_max) also increased with larger beam aspect ratio and tortuosity, respectively, and decreased with higher connectivity. The peripheral regions had lower node density and connectivity, and higher pore area fraction, tortuosity, and strains (except for E_rθ) than the central regions. The peripheral nasal region had the lowest E_max, Γ_max, radial strain, and pore area fraction.

Conclusions

Features of LC beam network microstructure that are indicative of greater collagen density and connectivity are associated with lower pressure-induced LC strain, potentially contributing to resistance to glaucomatous damage.

Scleral structure and biomechanics

As the eye's main load-bearing connective tissue, the sclera is centrally important to vision. In addition to cooperatively maintaining refractive status with the cornea, the sclera must also provide stable mechanical support to vulnerable internal ocular structures such as the retina and optic nerve head. Moreover, it must achieve this under complex, dynamic loading conditions imposed by eye movements and fluid pressures. Recent years have seen significant advances in our knowledge of scleral biomechanics, its modulation with ageing and disease, and their relationship to the hierarchical structure of the collagen-rich scleral extracellular matrix (ECM) and its resident cells. This review focuses on notable recent structural and biomechanical studies, setting their findings in the context of the wider scleral literature. It reviews recent progress in the development of scattering and bioimaging methods to resolve scleral ECM structure at multiple scales. In vivo and ex vivo experimental methods to characterise scleral biomechanics are explored, along with computational techniques that combine structural and biomechanical data to simulate ocular behaviour and extract tissue material properties. Studies into alterations of scleral structure and biomechanics in myopia and glaucoma are presented, and their results reconciled with associated findings on changes in the ageing eye. Finally, new developments in scleral surgery and emerging minimally invasive therapies are highlighted that could offer new hope in the fight against escalating scleral-related vision disorder worldwide.

Application of multiphoton imaging and machine learning to lymphedema tissue analysis

The results of in-vivo two-photon imaging of lymphedema tissue are presented. The study involved 36 image samples from II stage lymphedema patients and 42 image samples from healthy volunteers. The papillary layer of the skin with a penetration depth of about 100 μm was examined. Both the collagen network disorganization and increase of the collagen/elastin ratio in lymphedema tissue, characterizing the severity of fibrosis, was observed. Various methods of image characterization, including edge detectors, a histogram of oriented gradients method, and a predictive model for diagnosis using machine learning, were used. The classification by "ensemble learning" provided 96% accuracy in validating the data from the testing set.

Analysis of Collagen Spatial Structure Using Multiphoton Microscopy and Machine Learning Methods

Pathogenesis of many diseases is associated with changes in the collagen spatial structure. Traditionally, the 3D structure of collagen in biological tissues is analyzed using histochemistry, immunohistochemistry, magnetic resonance imaging, and X-radiography. At present, multiphoton microscopy (MPM) is commonly used to study the structure of biological tissues. MPM has a high spatial resolution comparable to histological analysis and can be used for direct visualization of collagen spatial structure. Because of a large volume of data accumulated due to the high spatial resolution of MPM, special analytical methods should be used for identification of informative features in the images and quantitative evaluation of relationship between these features and pathological processes resulting in the destruction of collagen structure. Here, we describe current approaches and achievements in the identification of informative features in the MPM images of collagen in biological tissues, as well as the development on this basis of algorithms for computer-aided classification of collagen structures using machine learning as a type of artificial intelligence methods.

Radial and Circumferential Collagen Fibers Are a Feature of the Peripapillary Sclera of Human, Monkey, Pig, Cow, Goat, and Sheep

Purpose

To test the hypothesis that human, monkey, pig, sheep, cow, and goat eyes exhibit circumferential, radial, and interweaving collagen architecture in the posterior sclera.

Methods

We analyzed 1,327 cryosections from the posterior poles of 4 human, 4 monkey, 5 pig, 8 sheep, 1 goat, and 2 cow eyes. Images were acquired using polarized light microscopy and processed to obtain polar fiber orientations relative to the center of the canal. Circumferential, radial, and interweaving regions were identified and analyzed for mean fiber orientation and anisotropy and region width and thickness.

Results

Every eye exhibited circumferential, radial, and interweaving fibers in consistent locations. Radial fibers extended out from near the canal into the peripapillary and peripheral sclera in the innermost sclera. Circumferential fibers were directly adjacent to the canal and most prevalent in the outermost, posterior sclera. Interweaving fibers were found throughout the sclera thickness. Across all species, median anisotropy in the radial, circumferential, and interweaving regions were 0.95, 0.96, and 0.28, respectively.

Conclusions

Regions of radial, circumferential, and interweaving fibers occur in the posterior pole sclera of human, monkey, pig, sheep, cow, and goat eyes. The consistency across species in scleral architecture suggests that they are primary organizational components whose functions should be better understood.

Quantification of collagen fiber structure using second harmonic generation imaging and two-dimensional discrete Fourier transform analysis: Application to the human optic nerve head

Second harmonic generation (SHG) microscopy is widely used to image collagen fiber microarchitecture due to its high spatial resolution, optical sectioning capabilities and relatively nondestructive sample preparation. Quantification of SHG images requires sensitive methods to capture fiber alignment. This article presents a two-dimensional discrete Fourier transform (DFT)-based method for collagen fiber structure analysis from SHG images. The method includes integrated periodicity plus smooth image decomposition for correction of DFT edge discontinuity artefact, avoiding the loss of peripheral image data encountered with more commonly used windowing methods. Outputted parameters are as follows: the collagen fiber orientation distribution, aligned collagen content and the degree of collagen fiber dispersion along the principal orientation. We demonstrate its application to determine collagen microstructure in the human optic nerve head, showing its capability to accurately capture characteristic structural features including radial fiber alignment in the innermost layers of the bounding sclera and a circumferential collagen ring in the mid-stromal tissue. Higher spatial resolution rendering of individual lamina cribrosa beams within the nerve head is also demonstrated. Validation of the method is provided in the form of correlative results from wide-angle X-ray scattering and application of the presented method to other fibrous tissues.

Thin Lamina Cribrosa Beams Have Different Collagen Microstructure Than Thick Beams

Purpose

To compare the collagen microstructural crimp characteristics between thin and thick lamina cribrosa (LC) beams.

Methods

Seven eyes from four sheep were fixed at 5 mm Hg IOP in 10% formalin. For each eye, one to three coronal cryosections through the LC were imaged with polarized light microscopy and analyzed to visualize the LC and determine collagen fiber microstructure. For every beam, we measured its width and three characteristics of the crimp of its collagen fibers: waviness, tortuosity, and amplitude. Linear mixed effects models were used to test whether crimp characteristics were associated with the LC beam width.

Results

For each eye and over all the eyes, LC beam width was positively associated with crimp waviness and tortuosity, and negatively associated with crimp amplitude (P's < 0.0001). Thin beams, average width 13.11 μm, had average (SD) waviness, tortuosity, and amplitude of 0.27 (0.17) radians, 1.017 (0.028) and 1.88 (1.41) μm, respectively. For thick beams, average width 26.10 μm, these characteristics were 0.33 (0.18) radians, 1.025 (0.037) and 1.58 (1.36) μm, respectively.

Conclusions

Our results suggest heterogeneity in LC beam mechanical properties. Thin beams were less wavy than their thicker counterparts, suggesting that thin beams may stiffen at lower IOP than thick beams. This difference may allow thin beams to support similar amounts of IOP-induced force as thicker beams, thus providing a similar level of structural support to the axons at physiologic IOP, despite the differences in width. Measurements of beam-level mechanical properties are needed to confirm these predictions.

Spatial Patterns and Age-Related Changes of the Collagen Crimp in the Human Cornea and Sclera

Purpose

Collagen is the main load-bearing component of the eye, and collagen crimp is a critical determinant of tissue mechanical behavior. We test the hypothesis that collagen crimp morphology varies over the human cornea and sclera and with age.

Methods

We analyzed 42 axial whole-globe sections from 20 normal eyes of 20 human donors, ranging in age from 0.08 (1 month) to 97 years. The sections were imaged using polarized light microscopy to obtain μm-scale fiber bundle/lamellae orientation from two corneal and six scleral regions. Crimp morphology was quantified through waviness, tortuosity, and amplitude.

Results

Whole-globe median waviness, tortuosity, and amplitude were 0.127 radians, 1.002, and 0.273 μm, respectively. These parameters, however, were not uniform over the globe, instead exhibiting distinct, consistent patterns. All crimp parameters decreased significantly with age, with significantly different age-related decreases between regions. The crimp morphology of the limbus changed the most drastically with age, such that it had the largest crimp in neonates, and among the smallest in the elderly.

Conclusions

Age-related decreases in crimp parameters are likely one of the mechanisms underlying age-related stiffening of the sclera and cornea, potentially influencing sensitivity to IOP. Further work is needed to determine the biomechanical implications of the crimp patterns observed. The comparatively large changes in the crimp morphology of the limbus, especially in the early years of life, suggest that crimp in this region may play a role in eye development, although the exact nature of this is unclear.

Optical phantoms for biomedical polarimetry: a review

Calibration, quantification, and standardization of the polarimetric instrumentation, as well as interpretation and understanding of the obtained data, require the development and use of well-calibrated phantoms and standards. We reviewed the status of tissue phantoms for a variety of applications in polarimetry; more than 500 papers are considered. We divided the phantoms into five groups according to their origin (biological/nonbiological) and fundamental polarimetric properties of retardation, depolarization, and diattenuation. We found that, while biological media are generally depolarizing, retarding, and diattenuating, only one of all the phantoms reviewed incorporated all these properties, and few considered at least combined retardation and depolarization. Samples derived from biological tissue, such as tendon and muscle, remain extremely popular to quickly ascertain a polarimetric system, but do not provide quantifiable results aside from relative direction of their principal optical axis. Microspheres suspensions are the most utilized phantoms for depolarization, and combined with theoretical models can offer true quantification of depolarization or degree of polarization. There is a real paucity of birefringent phantoms despite the retardance being one of the most interesting parameters measurable with polarization techniques. Therefore, future work should be directed at generating truly reliable and repeatable phantoms for this metric determination. Diattenuating phantoms are rare and application-specific. Given that diattenuation is considered to be low in most biological tissues, the lack of such phantoms is seen as less problematic. The heterogeneity of the phantoms reviewed points to a critical need for standardization in this field. Ultimately, all research groups involved in polarimetric studies and instruments development would benefit from sharing a limited set of standardized polarimetric phantoms, as is done earlier in the round robin investigations in ellipsometry.

Bulk changes in posterior scleral collagen microstructure in human high myopia

Purpose

We aimed to characterize any bulk changes in posterior scleral collagen fibril bundle architecture in human eyes with high myopia.

Methods

Wide-angle X-ray scattering (WAXS) was employed to map collagen orientation at 0.5 mm × 0.5 mm spatial intervals across the posterior sclera of seven non-myopic human eyes and three eyes with high myopia (>6D of refractive error). At each sampled point, WAXS provided thickness-averaged measures of the angular distribution of preferentially aligned collagen fibrils within the tissue plane and the anisotropic proportion (the ratio of preferentially aligned to total collagen scatter).

Results

Non-myopic specimens featured well-conserved microstructural features, including strong uniaxial collagen alignment along the extraocular muscle insertion sites of the mid-posterior sclera and a highly anisotropic annulus of collagen circumscribing the nerve head in the peripapillary sclera. All three myopic specimens exhibited notable alterations in the peripapillary sclera, including a partial loss of circumferential collagen alignment and a redistribution of the normally observed regional pattern of collagen anisotropic proportion. Linear mixed-model analysis indicated that the mean fiber angle deviation from the circumferential orientation in the peripapillary sclera of highly myopic eyes (23.9° ± 18.2) was statistically significantly higher than that of controls (17.9° ± 12.0; p<0.05).

Conclusions

Bulk alterations in the normal posterior scleral collagen microstructure occur in human eyes with high myopia. These changes could reflect remodeling of the posterior sclera during axial lengthening and/or a mechanical adaption to tissue stresses induced by fluid pressure or eye movements that may be exacerbated in enlarged eyes.

Structured polarized light microscopy for collagen fiber structure and orientation quantification in thick ocular tissues

Collagen is a major constituent of the eye and understanding its architecture and biomechanics is critical to preserve and restore vision. We, recently, demonstrated polarized light microscopy (PLM) as a powerful technique for measuring properties of the collagen fibers of the eye, such as spatial distribution and orientation. Our implementation of PLM, however, required sectioning the tissues for imaging using transmitted light. This is problematic because it limits analysis to thin sections. This is not only slow, but precludes study of dynamic events such as pressure-induced deformations, which are central to the role of collagen. We introduce structured polarized light microscopy (SPLM), an imaging technique that combines structured light illumination with PLM to allow imaging and measurement of collagen fiber properties in thick ocular tissues. Using pig and sheep eyes, we show that SPLM rejects diffuse background light effectively in thick tissues, significantly enhancing visualization of optic nerve head (ONH) structures, such as the lamina cribrosa, and improving the accuracy of the collagen fiber orientation measurements. Further, we demonstrate the integration of SPLM with an inflation device to enable direct visualization, deformation tracking, and quantification of collagen fibers in ONHs while under controlled pressure.

Peripapillary sclera architecture revisited: A tangential fiber model and its biomechanical implications

The collagen fiber architecture of the peripapillary sclera (PPS), which surrounds the scleral canal, is a critical factor in determining the mechanical response of the optic nerve head (ONH) to variations in intraocular pressure (IOP). Experimental and clinical evidence point to IOP-induced deformations within the scleral canal as important contributing factors of glaucomatous neural tissue damage and consequent vision loss. Hence, it is imperative to understand PPS architecture and biomechanics. Current consensus is that the fibers of the PPS form a closed ring around the canal to support the delicate neural tissues within. We propose an alternative fiber architecture for the PPS, in which the scleral canal is supported primarily by long-running fibers oriented tangentially to the canal. We present evidence that this tangential model is consistent with histological observations in multiple species, and with quantitative measurements of fiber orientation obtained from small angle light scattering and wide-angle X-ray scattering. Using finite element models, we investigated the biomechanical implications of a tangential fiber PPS architecture. We found that the tangential arrangement of fibers afforded better mechanical support to the tissues within the scleral canal as compared to a simple circumferential ring of fibers or a combination of fibers oriented radially and circumferentially. We also found that subtle variations from a tangential orientation could reproduce clinically observed ONH behavior which has yet to be explained using current theories of PPS architecture and simulation, namely, the contraction of the scleral canal under elevated IOP.

STATEMENT OF SIGNIFICANCE

It is hypothesized that vision loss in glaucoma is due to excessive mechanical deformation within the neural tissue inside the scleral canal. This study proposes a new model for how the collagen of the peripapillary sclera surrounding the canal is organized to support the delicate neural tissue inside. Previous low-resolution studies of the peripapillary sclera suggested that the collagen fibers are arranged in a ring around the canal. Instead, we provide microscopic evidence suggesting that the canal is also supported by long-running interwoven fibers oriented tangentially to the canal. We demonstrate that this arrangement has multiple biomechanical advantages over a circular collagen arrangement and can explain previously unexplained experimental findings including contraction of the scleral canal under elevated intraocular pressure.

Measurement of tissue optical properties in the context of tissue optical clearing

Nowadays, dynamically developing optical (photonic) technologies play an ever-increasing role in medicine. Their adequate and effective implementation in diagnostics, surgery, and therapy needs reliable data on optical properties of human tissues, including skin. This paper presents an overview of recent results on the measurements and control of tissue optical properties. The issues reported comprise a brief review of optical properties of biological tissues and efficacy of optical clearing (OC) method in application to monitoring of diabetic complications and visualization of blood vessels and microcirculation using a number of optical imaging technologies, including spectroscopic, optical coherence tomography, and polarization- and speckle-based ones. Molecular modeling of immersion OC of skin and specific technique of OC of adipose tissue by its heating and photodynamic treatment are also discussed.