Compensation method for obtaining accurate, sub-micrometer displacement measurements of immersed specimens using electronic speckle interferometry

Effect of different preconditioning protocols on the viscoelastic inflation response of the posterior sclera

Preconditioning by repeated cyclic loads is routinely used in ex vivo mechanical testing of soft biological tissues. The goal of preconditioning is to achieve a steady and repeatable mechanical response and to measure material properties that are representative of the in vivo condition. Preconditioning protocols vary across studies, and their effect on the viscoelastic response of tested soft tissue is typically not reported or analyzed. We propose a methodology to systematically analyze the preconditioning process with application to inflation testing. We investigated the effect of preconditioning on the viscoelastic inflation response of tree shrew posterior sclera using two preconditioning protocols: (i) continuous cyclic loading-unloading without rest and (ii) cyclic loading-unloading with 15-min rest between cycles. Posterior scleral surface strain was measured using three-dimensional Digital Image Correlation (3D-DIC). We used five variables of characterizing features of the stress-strain loop curve to compare the two preconditioning protocols. Our results showed protocol-dependent differences in the tissue response during preconditioning and at the preconditioned state. Incorporating a resting time between preconditioning cycles significantly decreased the number of cycles (10.5 ± 2.9 cycles vs. 3.1 ± 0.5 cycles, p < 0.001) but increased the total time (15.8 ± 4.4 min vs. 51.2 ± 8.3 min, p < 0.001) needed to reach preconditioned state. At the preconditioned state, 2 of 5 characteristic variables differed significantly between protocols: hysteresis loop area (difference=0.023 kJ/m³, p = 0.0020) and elastic modulus at high IOPs (difference=24.0 MPa, p = 0.0238). Our results suggest that the analysis of the preconditioning process is an essential part of inflation experiments and a prerequisite to properly characterize the tissue viscoelastic response. Furthermore, material properties obtained at the preconditioned state can be impacted by the resting time used during preconditioning and may not be directly compared across studies if the resting time varies by 15 min between studies. STATEMENT OF SIGNIFICANCE: Although applying a preconditioning protocol by repeated cyclic loads is common practice in ex vivo mechanical characterization of soft tissues, the tissue response is typically not reported or analyzed, and the protocol's potential effect on the response remains unclear. This is partially caused by lack of a standardized methodology to precondition soft tissues. We present the first systematic analysis of two representative preconditioning protocols used during inflation testing in ocular biomechanics. Our results show protocol-dependent differences in the viscoelastic response during the preconditioning process and at the preconditioned state. Consequently, the analysis of the preconditioning response represents an essential part of mechanical testing and a prerequisite to properly characterize the tissue viscoelastic response. The effect of preconditioning on the preconditioned state response must be considered when comparing results across studies with different preconditioning protocols.

Full-field displacement measurement of corneoscleral shells by combining multi-camera speckle interferometry with 3D shape reconstruction

Changes in the biomechanical properties of the connective tissue of the eye occur with age and underlie the development of several ocular diseases, such as glaucoma, myopia, and keratoconus. The biomechanical dynamics of ocular connective tissue are measured by ex vivo inflation testing, in which intraocular pressure (IOP) is varied and optical methods are used to produce maps of corneal and scleral displacement. Current optical methods are limited by acquisition rate, occlusions, poor spatial resolution, and insufficient 3D mapping. We developed an interferometric optical method integrates four-camera electronic speckle pattern interferometry (ESPI) and a novel three-dimensional (3D) shape reconstruction process to measure shape and full-field mechanical deformations of corneal and scleral shells during ex vivo inflation testing. Each camera provides accurate measurements of the laser beam phase related to deformations of the specimen surface; a multi-view stereovision method generates the shape of the specimen and a functional form that links every pixel of a given camera to 3D points on the specimen's visible surface. In this way, dynamic deformations of the specimen are localized, with quantification of the time-dependent 3D displacements of the specimen at nanometric accuracy. The ESPI-3D system is suitable for analyzing scleral deformation and morphological changes caused by time-varying IOP.

The Relationship Between Scleral Strain Change and Differential Cumulative Intraocular Pressure Exposure in the Nonhuman Primate Chronic Ocular Hypertension Model

Purpose

To determine the relationship between peripapillary scleral strain change and cumulative differential IOP exposure in nonhuman primates (NHPs) with unilateral chronic ocular hypertension.

Methods

Posterior scleral shells from 6 bilaterally normal and 10 unilateral chronic ocular hypertension NHPs were pressurized from 5 to 45 mm Hg, and the resulting full-field, three-dimensional, scleral surface deformations were acquired using laser speckle interferometry. Scleral tensile strain (local tissue deformation) was calculated by analytical differentiation of the displacement field; zero strain was assumed at 5 mm Hg. Maximum principal strain was used to represent the scleral strain, and strains were averaged over a 15°-wide (∼3.6-mm) circumpapillary region adjacent to the ONH. The relative difference in mean strain was calculated between fellow eyes and compared with the differential cumulative IOP exposure within NHPs during the study period. The relationship between the relative difference in scleral strain and the differential cumulative IOP exposure in fellow eyes was assessed using an F test and quadratic regression model.

Results

Relative differential scleral tensile strain was significantly associated with differential cumulative IOP exposure in contralateral eyes in the chronic ocular hypertension NHPs, with the bilaterally normal NHPs showing no significant strain difference between fellow eyes. The sclera in the chronic ocular hypertension eyes was more compliant than in their fellow eyes at low levels of differential cumulative IOP exposure, but stiffer at larger differential IOPs (P < 0.0001).

Conclusions

These cross-sectional findings suggest that longitudinal IOP-induced changes in scleral mechanical behavior are dependent on the magnitude of differential cumulative IOP exposure.

Bayesian Semiparametric Functional Mixed Models for Serially Correlated Functional Data, with Application to Glaucoma Data

Glaucoma, a leading cause of blindness, is characterized by optic nerve damage related to intraocular pressure (IOP), but its full etiology is unknown. Researchers at UAB have devised a custom device to measure scleral strain continuously around the eye under fixed levels of IOP, which here is used to assess how strain varies around the posterior pole, with IOP, and across glaucoma risk factors such as age. The hypothesis is that scleral strain decreases with age, which could alter biomechanics of the optic nerve head and cause damage that could eventually lead to glaucoma. To evaluate this hypothesis, we adapted Bayesian Functional Mixed Models to model these complex data consisting of correlated functions on spherical scleral surface, with nonparametric age effects allowed to vary in magnitude and smoothness across the scleral surface, multi-level random effect functions to capture within-subject correlation, and functional growth curve terms to capture serial correlation across IOPs that can vary around the scleral surface. Our method yields fully Bayesian inference on the scleral surface or any aggregation or transformation thereof, and reveals interesting insights into the biomechanical etiology of glaucoma. The general modeling framework described is very flexible and applicable to many complex, high-dimensional functional data.

Biomechanical assessment in models of glaucomatous optic neuropathy

The biomechanical environment within the eye is of interest in both the regulation of intraocular pressure and the loss of retinal ganglion cell axons in glaucomatous optic neuropathy. Unfortunately, this environment is complex and difficult to determine. Here we provide a brief introduction to basic concepts of mechanics (stress, strain, constitutive relationships) as applied to the eye, and then describe a variety of experimental and computational approaches used to study ocular biomechanics. These include finite element modeling, direct experimental measurements of tissue displacements using optical and other techniques, direct experimental measurement of tissue microstructure, and combinations thereof. Thanks to notable technical and conceptual advances in all of these areas, we are slowly gaining a better understanding of how tissue biomechanical properties in both the anterior and posterior segments may influence the development of, and risk for, glaucomatous optic neuropathy. Although many challenging research questions remain unanswered, the potential of this body of work is exciting; projects underway include the coupling of clinical imaging with biomechanical modeling to create new diagnostic tools, development of IOP control strategies based on improved understanding the mechanobiology of the outflow tract, and attempts to develop novel biomechanically-based therapeutic strategies for preservation of vision in glaucoma.

Changing material properties of the tree shrew sclera during minus lens compensation and recovery

PURPOSE

To estimate two collagen-specific material properties (crimp angle and elastic modulus of collagen fibrils) of the remodeling tree shrew sclera during monocular -5 diopter (D) lens wear and recovery.

METHODS

Tensile tests were performed on scleral strips obtained from juvenile tree shrews exposed to three different visual conditions: normal, monocular -5 D lens wear to induce myopia, and recovery. Collagen fibrils are crimped in the unloaded sclera and uncrimp as the tissue stiffens under load. Inverse numerical analyses were performed to estimate the (unloaded) crimp angle and elastic modulus of collagen fibrils using a microstructure-based constitutive model.

RESULTS

Compared with the control eye, the crimp angle was significantly higher in the treated eye after 2 days and remained significantly higher until 21 days of lens wear (P < 0.05). The difference between the crimp angle of the treated and control eye rapidly vanished during recovery in concert with the changes in axial elongation rate. A rapid and extensive increase in the elastic modulus was seen in both eyes after starting and stopping the lens wear.

CONCLUSIONS

The estimated change in the crimp of scleral collagen fibrils is temporally associated with the change in axial elongation rate during myopia development and recovery. This finding suggests that axial elongation may be controlled by a remodeling mechanism that modulates the collagen fibril crimp. The observed binocular changes in scleral stiffness are not temporally associated with the axial elongation rate, indicating that scleral stiffening may not be causally related to myopia.

Age- and race-related differences in human scleral material properties

PURPOSE

We tested the hypothesis that there are age- and race-related differences in posterior scleral material properties, using eyes from human donors of European (20-90 years old, n = 40 eyes) and African (23-74 years old, n = 22 eyes) descent.

METHODS

Inflation tests on posterior scleral shells were performed while full-field, three-dimensional displacements were recorded using laser speckle interferometry. Scleral material properties were fit to each eye using a microstructure-based constitutive formulation that incorporates the collagen fibril crimp and the local anisotropic collagen architecture. The effects of age and race were estimated using Generalized Estimating Equations, while accounting for intradonor correlations.

RESULTS

The shear modulus significantly increased (P = 0.038) and collagen fibril crimp angle significantly decreased with age (P = 0.002). Donors of African descent exhibited a significantly higher shear modulus (P = 0.019) and showed evidence of a smaller collagen fibril crimp angle (P = 0.057) compared to donors of European descent. The in-plane strains in the peripapillary sclera were significantly lower with age (P < 0.015) and African ancestry (P < 0.015).

CONCLUSIONS

The age- and race-related differences in scleral material properties result in a loss of scleral compliance due to a higher shear stiffness and a lower level of stretch at which the collagen fibrils uncrimp. The loss of compliance should lead to larger high frequency IOP fluctuations and changes in the optic nerve head (ONH) biomechanical response in the elderly and in persons of African ancestry, and may contribute to the higher susceptibility to glaucoma in these at-risk populations.

Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent

PURPOSE

We tested the hypothesis that the variation of peripapillary scleral structural stiffness with age is different in donors of European (ED) and African (AD) descent.

METHODS

Posterior scleral shells from normal eyes from donors of European (n = 20 pairs; previously reported) and African (n = 9 pairs) descent aged 0 and 90 years old were inflation tested within 48 hours post mortem. Scleral shells were pressurized from 5 to 45 mm Hg and the full-field, 3-dimensional (3D) deformation of the outer surface was recorded at submicrometric accuracy using speckle interferometry (ESPI). Mean maximum principal (tensile) strain of the peripapillary and midperipheral regions surrounding the optic nerve head (ONH) were fit using a functional mixed effects model that accounts for intradonor variability, same-race correlation, and spatial autocorrelation to estimate the effect of race on the age-related changes in mechanical scleral strain.

RESULTS

Mechanical tensile strain significantly decreased with age in the peripapillary sclera in the African and European descent groups (P < 0.001), but the age-related stiffening was significantly greater in the African descent group (P < 0.05). Maximum principal strain in the peripapillary sclera was significantly higher than in the midperipheral sclera for both ethnic groups.

CONCLUSIONS

The sclera surrounding the ONH stiffens more rapidly with age in the African descent group compared to the European group. Stiffening of the peripapillary sclera with age may be related to the higher prevalence of glaucoma in the elderly and persons of African descent.

Age-related changes in human peripapillary scleral strain

To test the hypothesis that mechanical strain in the posterior human sclera is altered with age, 20 pairs of normal eyes from human donors aged 20 to 90 years old were inflation tested within 48-h postmortem. The intact posterior scleral shells were pressurized from 5 to 45 mmHg, while the full-field three-dimensional displacements of the scleral surface were measured using laser speckle interferometry. The full strain tensor of the outer scleral surface was calculated directly from the displacement field. Mean maximum principal (tensile) strain was computed for eight circumferential sectors (45° wide) within the peripapillary and mid-peripheral regions surrounding the optic nerve head (ONH). To estimate the age-related changes in scleral strain, results were fit using a functional mixed effects model that accounts for intradonor variability and spatial autocorrelation. Mechanical tensile strain in the peripapillary sclera is significantly higher than the strain in the sclera farther away from the ONH. Overall, strains in the peripapillary sclera decrease significantly with age. Sectorially, peripapillary scleral tensile strains in the nasal sectors are significantly higher than the temporal sectors at younger ages, but the sectorial strain pattern reverses with age, and the temporal sectors exhibited the highest tensile strains in the elderly. Overall, peripapillary scleral structural stiffness increases significantly with age. The sectorial pattern of peripapillary scleral strain reverses with age, which may predispose adjacent regions of the lamina cribrosa to biomechanical insult. The pattern and age-related changes in sectorial peripapillary scleral strain closely match those seen in disk hemorrhages and neuroretinal rim area measurement change rates reported in previous studies of normal human subjects.

Regional variations in mechanical strain in the posterior human sclera

PURPOSE

The goal of this study was to establish sectorial and regional variability in the mechanical strain of peripapillary and mid-peripheral sclera in normal eyes from elderly human donors.

METHODS

Ten pairs of normal eyes from human donors aged 57 to 90 years old were mechanically inflation-tested within 48 hours post mortem. The intact posterior scleral shells were pressurized from 5 to 45 mm Hg while the full-field three-dimensional displacements of the scleral surface were measured using laser speckle interferometry. The displacement field was fit to continuous and differentiable analytical functions, from which the full strain tensor of the outer scleral surface was calculated. Mean maximum principal (tensile) strain was computed for eight circumferential sectors (45° wide) within the peripapillary and mid-peripheral regions surrounding the optic nerve head (ONH).

RESULTS

Overall, the peripapillary sclera exhibited significantly higher tensile strain (1.2%) than mid-peripheral sclera (0.95%) for a 40 mm Hg IOP elevation (P < 0.00001). In the peripapillary region, the inferotemporal sector exhibited the highest tensile strain (1.45%) while the superior sector had the lowest (1.19%; P < 0.00001). Mid-peripheral scleral strains were lower but exhibited a similar sectorial pattern.

CONCLUSIONS

Human posterior sclera exhibits complex regional mechanical behavior in response to acute IOP elevations from 5 to 45 mm Hg. Results indicate 1) the peripapillary sclera is subjected to significantly higher tensile strain than the adjacent mid-peripheral sclera, and 2) strains are significantly higher in the temporal and inferior quadrants of the peripapillary sclera, which may contribute to the increased prevalence of glaucomatous damage associated with these regions of the ONH.