Appropriate Objective Functions for Quantifying Iris Mechanical Properties Using Inverse Finite Element Modeling

A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues From Digital Image Correlation Measurements

We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledge of the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on three conventional constitutive models. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling.

In vivo biomechanical assessment of iridial deformations and muscle contractions in human eyes

The iris is a muscular organ whose deformations can cause primary angle-closure glaucoma (PACG), a leading cause of blindness. PACG risk assessment does not consider iridial biomechanical factors, despite their expected influence on iris deformations. Here, we exploited an existing biometric dataset consisting of near-infrared movies acquired during the pupillary light reflex (PLR) as a unique resource to study iris biomechanics. The PLR caused significant (greater than 100%) and essentially spatially uniform radial strains in the iris in vivo, consistent with previous findings. Inverse finite-element modelling showed that sphincter muscle tractions were ca fivefold greater than iridial stroma stiffness (range 4- to 13-fold, depending on sphincter muscle size). This muscle traction is greater than has been previously estimated, which may be due to methodological differences and/or to different patient populations in our study (European descent) versus previous studies (Asian); the latter possibility is of particular interest due to differential incidence rates of PACG in these populations. Our methodology is fast and inexpensive and may be a useful tool in understanding biomechanical factors contributing to PACG.

Three-dimensional topographic changes of anterior chamber depth following phacoemulsification with intraocular lens implantation in cataract patients

PURPOSE

To investigate the three-dimensional topographic changes of anterior chamber depth (ACD) following cataract surgery.

METHODS

Seventy-eight eyes with age-related cataract undergoing phacoemulsification and intraocular lens (IOL) implantation were retrospectively enrolled. Participants were evaluated with Pentacam for ACD topography before and approximately four weeks after the surgery. The absolute changes of ACD (AACD) and the relative changes of ACD (RACD) topography were calculated, and three-dimensional topographic contours were plotted. The influence of age, gender, distance to corneal apex (DCA), temporal-nasal and superior-inferior on AACD and RACD was analyzed.

RESULTS

Both AACD and RACD were negatively correlated with the DCA (p < 0.001; p < 0.001) and positively correlated with the age at all DCA (p < 0.05 for all the analyses). Significantly greater AACD and RACD were observed in female subjects (p < 0.05, respectively, at all DCA). AACD was significantly larger in the temporal compared with the nasal region (p < 0.001) and at the superior compared with the inferior region (p < 0.001), but not RACD. Subgroup analysis indicated that the significant difference of the AACD between the temporal and nasal regions was manifested at the DCA of more than 6 mm (p < 0.001), and the difference between the superior and inferior regions was observed at 2 mm DCA for both AACD (p < 0.001) and RACD (p = 0.001).

CONCLUSIONS

We depicted the topographic changes of ACD following cataract surgery and found that it was significantly influenced by age, gender, DCA and quadrant location. The research provided the basis for including postoperative ACD topography prediction before cataract surgery in the future.

Changes in Iris Stiffness and Permeability in Primary Angle Closure Glaucoma

Purpose

To evaluate the biomechanical properties of the iris by evaluating iris movement during pupil constriction and to compare such properties between healthy and primary angle-closure glaucoma (PACG) subjects.

Methods

A total of 140 subjects were recruited for this study. In a dark room, the anterior segments of one eye per subject were scanned using anterior segment optical coherence tomography imaging during induced pupil constriction with an external white light source of 1700 lux. Using a custom segmentation code, we automatically isolated the iris segments from the AS-OCT images, which were then discretized and transformed into a three-dimensional point cloud. For each iris, a finite element (FE) mesh was constructed from the point cloud, and an inverse FE simulation was performed to match the clinically observed iris constriction in the AS-OCT images. Through this optimization process, we were able to identify the elastic modulus and permeability of each iris.

Results

For all 140 subjects (95 healthy and 45 PACG of Indian/Chinese ethnicity; age 60.2 ± 8.7 for PACG subjects and 57.7 ± 10.1 for healthy subjects), the simulated deformation pattern of the iris during pupil constriction matched well with OCT images. We found that the iris stiffness was higher in PACG than in healthy controls (24.5 ± 8.4 kPa vs. 17.1 ± 6.6 kPa with 40 kPa of active stress specified in the sphincter region; P < 0.001), whereas iris permeability was lower (0.41 ± 0.2 mm2/kPa s vs. 0.55 ± 0.2 mm2/kPa s; p = 0.142).

Conclusions

This study suggests that the biomechanical properties of the iris in PACG are different from those in healthy controls. An improved understanding of the biomechanical behavior of the iris may have implications for the understanding and management of angle-closure glaucoma.

Quantification of iris elasticity using acoustic radiation force optical coherence elastography

Careful quantification of the changes in biomechanical properties of the iris can offer insight into the pathophysiology of some ocular diseases. However, to date there has not been much information available regarding this subject because clinical detection for iris elasticity remains challenging. To overcome this limitation, we explore, for the first time to our knowledge, the potential of measuring iris elasticity using acoustic radiation force optical coherence elastography (ARF-OCE). The resulting images and shear wave propagation, as well as the corresponding shear modulus and Young's modulus from ex vivo and in vivo rabbit models confirmed the feasibility of this method. With features of noninvasive imaging, micrometer-scale resolution, high acquisition speed and real-time processing, ARF-OCE is a promising method for reconstruction of iris elasticity and may have great potential to be applied in clinical ophthalmology with further refinement.

Iris stromal cell nuclei deform to more elongated shapes during pharmacologically-induced miosis and mydriasis

Nuclear shape alteration in ocular tissues, which can be used as a metric for overall cell deformation, may also lead to changes in gene expression and protein synthesis that could affect the biomechanics of the tissue extracellular matrix. The biomechanics of iris tissue is of particular interest in the study of primary angle-closure glaucoma. As the first step towards understanding the mutual role of the biomechanics and deformation of the iris on the activity of its constituent stromal cells, we conducted an ex-vivo study in freshly excised porcine eyes. Iris deformation was achieved by activating the constituent smooth muscles of the iris. Pupillary responses were initiated by inducing miosis and mydriasis, and the irides were placed in a fixative, bisected, and sliced into thin sections in a nasal and temporal horizontal orientation. The tissue sections were stained with DAPI for nucleus, and z-stacks were acquired using confocal microscopy. Images were analyzed to determine the nuclear aspect ratio (NAR) using both three-dimensional (3D) reconstructions of the nuclear surfaces as well as projections of the same 3D reconstruction into flat two-dimensional (2D) shapes. We observed that regardless of the calculation method (i.e., one that employed 3D surface reconstructions versus one that employed 2D projected images) the NAR increased in both the miosis group and the mydriasis group. Three-dimensional quantifications showed that NAR increased from 2.52 ± 0.96 in control group to 2.80 ± 0.81 and 2.74 ± 0.94 in the mydriasis and miosis groups, respectively. Notwithstanding the relative convenience in calculating the NAR using the 2D projected images, the 3D reconstructions were found to generate more physiologically realistic values and, thus, can be used in the development of future computational models to study primary angle-closure glaucoma. Since the iris undergoes large deformations in response to ambient light, this study suggests that the iris stromal cells are subjected to a biomechanically active micro-environment during their in-vivo physiological function.

Manifold learning based data-driven modeling for soft biological tissues

Data-driven modeling directly utilizes experimental data with machine learning techniques to predict a material's response without the necessity of using phenomenological constitutive models. Although data-driven modeling presents a promising new approach, it has yet to be extended to the modeling of large-deformation biological tissues. Herein, we extend our recent local convexity data-driven (LCDD) framework (He and Chen, 2020) to model the mechanical response of a porcine heart mitral valve posterior leaflet. The predictability of the LCDD framework by using various combinations of biaxial and pure shear training protocols are investigated, and its effectiveness is compared with a full structural, phenomenological model modified from Zhang et al. (2016) and a continuum phenomenological Fung-type model (Tong and Fung, 1976). We show that the predictivity of the proposed LCDD nonlinear solver is generally less sensitive to the type of loading protocols (biaxial and pure shear) used in the data set, while more sensitive to the insufficient coverage of the experimental data when compared to the predictivity of the two selected phenomenological models. While no pre-defined functional form in the material model is necessary in LCDD, this study reinstates the importance of having sufficiently rich data coverage in the date-driven and machine learning type of approaches. It is also shown that the proposed LCDD method is an enhancement over the earlier distance-minimization data-driven (DMDD) against noisy data. This study demonstrates that when sufficient data is available, data-driven computing can be an alternative method for modeling complex biological materials.

A computational multi-scale approach to investigate mechanically-induced changes in tricuspid valve anterior leaflet microstructure

The tricuspid valve is an atrioventricular valve that prevents blood backflow from the right ventricle into the right atrium during ventricular contractions. It is important to study mechanically induced microstructural alterations in the tricuspid valve leaflets, as this aids both in understanding valvular diseases and in the development of new engineered tissue replacements. The structure and composition of the extracellular matrix (ECM) fiber networks are closely tied to an overall biomechanical function of the tricuspid valve. In this study, we conducted experiments and implemented a multiscale modeling approach to predict ECM microstructural changes to tissue-level mechanical responses in a controlled loading environment. In particular, we characterized a sample of a porcine anterior leaflet at a macroscale using a biaxial mechanical testing method. We then generated a three-dimensional finite element model, to which computational representations of corresponding fiber networks were incorporated based on properties of the microstructural architecture obtained from small angle light scattering. Using five different biaxial boundary conditions, we performed iterative simulations to obtain model parameters with an overall R² value of 0.93. We observed that mechanical loading could markedly alter the underlying ECM architecture. For example, a relatively isotropic fiber network (with an anisotropy index value α of 28%) became noticeably more anisotropic (with an α of 40%) when it underwent mechanical loading. We also observed that the mechanical strain was distributed in a different manner at the ECM/fiber level as compared to the tissue level. The approach presented in this study has the potential to be implemented in pathophysiologically altered biomechanical and structural conditions and to bring insights into the mechanobiology of the tricuspid valve. STATEMENT OF SIGNIFICANCE: Quantifying abnormal cellar/ECM-level deformation of tricuspid valve leaflets subjected to a modified loading environment is of great importance, as it is believed to be linked to valvular remodeling responses. For example, developing surgical procedures or engineered tissue replacements that maintain/mimic ECM-level mechanical homeostasis could lead to more durable outcomes. To quantify leaflet deformation, we built a multiscale framework encompassing the contributions of disorganized ECM components and organized fibers, which can predict the behavior of the tricuspid valve leaflets under physiological loading conditions both at the tissue level and at the ECM level. In addition to future in-depth studies of tricuspid valve pathologies, our model can be used to characterize tissues in other valves of the heart.