Imaging shear stress distribution and evaluating the stress concentration factor of the human eye

Quantitative polarization microscopy as a potential tool for quantification of mechanical stresses within 3D matrices

3D mechanical stresses within tissues/extracellular matrices (ECMs) play a significant role in pathological and physiological processes, making their quantification a necessary step to understand the mechanobiological phenomena. Unfortunately, it is rather challenging to quantify these 3D mechanical stresses due to the highly nonlinear and heterogeneous nature of the fibrous matrix. A number of techniques have been developed to address this challenge, including 3D traction force microscopy (TFM), micropillar devices or microparticle-based force sensors; yet, these techniques come with certain drawbacks. Here, we are presenting quantitative polarization microscopy (QPOL) as a non-invasive and label-free technique to quantify mechanical stresses in 3D matrix without a necessity to assume a matrix material model. Taking collagen as a birefringent material, we demonstrated the correlation between the retardance signals obtained by QPOL and the mechanical parameters associated with the 3D collagen hydrogel, i.e. applied external forces and maximum shear stresses. Using cantilever-collagen systems wherein cantilevers applied external loads on the collagen hydrogel, we showed that the retardance signal within loaded collagen positively correlated with the applied load. Also, the retardance signal values within the collagen hydrogel correlated with the maximum shear stress values derived from computational finite element (FE) models. Finally, we obtained the retardance signals around the spheroids of different contractility levels embedded in collagen hydrogel, and the retardance distribution around the spheroids reflected the stress distribution and applied force. This study provides the framework to use QPOL as a tool for quantification of mechanical stresses within 3D ECM. STATEMENT OF SIGNIFICANCE: Mechanical stresses within the 3D extracellular matrix play an important role during physiological and pathological processes. Quantification of such 3D forces is paramount to our understanding of such phenomena and potentially developing therapeutic interventions based on mechanobiological status of the disease. The existing approaches to quantify these 3D mechanical stresses face certain drawbacks such as high computational cost or introduce discontinuities and alteration within the natural 3D microenvironment of the cells. Here, we provide the framework to use quantitative polarization microscopy (QPOL) as an optical-based, non-invasive and computationally efficient technique to quantify the 3D mechanical stresses within the 3D matrix.

Experimental evaluation of corneal stress-optic coefficients using a pair of force test

BACKGROUND

Topography and tomography are valuable techniques for measuring the corneal shape, but they cannot directly assess its internal mechanical stresses. And nonuniform corneal stress plays a crucial biomechanical role in the progression of diseases and postoperative changes. Given the cornea's inherent transparency, analyzing corneal stresses using the photoelasticity method is highly advantageous. However, quantification of photoelasticity faces challenges in obtaining the stress-optic coefficient due to wrinkles caused by the non-spherical geometry during tensional experiments.

OBJECTIVE

In this study, we propose an innovative experimental setup aimed at generating a gradient field of simple shear stress and achieving surface flatness during corneal stretching experiments, enabling the acquisition of the stress-optic coefficient through comparison with numerical results.

METHODS

Our designed setup applies fluid pressure and force couples on the cornea. The internal fluid pressure maintains the corneal shape, preventing wrinkles, while the force couples create a stress field leading to isochromatic fringes.

RESULTS

We successfully measured the stress-optic coefficients of the porcine anisotropic cornea in ex-vivo as 1.87 × 10-9 (horizontal) and 1.97 × 10-9 (vertical) (m2/N). Each isochromatic fringe order represents a shear stress range of 6.05 × 104 Pa under a low tension.

CONCLUSIONS

This study establishes a significant connection between corneal photoelastic patterns and the quantification of corneal stress by enabling direct measurement through advanced photoelastic visualization technology for clinical applications.

Birefringent properties of the cornea measured by a Mueller type polarimeter in healthy adults and children

Mueller type polarimeter was used for in vivo measurements of the anisotropic parameters (retardation and azimuth angle) of corneas. To determine birefringence, corneal thickness was measured with a Scheimpflug camera (Corvist ST). The retardation distributions in the nasal-temporal cross-section in both children (N=7) and adults (N=38) groups occurred asymmetrical. The asymmetry in birefringence distributions was observed only in adults group. The geometrical analysis of the first order isochromes in both age groups showed the asymmetry of its shapes. The changes of symmetry in birefringent properties with age may have potential relationship with changing corneal biometry.

Comparative analysis of the corneal birefringence pattern in healthy children and adults

PURPOSE

To undertake a comparative analysis of the corneal shape, thickness and isochromatics in the eyes of children and adults in order to determine the extent of similarities and differences between the cohorts.

METHODS

The study involved 24 children (aged 8 years) and 37 young White adults (aged between 22-24 years) with no apparent or known health or ocular conditions. Measurements were made of corneal radius of curvature, both central (CCT) and paracentral (PCT) corneal thickness and intraocular pressure (IOP). Images of the isochromatics were captured using a slit lamp and a circular polarizer. The geometry of fringe I and II of the isochromatics was analysed.

RESULTS

Statistically significant differences were found between CCT and PCT in nasal and temporal regions for both the children and adult cohorts. The same trends were observed in the radii of the cornea. Statistically significant differences between side lengths and angles of isochromatic fringes were found. No differences in asymmetry of shape for fringe I between adults and children were detected; greater symmetry was seen in fringe II in children than for adults.

CONCLUSIONS

The asymmetry in corneal shape and curvature contributes to the shape of the isochromatic fringes. This is likely linked to the orientation and parameters of the collagen fibres and to the muscles' forces, and be relevant for surgical procedures such as corneal transplantation.

Photonics and fracture toughness of heterogeneous composite materials

Fracture toughness measures the resistance of a material to fracture. This fundamental property is used in diverse engineering designs including mechanical, civil, materials, electronics and chemical engineering applications. In spite of the advancements made in the past 40 years, the evaluation of this remains challenging for extremely heterogeneous materials such as composite concretes. By taking advantage of the optical properties of a thin birefringent coating on the surface of opaque, notched composite concrete beams, here we sense the evolution of the maximum shear stress distribution on the beams under loading. The location of the maximum deviator stress is tracked ahead of the crack tip on the experimental concrete samples under the ultimate load, and hence the effective crack length is characterised. Using this, the fracture toughness of a number of heterogeneous composite beams is evaluated and the results compare favourably well with other conventional methods using combined experimental and numerical/analytical approaches. Finally a new model, correlating the optically measured shear stress concentration factor and flexural strength with the fracture toughness of concretes is proposed. The current photonics-based study could be vital in evaluating the fracture toughness of even opaque and complex heterogeneous materials more effectively in future.

Corneal structure and transparency

The corneal stroma plays several pivotal roles within the eye. Optically, it is the main refracting lens and thus has to combine almost perfect transmission of visible light with precise shape, in order to focus incoming light. Furthermore, mechanically it has to be extremely tough to protect the inner contents of the eye. These functions are governed by its structure at all hierarchical levels. The basic principles of corneal structure and transparency have been known for some time, but in recent years X-ray scattering and other methods have revealed that the details of this structure are far more complex than previously thought and that the intricacy of the arrangement of the collagenous lamellae provides the shape and the mechanical properties of the tissue. At the molecular level, modern technologies and theoretical modelling have started to explain exactly how the collagen fibrils are arranged within the stromal lamellae and how proteoglycans maintain this ultrastructure. In this review we describe the current state of knowledge about the three-dimensional stromal architecture at the microscopic level, and about the control mechanisms at the nanoscopic level that lead to optical transparency.