Stress–Strain Index Map: A New Way to Represent Corneal Material Stiffness

Abstract

PurposeTo introduce a new method to map the mechanical stiffness of healthy and keratoconic corneas.MethodsNumerical modeling based on the finite element method was used to carry out inverse analysis of simulated healthy and keratoconic corneas to determine the regional variation of mechanical stiffness across the corneal surface based on established trends in collagen fibril distribution. The Stress–Strain Index (SSI), developed and validated in an earlier study and presented as a parameter that can estimate the overall stress–strain behavior of corneal tissue, was adopted in this research as a measure of corneal stiffness. The regional variation of SSI across the corneal surface was estimated using inverse analysis while referring to the common features of collagen fibrils’ distribution obtained from earlier x-ray scattering studies. Additionally, for keratoconic corneas, a method relating keratoconic cone features and cornea’s refractive power to the reduction in collagen fibril density inside the cone was implemented in the development of SSI maps. In addition to the simulated cases, the study also included two keratoconus cases, for which SSI maps were developed.ResultsSSI values varied slightly across corneal surface in the simulated healthy eyes. In contrast, both simulated and clinical keratoconic corneas demonstrated substantial reductions in SSI values inside the cone. These SSI reductions depended on the extent of the disease and increased with more considerable simulated losses in fibril density in the cone area. SSI values and their regional variation showed little change with changes in IOP, corneal thickness, and curvature.ConclusionSSI maps provide an estimation of the regional variation of biomechanical stiffness across the corneal surface. The maps could be particularly useful in keratoconic corneas, demonstrating the dependence of corneal biomechanical behavior on the tissue’s microstructure and offering a tool to fundamentally understand the mechanics of keratoconus progression in individual patients.

Long-Term Clinical Outcomes of Small-Incision Femtosecond Laser-Assisted Intracorneal Concave Lenticule Implantation in Patients with Keratoconus

“…In addition, to eliminate the influence of other factors on corneal biomechanical examination, we observed a new detection index: the SSI. Zhang et al [ 42 ] reported that changes in SSI can be used as an assessment of the effectiveness of treatment in keratoconus. Unlike other stiffness parameters, the change of SSI is not affected by bIOP or CCT and can be used to evaluate the mechanical properties of corneal tissue accurately [ 43 ].…”

In vivo Assessment of Localised Corneal Biomechanical Deterioration With Keratoconus Progression

“…This approximation, which was necessary due to the lack of complete information on the through-thickness variation in behaviour, could have influenced the model’s outputs. In the numerical modelling used to develop the SSI maps, it was assumed that the areas outside the cone in keratoconic corneas shared the same microstructure as corresponding areas in healthy corneas ( Zhang et al, 2021 ). This assumption was necessary due to the lack of methods to measure corneal microstructure in vivo and was based on evidence from two earlier studies ( Boote et al, 2003 ; Zhou et al, 2019 ).…”

“…The first study reported only small inter-individual variations in collagen fibril content in healthy corneas of up to 2.9% ( Zhou et al, 2019 ), and the second reported little variation among individuals in fibril diameter ( Dias and Ziebarth, 2013 ). Another limitation is that the validation of the mapping method relied on comparing the numerically-predicted, SSI-based deformation of the cornea along only the cornea’s principal temporal-nasal meridian to that measured clinically by the Corvis ST ( Zhang et al, 2021 ). Further, the method to relate the fibril density reduction inside the cone with the cone morphology was based on information obtained from only 7 KC corneas ( Zhou et al, 2021 ).…”

“…The development of SSI maps for individual corneas followed the method proposed by Zhang et al to convert the single SSI value obtained from the Corvis exam into a 2D map ( Zhang et al, 2021 ). In brief, the process begins by estimating three KC cone features: apex location, cone height and KC area of pathology, based on a method proposed by Eliasy et al that was later clinically validated ( Eliasy et al, 2020 ; Lopes B. et al, 2021 ).…”

“…The assumption of homogeneity embedded in the SSI development, however, can mask the localised biomechanical deterioration that takes place in KC. To solve this problem, Zhang et al proposed a method to map SSI across the cornea based on known trends in collagen fibril density distribution and how these trends change in keratoconic corneas ( Zhang et al, 2021 ). This method is of particular importance in evaluating disease progression.…”