An Automated Approach for Direct Measurement of Two-Dimensional Strain Distributions Within Articular Cartilage Under Unconfined Compression

Abstract

An automated approachfor measuring in situ two-dimensional strain fields was developed and validated for its application to cartilage mechanics. This approach combines video microscopy, optimized digital image correlation (DIC), thin-plate spline smoothing (TPSS) and generalized cross-validation (GCV) techniques to achieve the desired efficiency and accuracy. Results demonstrate that sub-pixel accuracies can be achieved for measuring tissue displacements with this methodology with a measurement uncertainty ranging from 0.25 to 0.30 pixels. The deformational gradients (from which the strains are determined) can be evaluated directly using the optimized DIC, with a measurement uncertainty of 0.017 to approximately 0.032. In actual measurements of strain in cartilage, TPSS and differentiation can be used to achieve a more accurate measurement of the gradients from the displacement data. Using this automated approach, the two-dimensional strain fields inside immature bovine carpometacarpal joint cartilage specimens under unconfined compression were characterized (n=21). The depth-dependent apparent elastic modulus and Poisson's ratio were also determined and found to be smallest at the articular surface and increasing with depth. The apparent Poisson's ratio is found to decrease with increasing compressive strain, with values as low as 0.01 observed near the articular surface at 25% compression. The variation of the apparent Poisson's ratio with depth is found to be consistent with a theoretical model of cartilage which accounts for the disparity in its tensile and compressive moduli.

Heterogeneous three-dimensional strain fields during unconfined cyclic compression in bovine articular cartilage explants

“…Unlike previous 2D studies that documented strains perpendicular to the thickness direction either as generally zero [23,29] or at least an order of magnitude smaller than strains in the thickness direction [34], strains perpendicular to the thickness direction reported herein were in general large and on the same order as strains in the thickness direction. This primary difference can be attributed to the loading protocol used (i.e.…”

“…strain at equilibrium versus strain during cyclic loading). Another study reported that all strain components changed nonlinearly with increasing load [34], which is in contrast to the results reported herein for strain in the split-line and transverse directions. Further, the large strains observed were not unexpected based on rapid loading of the explants (in less than 200ms [24]) and the resulting pressure gradient in favor of interstitial fluid flow towards the outer boundary of the cylindrical cartilage samples [l].…”

“…Two-dimensional (2D) analyses employing video microscopy and image correlation techniques showed strain on the imaged (crosssectional) cartilage surface to be heterogeneous in the thickness direction. Important aspects and results of these analyses were that: (1) 2D cartilage strains were computed at equilibrium for both confined [29] and unconfined test protocols [23,36], (2) strains in the thickness direction varied as a function of depth, and (3) strains perpendicular to the thickness direction were either generally zero [23,29] or at least an order of magnitude smaller than strains in the thickness direction [34]. Based on these strain fields, it was possible to compute estimates for equilibrium moduli [28,33].…”

“…Based on these strain fields, it was possible to compute estimates for equilibrium moduli [28,33]. Also, all strain components changed nonlinearly with increasing load [34]. Additional studies note the anisotropy and depthdependent strains under applied loading [14,15,36].…”

A layered agarose approach to fabricate depth‐dependent inhomogeneity in chondrocyte‐seeded constructs

“…Due to the inhomogeneous depth-dependent properties of articular cartilage [27,32], there has been increased interest in developing methods to replicate this inhomogeneity and study its importance. A recently developed K. W. Ng et ul.…”