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Research Papers

Multiscale Strain as a Predictor of Impact-Induced Fissuring in Articular Cartilage

[+] Author and Article Information
Corinne R. Henak

Meinig School of Biomedical Engineering,
Cornell University,
Ithaca, NY 14853

Lena R. Bartell

Department of Applied and Engineering Physics,
Cornell University,
Ithaca, NY 14853

Itai Cohen

Department of Physics,
Cornell University,
Ithaca, NY 14853

Lawrence J. Bonassar

Meinig School of Biomedical Engineering,
149 Weill Hall,
Cornell University,
Ithaca, NY 14853;
Sibley School of Mechanical
and Aerospace Engineering,
Cornell University,
Ithaca, NY 14853
e-mail: LB244@cornell.edu

1Present address: Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706.

2Corresponding author.

Manuscript received May 4, 2016; final manuscript received October 4, 2016; published online January 23, 2017. Assoc. Editor: Michael Detamore.

J Biomech Eng 139(3), 031004 (Jan 23, 2017) (8 pages) Paper No: BIO-16-1182; doi: 10.1115/1.4034994 History: Received May 04, 2016; Revised October 04, 2016

Mechanical damage is central to both initiation and progression of osteoarthritis (OA). However, specific causal links between mechanics and cartilage damage are incompletely understood, which results in an inability to predict failure. The lack of understanding is primarily due to the difficulty in simultaneously resolving the high rates and small length scales relevant to the problem and in correlating such measurements to the resulting fissures. This study leveraged microscopy and high-speed imaging to resolve mechanics on the previously unexamined time and length scales of interest in cartilage damage, and used those mechanics to develop predictive models. The specific objectives of this study were to: first, quantify bulk and local mechanics during impact-induced fissuring; second, develop predictive models of fissuring based on bulk mechanics and local strain; and third, evaluate the accuracy of these models in predicting fissures. To achieve these three objectives, bovine tibial cartilage was impacted using a custom spring-loaded device mounted on an inverted microscope. The occurrence of fissures was modulated by varying impact energy. For the first objective, during impact, deformation was captured at 10,000 frames per second and bulk and local mechanics were analyzed. For the second objective, data from samples impacted with a 1.2 mm diameter rod were fit to logistic regression functions, creating models of fissure probability based on bulk and local mechanics. Finally, for the third objective, data from samples impacted with a 0.8 mm diameter rod were used to test the accuracy of model predictions. This study provides a direct comparison between bulk and local mechanical thresholds for the prediction of fissures in cartilage samples, and demonstrates that local mechanics provide more accurate predictions of local failure than bulk mechanics provide. Bulk mechanics were accurate predictors of fissure for the entire sample cohort, but poor predictors of fissure for individual samples. Local strain fields were highly heterogeneous and significant differences were determined between fissured and intact samples, indicating the presence of damage thresholds. In particular, first principal strain rate and maximum shear strain were the best predictors of local failure, as determined by concordance statistics. These data provide an important step in establishing causal links between local mechanics and cartilage damage; ultimately, data such as these can be used to link macro- and micro-scale mechanics and thereby predict mechanically mediated disease on a subject-specific basis.

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Figures

Grahic Jump Location
Fig. 1

Impact device and resulting fissures. Impact was applied via a custom spring-loaded impact device, which sat on an inverted microscope (a). The amount of spring compression controlled the upper bound on the impact energy and the microscope could be used either in epifluorescence mode with a high-speed camera or in confocal mode. Images taken during impact were used to calculate force from the backplate deflection, and to calculate strain ((a), inset). To produce a wide array of fissures, two different diameter rods were used: 1.2 mm diameter (b) and 0.8 mm diameter (c). Rods were oriented longitudinally such that a circular impact was visible through the objective and the impact geometry was as consistent as possible along the third dimension (optical axis). Both rods created some small angular fissures (filled arrow heads) and delamination near the articular surface (open arrow heads). Overall, the 1.2 mm rod created fissures with smaller open area postimpact ((b), arrows) compared to open fissures postimpact in the 0.8 mm rod group ((c), box). The variation in fissures between the two rod diameters suggested that local mechanics were important in the creation of fissures because the local impact mechanics are more distinct between the two scenarios than the bulk mechanics.

Grahic Jump Location
Fig. 2

Development and assessment of logistic regression models for predicting failure in cartilage. Models were developed using data from samples impacted with the 1.2 mm diameter rod (a). For local mechanics, the temporal peak of each mechanical variable was determined at each grid point. Regions near the articular surface that were fissured and intact were used to develop logistic regression models, providing multiple data points from each sample. For bulk mechanics, a single data point was used for each sample. Models were assessed using samples impacted with the 0.8 mm diameter rod (b). The predictor variable of interest (maximum shear strain rate in this example) was fed into the logistic regression model in order to yield the probability of fissure at each location on the sample.

Grahic Jump Location
Fig. 3

In general, bulk (a) and local (b) mechanics were larger in fissured samples than in intact samples when averaged across impact energies in each group. Large differences in magnitude between bulk and local mechanics reflect heterogeneity in the local strain fields that is averaged out in bulk strain. These differences are highlighted by the shading, which shows the average bulk results for the intact and fissured samples on the local plots. Local peak strain and strain rate were about two and five times larger, respectively, than their bulk measures. In particular, peak local second principal strain (most compressive strain) was 3.5 ± 2.4 times larger than peak bulk strain (also compressive). Further, peak local second principal strain rate was 4.4 ± 1.8 times larger than peak bulk strain rate. Within bulk mechanics, strain and strain rate were significantly larger in fissured than intact samples, but there were no significant differences in force or force rate (a). Within local mechanics, first principal strain and maximum shear strain, all three strain rates, and the gradients of first principal strain and maximum shear strain were significantly larger in fissured than intact samples (b). In contrast to bulk results, wherein bulk strain is analogous to local second principal strain, local second principal strain was not significantly different between groups. Error bars = standard deviation. Symbol indicates p ≤ 0.05 for select variable.

Grahic Jump Location
Fig. 4

First principal strain for a subset of time points during impact in representative intact (a) and fissured (b) samples. In both samples, large strains were concentrated under the impact location in the most superficial 500 μm of the sample (rod shaded for clarity). Peak magnitudes were larger in the fissured sample than in the intact sample. Following impact, the intact sample had an unchanged articular surface relative to the image before impact, while a fissure was visible in the fissured sample.

Grahic Jump Location
Fig. 5

Predictions of fissures from bulk mechanics. For individual samples, many of the predictions were inaccurate, including predictions of high probability of fissure for intact samples and low probability of fissure for fissured samples. Conversely, cohort average predictions were accurate for the entire cohort as can be seen by comparing with the experimentally observed fissure rate (dashed line). Cohort average predictions were calculated by averaging each predictor for the cohort, and then predicting the probability of fissure from the average value. For example, bulk force data were first averaged across all 12 intact and fissured samples. This average force was then used as input to the regression model (Eq. (4)), which resulted in the cohort average prediction. Error bars were calculated from the average of each predictor for the cohort plus or minus one standard deviation. Predictions were developed using data from samples impacted with the 1.2 mm diameter rod and evaluated on data from samples impacted with the 0.8 mm diameter rod. (For color in this figure legend, the reader is referred to the web version of this article.)

Grahic Jump Location
Fig. 6

Concordance statistics (c-statistics) for local predictors. Grid points near the articular surface were analyzed (a): for each predictor variable, the probability of fissure was calculated (i). Grid points above a probability threshold were selected and categorized as either true positives (locations that did fissure) or false positives (locations that did not fissure) (ii). Normalized true positives were plotted against normalized false positives for all samples (iii). Steps (ii) and (iii) were repeated for all probabilities from 0.001 to 1.000 in increments of 0.001. The result from this process was the ROC curve for each predictor variable (b). The area under the ROC curve was calculated using a Riemann sum. The area under the curve is the c-statistic, and was compared between predictor variables (c). Strain and strain rate c-statistics were all ≥0.75, while strain gradient c-statistics were all <0.75. The maximum c-statistic was for first principal strain rate, while the minimum was for the gradient of second principal strain.

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