Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 6, 19220

In Vivo Articular Cartilage Deformation: Noninvasive Quantification of Intratissue Strain During Joint Contact in the Human Knee


In Vivo Articular Cartilage Deformation: Noninvasive Quantification of Intratissue Strain During Joint Contact in the Human Knee

Deva D Chan et al. Sci Rep.


The in vivo measurement of articular cartilage deformation is essential to understand how mechanical forces distribute throughout the healthy tissue and change over time in the pathologic joint. Displacements or strain may serve as a functional imaging biomarker for healthy, diseased, and repaired tissues, but unfortunately intratissue cartilage deformation in vivo is largely unknown. Here, we directly quantified for the first time deformation patterns through the thickness of tibiofemoral articular cartilage in healthy human volunteers. Magnetic resonance imaging acquisitions were synchronized with physiologically relevant compressive loading and used to visualize and measure regional displacement and strain of tibiofemoral articular cartilage in a sagittal plane. We found that compression (of 1/2 body weight) applied at the foot produced a sliding, rigid-body displacement at the tibiofemoral cartilage interface, that loading generated subject- and gender-specific and regionally complex patterns of intratissue strains, and that dominant cartilage strains (approaching 12%) were in shear. Maximum principle and shear strain measures in the tibia were correlated with body mass index. Our MRI-based approach may accelerate the development of regenerative therapies for diseased or damaged cartilage, which is currently limited by the lack of reliable in vivo methods for noninvasive assessment of functional changes following treatment.


Figure 1
Figure 1. Displacements under applied loading by MRI (dualMRI) and selected techniques for hierarchical characterization of human biomechanics.
dualMRI synchronizes magnetic resonance imaging and mechanical loading to reveal intratissue strain (A). DENSE (displacement encoding by stimulated echoes) and ssFSE (single shot fast spin echo) enable tracking of the MRI phase signal before and during compressive loading applied to the foot. Medical imaging modalities, like MRI, radiography, and ultrasound, are capable of noninvasive measurement of cartilage biomechanics, and are limited ultimately by the spatial scale for acquisition (B). In contrast to other modalities, MRI allows for direct tracking of cartilage displacement and strain at a pixel-by-pixel basis at high spatial and temporal resolution.
Figure 2
Figure 2. MRI-compatible knee loading device for in vivo measurement of tissue deformation.
A loading device was manufactured to permit the cyclic loading of the leg of a human subject by a pneumatic actuator within the confines of a clinical MRI system (A). A laser displacement system, used only outside of the MRI, allowed for the measurement of leg motion across multiple loading cycles (B). Straps across the thigh and shin were used to restrict concomitant motion of the knee (flexed at ~10°) under compression, permitting a sagittal slice through the undeformed and deformed knee tissues to be imaged during cyclic loading (C). Although the cartilage can be imaged before and during loading, the measurement of nominal measures does not provide internal information, and there is insufficient image texture for digital image correlation techniques. Because dualMRI is based on phase contrast, internal displacements can be measured at each imaged pixel, providing intratissue deformations not otherwise measurable.
Figure 3
Figure 3. Displacement and strain–precision and effect of smoothing on displacement fields.
dualMRI experiments of a silicone imaging phantom were repeated at three different spatial resolutions to permit the calculation of displacement (A) and strain (B) precision. Precision improved with smoothing at all spatial resolutions but leveled off with less smoothing at coarser spatial resolutions, which also provided higher signal-to-noise ratios. Noise was added to simulated displacements of idealized cartilage-cartilage contact (C) to test the effect of smoothing in thin cartilage geometries. Displacement fields retained key features despite a general “flattening” of displacement gradients that is expected with smoothing (D).
Figure 4
Figure 4. Intratissue displacement fields in tibiofemoral articular cartilage.
dualMRI was used to measure in vivo displacements under cyclic loading and within a sagittal slice through the medial compartment of the knee (A) for a representative male subject. Displacements in the loading direction (y) and the direction transverse to loading (x) showed both rigid body displacement and intratissue deformation (B).
Figure 5
Figure 5. Complex finite strains in the load-based Cartesian coordinate system and principal directions.
After smoothing of displacement fields, in-plane Green-Lagrange strains (Exx, Eyy, Exy) could be computed at each pixel in the femoral and tibial cartilage (A). Exy was greatest at the middle of the cartilage-cartilage contact region. Computation of the principal strains (Ep1, Ep2) and maximum shear strains (Esm) for each pixel in the ROIs also showed that these values were the greatest at the middle of the cartilage-cartilage contact region (B).
Figure 6
Figure 6. Greater body mass index and estimated average cartilage stress correspond to larger strains.
BMI was linearly correlated, in the limited sample size, with contact area for all subjects (A) maximum Ep2 in the tibia of males (B) and maximum Ep1 and Esm in the tibia of females (B). Maximum Esm (A) also increased in magnitude with the average stress in the cartilage of one knee during two-legged standing, which was calculated as half the body weight divided by the estimated cartilage contact area. Solid regression line indicates p < 0.05; dashed line indicates p < 0.10.
Figure 7
Figure 7. Depth dependent strains in the femur and tibia.
Interpolated strain data show the relationship between cartilage depth and Exx (A) Eyy (B) and Exy (C) for each subject (thin lines), as well as the mean for male and female groups (thick line). These strains show a large variation among male and female subjects in Exx and Exy. Some of this variation may be explained by the differences in the tibiofemoral flexion angle of the subjects (D).
Figure 8
Figure 8. Patterns of shear strain in cartilage.
Large shear strains are generated by the contact of convex cartilage surfaces bound to rigid bony substrates (A). Volumetric strain was plotted against maximum in-plane shear strain (Exy) for each pixel in the cartilage ROIs of all subjects (B). Five different strain states of “isotropic tension,” “uniaxial tension,” “pure shear,” “uniaxial compression,” and “isotropic compression” were delineated with arrows, with the majority of the pixels more aligned with conditions of pure shear. Patterns of Exy as a function of anterior-posterior position (C) with respect to the center of the contact region (x = 0) were graphed for the femoral and tibial cartilage of male and female subjects (D).

Similar articles

See all similar articles

Cited by 26 articles

See all "Cited by" articles


    1. Grodzinsky A. J., Levenston M. E., Jin M. & Frank E. H. Cartilage tissue remodeling in response to mechanical forces. Annu Rev Biomed Eng 2, 691–713 (2000). - PubMed
    1. Guilak F. et al. The role of biomechanics and inflammation in cartilage injury and repair. Clin Orthop Relat Res. 423, 17–26 (2004). - PubMed
    1. Butler D. L., Goldstein S. A. & Guilak F. Functional tissue engineering: the role of biomechanics. J Biomech Eng 122, 570–575 (2000). - PubMed
    1. Butz K. D., Chan D. D., Nauman E. A. & Neu C. P. Stress distributions and material properties determined in articular cartilage from MRI-based finite strains. J Biomech 44, 2667–2672, 10.1016/j.jbiomech.2011.08.005 (2011). - DOI - PubMed
    1. Cao L., Guilak F. & Setton L. A. Three-dimensional finite element modeling of pericellular matrix and cell mechanics in the nucleus pulposus of the intervertebral disk based on in situ morphology. Biomech. Model. Mechan. 10, 1–10 (2011). - PMC - PubMed

Publication types