To investigate if multicompartment models provide increased sensitivity and specificity in detecting cartilage damage compared to the standard diffusion tensor (DT) model.

Cylindrical samples were drilled from human (aged 34±14y) patellae. Using a 17.6-T MRI (Bruker Advance) scanner with a 5-mm birdcage coil, the samples underwent MRI with a DTI protocol, and later histology with safranin-O staining to obtain an OA OARSI score (0=healthy to 6=bone remodelling). The DTI protocol had TR/TE=938/15.0ms, b-value=0 and 550s/mm², 6 directions, Δ=8 ms, δ=3 ms, FOV=12.8×12.8mm², slice thickness=800µm, and in plane resolution=50×100µm².

To test the potential use of multicompartent models we select 11 samples included in a previous study (Raya-2013), covering a broad range of the OARSI score (three at OARSI=0, two at OARSI=1, three at OARSI=2 and three at OARSI=3-4).

To the diffusion-weighted images we fit the three models described in figure 1. The first is the standard 6-parameter DT, which provides us with the derived metrics of mean diffusivity (MD) and fractional anisotropy (FA). The second is a 4-parameter cylindrically-symmetric DT, commonly called Zeppelin, from which MD and FA can be extracted. The third model, the 4-parameter Ball-Stick (Behrens-2003), is a multicompartment model which is often used in neuroimaging applications. In brain applications, the Ball compartment models the less anisotropic diffusion of water, which is more abundant in the extracellular space, whereas the Stick aims at capturing the more anisotropic component of diffusion ( intraaxonal diffusion). Even though the extracellular matrix in the cartilage is very different to that found in brain's white matter (e.g. cells only account for 3% of the total volume), the anisotropy induced by collagen fibers could be captured by the Stick component of the model. In this model, the Ball compartment is effectively an isotropic DT, while the Stick is a one dimensional DT.

The cartilage was then segmented on the b=0 image, and divided into two layers: the top 50% surface layer, and the bottom 50% deep layer. Averaged diffusion parameters for each model were calculated for the whole cartilage (bulk) and for the superficial and deep layers. We also investigated the correlation of the diffusion parameters with the OARSI score. Improvement of correlation is indicative of better ability to predict damage (p-value=0.05 indicates statistical significance).

Figure 2 shows the diffusivity maps from the three models, across six representative OARSI-scored samples. The first column shows the MD from the DT model, the second column shows the MD from the Zeppelin, and the third column shows the estimated diffusivity for both Ball and Stick compartments. In all samples, the DT diffusivity estimate is higher than Zeppelin's or Ball-Stick's (this is particularly visible from the diffusivity in water).

Figure 3 represents the anisotropic metric in the same samples of Fig. 2 (FA in DT and Zeppelin, and Stick volume fraction in the Ball-Stick). The simplicity of the Zeppelin and Ball-Stick benefits the fitting; the maps are clearly less noisy than those for DT.

We also fitted the models to a large ROI in the water, above the cartilage. Here, the standard DT gave an average FA of 0.043±0.018, the Zeppelin gave 0.0195±0.0124, and the Ball-Stick gave 0.004±0.008. Because of the isotropy of the water, we can deduce that the DT is more affected by SNR, hence giving the worst estimates. The estimated MD of DT was on average 1.941±0.014μm²/mm², versus 1.838±0.013 for Zeppelin and 1.846±0.024 for Ball-Stick.

In Figure 4 we compare the statistics (mean and std) of the models' parameters for the three segmentations of the cartilage. Across all OARSI grades, the bulk Zeppelin mean and variance are lowest among most entries, in both diffusivity and anisotropy. The DT and Ball-Stick are more alike in their mean estimates and variances.

Figure 5 provides the correlations of the models metrics with histology's OARSI scores. Here we see that the diffusivity correlations and significance are similar across both DT and the Zeppelin, while the Ball-Stick is only significant to the changes in the surface layer. In the anisotropy measures, however, the two new models provide more significance in the deep layer results than the DT. This is consistent with the findings in Raya-2013, which used a much larger sample size (n=43).

In this study we have shown that alternative models to DT, such as the Ball-Stick and Zeppelin, can provide more robust estimations of anisotropy. These models helped identify significant correlations with cartilage degradation that standard DT missed. These alternative models provide more robust estimation of diffusion parameters with potential application for in vivo DTI.