Classification of degraded cartilage through multiparametric MRI analysis

Abstract

MRI analysis of cartilage matrix may play an important role in early detection and development of therapeutic protocols for degenerative joint disease. Correlations between MRI parameters and matrix integrity have been established in many studies, but the substantial overlap in values observed for normal and for degraded cartilage greatly limits the specificity of these analyses. We implemented established multiparametric analysis methods to define data clusters corresponding to control and degraded bovine nasal cartilage in two-, three-, and four-dimensional parameter spaces, and applied these results to discriminant analysis of a validation data set. Analyses were performed using the parameters (T(1), T(2), k(m), ADC), where k(m) is the magnetization transfer rate and ADC is the apparent diffusion coefficient. Results were compared to univariate analyses. Multiparametric k-means clustering led to no improvement over univariate analyses, with a maximum sensitivity and specificity in the range of 60-70% for the detection of degradation using T(1), and in the range of 80% sensitivity but only 36% specificity using the parameter pair (T(1), k(m)). In contrast, model-based analysis using more general Gaussian clusters resulted in markedly improved classification, with sensitivity and specificity reaching levels of 80-90% using the pair (T(1), k(m)). Finally, a fuzzy clustering technique was implemented which may be still more appropriate to the continuum of degradation seen in degenerative cartilage disease. In view of its success in identifying mild cartilage degradation, the formal multiparametric approach implemented here may be applicable to the nondestructive evaluation of other biomaterials using MRI.

Figure 1

Images of BNC samples within the 4-well sample holder following 6-hour trypsin digestion. (A) Transverse slice showing all four wells in cross section. (B) Diffusion-weighted image used for delineation of ROIs, as indicated.

Figure 2

Bivariate scatter plots of data acquired from control and collagenase-digested BNC samples. Covariance matrices for each pair of MRI parameters were calculated for control (blue; ○) and degraded (red; ◊) BNC samples. The corresponding error ellipses illustrate the relationship between the parameter pairs indicated. (A) (k_m, T₁), (B) (T₁, T₂), (C) (k_m, T₂), (D) (T₁, ADC), (E) (T₂, ADC), and (F) (k_m, ADC) parameter pairs.

Figure 3

Model-based discriminant analysis based on MCLUST partitioning of control (blue; ○) and trypsin-degraded (pink; ◊) BNC samples. Models were developed based on 53 samples selected randomly from the total set of 80, with the remaining 27 samples forming a validation set. The MRI parameters T₁, T₂ and k_m are shown here for illustrative purposes. Error ellipsoids represent the 50% confidence surface. Incorrectly classified samples are indicated by solid symbols. Panels A and B illustrate the results with clusters restricted to single components, while Panels C and D illustrate clusters formed from multiple (two, in this case) components. Panel A: training set; five samples in the control group (specificity 80%) and one sample in the trypsin-degraded group (sensitivity 96.4%) were misclassified using single-component clusters. Panel B: validation set, with 5 control and 3 degraded samples being misclassified, resulting in sensitivity and specificity of 75% and 67%, respectively using single-component clusters. Panel C: training set; a single sample in both the control and degraded groups were misclassified, resulting in a sensitivity of 96.4% and a specificity of 96% using multiple-component clusters. Panel D: validation set, with 3 control samples and one degraded sample being misclassified, resulting in sensitivity and specificity of 91.7% and 80%, respectively, using multiple-component clusters.