MRI is increasingly used to assess cartilage, with the overall goal of relating noninvasive measurements to the actual biophysical status of the tissue. There are a variety of available MR techniques and image contrast mechanisms that can be evaluated in terms of their ability to characterize tissue status, both in experimental preparations and in the clinical setting: T2 is sensitive to tissue hydration, collagen content, and collagen orientation with respect to the main magnetic field; diffusion (D) is sensitive to macromolecular content and hydration; T1 is sensitive primarily to PG content, as is the dGEMRIC index. Magnetization transfer (MT) studies primarily reflect collagen content. Heteronuclear studies have also been performed, with the Na+ signal intensity being sensitive to local PG content. All of these measurements exhibit utility in certain circumstances. However, all are of limited specificity, with a large overlap observed between values measured in normal cartilage and e.g. degraded cartilage, or between different regions of cartilage. Parameter combinations can be more specific than single parameters; a variety of multi-parametric approaches have been applied, particularly to image segmentation. A robust approach is k-means clustering. In our application, cluster centroids are calculated based on a scatterplot with respect to measured parameters. A data point is then assigned to the cluster with the closer centroid. There will be a certain number of misclassifications with real, imperfectly clustered, data, but the analysis is expected to be substantially more accurate than univariate classifications. One factor determining the success of the algorithm is the degree of independence of the measured parameters, so that careful selection of these is essential. Similarly, clustering can be performed with any number of independent outcome variables; the two-parameter case was illustrated above. These outcome variables can also be derived from entirely different modalities, such as use of MRI in conjunction with FT-IRIS outcome measures. A further extension of the basic k-means clustering algorithm is fuzzy k-means, where tissue is designated as belonging to a particular cluster to a specified degree. This is of particular utility when the dataset does not break into defined clusters, as in cartilage analysis. An additional extension of the basic algorithm removes the requirement for pre-defining the number of clusters within the data. This may not be required in experimental situations in which the goal is to distinguish two discrete groups, such as normal and degraded cartilage. However, it may be very useful in realistic situations with more subtle gradations of tissue quality. Finally, we note that different distance metrics may be applied, permitting relative weighting of the outcome measures. We have tried multiple approaches to this problem, with the best results to date resulting from a cluster analysis based on parameterized cluster shapes, sizes, and orientations. Additional analysis has demonstrated that under severe degradation, the conventional univariate analysis based on comparison of sample values with category means provides reasonable sensitivity and specificity. However, with more subtle degradation, we have found that model-based classification using Gaussian clusters is substantially more effective for classification. The probabalistic nature of this analysis lends itself readily to fuzzy clustering as well. While our application has been to cartilage degradation, the approach is much more general and may be useful in materials classification in general with magnetic resonance. Current work is centered around development of support vector machine analysis of degraded cartilage. We find that this SVM approach may have significant advantages, in particular through a minimization of the over-training potential that occurs when developing a model with a training set for use on validation samples. In addition, the SVM, like the Gaussian clustering approach, lends itself to a graded assessment of cartilage degradation. This is through a sigmoidal probability function of the distance of a sample in parameter space from the decision hypersurface. We are currently developing discriminant functions based on three metrics in both one variable and two variables. These permit the translation of means and standard deviations to sensitivity and specificity of derived statistical tests.
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