Characterization of engineered cartilage constructs using multiexponential T₂ relaxation analysis and support vector regression

Increased sensitivity in the characterization of cartilage matrix status by magnetic resonance (MR) imaging, through the identification of surrogate markers for tissue quality, would be of great use in the noninvasive evaluation of engineered cartilage. Recent advances in MR evaluation of cartilage include multiexponential and multiparametric analysis, which we now extend to engineered cartilage. We studied constructs which developed from chondrocytes seeded in collagen hydrogels. MR measurements of transverse relaxation times were performed on samples after 1, 2, 3, and 4 weeks of development. Corresponding biochemical measurements of sulfated glycosaminoglycan (sGAG) were also performed. sGAG per wet weight increased from 7.74±1.34μg/mg in week 1 to 21.06±4.14μg/mg in week 4. Using multiexponential T₂ analysis, we detected at least three distinct water compartments, with T ₂ values and weight fractions of (45ms, 3%), (200ms, 4%), and (500ms, 97%), respectively. These values are consistent with known properties of engineered cartilage and previous studies of native cartilage. Correlations between sGAG and MR measurements were examined using conventional univariate analysis with T₂ data from monoexponential fits with individual multiexponential compartment fractions and sums of these fractions, through multiple linear regression based on linear combinations of fractions, and, finally, with multivariate analysis using the support vector regression (SVR) formalism. The phenomenological relationship between T₂ from monoexponential fitting and sGAG exhibited a correlation coefficient of r ²=0.56, comparable to the more physically motivated correlations between individual fractions or sums of fractions and sGAG; the correlation based on the sum of the two proteoglycan-associated fractions was r ²=0.58. Correlations between measured sGAG and those calculated using standard linear regression were more modest, with r² in the range 0.43-0.54. However, correlations using SVR exhibited r² values in the range 0.68-0.93. These results indicate that the SVR-based multivariate approach was able to determine tissue sGAG with substantially higher accuracy than conventional monoexponential T₂ measurements or conventional regression modeling based on water fractions. This combined technique, in which the results of multiexponential analysis are examined with multivariate statistical techniques, holds the potential to greatly improve the accuracy of cartilage matrix characterization in engineered constructs using noninvasive MR data.