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

Abstract

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±1.34 μg/mg in week 1 to 21.06±4.14 μg/mg in week 4. Using multiexponential T₂ analysis, we detected at least three distinct water compartments, with T₂ values and weight fractions of (45 ms, 3%), (200 ms, 4%), and (500 ms, 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 r²=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 r²=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.

FIG. 1.

Representative T₂ distribution from an engineered construct after 3 weeks of development. Three dominant water compartments are evident, with their corresponding T₂ values indicated on the horizontal axis. The vertical axis is in arbitrary units (a.u.), defined by the integrated areas summing to unity.

FIG. 2.

Linear regression analysis using component fraction sizes as dependent variables and sGAG concentration as an independent variable. (A) Correlation between sGAG concentration and w₁ (r²=0.43, p=0.001), (B) correlation between sGAG concentration and w₂ (r²=0.51, p=0.003), (C) correlation between sGAG concentration and w₃ (r²=0.46, p=0.001), and (D) correlation between sGAG concentration and w₁+w₂ (r²=0.58, p=0.02). The assignments of the component fractions are as discussed in the text, with w₁ and w₂ representing proteoglycan-bound water, and w₃ representing relatively unbound water. As shown, w₁+w₂ showed the best correlation with sGAG concentration. sGAG, sulfated glycosaminoglycan.

FIG. 3.

Correlations between predicted sGAG concentrations obtained from univariate linear regression analysis incorporating the indicated component fractions as described in the text, and biochemically determined sGAG content of the corresponding tissue-engineered constructs. Correlations between biochemically determined sGAG concentration and sGAG content calculated from magnetic resonance–measured weight fractions (A) w₁ (r²=0.43, p=0.001), (B) w₂ (r²=0.51, p=0.003), (C) w₃ (r²=0.46, p=0.001), and (D) w₁+w₂ (r²=0.54, p=0.02). As seen, the model based on w₁+w₂ was the best univariate predictor of sGAG concentration.

FIG. 4.

Correlation between biochemically measured sGAG concentration and transverse relaxation time calculated from monoexponential fitting. As expected, T_2,mono decreased with increasing sGAG concentration (r²=0.56, p<0.05).

FIG. 5.

Correlation between predicted sGAG concentration derived from MLR analysis using the component weight combination [w₁, w₂, w₃] and the biochemically determined sGAG content of the tissue-engineered constructs (r²=0.57). [w₁, w₂, w₃] was the best predictor of sGAG content among all possible parameter sets in MLR. MLR, multiple linear regression.

FIG. 6.

Correlations between predicted sGAG concentration derived from support vector regression analysis using the indicated component weight fraction combinations and the biochemically determined sGAG content of the tissue-engineered constructs. Combinations illustrated are (A) [w₁, w₂] (r²=0.68), (B) [w₂, w₃] (r²=0.93), and (C) [w₁, w₂, w₃] (r²=0.82). As seen, [w₂, w₃] was the best predictor of sGAG content.