1.

Introduction

Biochemical composition,^1–3 biomechanical properties,⁴ and grade of osteoarthritis^5,6 of articular cartilage (AC) have been evaluated with Fourier transform infrared (FT-IR) spectroscopic methods. There has been increasing interest toward multivariate analysis methods in FT-IR spectroscopic studies of AC. These methods include, e.g., principal component regression,^2,7 partial least squares (PLS) regression,^8,9 and cluster analysis.^10–14 Multivariate regression methods are attractive because they can utilize overlapping data, i.e., it is not necessary to find a characteristic absorption peak for each compound in the sample. Instead, multivariate models can be built using the whole acquired wavenumber range. However, some of the variables may be irrelevant, noisy, or otherwise unreliable in the situation of interest.¹⁵ Therefore, the model may benefit, if unnecessary variables are removed from the data before conduction of multivariate regression analysis.

In a recent study, genetic algorithm (GA) was applied for variable selection when compressive stiffness of AC was predicted from FT-IR spectra.⁴ Direct application of GA is problematic if the data contains lots of variables because the probability of finding chance correlation and overfitting increases. Therefore, in that study, the variables were averaged using a $10\text{-}{\mathrm{cm}}^{-1}$ spectral window to decrease the number of variables. Averaging effectively reduces the possibility of overfitting. Unfortunately, some narrow peaks can be lost as a result of averaging, which can decrease the prediction accuracy. Alternative means to reduce the number of variables are needed to obtain best results with GA.

Backward interval PLS (biPLS) is an algorithm that can be used to remove unnecessary spectral windows from the spectra before PLS regression.¹⁵ In biPLS, the spectral data is divided into equal-sized spectral windows. The effect of removal of each spectral window to the model prediction is calculated. After finding the best PLS regression model, the corresponding window is removed. The process can be repeated until there is only one window left or until enough windows have been removed. The PLS regression model could then be built using the best combination of spectral windows found from biPLS. Alternatively, variable selection can be further continued by applying GA to the variables that are left after biPLS. Thus far, the biPLS method has not yet been applied to FT-IR studies of AC.

The aim of this study was to predict the collagen and proteoglycan contents in bovine AC using FT-IR spectroscopy and PLS regression. Biochemical analysis of collagen and proteoglycan contents served as reference. As a second aim, it was evaluated whether the variable selection algorithms biPLS and GA can further improve the prediction results.

2.

Materials and Methods

3.

Results

3.2.

biPLS

The spectral regions that were selected for the prediction of the proteoglycan content by biPLS are shown in Fig. 1(a). The correlation coefficient between the uronic acid content and the content predicted by the biPLS regression model was $r=0.904$ ($p<0.01$) [Fig. 1(b)]. The correlation coefficient was statistically significantly higher than that of the full-spectrum model. The spectral regions that were selected for the prediction of the collagen content are shown in Fig. 2(a). The correlation coefficient between the hydroxyproline content and the content predicted by the biPLS regression model was $r=0.881$ ($p<0.01$) [Fig. 2(b)]. This correlation coefficient was also statistically significantly higher than that of the full spectrum model. Figure 3 shows the correlation coefficients as a function of the number of windows used in biPLS.

Fig. 1

(a) Spectral regions selected by biPLS for the prediction of the uronic acid content in AC are marked by a gray fill. (b) A scatter plot between the reference values of uronic acid content and the content predicted by the biPLS regression model.

Fig. 2

(a) Spectral regions selected by biPLS for the prediction of the hydroxyproline content in AC are marked by a gray fill. (b) A scatter plot between the reference values of hydroxyproline content and the content predicted by the biPLS regression model.

Fig. 3

Correlation coefficient between the reference values of uronic acid (white circles) and hydroxyproline (black squares) contents and biPLS regression models as a function of the number of windows used in biPLS. Correlation coefficients for the models using only the last windows are not visible in the plot as they were significantly smaller ($r=0.40$ and 0.30 for uronic acid and hydroxyproline, respectively) than the other values.

3.3.

GA after biPLS

biPLS was first used to remove 12 out of 20 spectral windows. The remaining eight spectral windows are shown in light gray shading in Figs. 4(a) and 5(a) for proteoglycans and collagen, respectively. GA was applied to the remaining spectral windows. The 11 spectral variables that were selected for the prediction of the proteoglycan content by the GA are shown in Fig. 4(a). The correlation coefficient between the uronic acid content and the content predicted by the PLS regression model was $r=0.923$ ($p<0.01$) [Fig. 4(b)]. The correlation coefficient was statistically significantly higher than that of the full-spectrum model. The 21 spectral variables that were selected for the prediction of the collagen content by the GA are shown in Fig. 5(a). The correlation coefficient between the hydroxyproline content and the content predicted by the PLS regression model was $r=0.896$ ($p<0.01$) [Fig. 5(b)]. The correlation coefficient was statistically significantly higher than that of the full-spectrum model. The results are summarized in Table 1.

Fig. 4

(a) The eight spectral regions remaining after biPLS for the prediction of the uronic acid content in AC are marked by a light gray fill. The spectral variables selected by GA for the prediction of the uronic acid content in AC are marked by a black fill. (b) A scatter plot between the reference values of uronic acid content and the content predicted by the PLS regression model that used the variables selected by GA.

Fig. 5

(a) The eight spectral regions remaining after biPLS for the prediction of the hydroxyproline content in AC are marked by a light gray fill. The spectral variables selected by GA for the prediction of the hydroxyproline content in AC are marked by a black fill. (b) A scatter plot between the reference values of hydroxyproline content and the content predicted by the PLS regression model that used the variables selected by GA.

Table 1

Linear correlation coefficients (r) between the different PLS regression models and biochemical reference information.

Content	PLS	biPLS	biPLS+GA
Uronic acid	0.862	0.904*	0.923*
Hydroxyproline	0.793	0.881*	0.896*

^*Significantly higher r compared with that of the full-spectrum PLS regression model (p<0.05).

4.

Discussion

The aim of this study was to predict the biochemical composition of AC using FT-IR spectroscopy, PLS regression, and variable selection algorithms. The major components of AC, proteoglycans, and collagen were successfully determined from FT-IR spectra using multivariate regression. The results of the study demonstrate that variable selection algorithms significantly improve the multivariate regression models when predicting uronic acid and hydroxyproline contents in AC. biPLS with or without GA showed improved correlation with the biochemically determined reference information as compared with the full-spectrum PLS regression models. GA seemed to improve the results as compared with biPLS but the difference did not reach the limit of statistical significance.

The spectral regions selected by the biPLS were very similar for both uronic acid [Fig. 1(a)] and hydroxyproline [Fig. 2(a)]. Both used the carbohydrate region (950 to $1050{\mathrm{cm}}^{-1}$), sulfate region (1250 to $1300{\mathrm{cm}}^{-1}$), and amide II region (1550 to $1560{\mathrm{cm}}^{-1}$). Hydroxyproline used fraction of amide I region (1650 to $1700{\mathrm{cm}}^{-1}$), while the spectral region of 1400 to $1450{\mathrm{cm}}^{-1}$ was included in the uronic acid model. The similarities in the spectral regions between these two are not that surprising, considering that the spectra of collagen and proteoglycans overlap each other.¹ Because there are no specific absorption peaks for either of these components, the multivariate regression model requires information on both collagen and proteoglycans. There are more significant differences between uronic acid and hydroxyproline in spectral variables selected by the GA. The uronic acid model heavily utilizes the carbohydrate region [Fig. 4(a)], which is known to be linked to proteoglycans.^1,23,24 In addition to the carbohydrate and the sulfate regions, the hydroxyproline model also uses amide I and amide II regions which are traditionally used for the analysis of collagen content¹ [Fig. 5(a)].

Collagen and proteoglycan contents in AC have earlier been predicted from FT-IR spectra using multivariate regression models.^2,7–9 These studies used a wide spectral region in the multivariate models but still indicated superior performance compared with traditional univariate methods. Collagen and proteoglycans form the majority of the dry matrix of AC. Therefore, it is not that critical to select the optimal spectral regions when predicting collagen and proteoglycan contents in AC. Although the earlier results have been good, the variable selection algorithms can be used to further improve the models. In this study, it was found that biPLS provides a relatively easy and objective way to select optimal spectral regions for PLS regression. The results could still be further optimized by testing different spectral window sizes in biPLS.¹⁵ GA is a more complicated and time-consuming method for variable selection, but it may improve the prediction accuracy over that of biPLS alone. Multivariate regression models may be built to predict smaller molecular components of AC such as collagen cross-links or different collagen types. Furthermore, these models may also be useful to predict more complex phenomena such as biomechanical function of AC or progress of osteoarthritis. As these are not expected to be the origins of main features of AC FT-IR spectra, the variable selection algorithms may become even more important in the future.

We used 10-year-old formalin-fixed paraffin-embedded (FFPE) samples in this study. In general, FFPE samples are highly stable.²⁵ Fixation and storage time of FFPE samples have been shown to hinder the analysis of ribonucleic acids. On the other hand, proteomic investigations of abundant proteins in FFPE samples have been successfully conducted even from older samples without problems.²⁶ There exists large number of FFPE samples in different laboratories, and some of these samples are decades old.²⁵ Therefore, it would be beneficial if the composition of old FFPE samples could be analyzed accurately. The results of this study show that the macromolecular composition of AC can be accurately determined from 10-year-old FFPE samples. However, we cannot say if the current models work equally well in case of FFPE samples of different ages. Further studies comparing FFPE samples of different ages are needed to clarify this matter.