Discrimination of healthy and osteoarthritic articular cartilage by Fourier transform infrared imaging and Fisher's discriminant analysis.

Fourier transform infrared spectroscopic imaging (FTIRI) technique can be used to obtain the quantitative information of content and spatial distribution of principal components in cartilage by combining with chemometrics methods. In this study, FTIRI combining with principal component analysis (PCA) and Fisher's discriminant analysis (FDA) was applied to identify the healthy and osteoarthritic (OA) articular cartilage samples. Ten 10-μm thick sections of canine cartilages were imaged at 6.25μm/pixel in FTIRI. The infrared spectra extracted from the FTIR images were imported into SPSS software for PCA and FDA. Based on the PCA result of 2 principal components, the healthy and OA cartilage samples were effectively discriminated by the FDA with high accuracy of 94% for the initial samples (training set) and cross validation, as well as 86.67% for the prediction group. The study showed that cartilage degeneration became gradually weak with the increase of the depth. FTIRI combined with chemometrics may become an effective method for distinguishing healthy and OA cartilages in future.


Introduction
Articular cartilage (AC) is a type of connective tissue that covers the end of bone to reduce friction, distribute pressure and buffer vibration [1]. It has a critical role during joint motion and loading. Structurally, the uncalcified cartilage can be subdivided into three histological zones (superficial zone (SZ), transitional zone (TZ) and radial zone (RZ)) from the articular surface to subchondral bone [2]. The primary molecular components of the extracellular matrix in AC are type II collagen and proteoglycan (PG) [3]. Collagen forms the essential structural framework of fibro network that enmeshes PG molecules [4]. PG keeps the resiliency and compressive strength of AC [5].
Either the disruption of collagen fiber or the loss of PG would lead to the onset of the functional degeneration of AC, eventually clinically osteoarthritis (OA) [6,7]. In the early stage of OA, the major characteristic represents as the concentration reduction of the principal components in cartilage matrix [8]. There is not yet macroscopic injury in this stage, which offers an opportunity for tissue repair. However, a sensitive and accurate method for the early OA monitoring and the evaluation to the therapy effect is still imperative. Several approaches have been used to investigate AC in recent years, including biochemical analysis, magnetic resonance imaging, biomechanical measurement and various forms of microscopy techniques [8]. It is still challenging to synchronously determine the PG and collagen content at 10s of micron resolution in these methods, which is critical in detecting OA.
Fourier transform infrared spectroscopic imaging (FTIRI) can synchronously achieve the infrared spectrum collection and image scanning of the cartilage samples with fine spatial and spectral resolutions [9]. By combining with chemometric methods, it can be used to measure the spatial distribution of the component concentrations in cartilage matrix [8,10]. Principal component analysis (PCA) has been used to extract the semi-quantitative information of the primary components from the spectral matrix [11]. One particular analysis approach, Fisher's discriminant analysis (FDA), could achieve the rapid classification for the data set through the analysis of the covariance [12]. FTIRI combining with PCA and FDA has shown new applications in biomedical filed [12,13]. In this work, this combined method were used to differentiate the healthy and OA cartilages. The depth-dependences of discrimination and degeneration were also investigated.

Sample preparation
The AC samples were harvested from ten dogs (5 healthy and 5 OA) after they were sacrificed, which was approved by the institutional review committees. All the dogs had similar individual features in age and weight. The OA samples had been induced by anterior cruciate ligament transection (ACLT) in one knee joint 2 years ago. Each cartilage attaching on bones was cut into several rectangular blocks with the size of 2mm × 2mm × 2mm. After washed in saline for 1 minute and frozen by liquid N 2 , these specimen blocks were sectioned into 10-μm-thick sections by cryostat (Leica CM 1950, Germany) at −20 °C, and then mounted on MirrIR slides (Kevley Technologies, Chesterland, OH). These sectioned specimens were dried in air for 2 hours to remove the moisture influence on infrared spectra before FTIRI.

FTIRI experiment
FTIRI was performed on a PerkinElmer Spotlight-300 infrared imaging system [8,14]. The specimen sections were mounted on a movable mechanical stage for FTIRI. The image data of cartilage sections were collected at 6.25-μm pixel size and 8 cm −1 wavelength spacing over the range of 4000-744 cm −1 . Background spectra (MirrIR slide) were also collected in the same range for the baseline correction.
FTIR spectra were extracted from the FTIR images of 10 sections (5 healthy and 5 OA), which were numbered in the order of AC-1 to AC-5 and OA-1 to OA-5, respectively. The most obvious concentration change in cartilage matrix is the loss of PG in SZ and TZ at the early stage of OA [14]. Therefore, the spectra extracted from SZ are optimal for the training set. In addition, owing to the scattering and diffuse reflection at the SZ edge of section, the IR spectrum from this area was distorted and could not accurately reflect the characteristics of the corresponding components so that first one or two spectra from SZ edge were excluded [8]. Therefore, 5 spectra were extracted from SZ of each sample with 10μm intervals for constructing FDA model (#1~25 from healthy sections and #26~50 from OA sections). Except for the above spectra, another 15 spectra were randomly extracted from three 50μm-wide continuous areas in each sample, including TZ and a followed part of RZ, for prediction. All of 200 spectra were sequenced from 1 to 200.

Principal component analysis and Fisher's discriminant analysis
PCA and FDA were both performed in SPSS software. The spectral range of 1800~1000 cm −1 was chosen for PCA. First, total 200 spectra extracted from the FTIR images were formed into a spectral matrix. Then, this matrix was decomposed to the factor loading matrix and score matrix by PCA, which were considered as the normalized spectra and relative concentration of the principal components in chemometrics, respectively [15]. The factor was chosen as the cumulative contribution exceeded 85%.
In FDA, the score matrix of the first 50 spectra (#1~50) was used to construct the FDA model for identifying the cartilage samples. The main process is to obtain the classification function and the cutoff threshold based on the Euclidean distance between the spectra and cluster center. In this study, when the score of the spectrum calculated with the classification function is less than 0, it belongs to the healthy group; otherwise it belongs to the OA group.
Leave-one-out cross validation (LOOCV) was used to evaluate the performance of the classification model constructed by the PCA-FDA method [16]. After the FDA model constructed, the rest of 150 spectra (#51~200) were calculated with the classification function based on the score matrix obtained in PCA. By comparing the score with the cutoff threshold, the spectra were attributed into different classes.  Figure 1 shows an infrared absorption spectrum. The characteristic bands of collagen and PG are in the range of 1800-1000 cm −1 , including amide I (1700-1600 cm −1 ), amide II (1600-1500 cm −1 ), amide III (1300-1200 cm −1 ) and sugar bands (1125-960 cm −1 ) [9,14]. In addition, the 1338 cm −1 band did not exist in pure PG spectrum so that it could be used to qualitatively estimate the collagen [8]. The intensity of each absorption peak is not directly associated with the concentration of the principal macromolecules in cartilage matrix since the multiple component information is superposed into one spectrum [8].  Figure 2 shows the IR (Fig. 2(a)) and visible (Fig. 2(d)) images of healthy and OA cartilage sections. Compared with the other bands, the band centering at 1338 and 1072 cm −1 is more suitable for characterizing collagen and PG [8]. Therefore, Fig. 2(b) and Fig. 2(c), the FTIR images of healthy and OA cartilage at 1338 and 1072 cm −1 , could qualitatively represent the relative distributions of collagen and PG in cartilage matrix, respectively. Compared with the FTIR images of healthy section, the infrared absorption intensity of OA section was significantly reduced, especially in SZ and TZ (Fig. 2(c)). differences could be small. Therefore PCA and FDA were needed to classify the healthy and OA samples as the quantitative methods.

Principal component analysis
The cumulative contribution of variance for the first four principal components calculated by PCA was shown in Table 1.The score matrix of the first two components would be used for FDA as the cumulative variance exceeded 85%. The scatter plot of PC1 and PC2 was shown in Fig. 3. The spectral data in healthy and OA group were represented as the solid triangles and circles, respectively. Compared with the spots from healthy group, the spots in OA group were relatively decentralized and distinguishable from the healthy one.

Fisher's discriminant analysis
As the principal component factor was 2, the initial samples in healthy group were all correctly identified, while three cases in OA group (#41, 42 and 46) were misjudged. The total accuracy for initial sample was 94%. The same results occurred in the case of cross validation, as shown in Table 2. As 150 spectra (#51-200) in prediction group were identified, 95 cases were attributed into healthy group; and the other 55 cases were attributed into OA group.

OA features
According to the morphological observation of knee cartilage, the OA cartilages were partly damaged in SZ. The major difference between the OA and healthy sections was the decrease of PG concentration in the corresponding areas [14,17], which could lead to the spectral change so as to be used as the main parameter in PCA-FDA. This confirmed the OA features, which may be caused by the deformation of joint motion and the cartilage injury after ACLT [8,18].

PCA and FDA
According to Table 1, the cumulative contribution of variance for the first two principal components was 90.08%, which means that most of information contained in the spectral matrix has been retained. And these spectra could be roughly divided into two classes (shown in Fig. 3), suggesting that there was a significant absorbance difference between healthy and OA samples [14]. In addition, the spots of OA group were decentralized when comparing with those of healthy group, which might result from the variations in the degeneration degree between different OA sections and areas. It was also inferred that the characteristic of healthy cartilage sections is quite similar with each other. In FDA, three misjudged cases (#41, 42 and 46) in Table 2 originated from OA-4 and OA-5, respectively. Since all the OA sections were obtained from the similar individual, the reasons mentioned below may lead to the misjudgment. First, the thickness gradient at the edge of SZ may cause the light scattering effect, shown as the brighter area in Fig. 2, and the eventual misjudgment. Second, the degeneration degree of each sample might be different to some extent. The degeneration degree of OA-4 and OA-5 was clearly weaker than the other OA samples. Therefore, all misjudged cases concentrated in the two samples. In addition, by comparing the results of initial sample and cross validation, it is demonstrated that the classification model built by the PCA-FDA method is reliable and steady.
In prediction group, the amount of the misjudged cases increased with the sampling depth and most of the misjudged cases originated from the last 50-μm region. It was inferred that the degeneration degree of the OA sections in TZ and RZ was clearly weaker than that in SZ, which also means the PG loss was heavier in SZ than that in TZ and RZ [14]. In addition, the cases misjudged as health almost concentrated in OA-2, OA-4 and OA-5, suggesting that the degeneration degree of these samples was weaker than the others. It further confirmed the second reason above.
According to the principle of PCA, every spectrum could be considered as a sample that is uncorrelated with each other relatively. And the spectra from the same section were more or less different because of the depth-dependent concentration of PG and collagen [8]. As the total accuracy was 86.67% for the prediction group, 94% for initial sample and cross validation, FTIRI combined with PCA-FDA was effective and reliable to identify the healthy and OA cartilages.

Conclusion
FTIRI was combined with PCA and FDA to identify the spectra from the healthy and OA sections at different depth. When the principal component factor was set as 2, all the cases in healthy group were correctly identified for initial sample; while 3 cases in OA group were misjudged. The total accuracy of initial sample (training set) was 94%, as well as that of cross validation. For prediction group, the accuracy was 86.67%. It was found that the degeneration degree of the OA sections in TZ and RZ was clearly weaker than that in SZ. FTIRI combined with PCA and FDA can be applied to identify the AC accurately and reliably, which would provide a newly potential and effective method for distinguishing healthy and OA cartilages when optical fiber spectroscopy can be used in clinic in expectable future.