Ensemble multivariate analysis to improve identification of articular cartilage disease in noisy Raman spectra

Abstract

The development of new methods for the early diagnosis of cartilage disease could offer significant improvement in patient care. Raman spectroscopy is an emerging biomedical technology with unique potential to recognize disease tissues, though difficulty in obtaining the samples needed to train a diagnostic and excessive signal noise could slow its development into a clinical tool. In the current report we detail the use of principal component analysis--linear discriminant analysis (PCA-LDA) on spectra from pairs of materials modeling cartilage disease to create multiple spectral scoring metrics, which could limit the reliance on primary training data for identifying disease in low signal-to-noise-ratio (SNR) Raman spectra. Our proof-of-concept experiments show that combinations of these model-metrics has the potential to improve the classification of low-SNR Raman spectra from human normal and osteoarthritic (OA) cartilage over a single metric trained with spectra from the same healthy and OA tissues. Scatter plot showing the PCA-LDA derived human-disease-metric scores versus rat-model-metric scores for 7656 low signal-to-noise spectra from healthy (blue) and osteoarthritic (red) cartilage. Light vertical and horizontal lines represent the optimized single metric classification boundary. Dark diagonal line represents the classification of boundary resulting from the optimized combination of the two metrics.

Keywords: Raman spectroscopy; articular cartilage; multivariate analysis; osteoarthritis.

Figure 1

A schematic representing the experimental process presented in this report. High-quality training spectra were first obtained from three sets of materials to model biochemical changes in osteoarthritis. The spectra from each set of materials was then subjected to multivariate analysis to create a scoring metric. Finally, the metrics were applied singly or in combination to maps of noisy spectra from healthy and osteoarthritic cartilage, the degree to which this produced separable groups of scores for the two tissues was measured. Abbreviations: OA (osteoarthritis), HOA (human osteoarthritis), HAC (human articular cartilage), SNR (signal-to-noise ratio), C (collagen metric), R (rat metric), H (human metric).

Figure 2

(a) The average spectra for the training sets acquired from rat articular cartilage (RAC), rat injury-induced fibrocartilage (RIF), human articular cartilage (HAC), human osteoarthritic cartilage (HOA), purified collagen type II (COL2), and purified collagen type I (COL1). The similarity of the tissue derived spectra to those from the purified collagens suggests that this component of the tissue dominates the spectral signature. Also included for reference is the average spectrum from 15 spectra taken from purified chondroitin sulfate (CS), which spectral has features distinct from the cartilage tissue spectra. (b) PCA-LDA coefficients for the metrics from the HAC vs. HOA (Human), RAC vs. RIF (Rat), and COL2 vs. COL1 (Collagen) analyses.

Figure 3

(a) A phase contrast image of a 10 μm-thick cross-section of osteochondral defect on rat femur condyle, 4 weeks post-injury. The red dotted line indicates the approximate injury site. The black dashed line marks the region covered by spectral Raman mapping. (b) Raman spectral map of the injury site, for which the coloration of each pixel (7 μm × 7 μm) represents the rat metric PCA-LDA score of the low signal-to-noise spectrum taken at that location. In this map the distinctive scoring of the cartilage and fibrocartilage region is visualized. (c) Raman spectral map scored with the collagen metric. The similarity between the two maps likely reflects the similarity between the model materials from which the metrics were derived. (d) Schematic of the relationship between a spectrum's score and its representative color.

Figure 4

(a) Histograms (red and blue bars) and fitted Gaussians (red and blue curves) of the PCA-LDA score distribution of the training sets for the HAC vs. HOA (Human, left), RAC vs. RIF (Collagen, middle), and COL2 vs. COL1 (Rat, right) metrics. (b) Low signal-to-noise Raman spectral maps taken from HAC (top) and HOA (bottom) samples, and scored by human (left), rat (middle), and collagen (right) metrics. (c) Distributions of PCA-LDA scores from the maps in (b) as scored by human (left), collagen (middle), and rat (right) metrics. The histograms and dark fitted Gaussians curves represent the combined distributions for the HAC maps (red) and HOA maps (blue). The light curves represent the distributions of individual HAC maps (red) and HOA maps (blue). The distributions of human metric scores from low-SNR human maps were broadened compared to scoring of the human training sets, highlighting the challenge of noisy spectra. Score distributions created by the rat metric scoring of the maps show a similar separation of the classes when compared to the human metric, but shifted towards the cartilage-like scores. The collagen metric does not perform as well in creating well-separated distributions for the two classes of spectra. Differential scoring of HOA maps 3 and 6 are highlighted by the darker dotted and dashed lines respectively, which indicates a tendency of the different metrics to vary in scoring of maps within a class, while still scoring the two classes as distinct groups.

Figure 5

Scatter plots of the human metric score versus collagen metric score (a), human metric score versus rat metric score (b), and rat metric score versus collagen metric score (c) of each spectrum from the HAC (blue) and HOA (red) low signal-to-noise maps. Light vertical and horizontal lines represent present the optimized single metric classification boundary. Dark diagonal lines represent the optimized classification of boundary resulting from the combination of two metrics through a second LDA (er = error rate). The relatively isotropic spread of the within-class scatter – as opposed to following a positive diagonal – shows the weak correlation between to scores of individual spectra produced by different metrics. In each of the plots the scatter points present that represent spectra misclassified by one or the other metric, but correctly classified by the combined boundary directly illustrate the improvement possible with ensemble classification. (d) Table summarizing the optimized classification of low signal-to-noise map spectra by single metric and ensemble methods.