Raman Spectra
The mean Raman spectra (background and baseline corrected) of each damage group compared to the control spectrum are shown in Figure 17-Figure 20. Raman peak assignments are presented in Table 6. COL24 group showed the most extreme variation relative to the control group as it represents severe OA. All peaks showed a decrease relative to the control group, except the peaks at 1610 cm-1 and 1510 cm-1 increased, the former corresponds to phenylalanine and tyrosine aromatic ring breathing and the latter is likely related to the collagenase itself. The SO3− symmetric stretch band at 1060 cm-1 increased significantly across all damage groups, except for the IMP group, for which it increased only slightly. The ABR group spectrum showed a slight increase of the bands at 1336 and 1381cm-1, which are attributed to CH2 wagging and glycosaminoglycans, respectively. TRYP30 spectrum showed a slight decrease in the glycosaminoglycan band at 1381 cm-1 accompanied by a decrease also in proline, hydroxyproline, and tyrosine bands. Notable changes in the COL90 spectrum include a subtle decrease in amide III doublet, hydroxyproline, tyrosine, proline, and tryptophan bands.
Figure 21 shows the mean of enzymatic damage groups vs the mechanical ones relative to the control group mean. The COL24 group was left out in the calculation of the enzymatic mean spectrum, as it represents severe OA, and it would greatly bias the spectrum. Notable peak differences occur at The SO3− symmetric stretch band at 1060 cm-1 increased significantly for both mechanical and enzymatic damage. On the other hand, a slight decrease of the proline and hydroxyproline bands at 938 and 855 cm-1 respectively was present in the enzymatic mean only.
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Figure 16:Impact mean spectrum vs Control mean
Figure 17:Abrasion mean spectrum vs Control mean
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Figure 18:Collagenase 90-minute mean spectrum vs Control mean
Figure 19:Trypsin 30-minute mean spectrum vs Control mean
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Figure 20:Collagenase 24-hours mean spectrum vs Control mean
Figure 21:Mean of Mechanical damage vs Mean of Enzymatic Damage vs Control group mean
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Table 6:Raman peak assignments
Raman Shift (Cm-1)
Peak
Letter Assignment Component Cartilage ECM
Component Reference
1660.7 A Amide I Protein Collagen 39,42,109
1610.6 B v C=C aromatic ring Phenylalanine, Tyrosine
42,109
1560.4 C v C=C aromatic ring Tryptophan, Tyrosine 42,109
1510.3 D unassigned Collagenase D
1450.5 E
d CH2/CH3 deformation Protein, Lipid Collagen 39,42,109
1425.4 F
COO– Glycosaminoglycans Proteoglycans 42,109
1381.1 G unassigned Glycosaminoglycans 42,109
1336.7 H
Delta CH2 waging Glycosaminoglycans 42,109
1317.4 I
CH2 twist
42,109
1265.4 J Amide III Protein Collagen 39,42,109,110
1242.2 K Amide III Protein Collagen 39,42,109,110
1201.7 L Hydroxyproline,
SO3− symmetric stretch Chondroitin sulfate Proteoglycans 39,42,109,110
1032.0 Q Phenylalanine Ring
deformation Phenylalanine 42,109
1001.2 R Phenylalanine (C-C) ring
breathing Phenylalanine 39,42,110
962.6 S
v1 PO43- Apatite Mineral 39,110
937.5 T v C–C Protein backbone
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854.6 W v C–C Proline Collagen 39,42,109,110
812.2 X v C–C Protein backbone Collagen (& other proteins)
42,109
762.1 Y Tryptophan ring
deformation Protein 109
Reference variables
Table 7 shows the average values for the mechanical properties, collagen orientation, and PG content of each damage group. A significant drop in biomechanical properties is observed in COL24 and IMP groups. In contrast, the ABR group’s biomechanical properties did not change much relative to the control group. COL90 and TRYP30 groups showed a moderate drop in their biomechanical properties. Regarding proteoglycans content, a relatively significant higher PG content was observed in the three zone ratios in the COL90 and ABR groups. Lastly, the collagen orientation in the superficial zone significantly increased for the COL24 group, along with an increase in the average orientation in the middle zone for COL90 and ABR groups accompanied by an increase in the deep zone also for the latter. Box-plot distributions of target variables are presented in Figure 22.
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Table 7: Average reference values of each damage group
Group Mechanical Moduli
Collagenase 90min 32.25 77.25 79.40
Abrasion 31.74 78.38 81.87
Trypsin 30min 30.80 72.67 78.90
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Figure 22:Target variables box-plot distributions. A) Dynamic and Instantaneous Moduli, B) Equilibrium Modulus, and C) Cartilage thickness, D) Proteoglycan
Content, and E) Collagen Orientation.
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Optimal Machine Learning Models
As previously mentioned, the model with the lowest RMSEP was chosen as the optimal model to predict each target. Table 8 shows the optimal machine learning algorithm and the corresponding hyperparameters that optimize the relationship between the Raman spectra and the different reference properties. It can be observed that the optimal PLSR models utilized only a few principal components (3-5), the optimal SVM models used linear and second-degree polynomial kernels, although higher degree polynomials and more complex kernel functions were present in the search. It can also be observed that none of the optimal models utilized second-degree differentiation preprocessing, and only two out of ten used first degree, while the rest used the undifferentiated spectra. Also, excessive smoothing was not ideal for the optimal models.
Table 8: Optimal models hyperparameters and pre-processing
Target Model Derivative Order Filter
Window SNV
Biomechanical Properties
Thickness PLSR (No. of Components = 5) 1 15 yes
Instantaneous Modulus SVM (C=100, degree=2, kernel='poly') 1 31 yes Equilibrium Modulus SVM (C=10, degree=2, kernel='poly') 0 31 yes
Dynamic Modulus
Superficial SVM (C=10, degree=2, kernel='linear') 0 31 yes
Middle SVM (C=1000, degree=2, kernel='poly') 0 7 yes
PLSR was the optimal algorithm for predicting the proteoglycan content across all zones, on the other hand, SVMs had similar success with collagen orientation. Figure 23 and Figure 24 show scatter plots of measured vs predicted targets, Table 9 presents the RMSE of cross-validation, calibration, and prediction percentages calculated by division over the target range.
Spearman correlation coefficient was also calculated for the training and test points along with their R-squared correlation.
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Table 9: Metrics of the optimal models that maximise the relationship between Raman spectra and cartilage reference properties
Target RMSECV
Figure 23: Scatter Plot of A) Equilibrium Modulus, B) Instantaneous Modulus, C) Cartilage Thickness, D) Dynamic Modulus.
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Figure 25 presents the feature importance for dynamic modulus, cartilage thickness, proteoglycan content across all zones and, collagen orientation for superficial zone only.
Feature importance was not provided for the rest of the targets as they were predicted using second-degree polynomial kernels in SVM models (non-linear functions), for which feature importance mapping is not possible.
Figure 24: Scatter Plot of Proteoglycan Content across A) Superficial, B) Middle, and C) Deep Zones and Collagen Orientation across D) Superficial, E) Middle, and F) Deep Zones
Figure 25:Feature Importance for A) Proteoglycan Content, B) Collagen Orientation, C) Dynamic Modulus and D) Cartilage Thickness
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