# Preprocessing Strategies for Sparse Infrared Spectroscopy: A Case Study on Cartilage Diagnostics

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## Abstract

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^{−1}, followed by peak normalization at 850 cm

^{−1}and preprocessing by MSC.

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Histology Reference Data

#### 2.2. FTIR Spectral Data

#### 2.3. Preprocessing Strategies for the Broadband Spectra

^{−1}, followed by peak normalization at 850 cm

^{−1}; (2, 3) MSC with and without weighting; (4, 5) EMSC1 with and without weighting; and (6, 7) EMSC2 with and without weighting. Broadband spectra preprocessed by EMSC1 with weights showed visually better results where all baseline variations were removed. The classification results for the weighted EMSC1 preprocessed broadband spectra were among the best results for all eight datasets (results not shown). Thus, the optimal preprocessing for the broadband spectra was identified to be weighted EMSC1 method. Figure 1b shows the spectra of the human dataset 2 preprocessed by weighted EMSC1 model. All broadband spectral datasets (human dataset 1 and 2, bovine and simulated data) preprocessed by this method were used as benchmark data for further analysis.

#### 2.4. Preprocessing Strategies for the Sparse Spectra

^{−1}with peak normalization at 850 cm

^{−1}) with MCR, FNR and FPR around 40%. Other approaches gave worse performances: MSC and EMSC1 gave almost 50% misclassification, while no preprocessing (raw data) gave very biased classification towards the healthy group (FNR raised to around 50% while FPR was close to 20%). Interestingly, sparse data of the benchmark spectra, i.e., spectra preprocessed before variables were selected, also gave quite unsatisfactory results with strong bias towards the healthy group.

^{−1}and 850 cm

^{−1}which were selected for the preprocessing purposes, and therefore were not supposed to be important for the discrimination of the cartilage quality.

## 3. Methods

#### 3.1. Measured Data

#### 3.1.1. Bovine Broadband Spectra

^{−1}spectral resolution, digital spacing of 0.2411 cm

^{−1}, and averaging 64 scans over the range from 4000 cm

^{−1}to 400 cm

^{−1}. The background spectrum of air was measured for each sample separately. Measurements were controlled by OMNIC software (Thermo Nicolet Corporation, Waltham, MA, USA). Thus, the dataset of treatment samples consists of 180 spectra in total with additional 180 spectra of controls.

#### 3.1.2. Human Broadband Spectra

^{−1}to 600 cm

^{−1}at a spectral resolution of 2 cm

^{−1}, and digital spacing of 1.0292 cm

^{−1}. All samples were measured in triplicates, resulting in 807 and 801 spectra in dataset 1 and dataset 2, respectively.

#### 3.1.3. Histology

#### 3.2. Simulated Broadband Spectra

^{−1}were simulated with the digital spacing of 1.0292 cm

^{−1}.

^{−1}by applying a window function based on Tukey [36] (see Figure S10). The EMSC1 corrected and transformed data were split into two groups ${\mathit{X}}_{i},\text{}i=1,2$: healthy and damaged samples, which were separately used for the simulation as follows:

- PCA decomposition of matrix ${\mathit{X}}_{i}$ as ${\mathit{X}}_{i}={\mathit{T}}_{i}{\mathit{P}}_{i}^{\prime}+{\mathit{E}}_{i}$ was done, where ${\mathit{T}}_{i}$ are scores and ${\mathit{P}}_{i}$ are loadings of matrix ${\mathit{X}}_{i}$.
- Calculation of mean ${\mu}_{{\mathit{T}}_{i}}$ and standard deviation ${\sigma}_{{\mathit{T}}_{i}}$ of scores ${\mathit{T}}_{i}$ for the chosen number of loadings A.
- New scores ${\tilde{\mathit{T}}}_{i}$ were drawn randomly from the respective normal distribution $N\left({\mu}_{{\mathit{T}}_{i}},{\sigma}_{{\mathit{T}}_{i}}\right)$ calculated for each score ${\mathit{T}}_{i}$. The random drawing had a feedback loop which was activated if scores higher than the maximum or lower than the minimum obtained in experimental dataset were drawn. This was done to prevent very unrealistic score values being drawn.
- The first set of simulated data were obtained by ${\tilde{\mathit{X}}}_{pure,i}={\tilde{\mathit{T}}}_{i}{\mathit{P}}_{i}^{\prime}$. These spectra generated for healthy and damaged groups separately were further merged into one dataset and corrected again by the EMSC1 method to avoid creating artificial physical effects by random recombination of loadings in the simulation.The resulting dataset ${\tilde{\mathit{X}}}_{pure}$ contained the final simulated pure absorbance spectra. To simulate apparent spectra which are “perturbed” by physical effects naturally present in the real data, the following was done.
- Group specific EMSC1 variations were added to simulated pure spectra using parameters ${\tilde{\mathit{\beta}}}_{i}=\left\{{\tilde{\mathit{c}}}_{i},{\tilde{\mathit{b}}}_{i},{\tilde{\mathit{d}}}_{i}\right\}$ drawn from the distributions $N\left({\mu}_{{\mathit{\beta}}_{i}},\text{}{\sigma}_{{\mathit{\beta}}_{i}}\right),\text{}i=1,2$.
- The spectra were merged into one dataset and white noise vectors
**w**were also added by randomly drawing from a uniform distribution $U\left(-\alpha ,\text{}\alpha \right)$ with the $\alpha $ level similar to experimental dataset.

#### 3.3. Sparse Spectra

^{−1}. These wavenumbers were selected as cartilage specific wavenumbers in the MIRACLE project for the production of custom-made fixed-wavelength QLC lasers. The positions of the preselected wavenumbers are shown on the broadband spectrum of human cartilage in Figure 6. The choice of the wavenumbers was based on the relevance of the wavebands for the discrimination of the cartilage quality, as well as the usefulness of the wavenumbers for the preprocessing of the spectra prior to the modelling.

^{−1}was selected as a reference variable for the baseline absorbance. As can be seen from the Figure 6, the spectral region between 2750 and 1780 cm

^{−1}is mostly devoid of strong chemical absorbance by the samples, and thus it can be used for determining baseline absorbance. However, strong absorbance between 2500 and 1900 cm

^{−1}, caused by the ATR diamond crystal, results in a relatively low signal-to-noise ratio in this region, and therefore 1800 cm

^{−1}was selected as an optimal baseline reference variable. Five out of seven wavenumbers were selected based on cartilage-specific absorbance, namely: 1745 cm

^{−1}, corresponding to the C=O stretching vibration of lipids present in the cartilage and synovial fluid; 1620 cm

^{−1}, corresponding to the C=O stretching vibration (amide I) of collagen; 1560 cm

^{−1}, corresponding to the C-N-H stretching and bending vibration (amide II) of collagen; 1210 cm

^{−1}, corresponding to the O=C-N-H stretching and bending vibration (amide III) of collagen, and 1080 cm

^{−1}corresponding to the C-O stretching vibration of carbohydrate residues in collagen and proteoglycans [37,38]. The seventh wavenumber, at 850 cm

^{−1}, is a band related to librations of water in the cartilage and synovial fluid. This wavenumber was selected as a reference variable since it is assumed that the chemical absorbance of water is mainly invariant in all the samples, and therefore it could be used for normalization of all measured variables.

#### 3.4. Spectral Preprocessing and Preclassification Strategies

^{−1}and 900–800 cm

^{−1}. The weights are presented in Figure S11. This weighting strategy was chosen to correct baseline variations.

^{−1}, followed by peak normalization at 850 cm

^{−1}; (2, 3) MSC with and without weighting; (4, 5) EMSC1 with and without weighting, and (6, 7) EMSC2 with and without weighting. The broadband data preprocessed by weighted EMSC1 are referred to as the benchmark data in this study.

^{−1}, followed by peak normalization at 850 cm

^{−1}; (2) MSC, and (3) EMSC1. The EMSC2 approach was not used in this study for two reasons. First, EMSC with its four parameters to be estimated for the sparse spectra containing seven channels has too few degrees of freedom to be implemented. Second, the spectra in this study were ATR-FTIR spectra and are thus devoid of complex spectral variations caused by radiation-sample interactions (such as scattering artifacts and interference fringes), that would have required correction by nonlinear EMSC terms. Simple baseline effects that can occur in ATR spectra can be corrected by MSC or EMSC1. To compare the performance of the preprocessing approaches for the sparse data, classification models were built, and the results were compared to the classification results using sparse data of the benchmark data - broadband spectra preprocessed by EMSC1 with weights.

#### 3.5. Classification Modelling

_{Opt}) corresponded to the maximum accuracy of the group with the lowest classification accuracy. Three different models were used in this study. First, binary classification using OARSI groups of the cartilage samples for human, bovine and simulated data. Second, multiclass classification into treatment groups of bovine samples: five groups G1–G5. Third, binary classification into treatment and control groups for bovine samples.

_{Opt}was obtained by $\underset{{A}_{Opt}}{\mathrm{max}}\left(\mathrm{min}\left(Accuracy\left(healthy\right),\text{}Accuracy\left(damaged\right)\right)\right)$, while in the case of multiclass classification by $\underset{{A}_{Opt}}{\mathrm{max}}\left(min\left(Accuracy\left({G}_{i}\right)\right)\right),i=1,\dots ,5$.

## 4. Conclusions

^{−1}and peak normalization by the water band at 850 cm

^{−1}. In some cases, preprocessing of sparse data by MSC showed good results as well. However, in most cases when extended by more terms, as in EMSC1 by a linear term, the performance of the classification dropped. Since the EMSC1 estimates three parameters from the seven selected wavenumbers in the sparse data, relevant chemical or physical information related to cartilage quality, may be modeled and removed from the data.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**Human dataset 2 samples: (

**a**) raw broadband spectra of after removing water spectra by EMSC pre-classification algorithm; (

**b**) spectra preprocessed by the weighted EMSC1 (MSC plus linear term) model.

**Figure 2.**Simulated human cartilage spectra: mean spectra of simulated healthy (in blue) and damaged (in red) spectra showing (

**a**) the full spectral range and (

**b**) the fingerprint region; (

**c**) all simulated apparent spectra in fingerprint region; (

**d**) simulated spectra preprocessed by the weighted EMSC1 (MSC plus linear term) model.

**Figure 3.**Binary PLSDA classification of healthy and damaged samples based on OARSI grades. Models were established using preprocessed spectra of human dataset 2. From left to right: (1) benchmark broadband data, (2) sparse spectra of the benchmark data, (3) sparse raw data, (4) sparse data with simple preprocessing, (5) sparse data preprocessed by MSC, (6) sparse data preprocessed by EMSC1. Overall misclassification rate (MCR = 1-Accuracy) as well as False Negative Rate (FNR = 1-Sensitivity) and False Positive Rate (FPR = 1-Specificity) for the damaged group are provided.

**Figure 4.**Binary PLSDA classification of healthy and damaged samples based on OARSI grades. Models were established using preprocessed simulated cartilage spectra. From left to right: (1) benchmark broadband data, (2) sparse spectra of the benchmark data, (3) sparse raw data, (4) sparse data with simple preprocessing, (5) sparse data preprocessed by MSC, (6) sparse data preprocessed by EMSC1. Overall misclassification rate (MCR = 1-Accuracy) as well as False Negative Rate (FNR = 1-Sensitivity) and False Positive Rate (FPR = 1-Specificity) for the damaged group are provided.

**Figure 5.**A flowchart for the PCA simulation of spectra. Blue blocks denote datasets, green blocks denote a computational action and yellow blocks denote results from the corresponding green block.

**Figure 6.**An average broadband spectrum of human cartilage obtained using dataset 2 in blue and the seven selected wavenumbers shown by red circles. The wavenumbers 1800, 1745, 1620, 1560, 1210, 1080, and 850 cm

^{−1}were selected based on their relevance to cartilage quality assessment and spectral preprocessing.

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**MDPI and ACS Style**

Tafintseva, V.; Lintvedt, T.A.; Solheim, J.H.; Zimmermann, B.; Rehman, H.U.; Virtanen, V.; Shaikh, R.; Nippolainen, E.; Afara, I.; Saarakkala, S.;
et al. Preprocessing Strategies for Sparse Infrared Spectroscopy: A Case Study on Cartilage Diagnostics. *Molecules* **2022**, *27*, 873.
https://doi.org/10.3390/molecules27030873

**AMA Style**

Tafintseva V, Lintvedt TA, Solheim JH, Zimmermann B, Rehman HU, Virtanen V, Shaikh R, Nippolainen E, Afara I, Saarakkala S,
et al. Preprocessing Strategies for Sparse Infrared Spectroscopy: A Case Study on Cartilage Diagnostics. *Molecules*. 2022; 27(3):873.
https://doi.org/10.3390/molecules27030873

**Chicago/Turabian Style**

Tafintseva, Valeria, Tiril Aurora Lintvedt, Johanne Heitmann Solheim, Boris Zimmermann, Hafeez Ur Rehman, Vesa Virtanen, Rubina Shaikh, Ervin Nippolainen, Isaac Afara, Simo Saarakkala,
and et al. 2022. "Preprocessing Strategies for Sparse Infrared Spectroscopy: A Case Study on Cartilage Diagnostics" *Molecules* 27, no. 3: 873.
https://doi.org/10.3390/molecules27030873