# Investigation of the Performance of Hyperspectral Imaging by Principal Component Analysis in the Prediction of Healing of Diabetic Foot Ulcers

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## Abstract

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_{2}) values from peripheral tissue. In an earlier study, HSI of 43 patients with diabetic foot ulcers at the time of presentation revealed that ulcer healing by 12 weeks could be predicted by the assessment of SpO

_{2}calculated from these images. Principal component analysis (PCA) is an alternative approach to analyzing HSI data. Although frequently applied in other fields, mapping of SpO

_{2}is more common in biomedical HSI. It is therefore valuable to compare the performance of PCA with SpO

_{2}measurement in the prediction of wound healing. Data from the same study group have now been used to examine the relationship between ulcer healing by 12 weeks when the results of the original HSI are analyzed using PCA. At the optimum thresholds, the sensitivity of prediction of healing by 12 weeks using PCA (87.5%) was greater than that of SpO

_{2}(50.0%), with both approaches showing equal specificity (88.2%). The positive predictive value of PCA and oxygen saturation analysis was 0.91 and 0.86, respectively, and a comparison by receiver operating characteristic curve analysis revealed an area under the curve of 0.88 for PCA compared with 0.66 using SpO

_{2}analysis. It is concluded that HSI may be a better predictor of healing when analyzed by PCA than by SpO

_{2}.

## 1. Introduction

_{2}) values from peripheral tissue [2,3,4,5,6,7,8,9].

_{2}was reduced in people with diabetes, and especially in those with neuropathy. Yudovsky et al. [6] also used HSI in the visible spectrum (450–700 nm) to predict tissue breakdown. A two-layer (epidermis, dermis) skin model was used to fit to the measured data and obtain an index of SpO

_{2}. The algorithm was able to predict tissue at risk of ulceration with a sensitivity and specificity of 95% and 80% respectively, 58 days before breakdown is visible to the naked eye [6].

_{2}from HSI was also used by Khaodhiar et al. [7] to estimate oxyhemoglobin and deoxyhemoglobin of 10 patients with type 1 diabetes with foot ulcers, 13 without ulcers, and 14 subjects without diabetes. A spectrum for each pixel was compared with standard tissue to determine measures of oxyhemoglobin and deoxyhemoglobin. Using this approach, the sensitivity and specificity of HSI in predicting ulcer healing were 93% and 86%, while the positive and negative predictive values for ulceration were calculated as 93% and 86%. Nouvong et al. [8] used a similar approach to estimate relative values of tissue oxyhemoglobin and deoxyhemoglobin in 66 people with diabetic foot ulcers and reported that the sensitivity of HSI to predict healing within 6 months was 80% and the specificity was 74%. As discussed in our previous work [9], both of these papers had weaknesses, which helps to explain the differences between results of [7,8,9]. The first study [7] was very small and acknowledged to be simply a pilot, and both studies based their analysis on outcome per ulcer rather than outcome per person. The population included in the second study [8] was also highly selected, with a mean age of participants of just over 50 years, much younger than a representative population with diabetic foot ulcers.

_{2}is more common in biomedical HSI. It is therefore valuable to compare the performance of PCA with SpO

_{2}measurement in the prediction of wound healing. PCA is a process that converts a number of possibly correlated variables into a set of linearly uncorrelated variables called principal components. PCA has been demonstrated to be an effective and efficient preprocessing method, as retaining only the first few principal components significantly reduces data [10]. In the food industry, PCA and HSI have been applied to tea classification [11], detection of bruise damage on mushrooms [12], and estimation of the quality of pork [13]. Some examples of the application of PCA in in vivo biomedical HSI are provided in useful reviews [14,15,16], with a focus on laparoscopic imaging [11,12]. PCA has also been used as a dimension-reduction algorithm for wavelet-based segmentation of hyperspectral colon tissue imagery [17]. For tissue measurement, the contiguous bands of a hypercube are highly correlated, as they are dominated by the oxy- and deoxyhemoglobin spectra. This has the benefit of being a data-reduction method for the hypercubes obtained from the tissues of feet affected by ulcers.

_{2}measurements in predicting whether a wound will heal within 12 weeks of presentation. More accurate prediction of wound healing will support earlier intervention and better treatment.

## 2. Method

#### 2.1. Experimental Setup

^{TM}Lighting, San Jose, CA, USA) with 8 units placed on either side of the camera. Light scattered from the foot was passed through an aperture, which controlled the amount of collected light and was focused onto a detector by a C-mount lens (f = 15 mm, f# = 2.2; Schneider).

_{sample}is the intensity measured from the raw image, and I

_{white}and I

_{dark}are the intensities of the white and dark references, respectively.

#### 2.2. Clinical Protocol

_{2}and PCA were obtained in a clinical study described previously [9]. The published study received research ethics approval and all participants provided written informed consent. Recruitment was of a consecutive cohort, and the only major prespecified exclusions were those with a unilateral major amputation and those who withheld or were unable to give informed consent [9]. There was therefore no control of gender balance, as one would expect a predominance of male patients in all studies of foot ulcers. There was also no control of diabetes type, as this is not a recognized significant factor associated with the outcome of diabetic foot ulcers.

_{2}algorithms and PCA, as described in Section 2.3 and Section 2.4, respectively.

#### 2.3. SpO_{2} Data Processing

_{2}is the concentration of oxyhemoglobin (mole L

^{−1}) and Hb is the concentration of deoxyhemoglobin (mole L

^{−1}).

_{a}(λ)) and attenuation (A(λ)) can be expressed as [18]:

^{−1}mole

^{−1}L), β(λ) is the specific absorption of deoxyhemoglobin (cm

^{−1}mole

^{−1}L), and d is the path length of the light (cm).

_{a}(λ) is known at 2 wavelengths, then it is straightforward to calculate SpO

_{2}from Equations (3) and (2), as α(λ) and β(λ) are known from literature values. A challenge is to relate measurements of A(λ) and μ

_{a}(λ). In the absence of light scattering, the path length is the geometric path length through the sample and the relationship is the Lambert–Beer law. In practice, the relationship between attenuation and absorption is nonlinear due to light scattering. An approximation is therefore needed to relate A(λ) and μ

_{a}(λ) in the presence of light scattering. The most commonly applied is the modified Lambert–Beer law [19,20]:

^{2}in an area of intact skin adjacent (typically 1–5 mm) to the edge of the ulcer and unaffected by callus.

#### 2.4. Principal Component Analysis

_{i}) is the attenuation at each pixel, i represents the wavelength bin number of the spectrum, and T denotes the transpose.

_{i}is expressed as:

_{i}by the eigenvector matrix provides a score matrix v

_{i}(Figure 2d), which can then be refolded to form a data cube that represents images of principal components.

_{1}≫ P

_{2}≫ … ≫ P

_{N}) enables data reduction, as usually only information is contained in the first few principal components. In this case, the oxy- and deoxyhemoglobin spectra are correlated and only the first two principal components (PC1 and PC2) are used for image classification.

_{2}values or PCA, receiver operating characteristic (ROC) curves are used to express the performance of a binary classifier system due to a varying discrimination threshold. An ROC curve is obtained by plotting true positive rate (TPR) against false positive rate (FPR). TPR is the fraction of true positives out of the total actual positives. FPR is the fraction of false positives out of the total actual negatives.

## 3. Results

#### 3.1. Oxygen Saturation Analysis

_{2}results from baseline were significantly different between ulcers that did and did not heal within 12 weeks, but not between those that did and did not by 24 weeks. Figure 3 shows measured SpO

_{2}at a point adjacent to the wound site against healing time (healed by 12 weeks represented by blue diamonds, unhealed at 12 weeks represented by red triangles). The dashed line shows the optimum threshold using Youden’s index [25] obtained from the ROC curve shown in the next section. An R

^{2}value of 0.4 was obtained when applying a linear fit to the data obtained for healing within the first 12 weeks.

_{2}classifier with the threshold set to 59.5%, the black dashed line (shown in Figure 3) can be used as the decision line where patients with SpO

_{2}values adjacent to the wound site lower than the threshold are classified as healing by 12 weeks. Only two of the unhealed ulcers were grouped incorrectly. The TPR was 50.0% (12 of 24) and the FPR was 11.8% (2 of 17). When using SpO

_{2}values to predict the healing of diabetic ulcers in 12 weeks, the sensitivity was 50% (12 of 24), the specificity was 88.2% (15 of 17), and the positive predictive value was 85.7% (12 of 14).

#### 3.2. Principal Component Analysis

_{2}and PC2 classifiers, the ROC curve in Figure 5 shows the PCA classifier (blue line) much closer to the ideal right-angled case than the SpO

_{2}classifier (red line). A common method to compare classifiers in a single scalar value is to calculate the area under the ROC curve (AUC) [26]. The AUC under the PCA classifier is 0.88, which is 33% more than the AUC for the SpO

_{2}classifier (0.66).

## 4. Discussion and Conclusions

_{2}values. Principal component analysis is an alternative approach that has not been investigated in the prediction of wound healing. It is therefore of value to investigate whether PCA improves the prediction of wound healing and to compare this with the performance of SpO

_{2}mapping.

_{2}values and PCA, and the principal finding was that classification of time to healing by 12 weeks based on PCA (sensitivity = 87.5%, specificity = 88.2%) outperformed that using SpO

_{2}(sensitivity = 50%, specificity = 88.2%). Comparison by receiver operating characteristic (ROC) analysis revealed an area under the curve of 0.88 for PCA, compared with 0.66 using oxygen saturation analysis. Thus, PCA based on the second principal component appeared superior to analysis using SpO

_{2}values in predicting healing of wounds by 12 weeks based on hyperspectral images taken at baseline.

_{2}measurement approaches. Due to the dominance of oxy- and deoxyhemoglobin, PCs greater than 2 provide no discriminatory value.

_{2}values may still be useful in cases where a hyperspectral camera is not available (as, for example, when making single point measurements using a lower-cost spectrometer-based method or when making measurements with a wound dressing with a fiber optic probe placed adjacent to the wound site). Furthermore, the previous demonstration that SpO

_{2}values on the top of the foot are well correlated with those on the underside means that precisely locating the fiber optic probe may not be necessary.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Hyperspectral imaging setup for imaging the foot (foot-to-lens distance typically 25–30 cm).

**Figure 2.**Principal component analysis (PCA) applied to a hypercube, where e-vector means eigenvector and e-value means eigenvalue: unfold (

**a**) 3-D datacube into (

**b**) 2-D matrix; (

**c**) obtain eigenvectors and eigenvalues from covariance matrix; (

**d**) multiply the 2-D matrix by the eigenvectors to obtain a score matrix; (

**e**) refold the score matrix to form images at each principal component.

**Figure 3.**Relationship between time to healing (days) and oxygen saturation in a region adjacent to the wound. In order to plot unhealed ulcers, their healing days were set at 200 (higher than all the healing days of the healed ulcers). The dashed line represents the optimum threshold calculated from Youden’s index.

**Figure 4.**Relationship between time to healing (days) and principal component 2 (PC2). In order to plot unhealed ulcers, healing days was set at 200 (higher than all the healing days of the healed ulcers).

**Figure 5.**Receiver operating characteristic (ROC) analysis: red line indicates classification based on SpO

_{2}values adjacent to the wound site and blue line represents classification based on the absolute value of the PC2 score. Black dashed line is the worst case.

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**MDPI and ACS Style**

Yang, Q.; Sun, S.; Jeffcoate, W.J.; Clark, D.J.; Musgove, A.; Game, F.L.; Morgan, S.P.
Investigation of the Performance of Hyperspectral Imaging by Principal Component Analysis in the Prediction of Healing of Diabetic Foot Ulcers. *J. Imaging* **2018**, *4*, 144.
https://doi.org/10.3390/jimaging4120144

**AMA Style**

Yang Q, Sun S, Jeffcoate WJ, Clark DJ, Musgove A, Game FL, Morgan SP.
Investigation of the Performance of Hyperspectral Imaging by Principal Component Analysis in the Prediction of Healing of Diabetic Foot Ulcers. *Journal of Imaging*. 2018; 4(12):144.
https://doi.org/10.3390/jimaging4120144

**Chicago/Turabian Style**

Yang, Qian, Shen Sun, William J. Jeffcoate, Daniel J. Clark, Alison Musgove, Fran L. Game, and Stephen P. Morgan.
2018. "Investigation of the Performance of Hyperspectral Imaging by Principal Component Analysis in the Prediction of Healing of Diabetic Foot Ulcers" *Journal of Imaging* 4, no. 12: 144.
https://doi.org/10.3390/jimaging4120144