Multispectral indices for real-time and non-invasive tissue ischemia monitoring using snapshot cameras

An adequate supply of oxygen-rich blood is vital to maintain cell homeostasis, cellular metabolism, and overall tissue health. While classical methods of measuring tissue ischemia are often invasive, localized and require skin contact or contrast agents, spectral imaging shows promise as a non-invasive, wide field, and contrast-free approach. We evaluate three novel reflectance-based spectral indices from the 460 - 840 nm spectral range. With the aim of enabling real time visualization of tissue ischemia, information is extracted from only 2-3 spectral bands. Video-rate spectral data was acquired from arm occlusion experiments in 27 healthy volunteers. The performance of the indices was evaluated against binary Support Vector Machine (SVM) classification of healthy versus ischemic skin tissue, two other indices from literature, and tissue oxygenation estimated using spectral unmixing. Robustness was tested by evaluating these under various lighting conditions and on both the dorsal and palmar sides of the hand. A novel index with real-time capabilities using reflectance information only from 547 nm and 556 nm achieves an average classification accuracy of 88.48, compared to 92.65 using an SVM trained on all available wavelengths. Furthermore, the index has a higher accuracy compared to reference methods and its time dynamics compare well against the expected clinical responses. This holds promise for robust real-time detection of tissue ischemia, possibly contributing to improved patient care and clinical outcomes.


Multispectral indices for real-time non-invasive tissue ischemia monitoring using snapshot cameras: supplemental document 1. WHITE BALANCING OF HYPERSPECTRAL IMAGES
Images are white balanced by dividing by an image of a uniform diffuse white reference tile covering the full field-of-view (Spectralon® 95%, SphereOptics GmbH), using the following equation: where I s is the measured irradiance at a pixel of the image using integration time t s , I ds the measured irradiance of that pixel in the dark reference image using the same integration time as the sample image, and I w the corresponding measured irradiance from the white reference image using integration time t w which we subtract with I dw , the dark reference value at the same integration time.The 0.95 value is the reflectance of the white reference target.

REFLECTANCE AND ABSORBANCE SPECTRA
Figure S1 shows the average reflectance and absorbance spectra of the hand during the initial experiment, both before and during occlusion, along with their standard deviation.Spectra are averages from all 15 subject, over all superpixels of the hand.The standard deviation is relatively high due to inter-subject variability and differences are subtle.The absorbance is estimated by negating the logarithm of the reflectance value.

SPECTRAL CORRECTION METHOD BASED ON COLOR CHART MEASUREMENTS
The spectral correction is based on a comparison between the color chart measurement (Col-orChecker Classic Mini, Calibrite) using the HSI camera and a spectrometer (HR4000, Ocean Optics).Using the spectrometer, specular and diffuse reflectance spectra were acquired for every color tile.The reflectance spectra from the HSI camera for every color tile is extracted by manually selecting a rectangular ROI in every tile.To minimize mismatch between the HSI camera and spectrometer, a weight and bias are optimized for every wavelength, minimizing the mean squared error (MSE) over all color tiles between the two.The optimization of weight and bias is performed via gradient descent, with a learning rate of 0.02 and a stopping threshold of 1e − 6. Optimized weight and bias were achieved after 4973 iterations.The optimized weight and bias for every wavelength are then added to the pre-processing pipeline.Every wavelength image of the hypercube is multiplied with the optimized weight for that wavelength and summed with the optimized bias for that wavelength.The spectra before and after correction are shown for one color tile in Fig. S2.The color of this tile is closest to the color of the actual skin tissue.The average MSE for all color tiles dropped from (710.70 + −579.12)e-5 to (8.88 + −6.48)e-5.

TISSUE OXYGENATION ALGORITHM
To compute the oxygenation values for every superpixel, we follow a similar approach as [1].As opposed to the ischemia indices, this method uses information from all available wavelengths in the hypercube.It should be noted that the application of this law comes with a few assumptions, assuming the light travels an equal path length in the tissue for every wavelength, that scattering is constant, and scattering is low compared to absorption.These assumptions do not fully hold up in real skin tissue, as red light penetrates the skin deeper compared to blue light, so not all wavelengths interrogate the same region of tissue.In addition, the scattering is wavelength dependent, decreasing with increasing wavelength [2].In the investigated spectral range of this study, the assumptions are taken as valid.The following relationship between absorption and concentration holds: where ε(b) denotes the molar extinction coefficient at wavelength b in cm −1 mol −1 L −1 , r(b) the reflectance at wavelength b, c the concentration in mol • L −1 , L the distance traveled by the photons in cm and G a constant accounting for losses due to scattering, which is geometry dependent.Considering oxy-and deoxyhemoglobin as absorbers in the formula above: Converting to vector notation: where H is a matrix consisting of (ε HbO2 , ε Hb , 1) and x equals (C HbO2 L, C Hb L, G) T .We then apply linear least-squares regression to determine the optimal solution ẋ: Then oxygenation is calculated as SatO2 = Note that no value is required for L as it drops out due to division.However, the calculation of total hemoglobin concentration would require a value of the path length.

PERFORMANCE OF SUPPORT VECTOR MACHINE VERSUS RANDOM FOREST REGRESSOR
To compare the performance of the proposed ischemia indices to a state-of-the-art machine learning classifier, both a support vector machine (SVM) and a random forest classifier were trained.For both, hyperparameter tuning was performed in the same manner and is described in section 2.5 of the main text.While tuning the random forest classifier, the following hyperparameters were tuned: the feature scaler (Normalizer, StandardScaler, RobustScaler, MinMaxScaler), the number of trees (10 to 500), the maximum depth of the three (1 to 20 or no maximum depth), the minimum samples per leaf (2 to 20) and the maximum amount of features (the square root or no maximum).Both classifiers were compared in terms of classification accuracy between healthy and ischemic superpixels on data from the initial experiment.Details of this comparison are provided in Table S1.During recursive feature selection, a subset of 12 wavelengths was found optimal in both models.Using this optimal subset or the complete wavelength set, an SVM achieves both the highest validation and test accuracy.Using a subset of 2 or 3 wavelengths, which is an equal amount to the proposed indices, a random forest classifier achieves higher accuracies.
As the goal of this study is to compare the proposed ischemia indices to a state-of-the-art reference method, the model with the highest accuracy is selected.Hence, the performance of the indices is compared to an SVM throughout the study.
Table S1.A comparison was made between the performance of a support vector machine and a random forest classifier in terms of their classification accuracy between healthy and ischemic superpixels on data from the initial experiment.Accuracy values are provided as mean values along with their standard deviations.

Fig. S1 .
Fig. S1.Average reflectance (a) and absorbance (b) spectra of the hand before and during occlusion in the initial experiment.The high standard deviation indicates high inter-subject variability.
Fig. S2.A spectral calibration step is applied to the images using a color chart to match the measured reflectance of the camera with that of a spectrometer by means of an optimized weight and bias for every wavelength.RGB image (a) of the ColorChecker Classic Mini, along with the spectra before and after the calibration of an ROI drawn in tile A5, which resembles skin color the most.The MSE in A5 drops from 116.3 × 10 −5 to 2.9 × 10 −5 .

Table S2 .
Statistical tests investigating whether there is a significant difference in classification accuracy between Asian and Caucasian participants for the proposed ischemia indices and all reference methods.* indicates a significant difference at α = 0.05.Accuracy scores are provided as mean value and standard deviation.