Accurate and early prediction of the wound healing outcome of burn injuries using the wavelet Shannon entropy of terahertz time-domain waveforms

Abstract

Significance: Severe burn injuries cause significant hypermetabolic alterations that are highly dynamic, hard to predict, and require acute and critical care. The clinical assessments of the severity of burn injuries are highly subjective and have consistently been reported to be inaccurate. Therefore, the utilization of other imaging modalities is crucial to reaching an objective and accurate burn assessment modality.

Aim: We describe a non-invasive technique using terahertz time-domain spectroscopy (THz-TDS) and the wavelet packet Shannon entropy to automatically estimate the burn depth and predict the wound healing outcome of thermal burn injuries.

Approach: We created 40 burn injuries of different severity grades in two porcine models using scald and contact methods of infliction. We used our THz portable handheld spectral reflection (PHASR) scanner to obtain the in vivo THz-TDS images. We used the energy to Shannon entropy ratio of the wavelet packet coefficients of the THz-TDS waveforms on day 0 to create supervised support vector machine (SVM) classification models. Histological assessments of the burn biopsies serve as the ground truth.

Results: We achieved an accuracy rate of 94.7% in predicting the wound healing outcome, as determined by histological measurement of the re-epithelialization rate on day 28 post-burn induction, using the THz-TDS measurements obtained on day 0. Furthermore, we report the accuracy rates of 89%, 87.1%, and 87.6% in automatic diagnosis of the superficial partial-thickness, deep partial-thickness, and full-thickness burns, respectively, using a multiclass SVM model.

Conclusions: The THz PHASR scanner promises a robust, high-speed, and accurate diagnostic modality to improve the clinical triage of burns and their management.

Keywords: Shannon entropy; burn assessment; machine learning; terahertz spectroscopic imaging; terahertz time-domain spectroscopy; wavelet packet transform.

Fig. 1

(a) The burn induction pattern on the dorsum in the first model. The burn locations created by scald and contact etiologies are shown by circle and square shapes, respectively. In this model, the exposure time is kept constant at 10 s, while the temperature is varied between 70°C, 80°C, and 100°C. (b) The burn induction pattern on the dorsum in the second model. The burns are created using the scald etiology. In this model, the temperature is kept constant at 100°C, while the exposure time is varied between 5, 25, 45, and 60 s. (c) The schematic of the optical components inside the PHASR scanner. This device incorporates a dual-fiber-laser spectrometer into a collocated, telecentric imaging configuration, which utilizes an $f\text{-}\theta$ lens and a two-axis motorized scanning system. (d) The PHASR scanner is shown as it is operated in the porcine imaging study.

Fig. 2

(a) The scale-frequency diagram of MODWPT. The first rectangle at level $j=0$ represents the entire spectrum of the original THz signal, $X$. At subsequent decomposition levels, the spectrum is divided into $2^j$ sub-bands of equal bandwidth by filtering the sub-bands of the previous stage with a pair of scaling and wavelet filters. The amplitude spectrum of the sub-bands are plotted for (b) MODWT and (c) MODWPT over $j=3$ levels of decomposition.

Fig. 3

The machine learning pipeline. The measurements are split randomly into the training (80%) and test (20%) sets. After band-pass filtering the signals and separating the main THz-TDS pulse, the MODWPT coefficients are calculated. The MODWPT sub-bands corresponding to the measurement bandwidth of $f=0.1-1\mathrm{THz}$ are selected. The ESER of selected sub-bands is calculated and normalized by the corresponding ESER of the reference air measurements to deconvolve the system response. These deconvolved ESER coefficients are used as the predictors. The dermal burn percentage on day 0 and the re-epithelialization rate on day 28 are used as the labels in training separate SVM classifiers. The hyperparameters of the classifiers, the choice of the mother wavelet function, and the level of decomposition of MODWPT are optimized over the five-fold cross-validation loss. The performance of the final trained model is evaluated over the 20% external test set. This process is iterated twenty times with the measurements being split randomly into the training and test sets at each iteration.

Fig. 4

(a) The anatomy of the skin layers, composed of epidermis, dermis, and hypodermis. Burn injuries can be divided into superficial (S), SPT, DPT, and FT groups, depending on the extension of the dermal burn depth. (b), (c) Two example microscopic images of the biopsy slices (H&E stained), extracted from a DPT and an FT burn, respectively. The blue arrows point at damaged microvasculature or necrotic cells, and the black ones point at the full dermis margin. (d) A schematic of the measured reflection pulses in the PHASR scanner. (e), (f) The images of an example contact burn obtained using a digital camera and the PHASR scanner, respectively. The color axis represents the peak-to-peak amplitude of the time-domain THz reflections at the burn and imaging window interface. (g)–(h) Similar to (e) and (f) for an example scald burn. (i) The mean and standard deviation of the pulses of an ROI delineated by a red square in (f). (j) A sub-sampled representative 3D data cube composed of spectral images of the burn in (g). The color axis is the normalized amplitude spectrum obtained by the Fourier transform of the THz pulses.

Fig. 5

(a) The THz electric field measurement of a representative DPT burn. The first five MODWPT sub-bands, including (b) ${\tilde{W}}_{\mathrm{8,0}}$; (c) ${\tilde{W}}_{\mathrm{8,1}}$; (d) ${\tilde{W}}_{\mathrm{8,2}}$; (e) ${\tilde{W}}_{\mathrm{8,3}}$; and (f) ${\tilde{W}}_{\mathrm{8,4}}$. The MODWPT coefficients are calculated using the db1 mother wavelet at the $J=8\mathrm{th}$ decomposition level. The wavelet coefficients of each sub-band are min–max normalized. (g) The ESER coefficients calculated for the $n=10$ to $n=80$ sub-bands, corresponding to the spectral range of $f=0.1-1\mathrm{THz}$, at the $J=12\mathrm{th}$ level of decomposition. The ESER of the burn measurements is normalized with the ESER of reference air measurements to deconvolve the system response. The black and red lines show the average and the 95% confidence interval of the ESER coefficients of all measurements belonging to the FR and NPR groups, respectively.

Fig. 6

(a) The ROC curves obtained by predicting the re-epithelialization status of the burn injuries on day 28 using the THz-TDS measurements on day 0 in a binary SVM model. The dashed diagonal line shows the ROC curve of a random predictor. (b) The bar plot shows the sensitivity, specificity, accuracy, and ROC-AUC values over the training, validation, and test sets. The error regions in (a) and the error bars in (b) give the standard deviation of each parameter over twenty random iterations of the training and testing of the model. (c) The effect of the MODWPT decomposition level on the accuracy rate of diagnosing FR versus NPR burns using the db1 mother wavelet function.

Fig. 7

The ROC curves obtained by classification of the burn injuries into SPT, DPT, and FT groups over the (a) training; (b) validation; and (c) test sets using the ESER of the THz-TDS measurements in a multi-class SVM model. The ground truth of each burn’s severity grade is measured histologically on biopsies obtained on day 0. The bar plots present the sensitivity, specificity, accuracy, and ROC-AUC values over the (d) training; (e) validation; and (f) test sets. The error bars give the standard deviation of each parameter over 20 random iterations of training and testing the model.