Machine-learning-based diabetes classification method using blood flow oscillations and Pearson correlation analysis of feature importance

The Animal Experiment Ethics Committee of Daegu Gyeongbuk Institute of Science and Technology approved this experimental protocol (approval no. DGIST-IACUC-21040201-0002). Twenty male Sprague-Dawley rats (7–8 weeks old, with an average weight of approximately 240 g at the beginning of the experiment) were divided into two groups of 10 animals each: a control group and a diabetes group. In the diabetes group, diabetes was induced by intraperitoneal injection of streptozotocin (STZ; 65 mg kg⁻¹, Sigma-Aldrich Co.) dissolved in 0.01 M sodium citrate buffer (pH 4.5) after fasting for at least 12 h [42]. Rats in the control group were injected with only 0.01 M sodium citrate buffer (pH 4.5). Forty-eight hours after the STZ injection, blood was collected from the tail vein of rats in the diabetes group, and the blood glucose level was measured using a glucose meter (Accu-Chek Performa, Roche Diagnostic). A 270 mg dl⁻¹ or higher blood glucose level indicated diabetes [43]. Then, the rats' blood glucose levels, body weight, and blood flow signals were measured weekly for ten weeks.

The blood flow signals of rats in the control and diabetes groups were measured using our custom-built DSCA system. This system consisted of an 830 nm wavelength laser (DL-830-100SO, CrystaLaser, 830 nm, 100 mW) and a charge-coupled device camera (F-033B, Stingray, cell size: $9.9\,\,\mu\mathrm{m}$) [44]. The DSCA system probe was made of polydimethylsiloxane with a distance of 5 mm between the source and detector. It was placed on the rat's right hind paw (figure 1). The DSCA system measured blood flow signals from all rats weekly for ten weeks after anesthesia with isoflurane (2.0%; 1.5 L min⁻¹). The DSCA signals were recorded at a sampling rate of 60 Hz using a fast pulsatile blood flow measurement method, and a reactive hyperemia test was performed to induce blood flow changes [44]. The reactive hyperemia test is used to noninvasively assess the peripheral microvascular function by briefly inducing ischemia through arterial occlusion [45]. In this study, an elastic band was used to briefly induce ischemia in the thigh of a rat during blood flow signal measurements (figure 1).

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The blood flow signals measured in the reactive hyperemia test were divided into three periods: baseline, occlusion, and release (figure 2). The rats' blood flow signals were measured at 1 min 40 s (baseline), 2 min 20 s (occlusion), and 6 min (release). The baseline is the usual period without stimulation; occlusion is when the rat's thigh is compressed with an elastic band to cause ischemia; and release is the period after the end of ischemia when blood flow temporarily increases significantly and stabilizes.

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The blood flow signals in the baseline, occlusion, and release periods were calculated as metabolism-related blood flow oscillations from 0.01 to 5 Hz by continuous wavelet transform using Morlet wavelets, which were used as input data for machine learning algorithms (figure 3).

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The blood flow oscillation data is calculated as the relative magnitude, the ratio of the average magnitude of five frequency bands related to the rat's metabolism [46]. Rat blood flow oscillations of 2–5 Hz, 0.7–2 Hz, 0.2–0.74 Hz, 0.08–0.2 Hz, and 0.01–0.08 Hz are associated with cardiac activities, respiratory activities [40], myogenic activities, neurogenic activities, and endothelial-related metabolic activities [41], respectively. All preprocessing code was implemented using MATLAB.

We analyzed and compared the performance of three machine learning algorithms, namely, gradient tree boosting, random forest, and Adaboost, to determine the classification potential of control and diabetes blood flow signals. The gradient tree boosting algorithm increases the model performance by sequentially combining weak learners to reduce the residual [47, 48]. It suffers from being easy to overfit; however, it generally performs better than the random forest algorithm [49]. The random forest algorithm builds a model with better performance by constructing multiple decision trees. Each decision tree is trained with bootstrap samples extracted from the training set. The tree is constructed by searching for the best split by randomly selecting a subset of the input variables at each node split. Consequently, the generalization error converges to a limit as the number of decision trees increases [50]. The Adaboost algorithm was the first in which the boosting method was used to increase the model performance by adjusting the sample weights while combining weak learners [51]. Like the gradient tree boosting algorithm, the Adaboost algorithm uses a boosting method to create a strong learner by sequentially combining weak learners; however, it performs poorer than the gradient tree boosting algorithm [52].

The 200-input data (100 control, 100 diabetes) were randomly divided into 160 (80 control, 80 diabetes) training data and 40 (20 control, 20 diabetes) test data for use in the machine learning algorithm (figure 4). The data was split using the train_test_split function, and then normalized using the MinMaxScaler function to ensure consistent data scaling across all models. The hyperparameters of the machine learning algorithm were tuned by applying fivefold cross-validation to the training data. For all three models–gradient tree boosting, random forest, and Adaboost–three hyperparameters were adjusted: min_samples_split (ranging from 2 to 101), max_features (ranging from 1 to 5), and n_estimators (ranging from 1 to 150), to improve the model's performance. Additionally, for gradient tree boosting and Adaboost, the learning_rate (ranging from 0.01 to 1) was also optimized. The hyperparameters that maximized the average validation accuracy were adopted. The validation accuracy, test accuracy, and AUC score were calculated to evaluate the classification performance of the three algorithms on the training and test data. Validation accuracy refers to the accuracy obtained by fivefold cross-validation using training data, and test accuracy refers to the accuracy obtained with the test data using the trained model. The AUC score is an effective way to evaluate the overall classification performance of a model; it is calculated as the area under the receiver operating characteristic curve. It takes a value between 0 and 1 [53]. We obtained ten validation accuracy, test accuracy, and AUC scores and evaluated the classification performance in terms of the average value of these scores. The best machine learning algorithm was selected for feature importance and Pearson correlation analysis.

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Through feature importance analysis, we confirmed the change in importance according to the machine learning algorithm and input data period. We obtained the Pearson correlation coefficient between the importance of each feature and the diabetes classification performance. By determining the correlation between the importance of blood flow oscillation data and the diabetes classification performance, we investigated which features most impact the classification of control and diabetes blood flow signals. The feature importance was calculated based on the Gini impurity. All code was implemented using Python and MATLAB.

This study measured blood glucose and body weight to confirm that diabetes was maintained during the experimental period. After STZ injection, the blood glucose levels of rats in the diabetes group increased significantly. In contrast, that of rats in the control group showed little change (figure 5(A)). For ten weeks after the STZ injection, the blood glucose level of rats in the control group remained between 100 and 200 mg dl⁻¹. By contrast, rats in the diabetes group consistently remained above 500 mg dl⁻¹ on average. In addition, the body weight of the rats in the control group continued to increase significantly. By contrast, that of the rats in the diabetes group increased very slowly (figure 5(B)). In a previous study in which STZ was used to induce diabetes in rats, the body weight of the diabetes group increased much slower than that of the control group. The blood glucose level of the diabetes group remained above 400 mg dl⁻¹ [42]. Observations of the changes in the blood glucose level and body weight before and after the STZ injection showed that diabetes was maintained in the rats in the diabetes group throughout the experiment.

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When analyzing blood flow signals for diabetes classification, the anesthesia status can be considered a factor influencing the results. Humeau et al (2007) reported that deeper anesthesia significantly reduces myogenic and neurogenic activities compared to lighter anesthesia, suggesting that anesthesia could affect diabetes classification based on blood flow signals [54]. However, in our study, since the blood flow oscillations corresponding to cardiac activities primarily affected diabetes classification, we think that the impact of anesthesia on classification performance was minimal.

Additionally, during the reactive hyperemia test, we observed a temporary increase in blood flow at the end of the baseline period and the start of the occlusion period. According to Rosenberry et al (2020), when a specific area is compressed with a cuff or a device with similar functionality, the tissue experiences hypoxia, strongly inducing vasodilation [45]. This vasodilation leads to a transient increase in blood flow, followed by a rapid decrease when additional blood flow cannot be supplied, explaining the observed phenomenon.

Moreover, to determine the influence of body weight on blood flow signals, we analyzed the correlation between body weight and the mean values of raw blood flow signals and the five types of blood flow oscillations (cardiac, respiratory, myogenic, neurogenic, and metabolic). The Pearson correlation analysis revealed little to no correlation, indicating that body weight does not influence the raw blood flow signals or blood flow oscillations. Thus, body weight is not expected to impact the classification results in our study significantly.

In this study, our custom-built DSCA system was used to measure the blood flow signals of rats in the control and diabetes groups. The measured blood flow signals were calculated as the ratio data of blood flow oscillations through wavelet transform, and they were used as input data for machine learning algorithms. The performance of the machine learning algorithms was evaluated in terms of the validation accuracy, test accuracy, and AUC score. The importance of blood flow oscillations and the correlation between the classification performance of blood flow signals in the control and diabetes groups were determined using feature importance and Pearson correlation analysis.

3.2.1. Performance evaluation results of machine learning algorithms for diabetes classification

As mentioned earlier, the three machine learning algorithms were trained by randomly splitting the calculated input data into training and test data in an 8:2 ratio. The input data was calculated from the blood flow signal data of four periods (baseline, occlusion, release, entire), where the entire period includes blood flow oscillation data of the baseline, occlusion, and release periods. The classification results were validated in terms of the validation accuracy, test accuracy, and AUC score by repeating the above process ten times. Figures 6(A)–(C) respectively show the classification results of the gradient tree boosting, random forest, and Adaboost algorithms. The gradient tree boosting algorithm using the baseline period data showed the highest classification performance among the results of the three machine learning algorithms, with validation accuracy, test accuracy, and AUC scores of 0.814 ± 0.012, 0.823 ± 0.025, and 0.853 ± 0.027, respectively. Figure 6(D) shows the ROC curves of the gradient tree boosting algorithm for the four periods with the highest classification performance, visualizing the classification accuracy across each period. AUC scores of approximately 0.5, 0.8–0.9, and more than 0.9 indicate poor, excellent, and outstanding classification performance, respectively [55]. The diabetes classification performance of the gradient tree boosting algorithm can be considered excellent. A comparison of the classification results obtained using input data from the baseline, occlusion, release, and entire periods showed that the baseline period data had the best performance. This is because each part of the blood flow signal obtained by the reactive hyperemia test has different characteristics [45]. The baseline period blood flow reflects stable metabolic information. The occlusion period blood flow contains very little metabolic information. The release period blood flow fluctuates over time, leading to considerable variations in the obtained results. Therefore, blood flow signals from the occlusion and release periods are unsuitable input data for machine learning algorithms to classify diseases. We performed a feature importance analysis to evaluate the impact of each feature in the input data on the obtained diabetes classification results.

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3.2.2. Feature importance analysis result

The impact of diabetes classification results on five features of input data, namely, the blood flow oscillations of cardiac, respiratory, myogenic, neurogenic, and metabolic activities, was observed by feature importance analysis. In feature importance analysis, a higher importance indicates that a feature plays a more critical role in the classification result [50, 56]. Figure 7(A) shows the feature importance results of five blood flow oscillation features (cardiac, respiratory, myogenic, neurogenic, and endothelial-related metabolic activities) for the three machine learning algorithms (gradient tree boosting, random forest, and Adaboost) using baseline period data. From the three machine learning algorithms, the importance of cardiac activities is 0.386 ± 0.041, 0.310 ± 0.017, and 0.266 ± 0.049, respectively, and that of respiratory activities is 0.435 ± 0.104, 0.299 ± 0.030, and 0.333 ± 0.070, respectively. The importance of cardiac and respiratory activities in the random forest and Adaboost algorithms accounted for more than 60% of the total, and the gradient tree boosting algorithm accounted for more than 80%. This is confirmed by other results indicating that features corresponding to cardiac and respiratory activities contribute the most to the explanation of diabetes classification data. The gradient tree boosting algorithm, which showed the best classification performance in figures 6(A)–(C), was adopted to classify diabetes blood flow signals for additional feature importance analysis. Figure 7(B) shows the feature importance results of the gradient tree boosting algorithm from three individual period data (baseline, occlusion, and release). The importance of cardiac and respiratory activities with the baseline period data is much more significant than the other features.

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In the occlusion period data results, the average importance of all features was not different, with values between 0.15 and 0.25. With the release period data, the importance of respiratory activities accounted for more than 50% of the total. Figures 8(A) and (B) shows the feature importance results of the gradient tree boosting algorithm using the entire period data. As mentioned earlier, the entire period refers to combined blood flow oscillation data for the baseline, occlusion, and release periods. Figure 8(A) shows that the sum of the importance for the baseline, occlusion, and release periods is 0.721 ± 0.059, 0.119 ± 0.026, and 0.159 ± 0.050, respectively. The importance of the occlusion and release period data is less than 30% of the total, and the performance increases when these data are not used. It means that even when classifying the control and diabetes blood flow signals using data from the baseline, occlusion, and release periods, the occlusion and release period data had little impact on the classification results, and the baseline period data played a vital role in the classification. In addition, in the total importance, the importance of cardiac and respiratory activities in the baseline period is 0.298 ± 0.019 and 0.327 ± 0.073, respectively (figure 8(B)). It means that these two features accounted for more than 60% of the total importance and had a more significant impact on the classification of diabetes blood flow signals than other features. The feature importance analysis results demonstrate that our proposed disease classification method does not require additional experiments to observe the blood flow reactivity, such as reactive hyperemia. Therefore, the time required for measuring blood flow signals for disease classification is significantly less than that in conventional methods. We performed Pearson correlation analysis to evaluate the impact of each feature in the input data on the diabetes classification performance.

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3.2.3. Pearson correlation coefficient and linear regression analysis

The Pearson correlation coefficient, the blood flow oscillation data, and diabetes classification performance were obtained. This coefficient takes a value between −1 and 1 [57]. Generally, an absolute value of around zero indicates no correlation between the features, whereas a value above 0.7 indicates strong correlation. We used 30 classification results from 10 baseline, 10 occlusion, and 10 release period data to calculate Pearson's correlation coefficient. The correlation values of the three machine learning algorithms using the 30 results are shown in table 1. As shown in table 1(A)–(C), Pearson's correlation coefficients between feature importance corresponding to cardiac activities and diabetes performance were above 0.8. Moreover, the gradient tree boosting algorithm showed Pearson's correlation coefficient above 0.9 as well as the best diabetes classification performance. In contrast, the absolute values of the correlation coefficient between the importance of features other than cardiac activities and diabetes classification performance were all below 0.7. The higher the diabetes classification performance, the higher the Pearson correlation coefficient. These results show that the blood flow oscillation data corresponding to cardiac activity in the blood flow signal was strongly correlated with the diabetes classification performance, and other blood flow oscillation data do not significantly impact the diabetes classification.

Table 1. Pearson correlation coefficient between test accuracy, AUC score, and feature importance calculated using the three machine learning algorithms: gradient tree boosting, random forest, and Adaboost.

	Feature importance	Cardiac activities	Respiratory activities	Myogenic activities	Neurogenic activities	Metabolic activities
Gradient tree boosting	Test accuracy	0.933	0.349	−0.629	−0.519	−0.547
	AUC score	0.928	0.399	−0.699	−0.538	−0.550
Random forest	Test accuracy	0.888	0.685	−0.449	−0.349	−0.371
	AUC score	0.888	0.696	−0.467	−0.288	−0.410
Adaboost	Test accuracy	0.858	0.287	−0.653	−0.436	0.378
	AUC score	0.839	0.216	−0.686	−0.289	0.297

Finally, we performed a linear regression analysis with the best-performing gradient tree-boosting algorithm. Figures 9(A)–(E) shows the results of the linear regression analysis between the AUC score of the gradient tree boosting algorithm and the feature importance of the five blood flow oscillations. Each linear regression graph was visualized using the data to calculate the Pearson correlation coefficient. Figure 9(A) shows the results of the linear regression analysis between the AUC score and the feature importance of cardiac activities; the R² value is 0.8608. Figures 9(B)–(E) shows the results of the linear regression analysis between the AUC score and the feature importance of the other activities; all R² values were below 0.5. The linear regression graph analysis showed that changes in blood flow related to cardiac activity contain important information for classifying diabetes, as shown in table 1. Considering that CVD is the leading cause of death in diabetics, the findings on blood flow oscillations corresponding to cardiac activity are noteworthy. This is because the blood flow oscillation data reflects metabolic information, and diabetes has the most significant impact on metabolism related to cardiac activity.

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