Detection of Diabetic Foot Using Statistical Features

Abstract

Diabetes is a serious threat to universal health that respects neither socioeconomic rank nor nationwide boundaries. Diabetic foot and lower extremities problems, which affect 40 to 60 million people with diabetes universally, are a significant source of morbidity in people with diabetes. Conducting regular screening and risk stratification for at-risk feet can be greatly used for the management of blood glucose levels. Recent studies revealed that qualitative evidence can be attained using temperature variations from the thermogram of the plantar foot. The changes in temperature distribution are vital in the investigation of diabetic foot, which assist in the early detection of foot ulceration. The main objective of this work is to perform statistical analysis of diabetic foot to draw reasonable and accurate inferences. Besides, there is no gold standard method in classifying the plantar thermal images into any particular group. This may be conquered by quantitatively analyzing the temperature distributions in each foot separately. Since, plantar thermal images are colored in nature, certain color statistical features which are statistically more significant are added with the quantitative temperature distribution to develop an efficient machine learning method to prognosticate the likelihood of diabetes in patients with maximum accuracy is explored.

1. Introduction

Globally, diabetes is among the top ten causes of death in adults and was estimated to have caused the 4.2 million deaths resulting from diabetes and its complications in 2019. India is ranked second with almost 77 million cases in the list of countries that are most affected with diabetes while China leads the list with over 116.4 million diabetics. An estimated 15.8% (20.4 million) of live births are affected by hyperglycemia in pregnancy in 2019. This represents 9.3% of the world’s population in this age group. In the International Diabetes Federation (IDF) South-East Asia Region, 57% of adults aged 20–79 years with diabetes are undiagnosed. An estimated 1.1 million children and adolescents (aged under 20 years) have type 1 diabetes. The total number is projected to rise to 578 million (10.2%) by 2030 and to 700 million (10.9%) by 2045. Annual worldwide health spending on diabetes is estimated to be USD 760 billion. It is projected that expenditure will reach USD 825 billion by 2030 and USD 845 billion by 2045 [1].

Fifty percentage of patients with diabetes have some degree of neuropathy, resulting in at least one-foot ulcer throughout the lifetime in 15% of the cases. Neuropathic foot ulceration is a foremost cause of illness in patients with diabetes [2]. Diabetes patients have demonstrated that there are significantly increased skin temperatures and recognizable thermal radiation patterns, which differentiate them from healthy people. Thermometry of the diabetic foot is an impressive way to evaluate the risks associated with foot ulceration [3]. It has been revealed that monitoring foot skin temperature contributes to the clinical information before other medical signs of the wound can be recognized [4]. Differences in plantar thermal patterns in normal controls and non-ulcer diabetic patients were studied using thermometry [5]. Though, it has not been abundantly clarified to what extent the individual inconsistency of the plantar thermal patterns shows different trends between healthy and diabetes patients. Thermal imaging technology is capable to measure insignificant temperature irregularities to oversee some physiological circumstances [6]. Understanding of the temperature profile of foot is quite important to evolve thermal imaging system for detection of diabetic foot.

1.1 Temperature profile of foot

A healthy foot having healthy blood flow through healthy blood vessels whereas the decreased blood flow in the diabetic foot cause damage to organs like the leg and foot. The lack of blood flow caused by diabetes decreases the body’s ability to heal from injuries. The assessment of raised temperature distribution with infrared thermometry in the diabetic foot is employed to identify the varying metabolic activity. Skin examination with an IR thermometer is flexible to repetitive wound care practice and home health. Nevertheless, the IR thermometry method becomes difficult and insufficient when measuring the temperature at many points on the foot [7, 8]. The liquid crystal thermograph methodology provides the temperatures pattern of the foot area as a colored foot imprint on a plate encompassed by layers of compressed thermochromics liquid crystals. The imprint persists for few minutes and then gradually disappear away. A temperature profile cannot be obtained for non-contact areas like an arch [9, 10].

Employing high-resolution and very sensitive thermal imaging cameras, the heat radiation from the matter is acquired and processed into an image of the thermal map which can then be stored and analyzed on screen and computer. Increased temperature investigation can be attained even for non-contact foot areas. Thermal images of diabetic feet reveal that it is 2.2°C colder than the lower leg, and usually the toes are not observable to the camera as they have become so hypothermic. Diabetic foot can arise several years before repetitive blood glucose levels indicate diabetes, and as such, can provide the patient time to treat the illness before everlasting nerve impairment occurs to the foot [11, 12, 13].

Though thermal imaging system is a promising screening tool for diabetic foot, diagnosis is usually done manually by skilled professionals. Hence, analyses made from thermograms are greatly subjective in nature. In order to overcome issues such as lack of proficient personnel, an efficient machine learning framework needs to be developed. The developments made in thermography and pattern recognition techniques are used to develop a competent system for detection of diabetic foot in plantar thermograms. Such a system can be used for screening of diabetes mellitus patients in developing countries, specifically by primary health care specialists in rural areas where health care expert is lacking.

2. Outline of the chapter

The main objective of this work is to perform statistical analysis in the thermal images to achieve reasonable and accurate inferences to make decisions accurately which aids in the prevention of numerous errors and biases. A Kernel Mixture Model (KMM) with four components approximates the plantar temperature distributions of the control group and DM group. Color texture features are extracted and analyzed to find the important features. A competent classification model to investigate the likelihood of diabetes in patients with maximum accuracy using the statistically significant temperature and color texture features is presented in Figure 1.

Figure 1.

Statistical analysis-based system for detection of diabetic foot.

2.1 Thermal camera and dataset details

The camera specifications, dataset details, and image acquisition protocol used in this study are presented in the following sections.

2.1.1 Thermal camera specifications

Most of the work in plantar foot thermography has been done on thermograms acquired using an infrared thermal imaging camera. Thermal imaging cameras with a high resolution made suitable for medical applications can measure subtle temperature changes and hence are capable of improved detection of diabetic foot complications. A FLIR E60 thermal imaging camera is used for the present study to acquire plantar foot thermal images. It has a resolution of 320x240 pixels and covers a Field of View (FOV) of 25°x19°. The range of operation of the camera is in the region of the infrared spectrum from 7.5 μm to 13 μm wavelength. It can detect the temperature in the range of −20–650°C with thermal sensitivity of less than 0.05°C at 30°C and has an onboard digital camera with a resolution of 3.1 megapixels (MP). The onboard digital camera covers the same FOV as that of the thermal imaging camera and acquired images are of size 2048x1536 pixels. The temperature values are associated with a color palette (Rainbow Color Scheme palette) to represent and distinguish them graphically, where blue and green shades represent cooler regions. Warmer regions are represented by yellow, orange, and red colors in the increasing order of temperature respectively. Maximum temperature (intensity) is represented in white. It is ensured that the thermal imaging camera is calibrated against a black body reference as per the manufacturer’s recommendations [14].

2.1.2 Laboratory and patient preparation protocols

In order to acquire accurate and convenient outcomes for clinical practice, the thermal images of the participants in the study were carried out in compliance with the protocols and guidelines set by the International Academy of Clinical Thermology Standards and Protocols [15, 16, 17] are listed below:

• The examination was performed in a steady-state 20 ± 1°C environment.

• The thermal images were acquired when the subject is sitting in a podiatric chair or comfortable and adequate position.

• The thermal imaging system emissivity is set to 0.98

• The thermal camera is calibrated prior to image acquisition by focusing lens on a black body

• After socks have been removed, the foot regions are cleaned with a damp towel

• All the subjects/patients are requested to remain in bare foot for 10–20 minutes before performing the actual measurements to eliminate the effect of external aspects on the temperature distributions of the foot

• The camera should be placed at a distance of 1.1 m

• During the investigation, the patient should be able to be placed relatively middle and sufficiently spaced from each wall

• Any IR radiation source is available in the investigational room that should be shielded/covered

The schematic representation of the acquisition of plantar thermal image is depicted in Figure 2.

Figure 2.

Schematic arrangement for acquisition of thermal image.

2.1.3 Dataset details

The control subjects and Diabetes Mellitus (DM) patients were considered in this study. A total of 35 control subjects and 35 DM patients were recruited from and Hycare for Wounds, Chennai. Both control and DM groups comprise male and female participants, aged between 30 and 65 years. The DM group thermal image collection has been granted by Hycare for Wounds – Institutional Review Board. The participants were informed about the study beforehand and written informed consent forms were obtained from the participants of the study. Sample color and thermal images of the control group and DM group are acquired by the highly sensitive FLIR E60 IR thermal imaging system and are shown in Figures 3 and 4 (a, b) respectively.

Figure 3.

Control group samples images. (a) Color image of the foot. (b) Thermal image of the foot.

Figure 4.

DM group samples images. (a) Color image of the foot. (b) Thermal image of the foot.

This study is carried out both on acquired and publicly available plantar thermogram database [17, 18, 19, 20, 21] for the early detection of diabetic foot. The plantar thermogram database was obtained in a controlled environment 20 ± 1°C using FLIR E60 and FLIR E6 IR thermal imaging system from 122 subjects diagnosed with diabetes (DM group) and 45 healthy subjects (control group). During the thermogram acquisition, the position of the camera is fixed by an adjustable vertical tripod to avoid any undesirable movement. The tripod is placed one meter away from the feet. The participants were asked to remove their shoes and socks and clean their feet with a damp towel. After that, the subjects were invited to maintain a supine position for 15 minutes (Figure 5).

Figure 5.

(a) Database thermal image of the foot – Control group. (b) Database thermal image of the foot – DM group.

For each plantar thermogram, the left and right foot were extracted and was taken as a separate thermogram, obtaining a database of 334 individual thermograms. The subjects were recruited from the General Hospital of the North, the General Hospital of the South, the BIOCARE clinic, and the National Institute of Astrophysics, Optics and Electronics (INAOE) over 3 years (from 2012 to 2014). The sample thermal image from the control group and DM group of the database is depicted in Figure 4(a) and (b), respectively. The total number of images used in the study is tabulated in Table 1, where the left foot and right foot is denoted by LF and RF respectively.

	Control Group	DM Group
Acquired images	70 (35 LF & 35 RF)	70 (35 LF & 35 RF)
Plantar thermogram database	90 (45 LF & 45 RF)	244 (122 LF & 122 RF)
Total	160 (80 LF & 80 RF)	314 (157 LF & 157 RF)

Table 1.

Number of images in the dataset.

Since the database images are having only the foot region, the segmentation is performed only for the acquired plantar thermal images. The left and right foot regions are segmented from each color image using the region growing algorithm [22]. The red, green, and blue planes are extracted from thermal images and multiplied with the corresponding segmented foot region to get the ROI as a thermal image. The foot position of the left and right foot regions is corrected. Figure 6(a) and (b) show the segmented plantar foot regions of the control group and DM group, respectively. The raw temperature profiles of the acquired thermal images are exported as a.csv file from FLIR Tools® thermal analysis and reporting software. The binary image of the segmented foot regions is multiplied with the raw temperature profile of the corresponding foot regions to obtain the temperature distribution for the foot regions.

Figure 6.

(a) Segmented LF and RF regions of the control group. (b) Segmented left and right foot regions of the DM group.

3. Temperature distribution analysis

The plantar foot region is divided into four regions covering the toe region, metatarsal heads, medial arch and heel region to quantitatively analyze the temperature distribution. Histogram plot of the temperature distributions is accomplished by computing the mean temperature for each row of the plantar raw temperature profile for both left and right foot. The temperature values which are greater than 0°C are alone used to compute the mean temperature while those temperature values that are equal to 0°C are related to background and hence eliminated in each row. The histogram plot of the temperature distributions was offset corrected and normalized. The balance of every single distribution is eliminated by deducting the smallest temperature value either at the start or termination of the distribution. Later it is normalized by selecting a precision of three decimal figures to differentiate deviations in temperature from one pixel to another pixel.

3.1 Kernel density estimation

Once the final histogram is obtained, an approximation of density function is estimated using Kernel Density Estimation (KDE). A kernel distribution is a non-parametric representation of the probability density function (pdf) of a random variable. Let $x{}_1,x{}_2,\dots ,x{}_n$ be observations drawn independently from a distribution P with density p. The kernel density estimate ${\widehat{g}}_h\left(x\right)$ is defined as

$${\widehat{g}}_h\left(x\right)=\frac{1}{\mathit{nh}}\sum _{i=1}^{n}K\left(\frac{x-x_i}{h}\right)$$E1

Where $K\left(\cdot \right)$ denotes the smoothing kernel function, and h > 0 is the smoothing bandwidth criterion which regulates the amount of smoothing. The kernel function is balanced and unimodal about the origin. The Gaussian kernel with normal distribution is utilized in this work. Bandwidth controls the smoothness of the density estimation. A smaller value of h will result in a rough estimation, while a higher value of h will result in a remarkably smooth estimate. The KDE smoothens every observation into a smaller density and the summation of these smaller densities together is used to attain the ultimate density estimate. The KDE is used to smooth the histogram plot of the temperature distribution and investigate the statistical significance [23, 24]. The temperature distributions of the four ROI (toes, metatarsal heads, medial arch and heel) in each foot are estimated using kernel density estimation. The histogram of the mean temperature distribution was smoothened using kernel density estimation which follows the non-parametric distribution. Figures 7 and 8 (a)-(d) illustrates the histogram and smoothened histogram of the left and right foot for the control and DM group.

Figure 7.

Smoothened temperature distribution - control group.

Figure 8.

Smoothened temperature distribution - DM group.

The smoothening is repeated for all the four regions of each left and right foot of the control and DM group. The region-wise smoothened temperature distribution is superimposed on the whole foot smoothened output for the control and DM groups depicted in Figures 9 and 10, respectively. From the mean temperature distribution histogram plot it was observed that the control group have a larger mean temperature around 21–22°C with a smaller number of occurrences of temperatures distribution while the DM group have a larger mean temperature around 23–24°C with a larger number of occurrences of particular temperatures values. Similar kinds of deviations are observed in all the four ROIs of the left foot and right foot in the control and DM groups.

Figure 9.

Region wise smoothened temperature distribution superimposed on the whole foot - control group.

Figure 10.

Region wise smoothened temperature distribution superimposed on the whole foot output - DM group.

Since the KDE, which is a non-parametric distribution utilized to smoothen the temperature distribution, the central tendency among the control and DM groups was calculated by arranging the temperature distribution in ascending order to determine median and interquartile range for statistical analysis. Similarly, the median and interquartile range are also obtained for all the four ROIs with the corresponding smoothened temperature distribution for both control and DM groups. The computed median and interquartile range extracted from whole foot and region-wise for both groups are shown in Tables 2 and 3.

Group	Median (°C)		Interquartile Range (°C)
	Left Foot	Right Foot	Left Foot	Right Foot
Control Group	27 ± 1.80	26.98 ± 1.77	1.92 ± 0.60	1.94 ± 0.49
DM Group	29.64 ± 2.85	29.84 ± 2.85	1.55 ± 0.66	1.59 ± 0.74

Table 2.

Median and interquartile range for whole foot.

Group	Region of Interest	Median (°C)		Interquartile Range (°C)
		Left Foot	Right Foot	Left Foot	Right Foot
Control Group	Toes	25.3 ± 2.17	25.33 ± 2.32	1.68 ± 0.69	1.68 ± 0.64
	Metatarsals	26.9 ± 1.99	26.82 ± 1.93	1.00 ± 0.38	1.03 ± 0.35
	Arch	28.23 ± 1.63	28.19 ± 1.61	1.79 ± 0.56	1.82 ± 0.55
	Heel	26.69 ± 1.76	26.68 ± 1.75	1.19 ± 0.42	1.18 ± 0.41
DM Group	Toes	29.50 ± 3.66	29.72 ± 3.70	1.24 ± 0.79	1.32 ± 0.95
	Metatarsals	29.89 ± 3.15	30.12 ± 3.15	0.92 ± 0.52	0.89 ± 0.47
	Arch	29.86 ± 2.55	30.06 ± 2.52	1.24 ± 0.58	1.19 ± 0.56
	Heel	29.17 ± 2.73	29.45 ± 2.79	1.02 ± 0.42	1.08 ± 0.48

Table 3.

Region wise median and interquartile range.

Thus, between Tables 2 and 3 it was observed that the control group has a lower median temperature than the DM group. Since the mean temperature distribution is having a higher value in the lower quartile and upper quartile for the whole foot and region-wise, the interquartile range for the DM group is lesser than the control group.

The Chi-square goodness-of-fit [25] test was employed to assess the null hypothesis statistically for all the smoothened temperature distribution of left foot and right foot among control and DM group as shown in Table 4. This test is utilized to determine whether the variables are attained from the particular group temperature distribution or not and also to evaluate whether the sample data is representative of the full population of the temperature distribution. For both control and DM groups, the test returned an h value equivalent to one which specifies that chi-square goodness-of-fit rejects the null hypothesis at 5% significance level. Hence, these median and interquartile ranges are utilized to detect the diabetic foot in the classification process.

Group	Null Hypothesis (h)		Probability
	Left Foot	Right Foot	Left Foot	Right Foot
Control Group	1	1	0.00459	0.00290
DM Group	1	1	0.00477	0.00448

Table 4.

Chi-square goodness-of-fit test results.

4. Extraction of color texture features

Color is one of the better notable and striking visual aspects that is employed in image retrieval and pattern recognition. Color moment (CM) is a computation technique utilized to discriminate images based on their color distribution in the image similar to the central tendency of the probability distribution. It is a potential technique for the description of color features [26, 27]. Once determined, these moments contribute a quantity for color resemblance among images. The red plane, green plane and blue plane images are extracted from each of the segmented thermal images for the control and DM groups. In this study, the mean (first moment), standard deviation (second moment), skewness (third moment), kurtosis (fourth moment), variance and entropy are extracted for all the four ROIs in each foot of all three color planes of images. The mean represents the average color value existing in the image. Variance is a measure of the color distribution of the image. Standard deviation is attained by executing a square root of the variance of the color distribution. Skewness is a measure of the degree of symmetry distribution of the color. The color textural features extracted from the green plane images of the left and right foot are highly correlated and shows very few dissimilarities within the values for all the four ROIs. Hence, the color texture features extracted from red and blue plane images alone are used for further processing. The skewness is having negative values for a few ROIs is the representation of the tail at the smaller end of the textural distribution is more pronounced than the tail at the larger end of the textural distribution.

5. Classification using machine learning techniques

5.1 Support vector machine

Support Vector Machine (SVM) is a discriminative classifier algorithm, concerning the patterns represented by the subset $d_i=+1$ and the patterns represented by the subset $d_i=-1$ are linearly separable. The decision surface that is in the form of a hyperplane that does the separation is given as follows.

$$w^{T}x=\sum _i{w}_i{x}_i$$E2

$$w^{T}x+b=0$$E3

where x is an input vector, w is an adjustable weight vector, and b is bias. The point closest to the hyperplane is called the ‘support vector’. The SVM classifier maximizes the margin of separation between the classes and minimizes the classification errors [28, 29]. The best hyperplane for SVM is the one with the largest margin between the two classes.

5.2 K-nearest neighbors (KNN) classifier

The KNN classifier is a non-parametric, non-linear, and simple method that is used to classify the features. In this algorithm, the classification of test data is executed by finding a majority vote of the known class, and the input data will attain the class that is most common among its k-nearest neighbors [30, 31]. It is obtained using a distance metric such as Euclidean distance between the training and test data set which is calculated by

$$D_e\left(x_1,x_2\right)=\sqrt{{\sum }_{i=1}^n{\left(x_{1i}-x_{2i}\right)}^2}$$E4

where, $x_1=\left(x_{11},x_{12},\dots ,x_{1n}\right)\text{and}{x}_2=\left(x_{21},x_{22},\dots ,x_{2n}\right)$.

The test data is assigned to a class based on closest k-datasets for training based on resemblance measures, subsequently, the majority vote of the case neighbors is determined to categorize the case [32, 33].

The textural color features, median temperature and interquartile range forms the feature sets for detection of the diabetic foot using SVM and KNN classifier. The different grouping of feature sets which are extracted from the control and DM group was investigated in this study as follows:

• Group 1 (RBT) contains 14 features as it is formed with the statistical measure of the median, interquartile range with color textural features extracted from red and blue plane images

• Group 2 (RB) consists of 12 features as it is formed with the color textural features extracted from red and blue plane images

• Group 3 (RT) contains 8 features as it is formed with the statistical measure of the median, interquartile range with color textural features extracted from red plane images

• Group 4 (BT) consists of 8 features as it is formed with the statistical measure of the median, interquartile range with color textural features extracted from blue plane images

In all the combination, 80% of features are used to train and the remaining 20% of features are used to test the performance of the classifier. In this study, the classification is carried out using the SVM classifier and K-Nearest Neighbors (KNN) classifier for automatic classification of the plantar thermal images into two classes. The performance evaluation metrics of SVM and KNN classifiers for the detection of diabetic foot are shown in Figure 11. It was realized that the SVM classifier has obtained a higher classification accuracy of 92.86%, a sensitivity of 96.55%, specificity of 84.62%, a precision of 93.33%, and an F1-score of 94.92% for Group 1 (RBT) features combination than other combinations of feature set.

Figure 11.

Performance of SVM and KNN classifier in various combinations of feature set.

6. Conclusion

In this study, the statistical analysis of plantar temperature distribution based non-parametric way was done by using kernel density estimation. This approach showed the temperature distribution changes in different areas of the plantar region between the control and DM groups. The median and interquartile ranges are obtained from the statistical analysis. The extracted color features are grouped with the statistical measures of temperature distribution to automatically classify the data using SVM and KNN classifiers. Four different combinations of features sets were used to train and test the performance of the classifier. The SVM classier obtained better accuracy with Group 1 (RBT) feature sets.

Acknowledgments

Authors would like to register their profound gratitude to Dr.V.B.Narayanamurthy, Dr.K.Rajesh and Dr.R.Arvind, Directors of Hycare for Wouds, Chennai, India, for their help to get the ethical approval from Institutional Review Board (IRB) for acquisition of thermal images and Clinical inputs for the same. The authors are also thankful to the patients and healthy volunteers who actively participated in the data collection and the clinicians in the Hycare for Wounds, Chennai.

Conflict of interest

The authors declare no conflict of interest.