Non-Invasive and Accurate Blood Glucose Detection Based on an Equivalent Bioimpedance Spectrum

Abstract

Accurate blood glucose monitoring is a key issue for the diagnosis and treatment of diabetes. For this purpose, a non-invasive blood glucose detection method is proposed, which makes use of the equivalent bioelectric impedance spectrum. An impedance detection platform is designed using an automatic balance bridge technique, which can acquire an impedance spectrum within the range of dispersion. Then, the K-nearest neighbor algorithm is used to extract the characteristics of the impedance spectrum. Furthermore, higher-order multiple regression methods are used to establish a blood glucose–electrical impedance spectrum model. Experimental results show that the proposed blood glucose–electrical impedance spectrum model can estimate the change in blood glucose and reliably identify the high blood glucose samples. The correlation between the proposed method and the biochemical blood glucose values can reach 0.89 and 0.87 in personal and multi-person blood glucose tests, respectively. Thus, the proposed method provides a feasible solution for non-invasive blood glucose detection and can help us identify diabetes mellitus.

1. Introduction

Diabetes is a chronic disease and ranks as the third leading cause of death worldwide [1,2]. It denotes a disorder from insulin secretion or action defects, causing metabolism disruptions in blood glucose, fat, and protein [3]. On 22 June 2023, $\mathit{The}\mathit{Lancet}$ published the Global Burden of Disease Study 2021, estimating diabetes’s global impact from 1990–2021 and forecasting trends for 2050 [4]. In 2021, 529 million people had diabetes, with a 6.1% prevalence rate. This resulted in 37.8 million YLLs, 41.4 million YLDs, and 79.2 million DALYs, 95.4% of which were due to type 2 diabetes [5]. By 2050, 1.31 billion people may have diabetes. Prolonged high blood glucose can cause irreversible tissue and organ damage, leading to complications like heart disease, kidney failure, eye issues, and nerve damage [6]. The WHO recommends that individuals with diabetes monitor their blood glucose levels four to five times daily [7]. This underscores the immense need for blood glucose monitoring among hundreds of millions of diabetes patients. The 2019 ADA Standards of Care for Diabetes elevated ‘blood glucose monitoring’ to a status equal to drug therapy, dedicating a separate chapter to it, highlighting the importance of blood glucose testing tech [8]. Moreover, real-time blood glucose monitoring offers daily data for diabetes patients and high-risk individuals, aiding in diet, medication, and achieving glucose control through lifestyle and medication coordination [9,10]. Recently, tech advances and rising health awareness, especially among the youth, have increased acceptance of “three highs” and demand for convenient health monitoring devices [11,12]. Blood glucose detection methods are invasive or minimally invasive, painful, and can cause infection. Non-invasive methods are painless, infection-free, convenient, comfortable, and cost-effective, offering accurate, real-time monitoring and early detection of metabolic abnormalities with substantial value. Therefore, non-invasive blood glucose detection technology has become a research hotspot in recent years [13,14].

The concept of non-invasive blood glucose detection was proposed in the 1980s. Currently, non-invasive blood glucose detection methods can be broadly categorized into two types based on their detection principles: optical methods and non-optical methods. Non-optical methods primarily include the energy metabolism conservation method [15], the microwave detection method (MS) [16], the electromagnetic detection method (ES) [17], and bioelectrical impedance spectroscopy (BIS) [18]. BIS refers to the conductive and dielectric properties exhibited by organisms when weak alternating currents below the excitation threshold are applied. This technique can estimate fluctuations in blood glucose levels, thereby facilitating the prediction of blood glucose concentrations [19].

In this paper, a type 2 diabetes mellitus recognition method based on an equivalent bioelectric impedance spectrum is introduced. It uses automatic balance bridge technology to design an impedance spectrum acquisition circuit and then extract impedance spectrum characteristics using the K-nearest neighbor algorithm [20]. Then, blood glucose samples are processed via multiple regression to establish a blood glucose–electrical impedance spectrum model and implement non-invasive blood glucose detection. According to the experimental results, the proposed method can accurately detect the fluctuation of personal blood glucose and reliably identify high blood glucose samples in multi-person tests.

2. Non-Invasive Blood Glucose Detection Mechanism Based on BIS

In physiology, glucose, as a monosaccharide that can be directly absorbed by the human body, dissolves in the blood and provides energy for the human body as the blood flows. In the physiological process of the body providing energy by absorbing glucose, the main participant is the glucose transporter protease embedded in the phospholipid bilayer of the cell membrane. Glucose-transported protease is embedded in the phospholipid bilayer of the human cell membrane. It acts as a target-recognition protein substance for glucose in the human body and passes glucose through the cell membrane into the cell to complete the physiological activity of energy supply. In this process, the transport speed of transport protease is limited by the difference in blood glucose concentration between the intracellular and external fluids, as well as the body’s temperature. Generally, the difference in blood glucose concentration plays a key role. The transfer rate of glucose will increase as the difference in blood glucose concentration increases. Glucose transport protease has two states: when it is involved in glucose transport, it is in an activated state; when it is not involved in glucose transport, it is in a resting or idle state. The amount of activated transport proteases can influence the dielectric constant of the cell membrane, as shown in (1) [21,22].

$${\epsilon }_{mem}={\epsilon }_{mem,0}\left[1+{\displaystyle \frac{(N_{free}+N_{glu}){{\mu }_{glu}}^2}{3kT{\epsilon }_0{\epsilon }_{mem,0}(1+\raisebox{1ex}{$K_m$}\!\left/ \!\raisebox{-1ex}{${\mathrm{C}}_{glu}$}\right.)}}]\right.$$

(1)

Formula (1) describes the relationship between the cell membrane dielectric constant ${\epsilon }_{mem}$ and the glucose concentration $c_{glu}$. In (1), $N_{free}$ refers to the volume concentration of the transporter in an idle state; $N_{glu}$ is the volume concentration of the transporter in activated state, and ${\mu }_{glu}$ is the dipole moment; ${\epsilon }_0$ represents the dielectric constant of the cell membrane in vacuum state. According to (1), the glucose concentration can be acquired indirectly by measuring the dielectric constant of the cell membrane. In addition, since the complex permittivity of human tissue is related to the complex impedance of the human body, it is possible to measure the complex permittivity of the cell membrane through the equivalent biological complex impedance of the human body. The relationship between complex impedance $Z^{\prime }$ and complex permittivity ${\epsilon }_{mem}$ is shown in (2) [23]:

$$Z^{\prime }={\displaystyle \frac{\kappa }{j\omega {\epsilon }_{mem}{\epsilon }_0}}.$$

(2)

According to (1) and (2), the mathematical relationship between the equivalent complex impedance of the human body and the blood glucose concentration is obtained. Therefore, the blood glucose value can be acquired by measuring the bioelectrical impedance. We establish a second-order linear regression model to examine the relationship between blood glucose values and impedance values, with the aim of predicting real-time blood glucose levels.

3. Bioelectrical Impedance Technology

The basic units of the human body are cells, the intracellular fluid inside cells, and the extracellular fluid between cells, all of which are components of bodily fluids. Since human bodily fluid contains a number of ions, when an AC excitation signal enters the human body, the current will propagate in the bodily fluid with lower impedance and stronger conductivity. As the frequency of the excitation signal increases, the propagation of the current will also be enhanced, as shown in Figure 1. This implies that the current-carrying human body may be equivalent to an impedance model. According to the classic Cole–Cole model, the human body shows resistance and capacitance characteristics when driven by an AC signal. Therefore, the human body can be equivalent to an R–C (resistance–capacitance) model in such cases [24], which is the basis of bioelectrical impedance technology.

Bioelectrical impedance technology can reveal the characteristics of different human body tissues by measuring their impedances. According to Schwan’s frequency dispersion theory, there are three different frequency bands [25], namely the $\alpha$ frequency area, the $\beta$ frequency area, and the $\gamma$ frequency area, as shown in Figure 2. The $\alpha$ band mainly reflects the characteristics of the ionic environment in biological fluids and is mostly used in biological component analysis and organ inspection. In the $\beta$ frequency region, with the increase in the excitation signal, the equivalent capacitance of the cell membrane remains relatively stable, so a relatively stable impedance characteristic can be obtained. The $\beta$ band is used in blood glucose detection and blood-related information detection, and the $\gamma$ band reflects some characteristics related to water molecules in cells. The frequency band characteristics appear because the applied electric field causes the dipole moment of protein binding water and protein molecules to rotate. Currently, the $\gamma$ band cannot be effectively applied to equivalent bioimpedance research, mainly because the interior of the human body is very complicated. For the non-invasive blood glucose detection model in this paper, band $\beta$ is selected for the excitation signal on the hardware platform.

In summary, when conducting research on bioelectrical impedance, the $\alpha$ frequency band and the $\beta$ frequency band are concentrated. But, the study found that it is difficult for a current to enter the cell in the $\alpha$ frequency region. As the frequency band of the test signal rises, an electric current will penetrate the cell membrane and flow into the intracellular fluid. In the $\beta$ band, the conductivity of the extracellular fluid increases with the frequency, and the relative dielectric constant value of the cell membrane decreases with the frequency. Within the $\beta$ dispersion frequency, the dielectric properties of biological tissues can effectively reflect the internal state of the cell, especially for the equivalent impedance change caused by the difference in blood glucose concentration inside and outside the cell. For the non-invasive blood glucose detection model designed in this paper, the $\beta$ band is selected as the signal frequency band of the excitation signal to design the hardware detection platform.

4. Electrode Tests and Measurement Band Selection

In the process of impedance spectrum measurement, once the signal is applied, a reverse electromotive force will arise between the test electrode and the skin, and it will prevent the current from entering organic tissues. This phenomenon is called the polarization of the electrode, and the reverse electromotive force is called the polarization potential, as shown in Figure 3. In non-invasive blood glucose detection based on bioelectrical impedance, the polarization of the electrode has different influences among persons under test, and that will make the excitation signal unable to effectively penetrate the skin and bodily fluids, eventually leading to inaccurate results. This chapter conducts experiments on the scattering parameter S of the test electrode, analyzes the return loss of the electrode in different frequency bands, and determines the frequency range of the test excitation signal in the hardware acquisition platform.

In order to reduce the polarization of the electrodes, experiments were carried out on the electrodes in different concentrations of blood glucose solutions to simulate the conditions of human bodily fluids with different blood glucose levels. Electrocardiogram electrodes are utilized in the tests. Different amounts of pure glucose are added to 0.9% normal saline to obtain blood-like solutions with different blood glucose concentrations. According to the physiological significance, the normal blood glucose concentration is in the range of 0.68∼1.3 g/L, so five different glucose ratios are selected: 0.3 g/L, 0.6 g/L, 0.9 g/L, 1.2 g/L, and 1.5 g/L. The concentration of blood-like solution required to simulate changes in the blood glucose varies. The instrument used is Keysight Technology’s E5061B vector network analyzer with a 10 kHz–50 GHz frequency range, which meets the experimental requirements.

When bioelectrical impedance technology is used for blood glucose detection, the selected excitation signal is a high-frequency signal, so the concept of a two-port network needs to be used for circuit analysis. As shown in Figure 4, if $a_1$ is represented as the signal incident wave, then $a_2$ can be represented as the outgoing wave after $a_1$ penetrates the network, and $b_1$ is represented as the signal reflected wave of $a_1$. Then, the return loss degree $S_{11}$ is as follows:

$$S_{11}=20\ast log(\raisebox{1ex}{$b_1$}\!\left/ \!\raisebox{-1ex}{$a_1$}\right.)$$

(3)

Due to impedance mismatch and other factors, the signal will be partially reflected on the electrode, and that will cause energy loss of the signal. In addition, according to the principle of radio frequency, a smaller $S_{11}$ means a smaller return loss of the signal, and thus, more energy of the signal can penetrate the skin in non-invasive blood glucose detection. In that case, the electrical characteristics of human tissues, as well as the blood glucose concentration, can be acquired with better reliability. Physiological parameters are primarily acquired using biomedical electrode pads. However, biological signals are inherently weak and prone to interference. The material and design of the electrode pads significantly influence return loss and polarization voltage. While this aspect is not the primary focus of the article, it is important to note that we have opted for well-established traditional silver/silver chloride electrode pads.

The relationship between parameter $S_{11}$ and the frequency obtained through the experiment is shown in Figure 5. It was observed that the glucose concentration in the blood-like solution increases, and the amplitude of the $S_{11}$ parameter decreases. With the increase in the test signal frequency, the $S_{11}$ parameter shows a downward trend and reaches the lowest point at 60–70 MHz. In the frequency range of 20–60 MHz, the falling rate of $S_{11}$ is the fastest in the whole process, and good linear results can be obtained in this frequency range. In the frequency range of 1–140 MHz, for ECG electrodes, the excitation signal in the frequency band of 60–70 MHz has lower return loss of the signal, stronger penetration to the skin, and contact with blood, cells, and other tissues. It is more sufficient to detect blood glucose information more accurately, so this frequency band should be included in the measurement frequency range.

The above experiment shows the optimal frequency range with respect to the $S_{11}$ parameter. The collected electrical impedance data revealed that at approximately 30 MHz, the impedance value reached its minimum, coinciding with the resonance point of the biological tissue’s RC equivalent circuit. At this frequency, the impedance of the biological tissue was at its highest, while the capacitive reactance was at its lowest. Considering the above, the frequency band of the excitation signal was finally determined as 25–60 MHz.

5. An Equivalent Bioelectrical Impedance Spectrum Acquisition Platform Based on the Electric Bridge Method

As stated above, bioelectrical impedance technology can physiologically analyze the human body via the characteristics of electrical signals. However, blood glucose information cannot be represented by only one or several specific impedance values; thus, the bioelectrical impedance spectroscopy method is used for detection [26]. This method scans the equivalent bioelectrical impedance of the human body within a certain frequency range. In non-invasive blood glucose detection, blood glucose information can be extracted from the impedance spectrum. Moreover, by controlling the frequency band of the excitation signal, the influence of individual differences can be greatly reduced so as to enhance the accuracy and generalization ability of the measurement mode.

According to the above-mentioned frequency range selection, a hardware platform for equivalent bioimpedance spectrum analysis has been designed, and its block diagram is shown in Figure 6.

The proposed hardware platform contains a microprocessor, a signal source, a phase detector, a power supply module, and other related parts. The microprocessor controls the signal source and communicates with the PC. The signal source generates excitation signals and implements frequency sweeping. The self-balance bridge module is the measurement unit for non-invasive tests. The phase detector measures the modulus and phase of the equivalent bioelectrical impedance from test signals. All the above modules are powered by the power supply module. This platform can acquire the impedance spectrum in 25–60 MHz.

The next step is to use the designed hardware platform to measure the impedance of the fixed part of the human body and process the obtained impedance data to fit a model that can indirectly measure blood glucose. The test electrodes of the system are disposable ECG electrodes produced by Hangzhou Schindler Radio Equipment Co., Ltd in China Zhejiang. The electrode materials are silver/silver chloride (Ag/AgCl), and the mesh non-woven backing is used for full contact with human skin. The specific measurement point is the inner side of the human forearm. The pasting distance between the two ECG electrodes is about 10 cm. Before attaching it to the skin, wipe the measurement site with medical alcohol and dry it with a dry face to reduce the influence of skin sweat on the measurement results.

6. Classification of Blood Glucose Parameters Based on the K-Proximity Method

6.1. Impedance Spectra Features of Different Blood Glucose Samples

The equivalent bioelectrical impedance acquisition platform designed in this paper is used for impedance spectrum acquisition and data preprocessing. The preprocessed impedance spectra are classified into “standard blood glucose samples” and “hyperglycemia samples” according to the threshold of 7.0 mmol/L biochemical blood glucose. The impedance spectra of standard blood glucose samples and hyperglycemia samples are shown in Figure 7 and Figure 8, respectively. For hyperglycemia samples, it is found that the impedance shows a decreasing trend at 25–30 MHz and fluctuates at 40–60 MHz. In contrast, for standard blood glucose samples, the impedance increases at 25–35 MHz, then gently changes in the higher frequency band without clear regularity.

For samples near the 7.0 mmol/L threshold (6.7–7.3 mmol/L, named as near-threshold samples hereafter), their impedance spectra are shown in Figure 9. It is found that, for most near-threshold samples, the impedance changes smoothly at 25–35 MHz, and only samples of 7.3 mmol/L show a decreasing trend. All spectra fluctuate slightly at 45–60 MHz, and some of them decrease at the higher end of frequency. Compared to Figure 7 and Figure 8, there is no distinct feature among the impedance spectra of near-threshold samples.

6.2. Hyperglycemia Recognition Using the K-Nearest Neighbor Algorithm

Based on impedance spectra of hyperglycemia samples, the K-nearest neighbor algorithm [27,28] is used to recognize type 2 diabetes mellitus. Considering the small sample size of the electrical impedance spectrum, the KNN algorithm performs effectively in processing small-scale datasets with limited features. Notably, it does not require model retraining when new samples are added; instead, it simply incorporates these samples into the training set. This characteristic aligns well with the real-time requirements of blood glucose prediction scenarios. In contrast, other algorithms, such as CNN and SVM, are more susceptible to overfitting when handling small-scale data, with CNN being primarily suited for image processing. Meanwhile, SVM demonstrates significant advantages in processing high-dimensional data. The training set T is a d-dimensional feature space containing two categories, namely “hyperglycemia samples” and “standard blood glucose samples”, and it is denoted as $T=\left\{{{\left.x_i\in R^d\right\}}_{i=1}}^N\right.$. The corresponding sample label of the training set is $\left\{\left.y_1,y_2,\cdots ,y_N\right\}\right.$, in which $y_i\in \left\{\left.0,1\right\}\right.$. Label $\left\{\left.0\right\}\right.$ and $\left\{\left.1\right\}\right.$ stand for hyperglycemia and standard blood glucose samples, respectively. Furthermore, $x_i$ is a sample to be tested. The characteristics of the K-nearest neighbor algorithm are $\alpha =\left[{\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4\right]$. Here, ${\alpha }_1$ and ${\alpha }_2$ indicate the spectrum features at 25–35 MHz and 40–60 MHz, respectively; ${\alpha }_3=1$ means the person under test is male, and ${\alpha }_3=0$ means female; ${\alpha }_4$ is the body surface temperature of the tested person.

The process of determining parameter ${\alpha }_1$ is as follows:

(1)

Find out the maximum and minimum in the frequency range of 25–35 MHz, denoted as ${\mathrm{Z}}_{(25-35)-max-1}$ and $Z_{(25-35)-min-1}$, respectively.

(2)

Find out the frequency values corresponding to the maximum and minimum, denoted as $f_{(25-35)-max-1}$ and $f_{(25-35)-min-1}$, respectively.

(3)

Let ${\alpha }_1=f_{(25-35)-max-1}-f_{(25-35)-min-1}$. The parameter ${\alpha }_2$ is calculated in a similar way among 40–60 MHz, i.e., ${\alpha }_2=f_{(40-60)-max-1}-f_{(40-60)-min-1}$. The Euclidean distance is calculated using the K-nearest neighbor algorithm. Furthermore, k is set to 5 for classification of the sample size and classification effect, and the results are shown in Figure 10.

In the experiment, it is found that the near-threshold samples have “high blood glucose characteristics” but may be identified as “standard blood glucose”. The reason is that such samples have “declining” trends in 25–30 MHz, which is in line with the judgment standard of a “hyperglycemic sample”. But, in group recognition, the Euclidean distance only involves the absolute distance between sample points, which makes it impossible to judge the trend of the impedance spectrum. To solve this problem, the Manhattan distance is used along with the Euclidean distance to identify “hyperglycemic samples”. The identification process is shown in Figure 11.

The classification result is defined as follows: in the K-nearest neighbor algorithm using the Euclidean distance, $x_1=0$ indicates a “hyperglycemic sample”, otherwise $x_1=1$; in the K-nearest neighbor using the Manhattan distance, $x_2=0$ indicates a “hyperglycemic sample”, otherwise $x_2=1$; if both algorithms classify the test sample as a “hyperglycemic sample”, the output will be a “hyperglycemic sample”.

The proposed classification algorithm is evaluated by the classification accuracy rate or classification accuracy. Let $n_{Acctest}$ be the number of samples correctly classified in the test set and $n_{test}$ be the number of all samples in the test set. The classification accuracy rate is calculated according to (4).

$$Ac{c}_{test}={\displaystyle \frac{n_{Acctest}}{n_{test}}}.$$

(4)

The classification accuracy rate for the test set is 0.86. Furthermore, the “Euclidean distance” K-proximity classification with k = 7 and the “Manhattan distance” K-proximity classification with k = 9 are combined for “hyperglycemic sample” recognition.

7. A Non-Invasive Blood Glucose Detection Model Based on Multiple Regression

The relationship between the dielectric constant of human tissues and blood glucose concentration was given in (1), and it can be further converted to equivalent biological complex impedance according to (2). Therefore, a regression model can be established to estimate the blood glucose value.

However, according to previous studies, the mathematical relationship between blood glucose and complex impedance is not a simple first-order linear relationship. As an example, the complex permittivity of the human cell membrane in the $\beta$ band follows fourth-order Cole–Cole expansion. The microscopic parameters in fourth-order Cole–Cole expansion and (1) cannot be obtained directly, but the impedance Z, the phase angle $\phi$, and the resistance R are positively correlated with the blood glucose concentration $c_{glu}$. Therefore, these three parameters can replace the microscopic parameters in fourth-order Cole–Cole expansion and (1) in order to effectively estimate the equivalent cell membrane dielectric constant [29,30], as shown in (5).

$$C_{glu}=f\left({\epsilon }^{\ast }\right)=g(\sum _{i=1}^4{a}_i{Z}^i),C_{glu}=f\left({\epsilon }^{\ast }\right)=g(\sum _{i=1}^4{b}_i{R}^i),C_{glu}=f\left({\epsilon }^{\ast }\right)=g(\sum _{i=1}^4{c}_i{\phi }^i).$$

(5)

The higher-order multiple regression model is shown in (6).

$$y={\beta }_0+\sum _{i=1}^4{\beta }_i{X}^i+\sum _{k=1}^4{\beta }_k{R}^k+\sum _{j=1}^4{\beta }_j{\phi }^j.$$

(6)

Then, the higher-order multiple regression equation can be written as (7) and (8).

$$\begin{array}{cc}\hfill {\tilde{y}}_{normal}& =-83\ast Z+0.8\ast Z^2-0.04\ast Z^3+18.0\ast \phi -25.2\ast {\phi }^2-0.07\ast {\phi }^3\hfill \\ \hfill & +162.9\ast R-2.8\ast R^2+0.02\ast R^3,\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill {\tilde{y}}_{high}& =147.38\ast Z-1.6\ast Z^2+0.08\ast Z^3+184.9\ast \phi -404.9\ast {\phi }^2+205.1\ast {\phi }^3\hfill \\ \hfill & -3.5\ast {\phi }^4+242.8\ast R+3.9\ast R^2-0.03\ast R^3.\hfill \end{array}$$

(8)

The obtained regression function can be validated through various statistical tests that assess the reliability of the regression model, primarily including goodness-of-fit tests, significance tests, and residual analysis. Among these, the goodness-of-fit test, denoted as $R^2$, reflects the degree of dispersion between the data points of the training sample and the regression function. It is straightforward to calculate and does not require extensive consideration of the model’s specific parameters. The formula for this calculation is presented in Formula (9). The range of the goodness-of-fit test $R^2$ is (0, 1), where a larger value indicates a better fit of the regression function.

$$R=\sqrt{1-{\displaystyle \frac{{\sum }_i^n{\left(y_i-\widehat{y_i}\right)}^2}{{\sum }_i^n{\left(y_i-\overline{y_i}\right)}^2}}}.$$

(9)

The F-test is a statistical method employed to assess the overall significance of a regression model. It represents the ratio of the mean square regression (MSR) to the mean square error (MSE) of the residuals. This test takes into account the complexity of the model and evaluates the significance of the model as a whole. The specific calculation formula is provided in Formulas (10) and (11). Additionally, a residual analysis is conducted to ascertain whether the residuals follow a normal distribution.

$$F={\displaystyle \frac{U/m}{Q/\left(n-m-1\right)}}\sim F\left(m,n-m-1\right),$$

(10)

$$Q=\sum {\left(y_i-\widehat{y_i}\right)}^2,U=\sum {\left(\widehat{y_i}-\overline{y_i}\right)}^2.$$

(11)

The statistical test results of the above higher order multiple regression model are listed in

Table 1. Statistical test of the higher-order multiple regression model.

Regression Model	Statistical Detection Value
	Correlation	F Value
		Lookup Table Data	Regression Model Data
Standard blood glucose
sample regression model	0.89	$F(12,20)=2.54$	4.6384
High blood glucose
sample regression model	0.87	$F(12,20)=2.54$	8.1599

.

According to Table 1, the correlation of the standard blood glucose regression model is 0.89, while that of the hyperglycemia regression model is 0.87. Thus, the above regression model is feasible for blood glucose estimation. Furthermore, in the significance test, the F value of the proposed regression model is greater than that of the lookup table, which proves that the selection of independent variables in the regression model is appropriate. Figure 12 and Figure 13 demonstrate the residual of the proposed regression model. It can be seen that the test samples are within the confidence interval of the residual, which further proves the effectiveness of the proposed regression model.

In addition, the residual value is analyzed using the quantile graphic method. A Q–Q diagram of the regression model is shown in Figure 14 and Figure 15, respectively. It can be found that the samples are distributed around the 45° diagonal in these two figures, which indicates that there is a correlation between the expected value and the observed value. It can be proved that the residual distribution of the regression model belongs to the normal distribution and can meet the theoretical requirements of the regression model.

According to the above results, the proposed regression model can reliably estimate the blood glucose concentration.

8. A Non-Invasive Blood Glucose Detection Experiment

Impedance spectra of the tested persons are acquired using the proposed hardware platform. Then, the non-invasive blood glucose detection model is used for blood glucose estimation so as to evaluate its accuracy and generalization ability. The experiment consists of two parts: a personal blood glucose test and a multi-person blood glucose test.

In this section, the designed impedance acquisition platform is used to obtain the bioimpedance spectrum of the tested person, and the non-invasive blood glucose detection model is used to calculate the blood glucose estimation to judge the accuracy and generalization ability of the model. Specific experiments include single-person blood glucose experiments and multi-person blood glucose experiments. The single-person blood glucose experiment focuses on testing the blood glucose fluctuation process, aiming to describe the trend of single-person blood glucose changes; the multi-person blood glucose experiment focuses on the generalization of the blood glucose model and identifies “high blood glucose samples” from the impedance spectrum data of different testers. The present study tested the developed non-invasive measurement method to obtain blood glucose-related properties. The connection between the measurement system and the human body is shown in Figure 16.

8.1. Single-Person Blood Glucose Experimental Design

The experimental conditions of the single-person blood glucose experiment include the following: (1) the physical condition of the tested person, (2) the test time, (3) the test attitude control, and (4) the test environment and other related information. Among them, the selected subjects are as follows: male, 26 years old, height 174 cm, weight 83 Kg, and BMI value 23.5. The test time starts from the fasting state in the morning, and the experiment is carried out every 1 h. The control of the test posture includes keeping the body stable during the test, emotional stability, no drinking water 20 min before the test, etc. The test environment requires that the external test environment temperature is stable, e.g., at room temperature, and there is no obvious temperature change during multiple measurements.

The specific test steps are as follows:

1.

Before taking the equivalent bioelectrical impedance readings, ask the tested person to sit still for 10 min before starting the test. The research protocol and experimental methods are explained to each volunteer, and then they are asked to sign a consent form.

2.

During the experiment, the tested persons continue to keep their bodies in a stable state. The impedance acquisition platform designed in this paper is used to conduct the experiment. The inner side of the forearm of the tested person is selected as the test point, and the corresponding electrode pads are pasted on the skin to start the test. The complete test time is about 2 min.

3.

After the impedance collection test is completed, biochemical blood glucose collection is performed. The Ulite URI0-26 blood glucose analyzer was selected as the biochemical blood glucose collection instrument for blood collection experiments.

4.

Arrange the impedance data obtained from the above experiments and the biochemical blood glucose data at the same time and label them.

8.2. Personal Blood Glucose Test

The experiment of personal blood glucose test lasts for 10 h, and it starts in the fasting state. After the first test, the tested person has a nutritional supplement, and then the test repeats every 1 h. In addition, there will be a 30 min lunchtime. The test results are shown in

Table 2. Single-person blood glucose experiment and blood glucose estimation.

Testing Time	Classification Model Judgment			Blood Glucose Model Estimation	Biochemical Blood Glucose Level	Absolute Error	Relative Error
	European K-Approaching	Manhattan K-Approaching	Whether It Is High Blood Glucose
Fasting state	1	1	no	4.837	4.3	−0.537	12.48%
1 h after meal	1	1	no	5.621	5.4	−0.221	4.09%
2 h after meal	0	0	Yes	7.986	6.9	−1.086	15.73%
3 h after meal	1	1	no	6.032	6.5	0.468	7.20%
4 h after meal	1	0	no	6.121	5.8	−0.321	5.53%
1 h after lunch	0	0	Yes	8.775	7.7	−1.075	13.96%
2 h after lunch	1	0	no	6.668	6.5	−0.168	2.58%
3 h after lunch	0	1	no	6.325	6.1	−0.225	3.68%
4 h after lunch	1	1	no	5.378	5.8	0.422	7.27%
Fasting before dinner	1	1	no	5.253	5.6	0.347	6.19%

and Figure 17.

In Table 2, the K-proximity classification model identified two hyperglycemia samples with biochemical blood glucose values of 6.9 and 7.7. The hyperglycemia sample with a biochemical blood glucose value of 7.7 appears 1 h after lunch, and it meets the physiological diagnostic criteria. On the other hand, the hyperglycemia sample with a biochemical blood glucose value of 6.9 does not strictly meet the physiological diagnostic criteria. According to the manual of the Unitech URI0-26 blood glucose analyzer, the measurement error of biochemical blood glucose can be up to $\pm 0.5$. Meanwhile, this suspicious sample appears at 2 h after the meal, just within the period that the blood glucose rises rapidly based on physiological knowledge. Therefore, this sample can also be judged as a high blood glucose sample, and it can be concluded that the proposed blood glucose detection model can accurately identify high blood glucose samples in personal tests and achieve type 2 diabetes mellitus detection.

Further analysis of the data in Table 2 shows that large errors are found in hypoglycemia (biochemical blood glucose value of 4.3) and near-threshold (biochemical blood glucose value of 6.9) samples. As pointed out by physiological knowledge, when the human body is in a water-deficient state after exercise, there will be a temporary decrease in impedance, and the human body in a “fasting state” has the same characteristics as that of a “water-deficient state”. Furthermore, in the regression fitting Equation (7), the impedance value has a negative correlation with blood glucose estimation. As a result, the impedance reduction causes a positive error in blood glucose estimation. Therefore, it is necessary to drink an appropriate amount of water before the experiment to ensure that the human body is only in an empty stomach state so as to reduce the measurement error caused by “water shortage”. In Table 2, the absolute error of blood glucose estimation in the “fasting state” is 0.53. In subsequent tests, the impedance in either the “hydration supplement” or “water shortage state” case is tested, respectively. It is found that the results are consistent with the above analysis, which can prove its correctness.

Figure 17 further demonstrates the blood glucose values versus time, in which the results of the proposed blood glucose detection model are consistent with biochemical blood glucose values. Therefore, the proposed model is applicable for blood glucose detection.

8.3. Multi-Person Blood Glucose Test

The proposed blood glucose detection model is applied to different subjects in order to further verify its accuracy and generalization ability. For multi-person blood glucose testing experiments, the testing process is basically the same as that of single-person testing. The external experimental conditions, such as the test posture and the test environment, are consistent with the single-person blood glucose test, including keeping the subject’s body stable and emotionally stable during the complete test process, drinking no water within 20 min of the test, etc., and controlling the ambient temperature during the test to be stable at room temperature. The subjects selected for this experiment consist of 16 males and 4 females, aged from 20 to 26 years old. Their physical types include thin, standard, overweight, etc. Their BMI values range from 13.7 to 31.8. The results are shown in

Table 3. Single-person blood glucose experiment and blood glucose estimation.

Tested Person	Gender	Classification Model Judgment			Blood Glucose Model Estimation	Biochemical Blood Glucose Level	Absolute Error	Relative Error
		European K-Approaching	Manhattan K-Approaching	Whether It Is High Blood Glucose
1	male	1	0	no	4.985	4.3	−0.685	15.93%
2	Female	1	1	no	5.198	4.4	−0.798	18.14%
3	male	1	1	no	5.421	4.7	−0.721	15.34%
4	male	1	1	no	5.567	4.9	−0.667	13.61%
5	male	0	1	no	5.858	5.2	−0.658	12.65%
6	Female	1	0	no	4.788	5.3	0.512	9.66%
7	male	1	0	no	5.354	5.4	0.046	0.85%
8	male	1	1	no	5.632	5.5	−0.132	2.4%
9	male	1	1	no	6.035	5.8	−0.235	4.05%
10	Female	0	0	Yes	8.856	7.3	−1.556	21.32%
11	male	0	0	Yes	8.736	7.7	−1.036	13.45%
12	male	0	1	no	6.498	7.4	0.902	12.19%
13	male	0	0	Yes	8.522	7.8	−0.722	9.26%
14	male	1	1	no	6.023	6.3	0.277	4.39%
15	male	0	0	Yes	9.398	8.5	−0.898	10.56%
16	male	1	1	no	6.385	6.4	0.015	0.23%
17	male	1	1	no	5.494	6.1	0.606	9.93%
18	male	0	1	no	6.853	6.5	−0.353	5.43%
19	male	1	1	no	6.757	6.0	−0.757	12.62%
20	Female	0	0	Yes	8.254	6.1	−2.154	35.31%

and Figure 18.

In Table 3, the K-proximity classification model identified five hyperglycemic samples, including those from three males and two females. The biochemical blood glucose values of male hyperglycemia samples are 7.7, 7.8, and 8.5, respectively. The proposed classification algorithm can identify these samples accurately. For these three samples, the absolute error of blood glucose estimation obtained by the higher order multiple regression equation is greater than 0.5 (range from 0.7 to 1.03). On the other hand, for female hyperglycemia samples, the biochemical blood glucose values are 7.3 and 6.1, respectively. The former sample meets the characteristics of hyperglycemia according to the physiological diagnosis standard, and it has been correctly classified by the proposed model. However, the latter sample with a biochemical blood glucose value of 6.1 is not a hyperglycemia sample according to the physiological diagnostic criteria, so the proposed model makes an incorrect identification for it. The main reason is that the accuracy of the K-proximity classification algorithm depends on the value of k and the sample size of the known class. When the capacity of one sample is too large and the capacity of another sample is small, the test sample cannot be close to the target sample. For the above sample with incorrect classification, the corresponding information of the tested person is as follows: female, age 25, height 162, weight 43, and a BMI value of 13.7. This sample has the lowest BMI in the experiment, and its impedance spectrum shows less relevance to the above-mentioned features of hyperglycemia samples. Thus, it can be treated as a “singular value” and removed.

After removing the sample of singular value, there are still two samples in Table 3 that have larger errors, both of which are females (with biochemical blood glucose values of 7.3 and 4.4). This may be caused by various gender differences, including skin impedance, basal metabolic rate, water content, and protein activity in human tissues.

In samples where blood sugar levels are either slightly above or below the normal range, the relative prediction error increases, indicating that the model’s predictive capability diminishes in sparse or boundary areas. An analysis of the blood sugar values presented in Figure 18 reveals no correlation, as the individuals tested are independent of one another. Figure 4 and Figure 5 illustrate the discrepancies between biochemical blood sugar values and non-invasive blood sugar estimates. It is observed that the majority of non-invasive blood sugar estimates are excessively high, while a few are lower than the biochemical blood sugar values. The mean absolute error is approximately 0.5. In conclusion, the blood glucose detection model developed in this study effectively captures the changing trends of an individual’s blood sugar levels and can accurately identify high blood sugar samples in multi-person experiments.

According to the above results, the proposed blood glucose detection model can feasibly identify high blood glucose samples in multi-person tests. Statistical analyses of big data indicate that factors such as gender, height, weight, age, waist circumference, and meal timing exhibit significant correlations with blood sugar levels. These variables can be utilized as features or independent variables in predictive models to enhance the accuracy of the predicted values.

9. Conclusions

The bioimpedance acquisition platform built in this paper, combined with the KNN algorithm for blood glucose sample classification and higher-order multivariate regression processing, can achieve real-time prediction of blood glucose levels, reaching the expected goal of this paper, but there are still areas for improvement.

(1). Through the measurement of electrode plate echo loss, it was found that the 60–70 MHz range is the frequency band with the strongest excitation current transmissivity, but the existing data lack this information. The next step is to expand the frequency scanning range of the bioimpedance acquisition platform to include the 60–70 MHz frequency band with less echo loss.

(2). Due to the limitation of sample sources, in real life, abnormal blood glucose data are naturally scarce, and there are problems such as a small sample size, a concentrated age range, and a lack of abnormal blood glucose samples, which limits the generalization ability of the model. In future research, it is necessary to continuously increase the sample size and explore data augmentation methods to solve the data imbalance problem.

(3). In this paper, the impedance value, phase value, and resistance value are used as features of the multivariate regression model, while physiological parameters such as age, height, and weight, which are correlated with blood glucose, may also contribute to blood glucose prediction. In the future, machine learning models based on decision trees or SVMs can be tried to improve the accuracy of blood glucose prediction.