**1. Introduction**

The number of people with diabetes is growing every year. Back in 2002, Jones M. and Harrison J. M. described in their article [1] that the World Health Organization (WHO) expects an increase in the number of people with diabetes to 300 million by 2025. According to a survey conducted by the International Diabetes Federation (IDF) already in 2013, three-hundred eighty-two million patients worldwide had diabetes. Seven years later, in 2020, the number of people living with diabetes was 463 million. Diabetes mellitus is a serious disease that can lead to many complications. There are several types of the disease. The main types are type 1 and type 2 diabetes. They are the most prevalent. In both of these cases, a person with diabetes needs to control blood sugar levels to avoid the complications of the disease. Self-testing devices require small blood sampling using different needles, which cause pain and discomfort to the user of the device. Today, a large number of methods and devices are being developed for determining glucose levels using non-invasive and continuous methods. This approach will allow people with diabetes to avoid the discomfort of measuring blood sugar and monitor it throughout the day. The most well-known non-invasive methods for measuring blood glucose are Raman spectroscopy, impedance spectroscopy, near-infrared spectroscopy, photoacoustic spectroscopy, and others.

Raman spectroscopy [2,3] is based on the measurement of scattered light. The disadvantages of this method are the instability of the intensity and wavelength of laser

beams during probing, a long time for obtaining data, as well as errors associated with chemical substances in the tissues. Impedance spectroscopy is based on the measurement of resistance when the radiation frequency changes. To measure the glucose level, several sensors located in the area of the veins in human hands are needed [4]. Near-infrared spectroscopy is based on the transmission of near-infrared radiation through a vascular region of the body (finger, earlobe, etc.). In this case, the glucose concentration is calculated on the basis of the received spectral information [5,6]. All measurements in near-infrared spectroscopy are based on the transmission of light through or into the sample and the measurement of the intensity (transmitted or reflected) of the beam. Spectrometers for measurements in near-infrared spectroscopy have a suitable light source (such as a highly stable quartz tungsten lamp), a monochromator or interferometer, and a detector. Conventional monochromators are acousto-optic tunable filters, diffraction gratings, or prisms. Mid-infrared spectroscopy is based on the absorption of light by glucose molecules [7–9]. This method uses a beam of light to travel through a crystal in contact with the skin. Thus, the electromagnetic field generated by the reflected light reaches the dermis (the layer of skin that contains the most glucose). The disadvantage of this method is the dependence of the obtained data on the water content in the dermis. Therefore, the reliability of the results largely depends on the degree of hydration. There is a technology based on ultrasonic sensing: photoacoustic spectroscopy [10,11]. This method is based on the acoustic response of a liquid using laser light. This method is similar to mid-infrared spectroscopy. There are also other less known methods for determining the level of glucose in the blood [12,13].

With the existing variety of physical methods used for the non-contact determination of blood glucose concentration, the problem of creating non-invasive glucometers has not ye<sup>t</sup> been solved. At the same time, conventional invasive glucometers have been actively improving over the past twenty years: chemical analysis has been replaced by electrochemistry; the devices are equipped with internal memory and other conveniences; their use has become easier, but still painful. It should be noted that invasive analysis is a direct method; in this case, a sample (blood drop) containing glucose is directly examined. While analyses of non-invasive glucometers are indirect methods, they are based on data obtained, as a rule, by spectral means. In some cases (IR spectroscopy), an attempt is made to quantitatively analyze blood glucose without removing a sample from the body; in others (for example, electrical and thermal characteristics), the study of factors associated with glucose levels is carried out in a very complex and ambiguous way. In any situation, the influence of surface tissue structures, the individual characteristics of the skin and the composition of the intercellular fluid, the functional complexity of blood components, and many difficult parameters of the external and internal environment are very great. The glucose percentage is a continuously changing parameter.

At the same time, in recent years, many laboratories and companies have been developing non-invasive glucometers, and some of the ready-made solutions have even received certification. In 2014, French researchers Chretiennot T., Dubuc D., and Grenier K.proposed a resonant microwave biosensor, which, according to the authors, achieved the accuracy of chemical glucometry methods. They published the paper [14]. However, this method cannot be rightfully considered non-invasive: it still requires the extraction of physiological fluids for analysis. A glucometer in the form of a patch (sugarBEAT) was created by the British company Nemaura Medical and certified in Europe. The sugarBEAT patch is only 1mm thick. It measures the glucose level in the tissue fluid of the upper layer of the skin (in sweat) and transmits the measurement results every 5 min via a digital interface. It is worth noting that sugarBEAT does not relieve the traditional finger puncture procedure, but it only needs to be done once to calibrate the meter before attaching it. The term of its operation can be up to two years. The American company M10, together with Seoul National University, created a prototype of a wearable device. It can not only measure the level of glucose in the blood, but also administer the required dose of insulin. The small patch contains sensors for glucose, temperature, humidity, and pH (sweat particles are

used for measuring), as well as microneedles for injecting the drug and a heater (with its help, the needles are activated).

The SugarSenz Velcro glucometer of the American company Glucovation is attached to the stomach and constantly measures the glucose level with the possibility of digital data transmission. However, it also pierces the skin, not like conventional glucometers, but to the subcutaneous layer, in which the glucose level can also be measured. Google X lab worked on the creation of contact lenses, which, using a special sensor, could measure glucose levels not in blood, but in tears. However, glucose in the extracellular fluid is different from blood glucose. On average, the physicochemical reaction between glucose and the electrode surface takes three to 20 min. During this time, glucose passes from the blood into the intercellular fluid, and only then, the received signal undergoes algorithmic processing. Therefore, such devices are suitable for detecting trends in sugar levels, but are not suitable for the instant and accurate analysis required in real conditions. GlucoTrack DF-F is a non-invasive blood glucose meter of the Israeli company Integrity Applications (received a certificate from the European Commission). It uses three ways to measure blood sugar: ultrasonic, electromagnetic, and thermal. All of these measurements are taken using a miniature clip-on transducer that clings to the ear. With three measurements, the meter can give a more accurate reading. The disadvantages are the need for regular device calibration and the lack of accuracy.

Scientists at the Swiss Institute in Lausanne (EPFL) have created a miniature implant that can measure various parameters of a person's blood, such as glucose or cholesterol levels. The sensor is installed under the skin, and above it, a small unit with a battery and a wireless transmitter is attached to the skin. C8 MediSensors (a non-invasive blood glucose meter of the American company C8 MediSensors (European certificate)) is based on the optical principle and does not require a blood sample. The meter sensor is attached to the skin in the abdomen and transmits measurements digitally. The measurement uses Raman spectroscopy technology.

GlucoWatch is a glucometric watch developed by Cygnus Inc (Petoskey, MI, USA). The sensing element is a sensor in contact with the skin. Using a weak electrical current, the sensors pull glucose out of the skin cells. The glucose entered into the sensor is measured and converted into blood glucose, and the result is displayed on the screen and, together with the date and time of the analysis, is recorded in the device's memory. Measurements are taken every 10 min for 13 h. The tests revealed the following: (1) the device is inconvenient in operation (the manual is a book of 112 pages) and expensive to maintain; its use requires a complex individual calibration; it is not suitable for some types of skin; the analysis area on the hand must change every time; (2) the data obtained with its help are less accurate than measurements on a conventional glucometer; in some cases, the error can reach 25–30%; (3) the change in the level of glucose in the cell fluid occurs with a delay in relation to the change in blood glucose, and as a result, GlucoWatch lags behind the true state of affairs by ten or more minutes.

Omelon V-2 is a technology developed in Russia. The principle of its action is based on the fact that muscle and vascular tone are dependent on glucose levels. The device measures the pulse wave, vascular tone, and blood pressure several times, based on which it calculates the sugar level. The high percentage of coincidences of the calculated indicators with laboratory data allowed this blood glucose monitor to be launched into mass production. However, the device has dimensions of 155 × 100 × 45 cm, which does not allow carrying it in a pocket, and the correctness of the readings depends on the observance of the rules for measuring pressure: the correspondence of the cuff to the girth of the arm, the patient's calmness, and the absence of movement during the operation of the device.

The Israeli firm Integrity Applications solved the problem of painless, fast, and accurate blood sugar measurement by combining ultrasonic, thermal, and electromagnetic technologies in the GlucoTrack DF-F glucometer model. The GlucoTrack Model DF-F is

intended for use by adults (over 18 years of age) with type 2 diabetes. The GlucoTrack Model DF-F is an expensive monitoring device and cannot be used for diagnostics.

The Symphony tCGM System, developed by Echo Therapeutics (Franklin, MA, USA), measures sugar levels transdermally. However, for the correct installation of the sensor and its accurate operation, it is necessary to pre-treat the skin with a special device, the Prelude SkinPrep System; it performs a superficial peeling of the skin area on which the study will be carried out by improving the electrical conductivity of the skin. After preparation, a sensor is attached to the skin area, and after a while, the device displays data, including indicators of glycemia and the percentage of body fat. This information can also be transferred to a smartphone. The accuracy of the device reaches 95%, which is slightly lower than that of standard invasive glucometers. This technology is under development.

Japanese startup Quantum Operation unveiled at CES 2021 a smartwatch-style device that is supposedly capable of accurately measuring blood glucose without puncturing the skin. The principle of action is based on spectroscopy (Raman spectroscopy). Judging by the information from the sources, the watch does not constantly monitor the glucose level, but does it after activating the corresponding function, and one must wait for about 20 s for the result. This is less effective than real-time monitoring, which is provided, for example, by the well-known partially invasive FreeStyle Libre device.

The large number of technologies presented to date for non-invasive glucometers shows the extreme popularity of the research area (only a few of them are noted above). However, despite the variety of methods being developed, a device that meets all the necessary requirements such as complete non-invasiveness, the accuracy of readings within the permissible error (laboratory tests are taken as basic ones, and it is believed that the readings of the glucometer should not differ from them by more than 10–15%), ease of use, lack of consumables, price, etc., has not ye<sup>t</sup> been created. Thus, the development of a non-invasive method for the determination of glucose remains an urgen<sup>t</sup> task today. This article is devoted to the development of a sensor based on near-field microscopy. The near-field method provides deep penetration of electromagnetic waves even in a highly absorbing environment, which, in particular, is human biological tissue.

The work is organized as follows. At the beginning of the work, a model of the sample of the biological medium in the form of a human hand is calculated, and the dependences of the real part of the dielectric permittivity of various concentrations of glucose in physiological saline on the frequency are plotted based on the experiment. This is done to bring numerical simulations closer to real conditions. Next, a numerical simulation of the sensor is carried out, based on which a real model of the sensor is created. Furthermore, a flat-layered phantom of a human hand is created for the experiments. Then, the analysis and results of numerical and field experiments of the proposed sensor design are presented.

#### **2. Materials and Methods**

### *2.1. Hand Model*

To develop a new sensor for non-invasive diagnostics of glucose levels, it is necessary to take into account several factors that can influence the measured value of the reflected electromagnetic signal. It should also be borne in mind that the concentration of glucose in different tissues of a human is distributed differently; the thickness of tissue layers of different people is different; and these are previously unknown values for noninvasive measurements. When developing non-invasive methods for measuring glucose by electromagnetic methods, first of all, it is necessary to consider the effect of skin layers.

This is important because skin, like blood, has a high dielectric permittivity. Therefore, the electromagnetic wave attenuates in it more strongly than in other layers. Each layer of the skin has its dielectric characteristics, which may differ from human to human due to differences in the morphology and thickness of skin layers, the concentration of tissue/blood components (such as glucose), cutaneous blood perfusion, etc.

The skin has a grea<sup>t</sup> influence on glucose measurement; it can vary in the range of 2–10 mm when looking at the whole human body. The skin has a multilayer structure and includes stratum corneum; its thickness ranges from 15 to 150 microns in various parts of the body; the epidermis, the upper outer layer of human skin, which includes about 15–35% interstitial fluid, without blood vessels; the dermis, the skin itself, is a connective tissue and contains arterioles, venules, capillaries, and about 40% interstitial fluid. Furthermore, the dermis includes subcutaneous fatty tissue and loose fibrous connective tissue. The distribution and thickness of the skin depend on heredity, sex hormones, and human living conditions. On average, the thicknesses vary in the following ranges: the epidermis thickness is 0.068–0.146 mm; the stratum corneum of the epidermis is 0.021–0.049 mm; dermis is 1.89–3.04 mm; the subcutaneous fat is 0.03–1.41 mm. The next layer is subcutaneous fat, which has a wide range of thicknesses. The thickness of the fat layer on the forearm is the smallest compared to other parts of the body. Before considering muscle fibers, it is required to consider the saphenous veins passing through the human forearm.

To measure glucose with a standard glucometer, blood is drawn from the subcutaneous capillary vessels. In a medical examination, blood is drawn from a vein. The fundamental difference between these two methods is measurement accuracy. It should be understood that in medicine, the level of glucose (glycated hemoglobin) is determined in practice by venous blood. The content of these substances in venous and arterial blood is somewhat different. For a more accurate calculation of the concentration of glucose, the venous blood was considered in our study. A vein has a multi-layered structure. Depending on the type of vessels, they have different thicknesses, densities, and permeabilities. Large vessels additionally contain small blood and lymphatic capillaries.

Due to different pressures during the entire period of a person's life, the blood supply (blood volume in the measurement area) changes; along with this, the diameter of the vessels also changes. People with symptoms of tachycardia (increased heart rate) have smaller vessels because a rapid heartbeat decreases the efficiency of the heart since the ventricles do not have time to fill with blood. As a result, blood pressure decreases, and blood flow to organs decreases; hence, the area for the microwave signal response is smaller.

Another factor that can affect the dielectric properties of blood is blood hematocrit. Blood hematocrit refers to the percentage of red blood cells in the blood. Differences in the size, morphology, and distribution of red blood cells in human blood lead to changes in its dielectric properties, regardless of glucose concentration, and thereby affect the accuracy of glucose determination using measurement methods based on dielectric properties. Normally, this indicator is 40–48% for men and 36–42% for women. At low frequencies (about 3 MHz), the spread in the dielectric permittivity is quite high in the region of 30% with a change in hematocrit of 5% [15]. This scatter is associated with a rapid change in blood dielectric permittivity from frequency, which is clearly shown in Figure 1. With increasing frequency, this effect disappears due to the linear behavior of the dependence of the real part of the dielectric permittivity. In this case, the change will vary by 0.01–0.02%.

**Figure 1.** Dependence of the real part of the dielectric permittivity on frequency.

Based on the results of the literature review and the analysis of the studied information, the summary Table 1 was formed. It shows the thicknesses of all materials used for modeling.


**Table 1.** Thickness of the materials used in modeling.

The values for the thicknesses of the muscles and bones of the human forearm are not given in the table, since when the near-field penetrates these tissues, a strong signal attenuation occurs, and the response from them will be at the noise level. Therefore, these layers in the calculation of the thicknesses of the materials used in the simulation can be neglected. Based on the given data, we created the model of a biological medium sample in the form of a human hand (Figure 2).

The model has a flat-layered structure. All previously described materials were modeled, and a 13 mm thick muscle layer was added. We used a flat structure because the used antenna substrate is flexible. In the future, when creating a real prototype of the sensor, this will make it possible to attach it directly to the area of human skin.

**Figure 2.** Model of the sample of the biological medium in the form of a human hand.

In the hand blood model, we used the data of the dielectric permittivity of saline with the following glucose concentrations: 0, 1, 3, 4, 5, 7, 9, and 10 mmol/L (Figure 3).

The data were analyzed using a PNA-L Network Analyzer (N5230C) and Dielectric Probe Kit-85070E Slim Form from Agilent Technologies. In subsequent simulations for blood with varying glucose concentrations, we used data obtained experimentally for physical solutions (saline) with different dextrose concentrations. Thus, it was possible to bring numerical modeling closer to real conditions.

**Figure 3.** Dependence of the real part of the dielectric permittivity of solutions on frequency.

### *2.2. Sensor Design*

The development of the near-field sensor was based on a combined slot antenna. The brown color in Figure 4 indicates the ideal conductor and green the flexible dielectric RO3003 with relative permittivity *ε* = 3. The shape of the sensor resembles a coin in the center of which there is a metalized circle with a slot in it. Then, using two rectangular metalized sections, the circle is connected to a conductive frame (Figure 4a). The backside of the sensor is a dielectric layer with a microstrip line close to a central circle and a small cut in the dielectric up to the conductive frame for connecting to the supply element (Figure 4b). The probing near-field is formed on the side with a slot (Figure 4a). Due to the presence of several radiating elements (slit and frame), the formation of the reactive parts of a specific interference energy flow takes place. These features can increase the sensor's sensitivity for near-field diagnostics of biological media and objects.

**Figure 4.** Near-field sensor model. Front (**a**) and back (**b**) views.

The VSWRof the sensor is also considered in terms of coherence with a sample of a biological medium in the form of a model of a human hand (Figure 5). The graph shows two sections of the curve with the highest matching of the sensor and the sample under study: the first at a frequency of 1 GHz (VSWR = 1.4) and the second in the range of 2.1–5 GHz (VSWR = 1.4). Note that almost the entire VSWR graph is below Level 3.

**Figure 5.** VSWRsensor coherence with the sample of the biological medium.

In the numerical simulation of the experiment to determine the concentration of glucose, the sensor was closely applied to a sample of a biological medium in the form of a human hand. The measurements were carried out in the frequency range of 0.5–5 GHz. We used this range to cover the entire frequency range in which the VSWR of the sensor is less than Level 3.
