Application of Broadband Microwave Near-Field Sensors for Glucose Monitoring in Biological Media

: The paper presents results of numerical simulation and experimental testing of a microwave sensor for non-invasive glucose monitoring. The sensor represents a conical horn with a conical conductor inside expanding toward the horn aperture. Such a sensor has a signiﬁcantly wider passband in comparison with sensors of other designs. It is essential that the sensor geometry provides formation of an extended near-ﬁeld zone with high electric ﬁeld strength near the sensor aperture. A clear relationship between the dielectric permittivity of the phantom biological tissue and the frequency dependence of the parameter S11 of the sensor is observed at frequencies in the range from 1.4 to 1.7 GHz. This circumstance can be used to develop a procedure for measuring the glucose level in blood that correlates with the parameter S11 of the sensor. From the viewpoint of monitoring of the glucose content in blood, the most convenient body sensor location is on the hands or feet, in particular, wrists.


Introduction
At present there is no effective medicine for diabetes treatment all over the world. Therefore, regular and reliable measuring of the blood glucose level in diabetes patients and procedures of insulin injections play an exclusive role in saving the lives of patients. Unfortunately, invasive methods of measuring the glucose level involve clearly inadequate medical instruments. Therefore, much attention has recently been paid to the development of new methods of determining the glucose level in blood, in particular, by using radio waves. Tamar L. et al. [1] subdivided the currently known methods of non-invasive determination of the glucose level in blood into three groups. In doing so, they considered the method of radio wave spectroscopy. In their review, the progress reached by several companies was pointed out, including Integrity Applications Inc. GlucoTrack ® (Israel), Cnoga Medical Ltd. (Israel), Combo Glucometer (Israel), Nemaura Medical SugarBEAT™ (Great Britain), and MediWise GlucoWise™ (Great Britain).
The glucose meters produced by the first of the above-listed companies have been certified and are already available in markets of several countries. An interesting feature of these glucose meters is that they use three fundamentally different technologies of determining the glucose level in blood. Of great interest is the product of the fourth company based on radio wave spectroscopy. Experts within the company found it expedient to use electromagnetic radiation with a frequency of 65 GHz applied to the skin between thumb and forefinger or to the earlobe. The wavelength of such radiation is sufficiently large to penetrate through the skin layer into biological tissues, and at the same time, is sufficient to resolve small blood vessels. It is also important that the sensors are equipped with special nanocomposite films providing good matching with the probed skin. It is stated that this guarantees the reliability of measurements in all patients, irrespective of race, age, and skin type. The glucose meter has good ergonomic characteristics. It is expected that after a cycle of clinical tests, it can be commercialized successfully. At the same time, there is no information on the accuracy of the glucose meter and its advantages over other known meters.
In addition to the abovementioned review, more reviews have recently been published (for example, see [2][3][4]). It is remarkable that in these reviews, attention is focused on radio wave methods of measurements that have undeniable advantages over other methods.
It should be noted that attempts to develop productive technologies for measuring and monitoring the glucose level in the human body using microwave radiation have been undertaken already for a long time. For example, detailed experimental studies reported in master dissertations [5,6] culminated in a thoughtful publication [7] where an openterminated spiral-shaped microstrip line was used as a resonant probe for non-invasive determination of blood glucose level. The resonant probe was built into the device for express analysis. An analysis is carried out by pressing the thumb of the patient on the microstrip line.
The potential of this probe for estimating the blood glucose level was theoretically investigated in [8] by a numerical simulation method. Malaysian scientists specializing in neural networks of artificial intelligence proposed a super-wideband system for reliable non-invasive determination of the blood glucose level. The system used a pair of microstrip antennas and ensured, according to the developers, an 82% accuracy when determining the blood glucose concentration [9]. Neural networks are used for signal processing in this system. However, the neural networks are rather sensitive to the learning sample and do not guarantee an accurate result when measurement conditions change. This is a disadvantage of the proposed system.
In a series of publications [4,[10][11][12] by the authors from Cardiff University, the design of a microwave non-invasive sensor for continuous monitoring of the blood glucose level was described in detail. The novelty of the design was that the sensor contained two splitring resonators with a gap. One of the resonators responded to changes in the glucose level, and another was used as a reference. The frequency of microwave radiation was about 1.4 GHz for greater penetration of radiation into biological tissues. The required power level did not exceed 1 mW to eliminate ionization processes in tissues. The authors considered their sensor to be exact, safe, and fast, providing continuous readings in fractions of a second.
Interesting data on measurements of glucose concentration in real time were reported in [13,14]. The authors used a sensor consisting of a dielectric resonator coupled with a probe-tip. Based on measurement of the reflection coefficient, they observed small changes in the glucose concentration in the range 0-300 mg/mL. At the working frequency changing from 4 to 5 GHz, they succeeded in tracing changes in the glucose concentration with a resolution of 1 mg/mL. The measured signal/noise ratio was about 37 dB, and the minimal detectable signal was about 0.003 dB/(mg/mL).
The theory [15] and practice [16] of near-field resonant microwave sensing of different biological media have recently been developed very intensively. Scientists from the Institute for Physics of Microstructures of the Russian Academy of Sciences have demonstrated convincingly that the method permits determining the filling degree of blood in the small vessels of human bodies and tissues and that the corresponding measuring complex is sensitive to any, even minor, changes in the blood flow in tissues rich with blood vessels. This method has already been partially implemented in clinical practice. It is pertinent to note that the developed resonant measuring systems provide penetration depths from 0.1 to 5 mm (in this case, the natural resonant frequencies of sensors were about 600 MHz, and their Q-factors were of the order of 150). Exactly these circumstances allow us to conclude that the method of near-field microwave sensing can be used for non-invasive determination of the blood glucose level in a patient.
From the foregoing it follows that to develop a reliable method of non-invasive microwave monitoring of the glucose level, further theoretical and experimental investigations of the physical processes of the interaction of electromagnetic fields with biological tissues containing blood vessels at small depths are required.
In the present work, an approach is proposed aimed at developing a near-field microwave sensing system for regular non-invasive monitoring of the glucose level. The paper is organized as follows. In the beginning of the paper, results of simulations of dependences of real parts of the dielectric permittivities ε of blood, fat, muscles, and bones at frequencies of electromagnetic oscillations in the range from 10 MHz to 10 GHz are discussed. Then the results of a computer simulation of the interaction of the wideband near-field probe having a special design with phantoms of different biological tissues are presented. This part of our research has allowed us to establish the special features of the attenuation of sensing radiation power density in the near-field zone in the above-indicated tissues. Based on the experimental investigations, opportunities for measuring the glucose content in phantoms of biological tissues (physiological solutions with different dextrose contents) are investigated. Finally, prospects for practical implementation of this approach are briefly discussed.
It should be noted that the ideological basis of our work was provided by pioneer research [17] in which the new concept of microwave tomography of absorbing media was proposed. Within the framework of this concept, essential changes in the near-field phase state of the probe in the vicinity of the so-called causal surface are effectively used for sensing of the medium.

Numerical Simulations
The main components of the biological tissue are blood, fat, muscles, and bones. From the viewpoint of monitoring the blood glucose level in patients, the simplest and most convenient places for sensor location are the hands and feet, in particular, the wrists. They conditionally have the following layers: the skin subdivided into epidermis and dermis (the main component of this layer); the hypodermis that forms the cell space with fatty deposits and blood vessels; the biological layer of muscles occupying the greatest part of the feet or hands; and the bone in the center of all layers. As is well known, microwave monitoring is based on the established interrelation between changes in the dielectric permittivity of the propagation medium and the sensing signal parameters. In theoretical investigations, the dielectric permittivity is usually approximated by the Debye model or its slightly modified variant-the Cole-Cole model. Exactly the latter model was used to calculate the dielectric permittivity of the above tissues in a wide frequency range [18,19]. We calculated independently the dependences of the real part of the dielectric permittivity ε of blood, fat, muscles, and bones at frequencies in the range from 10 MHz to 10 GHz [20]. As expected, the tissues comprising aqueous solution (blood, muscles, and skin) have high dielectric permittivity in a wide frequency range. The same special feature is also peculiar to the imaginary part of the dielectric permittivity.
In problems of near-field microwave sensing, the quality of the employed active probes is important. Therefore, we calculated in CST Microwave Studio the electric field distribution for the probe shaped like a conical horn with a conic wire placed inside that expanded toward the horn aperture (Figure 1a). Such a probe has a much wider band in comparison with the open end of a waveguide of the simplest narrow-band probe. The probe geometry provides formation of an extended near zone at its aperture with high electric field strength (Figure 1b). Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 9 (a) Probe geometry (b) Electric field distribution inside the probe and near its aperture The special features of the near-field probe interaction with different biological tissues were studied by analyzing the behavior of the real part of the radiation flux power density (the Poynting vector). The formation of such flux is a characteristic feature of interference interaction of overlapping evanescent fields, irrespective of their sources (in this case, the counter-propagating probe field and the field reflected from the phantom of the tissue were overlapped) [21]. Results of the calculations allowed us to estimate the depth of radiation penetration into the examined phantoms of tissues. The probe was placed at a distance of 1 mm from the examined phantom of the biological tissue ( Figure  2), and the Poynting vector was calculated at a frequency of 4 GHz at points of the segment of the straight line orthogonal to the probe aperture ( Figure 2).  The special features of the near-field probe interaction with different biological tissues were studied by analyzing the behavior of the real part of the radiation flux power density (the Poynting vector). The formation of such flux is a characteristic feature of interference interaction of overlapping evanescent fields, irrespective of their sources (in this case, the counter-propagating probe field and the field reflected from the phantom of the tissue were overlapped) [21]. Results of the calculations allowed us to estimate the depth of radiation penetration into the examined phantoms of tissues. The probe was placed at a distance of 1 mm from the examined phantom of the biological tissue (Figure 2), and the Poynting vector was calculated at a frequency of 4 GHz at points of the segment of the straight line orthogonal to the probe aperture ( Figure 2).  The special features of the near-field probe interaction with different biological tissues were studied by analyzing the behavior of the real part of the radiation flux power density (the Poynting vector). The formation of such flux is a characteristic feature of interference interaction of overlapping evanescent fields, irrespective of their sources (in this case, the counter-propagating probe field and the field reflected from the phantom of the tissue were overlapped) [21]. Results of the calculations allowed us to estimate the depth of radiation penetration into the examined phantoms of tissues. The probe was placed at a distance of 1 mm from the examined phantom of the biological tissue ( Figure  2), and the Poynting vector was calculated at a frequency of 4 GHz at points of the segment of the straight line orthogonal to the probe aperture ( Figure 2).  Results of the numerical simulation of the attenuation of the near field of the probe in different biological tissues are illustrated by Figure 3. It can be seen that the radiation attenuation by blood, muscles, and skin had an analogous exponential character. Such behavior was due to the dielectric properties of these tissues, namely, the presence of a considerable amount of liquid in their structure (86.3% of water in muscles; blood consists of plasma with 85% of water and platelets; the skin contains sebaceous glands composed of two-thirds water) [22]. As can be seen, the radiation flux power density almost vanished for radiation that penetrated through blood, muscles, and skin at a depth of 30 mm, through bone at a depth of 60 mm, and through fat at a depth of more than 100 mm. ci. 2021, 11, x FOR PEER REVIEW 5 of 9 Results of the numerical simulation of the attenuation of the near field of the probe in different biological tissues are illustrated by Figure 3. It can be seen that the radiation attenuation by blood, muscles, and skin had an analogous exponential character. Such behavior was due to the dielectric properties of these tissues, namely, the presence of a considerable amount of liquid in their structure (86.3% of water in muscles; blood consists of plasma with 85% of water and platelets; the skin contains sebaceous glands composed of two-thirds water) [22]. As can be seen, the radiation flux power density almost vanished for radiation that penetrated through blood, muscles, and skin at a depth of 30 mm, through bone at a depth of 60 mm, and through fat at a depth of more than 100 mm.

Experiments and Results
From the results of the numerical simulation it followed that the signal changes caused by changes in the electromagnetic parameters of blood, skin, and muscles could be detected with the probe placed in immediate proximity to the surface of the examined biological tissues. Since changes in the blood sugar level lead to changes of the dielectric permittivity, the maximum changes of the signal level are expected for radiation that has penetrated through blood vessels. Thus, the results of the numerical simulation confirmed the theoretical possibility of non-invasive near-field monitoring of blood sugar level in a patient.
In this case, the question arises: is it possible to detect minor changes in the sugar content in blood in an actual experiment? To answer it, we performed additional experimental investigations. As an object of research, a sodium chloride (physiological) solution with different contents of dextrose (glucose) was chosen. These two liquids, when mixed, allow sufficiently adequate experimental models of biological tissues and liquids to be obtained (more complicated phantoms of biological tissues were proposed, for example, in [23,24]). The employed experimental setup included the following main parts: (1) N5230C PNA-L Network Analyzer (Agilent Technologies) with working frequencies in the range 10 MHz-40 GHz; (2) coaxial line with variable cross section shaped like a coaxial conic probe; and (3) plastic container filled with the examined liquid located in immediate proximity to the probe aperture ( Figure 4).

Experiments and Results
From the results of the numerical simulation it followed that the signal changes caused by changes in the electromagnetic parameters of blood, skin, and muscles could be detected with the probe placed in immediate proximity to the surface of the examined biological tissues. Since changes in the blood sugar level lead to changes of the dielectric permittivity, the maximum changes of the signal level are expected for radiation that has penetrated through blood vessels. Thus, the results of the numerical simulation confirmed the theoretical possibility of non-invasive near-field monitoring of blood sugar level in a patient.
In this case, the question arises: is it possible to detect minor changes in the sugar content in blood in an actual experiment? To answer it, we performed additional experimental investigations. As an object of research, a sodium chloride (physiological) solution with different contents of dextrose (glucose) was chosen. These two liquids, when mixed, allow sufficiently adequate experimental models of biological tissues and liquids to be obtained (more complicated phantoms of biological tissues were proposed, for example, in [23,24]). The employed experimental setup included the following main parts: (1) N5230C PNA-L Network Analyzer (Agilent Technologies) with working frequencies in the range 10 MHz-40 GHz; (2) coaxial line with variable cross section shaped like a coaxial conic probe; and (3) plastic container filled with the examined liquid located in immediate proximity to the probe aperture (Figure 4). Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 9 During the experiments, the complex reflection coefficient from the probe input was measured depending on the frequency of arriving oscillations. The experiments were organized as follows. First, the reflection coefficient was measured for the sensing of solutions containing dextrose. Then the same procedure was repeated for the sensing of a pure physiological solution. Then the measured values of the reflection coefficients were digitized and subsequently normalized (in so doing, we fully took into account recommendations [25] concerning the reduction of the negative influence of various factors). As a result, we obtained data convenient not only for perception, but also for their substantial analysis. The spectral behavior of the reflection coefficient (the parameter S11) was investigated at frequencies in the range 0.1-10 GHz. We studied solutions with the following concentrations: 1 mmol/l (18.02 mg/dL), 3 mmol/l (54.05 mg/dL), 5 mmol/l (90.09 mg/dL), 7 mmol/l (126.13 mg/dL), and 25 mmol/l (450.45 mg/dL). Results of the investigations are shown in the figures below in red, dark blue, green, violet, and blue ( Figure  5). It can be seen that at frequencies higher than 3.5 GHz it became impossible to highlight the differences between signals for different concentrations due to the signals being superimposed on each other and having intersections. The same picture was observed at During the experiments, the complex reflection coefficient from the probe input was measured depending on the frequency of arriving oscillations. The experiments were organized as follows. First, the reflection coefficient was measured for the sensing of solutions containing dextrose. Then the same procedure was repeated for the sensing of a pure physiological solution. Then the measured values of the reflection coefficients were digitized and subsequently normalized (in so doing, we fully took into account recommendations [25] concerning the reduction of the negative influence of various factors). As a result, we obtained data convenient not only for perception, but also for their substantial analysis. The spectral behavior of the reflection coefficient (the parameter S11) was investigated at frequencies in the range 0.1-10 GHz. We studied solutions with the following concentrations: 1 mmol/l (18.02 mg/dL), 3 mmol/l (54.05 mg/dL), 5 mmol/l (90.09 mg/dL), 7 mmol/l (126.13 mg/dL), and 25 mmol/l (450.45 mg/dL). Results of the investigations are shown in the figures below in red, dark blue, green, violet, and blue ( Figure 5).  During the experiments, the complex reflection coefficient from the probe input was measured depending on the frequency of arriving oscillations. The experiments were organized as follows. First, the reflection coefficient was measured for the sensing of solutions containing dextrose. Then the same procedure was repeated for the sensing of a pure physiological solution. Then the measured values of the reflection coefficients were digitized and subsequently normalized (in so doing, we fully took into account recommendations [25] concerning the reduction of the negative influence of various factors). As a result, we obtained data convenient not only for perception, but also for their substantial analysis. The spectral behavior of the reflection coefficient (the parameter S11) was investigated at frequencies in the range 0.1-10 GHz. We studied solutions with the following concentrations: 1 mmol/l (18.02 mg/dL), 3 mmol/l (54.05 mg/dL), 5 mmol/l (90.09 mg/dL), 7 mmol/l (126.13 mg/dL), and 25 mmol/l (450.45 mg/dL). Results of the investigations are shown in the figures below in red, dark blue, green, violet, and blue ( Figure  5). It can be seen that at frequencies higher than 3.5 GHz it became impossible to highlight the differences between signals for different concentrations due to the signals being superimposed on each other and having intersections. The same picture was observed at It can be seen that at frequencies higher than 3.5 GHz it became impossible to highlight the differences between signals for different concentrations due to the signals being superimposed on each other and having intersections. The same picture was observed at low frequencies up to 1.5 GHz. Of particular interest was the signal in the frequency range 1.4-1.7 GHz. In this range of frequencies, a clear correlation was observed between the signal amplitudes and the solution concentrations. The signal received from the solution with the least dextrose concentration-1 mmol/L-had the least modulus of the complex reflection coefficient (Figure 6). l. Sci. 2021, 11, x FOR PEER REVIEW low frequencies up to 1.5 GHz. Of particular interest was the signa range 1.4-1.7 GHz. In this range of frequencies, a clear correlation was the signal amplitudes and the solution concentrations. The signal rec lution with the least dextrose concentration-1 mmol/L-had the le complex reflection coefficient ( Figure 6).

Conclusions
The interaction of the near-field coaxial conic probe with phan tissues was investigated both theoretically and experimentally. The pr a piece of coaxial line with a variable cross section that supported the This ensured the possibility of carrying out investigations in the wid namely, from 10 MHz to 10 GHz. Blood, skin, muscles, and bones wit permittivities were used as phantoms of biological tissues. As the wa there was a deeper penetration of radiation into biological tissue. Thi significant reflections of radiation from dense bone tissue and, conseq oration in the signal-to-noise ratio. In the range we used, the radiatio short and could not penetrate through the skin layer into the biolo same time, it provided the necessary near-field resolution of small b the human body.
The main goal of the theoretical study was the primary substant bility of using the proposed design of the probe for the purposes of ne of blood glucose in a wide frequency range. The experimental study confirmation of this possibility.

Conclusions
The interaction of the near-field coaxial conic probe with phantoms of biological tissues was investigated both theoretically and experimentally. The probe essentially was a piece of coaxial line with a variable cross section that supported the fundamental wave. This ensured the possibility of carrying out investigations in the wide frequency band, namely, from 10 MHz to 10 GHz. Blood, skin, muscles, and bones with known dielectric permittivities were used as phantoms of biological tissues. As the wavelength increased, there was a deeper penetration of radiation into biological tissue. This can lead to rather significant reflections of radiation from dense bone tissue and, consequently, to a deterioration in the signal-to-noise ratio. In the range we used, the radiation wavelength was short and could not penetrate through the skin layer into the biological tissue. At the same time, it provided the necessary near-field resolution of small blood vessels inside the human body.
The main goal of the theoretical study was the primary substantiation of the possibility of using the proposed design of the probe for the purposes of near-field diagnostics of blood glucose in a wide frequency range. The experimental study was aimed at real confirmation of this possibility.
Results of this experimental research demonstrated that the dielectric permittivities of these phantoms increase with increasing dextrose concentration in the sodium chloride solution. In experimental studies, we changed the glucose concentration in the range of 0-25 mmol/L (0-450 mg/dL). At the same time, in the frequency range 1.4-1.7 GHz, the possibility of monitoring the glucose concentration with a resolution of 1 mmol/L (18 mg/dL) was noted. The measured signal-to-noise ratio in the experiments was about 30 dB. This fact was also confirmed by the independent research of other scientific groups [9]. Thus, the possibility of near-field electromagnetic sensing of phantoms of biological tissues for the determination of the dextrose concentration in them was justified.
We believe that the procedure described above of the sensing of biological tissues can be embodied in an effective sensor for non-invasive glucose monitoring.