Daily monitoring of blood glucose levels is vital for managing diabetes; however, invasive blood sampling is a burden on patients. To improve patients’ quality of life, bioimpedance-based noninvasive blood glucose monitoring (BI-NIBGM) that involves wearable electrodes on the wrist has been proposed. In this study, we investigated the validity of applying a simple NaCl solution to a blood phantom for in vitro evaluation of BI-NIBGM. The electrical properties of cow blood and various blood phantoms with different NaCl concentrations were measured based on the parallel-plate method at frequencies from 200 kHz to 100 MHz. The following observations were made: (1) the conductivity of blood can be mimicked accurately with simple NaCl solutions, and the optimal concentration of the phantom depends on the operating frequency and (2) it is challenging to mimic the relative permittivity of blood with simple NaCl solutions because NaCl lacks a cellular structure. Furthermore, the relationship between the bioimpedance and electrical properties of the phantom was examined using a simplified arm model. The results indicate that the relative permittivity of the blood layer has little effect on the bioimpedance and that only the conductivity determines the bioimpedance. Therefore, the NaCl concentration of the phantom can be adjusted from the viewpoint of conductivity for BI-NIBGM.

Diabetes can cause serious complications, including blindness, kidney failure, heart attacks, strokes, and lower-limb amputation. The number of diabetic patients worldwide was 420 million in 2014, and this number is expected to reach 700 million in 2045.1 Daily monitoring of blood glucose levels (BGLs) is vital for managing diabetes. The most common monitoring technique employs an enzymatic electrode, which requires invasive blood sampling from patients.2 However, invasive blood sampling is uncomfortable, leaves patients vulnerable to infection, and can be relatively high in cost. To address these drawbacks and to improve patients’ quality of life, noninvasive blood glucose monitoring (NIBGM) has been proposed.3–6 Among various NIBGM techniques, those based on electromagnetic response (e.g., reflection and transmission characteristics) are the most promising.7–12 The monitoring method we have proposed is bioimpedance-based NIBGM (BI-NIBGM),12 which utilizes changes in a patient’s bioimpedance as an indicator of the BGL concentration; therefore, accurate measurement of the electrical properties of patients is required.

In a previous study, we evaluated the optimal bioimpedance measurement frequency via a multiple-subject experiment.12 However, a subject experiment is unsuitable for initial examination of BI-NIBGM from the viewpoint of reproducibility because subjects’ physical condition, body movement, and skin moisture condition affect the bioimpedance characteristics. To solve these problems, electromagnetic phantoms mimicking the electrical properties of biological tissues have been developed for in vitro experiments of electromagnetic wave exposure and human body communication as well as NIBGM.13–17 In this study, we investigated the validity of applying a simple NaCl solution to a blood phantom for in vitro evaluation of BI-NIBGM. In particular, the electrical properties of cow blood and various blood phantoms with different NaCl concentrations were measured based on the parallel-plate method at frequencies from 200 kHz to 100 MHz.

Ionization of the blood is inhibited when the BGL increases because the molecular weight of glucose is higher than that of conductive ions, such as Na+ and Cl.18 In addition, in terms of molecular interactions, glucose associates with electrolytes in aqueous solution.19 Therefore, the electrical characteristics of the blood change depending on the BGL; namely, as the BGL rises, the conductivity σ decreases and the permittivity εr increases.8,20Figure 1 models the bioimpedance of the human body as a resistor–capacitor (RC) parallel circuit. In this circuit, the bioimpedance Z is represented as

(1)

where C and R are the capacitance and resistance determined by the electrical properties of biological tissues, respectively. Changes in the electrical properties of blood result in changes in the bioimpedance Z. Therefore, the BGL can be estimated based on the change in bioimpedance, which is the input impedance of electrodes attached to a human body.

FIG. 1.

Measurement mechanism of bioimpedance-based noninvasive blood glucose monitoring.

FIG. 1.

Measurement mechanism of bioimpedance-based noninvasive blood glucose monitoring.

Close modal

The electrical properties, such as electrical conductivity σ and relative permittivity εr, of cow blood and various blood phantoms with different NaCl concentrations were measured based on the parallel-plate method at frequencies from 200 kHz to 100 MHz. For practicality in the in vitro experiments, the phantom consisted of liquid aqueous solution composed of pure water and NaCl. Figure 2 displays a measurement cell connected to an impedance analyzer (Agilent, 4294A). The cell comprised two circular platinum electrodes (diameter of 10 mm) and an acrylic sheath for loading liquid samples. The thickness of the acrylic sheath (i.e., distance between two platinum electrodes) was 5 mm. To reduce electrode polarization at the surfaces of the parallel electrodes due to the high conductivity of biological samples,21 platinum electrodes with large electrochemical surface areas were employed. This measurement cell could be used repeatedly because the detachable electrode structure allowed the loading/unloading of liquid samples.

FIG. 2.

(a) Measurement cell and connection to the impedance analyzer. (b) Schematic diagram of the measurement cell.

FIG. 2.

(a) Measurement cell and connection to the impedance analyzer. (b) Schematic diagram of the measurement cell.

Close modal

Figures 3 and 4 display the conductivity and relative permittivity, respectively, of cow blood and NaCl solutions with concentrations ranging from 0.30% to 0.90% as a function of frequency. As illustrated in Fig. 3, the conductivity of the NaCl solution increased as the concentration of NaCl increased due to increased ionization. The conductivity of cow blood was similar to that of 0.40% NaCl solution at frequencies from 200 kHz to 3 MHz and close to that of 0.45% and 0.50% NaCl solutions at frequencies higher than 3 MHz. This result demonstrates that the conductivity of blood can be mimicked accurately using simple NaCl solutions and that the optimal concentration of the phantom depends on the operating frequency.

FIG. 3.

Conductivity characteristics of blood and phantom as a function of frequency.

FIG. 3.

Conductivity characteristics of blood and phantom as a function of frequency.

Close modal
FIG. 4.

Relative permittivity characteristics of blood and phantom as a function of frequency.

FIG. 4.

Relative permittivity characteristics of blood and phantom as a function of frequency.

Close modal

As illustrated in Fig. 4, the relative permittivity of the NaCl solution increased as the concentration of NaCl increased. Notably, there was a considerable difference between the relative permittivity of blood and that of the NaCl solutions. This is because blood has a cellular structure composed of a cell membrane, intracellular fluid, and extracellular fluid, whereas the NaCl solution does not have a cellular structure. In cow blood, beta dispersion was observed at frequencies around 6 MHz. By contrast, no dispersion was observed in the NaCl solutions. These results imply that it is challenging to mimic the relative permittivity of blood with simple NaCl solutions without a cellular structure. However, the difference in relative permittivity between real blood and the phantom may be acceptable because the final measured parameter in BI-NIBGM is bioimpedance, not relative permittivity. In Sec. IV, the measured electrical properties are applied to a biological tissue model to calculate and evaluate the bioimpedance in BI-NIBGM.

In BI-NIBGM, the directly measured parameter is the bioimpedance. Based on the electrical properties discussed in Sec. III, we estimated the input impedance measured by wearable electrodes placed on a user’s wrist (i.e., bioimpedance). Figure 5 displays the structure of a simplified arm model and wearable electrode model for bioimpedance calculation. The arm model includes three layers: skin, blood, and a mixture of fat and muscle. In our previous studies, the biological tissues included in the simplified model were the dominant body tissue that determined the bioimpedance of the arm. Other body tissues below the muscle, such as tendon and bone, had little influence on the input impedance because the electric current is small in these tissues.22 

FIG. 5.

Structure of a simplified arm model and wearable electrode model.

FIG. 5.

Structure of a simplified arm model and wearable electrode model.

Close modal

The thickness of the skin and fat layer was determined based on the range of variation in the thickness of each tissue of the forearm,23 and the thickness of the blood layer was determined based on the general range of blood vessel diameters.24 These thicknesses were within a reasonable range based on the volume ratio25 of each biological tissue in a standard arm. To facilitate the theoretical calculation of bioimpedance, the thickness of the muscle layers and the plane of each layer were assumed to be infinitely wide. Frequency-dependent electrical properties26 were applied to layers other than the blood layer. The electrical properties of the mixture layer of fat and muscle were determined based on the tissue volume ratio of fat and muscle.25 The electrical properties presented in Figs. 3 and 4 were applied to the blood layer. Wearable electrodes were placed on the center of the arm model. The structure of the electrodes was the same as that of the electrodes used for the subject experiment.12 The entire bottom of the electrode was assumed to be in perfect contact with the skin layer. As illustrated in Fig. 5, when a semicircular current path connecting the centers of both electrodes (d = 25.1 mm) was dominant, the input impedance of the electrodes could be regarded as the impedance of a parallel-plate capacitor in which each tissue layer was sandwiched by electrodes.

As mentioned in Sec. II, the bioimpedance Z is represented as formula (1). Herein, C and R can be calculated as follows, using the electrical conductivity σ and relative permittivity εr of each biological tissue in the arm model, each electrode area S, and the distance between the electrodes d,

(2)
(3)

By substituting formulas (2) and (3) into (1), the absolute bioimpedance |Z| can be expressed as follows:

(4)

In Sec. IV B, differences in the electrical properties between real blood and the phantom are evaluated based on formula (4).

Figure 6 presents the bioimpedance characteristics calculated by formula (4) in the frequency range of 200 kHz to 200 MHz. Broken and solid lines represent the bioimpedance obtained from the simplified arm model with the electrical properties of blood (i.e., the blood-applied model) and the electrical properties of blood phantoms with different NaCl concentrations (i.e., the phantom-applied model), respectively. The bioimpedance characteristics obtained from the blood-applied model were similar to those obtained from the 0.40% NaCl solution phantom-applied model at frequencies from 200 kHz to 3 MHz. At frequencies higher than 3 MHz, the bioimpedance characteristics obtained from the blood-applied model were similar to those of the 0.45% and 0.50% NaCl solution phantom-applied models. This tendency was the same as that of the electrical properties discussed in Sec. III. Figure 7 illustrates the difference in bioimpedance between the blood-applied model and phantom-applied models. For all frequencies, the phantom with an appropriate NaCl concentration achieved a bioimpedance error within 1% of the target value. This indicates that a blood phantom composed of a simple NaCl solution can be applied for BI-NIBGM evaluation.

FIG. 6.

Bioimpedance characteristics calculated using the blood-applied model and phantom-applied models.

FIG. 6.

Bioimpedance characteristics calculated using the blood-applied model and phantom-applied models.

Close modal
FIG. 7.

Differences in bioimpedance between the blood-applied model and phantom-applied models.

FIG. 7.

Differences in bioimpedance between the blood-applied model and phantom-applied models.

Close modal

Furthermore, considering the fact that a simple NaCl solution cannot mimic the relative permittivity of real blood, we examined the relationship between the bioimpedance and relative permittivity of the phantom. To examine the effect of only the relative permittivity on the bioimpedance, the relative permittivity obtained from the phantom and the conductivity obtained from real blood were applied to the blood layer of the simplified model. These models are referred to as the permittivity evaluation models. Figure 8 presents the difference in bioimpedance between the blood-applied model and permittivity evaluation models. For all frequencies, the bioimpedance characteristics obtained from both models were in good agreement. This result indicates that the relative permittivity of the blood layer had little effect on the bioimpedance and that only the conductivity determined the bioimpedance in the BI-NIBGM setup. Therefore, the NaCl concentration of the phantom can be adjusted from the viewpoint of conductivity for BI-NIBGM.

FIG. 8.

Difference in bioimpedance between the blood-applied model and permittivity evaluation models.

FIG. 8.

Difference in bioimpedance between the blood-applied model and permittivity evaluation models.

Close modal

In this study, we investigated the validity of applying a simple NaCl solution to blood for in vitro evaluation of BI-NIBGM. The electrical properties of cow blood and various blood phantoms with different NaCl concentrations were measured based on the parallel-plate method at frequencies from 200 kHz to 100 MHz. The results revealed that the conductivity of blood can be mimicked accurately with simple NaCl solutions and that the optimal concentration of the phantom depends on the operating frequency. However, it is challenging to mimic the relative permittivity of blood with simple NaCl solutions because NaCl does not have a cellular structure comprising a cell membrane, intracellular fluid, and extracellular fluid. To investigate the effect of the differences in the electrical properties of real blood and a phantom on bioimpedance, a simplified arm model was introduced. For all frequencies, the phantom with an appropriate NaCl concentration achieved a bioimpedance error within 1% of the target value. This result indicates that a blood phantom composed of a simple NaCl solution can be applied for BI-NIBGM evaluation. Furthermore, the relationship between the bioimpedance and relative permittivity of the phantom was examined. The results revealed that the relative permittivity of the blood layer had little effect on bioimpedance and that only the conductivity determined the bioimpedance. Therefore, the NaCl concentration of the phantom can be adjusted from the viewpoint of conductivity for BI-NIBGM. These results can be applied to other systems using the interaction between biological tissues and electromagnetic waves, such as vital signal measurement systems and human body communication.

A part of this research was funded by the Grant-in-Aid for Young Scientists (A), Grant No. 17H04929.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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