# Non-Invasive and Accurate Blood Glucose Detection Based on an Equivalent Bioimpedance Spectrum
## 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].  
\[\varepsilon_{mem}=\varepsilon_{mem,0}\left[1+\frac{(N_{free}+N_{glu})\mu_{glu} ^{2}}{3 kT\varepsilon_{0}\varepsilon_{mem,0}(1+K_{m}\Big{/}C_{glu})}\right]. \tag{1}\]  
Formula (1) describes the relationship between the cell membrane dielectric constant \(\varepsilon_{mem}\) 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; \(\varepsilon_{0}\) 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 \(\varepsilon_{mem}\) is shown in (2) [23]:  
\[Z^{\prime}=\frac{\kappa}{j\omega\varepsilon_{mem}\varepsilon_{0}}. \tag{2}\]  
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.