Design, Development and Comparison of two Different Measurement Devices for Time-Resolved Determination of Phase Shifts of Bioimpedances

Bioimpedance measurements are a non-invasive method for determining the electrical characteristics of organic tissues [2]. With time-resolved measurements, it is possible to determine dynamic characteristics like the pulse wave or the effect of breathing [3].

For measuring the magnitude and phase of the unknown bioimpedance, a small known alternating current is injected into the tissue. This current produces a voltage drop across the bioimpedance, which is measured and used to calculate the complex bioimpedance. Usually the measured impedance phase of organic tissues is negative. This behavior can be explained by the capacitive behavior caused by the cell structure of biological matter [4]. Fig. 1 shows a simplified electrical equivalent circuit, whereby $R_{2}$ represents the extracellular fluid and $R_{1}$ and $C_{1}$ represent the cell impedance with cell membrane and intracellular fluid.

When the bioimpedance is measured time resolved a small variation of the impedance magnitude can be observed which is synchronous with the heart beat.

The reason for this effect is the pulsation of the blood in the tissue under test. When the heart is pumping blood through the bloodvessels, the pressure in the arteries increases abruptly and then falls again. Because of this variation of pressure, the arteries diameter and thus the volume of blood in the tissue under test changes. Since the conductivity of blood is significantly higher than that of tissue, this leads to a change of the impedance. One may assume that besides the magnitude also the phase of the complex bioimpedance is influenced by the blood pulsation. The changing of the bioimpedance phase shift would indicate that the blood additionally has a different phase shift than the tissue. Typical bioimpedance phase shifts of living tissues are between $\approx-10^{\circ}$ to $0^{\circ}$, with a maximum at about $50~{}kHz$ [5].

This work compares two different phase shift measurement methods. The first method is an analog circuit, realized with Operational Amplifiers (OPA). The second method is implemented by the IC (Integrated Circuit) AFE4300 from Texas Instruments. For the evaluation of the different measurement methods, both methods are realized together with an Electrocardiography (ECG) circuit, as a physiological time reference, on the same Printed Circuit Board (PCB). The PCB also contains a microcontroller system for Analog to Digital Conversion (ADC), basic signal preprocessing and USB for data transmission to a host PC for further signal processing and displaying of the measurement data.

The block diagram in Fig. 2 shows the schema of the developed PCB for interfacing the object under test to the host PC. For the communication between the AFE4300 and the microcontroller, a SPI bus is used. However the external analog phase shift measurement circuit uses the PCB’s analog inputs.

The development of the software can be separated into two parts. The first part is programming the microcontroller’s firmware. In the second part the LabView Software for the PC is programmed.

For the verification of the phase shift measurements an equivalent circuit for bioimpedances according to Fig. 6 is used. The result of an error estimation, executed with the total differential, is that this circuit is more insensitive to the components tolerances than the circuit shown in Fig. 1.

To realize the desired magnitudes and phase shifts only the resistors were changed. The reason is the higher tolerance of the capacitance. It is 1% whereas the resistors tolerance is just 0.1%. An additional advantage is that resistors are available in a wide range of values. The verification of both systems was executed with a frequency of $62.5~{}kHz$. An error estimation resulted to a maximal phase shift error of the equivalent circuit of less than $\pm 0.1^{\circ}$ in the interesting range.

The impedances were realized on a separate PCB where switches are used to change the resistances. Fig. 7 shows the result of the analog phase shift measurement system. Achieving this characteristic was only possible by adapting the system’s shunt resistance to the magnitude of the measured impedance. This measurement system shows a good linearity but some offset depending on the magnitude of the measured impedance.

Fig. 8 shows the results of the AFE4300. The measurements depend on the impedance’s magnitude, too. Furthermore the results have large offsets and are inverted. Especially for small phase shifts below $4^{\circ}$ there are strong deviations from a linear relation.

The linear behavior of the analog measurement system, especially when there are small phase shifts, is an advantage. However the system’s major disadvantage is that an external current source is needed. For suitable results it is also important to adjust the shunt resistor. As a consequence the magnitude of the impedance under test has to be known. The IC does not have such a linear behavior as the analog circuit. Although up to four calibration impedances can be connected to the IC pins. With these known impedances and a microcontroller program it is possible to automate the calibration. The disadvantage of using an IC with such a small housing (LQFP80) is the effort of implementation for experimental purposes. A complete PCB with a microcontroller has to be developed and manufactured. However there is an essential advantage that the whole measurement is done by just one component. Thus no external current source and shunt resistor is needed. Furthermore the AFE4300 is low priced (2.50 $ per 1000 pcs.) and no additional ADC is required. For reliable measuring of absolute phase shifts both systems have to be calibrated comprehensively. The effective resolution of both systems is about $0.3^{\circ}$. Measurements of real bioimpedances could not exhibit a relationship between the pulse and the phase shift. Using another impedance measurement instrument, which has also been developed in the work group [8, 9], it could be shown that the blood pulsation induced phase shift changes are only in a range of about $0.01^{\circ}$. Hence for this application both the analog and the integrated phase shift measurement systems are inappropriate.

For time depending measuring of the bioimpedances phase shift, two different measurement systems were compared.

The contrasted systems are the integrated circuit AFE4300 from Texas Instruments and an analog phase shift measurement circuit realized on a separate board.

To compare both systems a microcontroller based hardware system was developed and manufactured. Additionally the resulting PCB is able to measure an ECG simultaneously. A firmware was programmed for sending the measurement data from the microcontroller via the USB interface to a PC. Furthermore a LabView software was developed for signal processing and data logging. The systems were verified with the help of a RC-phantom with known magnitudes and phases. The result of the verification was that both circuits do have advantages and disadvantages in implementation as well as in the measuring results. But the effective phase shift resolution of both systems is far to low to detect the pulse induced phase variation of living tissue. With the developed PCB it is possible to test further measurement methods in the future.