Research on the measurement of intracranial hemorrhage in rabbits by a parallel-plate capacitor

Head capacitance measurement theory

According to the Cole-Cole model of biological tissue and the principle of high frequency capacitance coupling, a head capacitance measurement model as shown in Fig. 1 is proposed. C ₁ and C ₂ are the equivalent capacitance between the capacitor plate and the skull, C_x is the equivalent capacitance of brain tissue, and R_x is the equivalent resistance of brain tissue. The total capacitance C_total between the two plates satisfies Eq. (1), where ε_r is the equivalent permittivity of the head between the two plates, ε₀ is the vacuum permittivity, S and d are the surface area of the plate and the distance between the two plates respectively. According to Fig. 1, when the measuring position remains unchanged, C ₁ and C ₂ remain unchanged, the total capacitance C_total between the two plates is only related to C_x, that is, only to the equivalent permittivity of the measured head. When intracranial hemorrhage occurs, the head equivalent permittivity increases, C_x increases. (1)${\displaystyle \frac{1}{C_{total}}\approx \frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_x}\to \Delta C\propto C_x=\frac{{\epsilon }_r\cdot {\epsilon }_0\cdot S}{d}}$

Parallel-plate capacitance measurement system

The principle of the parallel plate capacitance measurement system is shown in Fig. 2A, and the photo of the system is shown in Fig. 2B. The parallel plate capacitor consists of two identical parallel copper clad laminates. Electrode plate is cut with epoxy glass fiber copper clad panel, and the thickness of the base plate is two mm. During measurement, the measured object is placed in parallel between two plates. This paper uses FDC2214 capacitance measuring chip (Ti) to measure the capacitance of the parallel-plate capacitor (Texas Instruments, 2015). The chip measures the total capacitance in parallel to the two ports of one channel and directly converts the measured capacitance into digital signal output. The specific measurement tool is the FDC2214 EVM development board of Texas Instruments (Texas Instruments, 2016). This development board mainly integrates a FDC2214 chip and a MSP430 MCU. MSP430 communicates with the computer through a USB cable. On the one hand, it receives the control command from the computer, sets the parameters of FDC2214 chip and controls its work; on the other hand, it uploads the capacitance data measured by FDC2214 to the computer. A FDC2214 data acquisition software (sensing solutions EVM GUI, Ti) is used to collect and display the measured data of FDC2214. FDC2214 EVM board has a channel port for connecting external capacitor, which is easy to use. Therefore, we directly welded the parallel plate capacitor to the measurement port of FDC2214 EVM board through wires. FDC2214 EVM board and data acquisition software are shown in Fig. 2B.

FDC2214 needs to connect a reference inductance and capacitance between two pins of the channel to form a parallel LC circuit, as the L ₀ and C ₀ shown in Fig. 2A. The measured external parallel plate capacitor C_sensor is also connected to the channel pins. So L ₀, C ₀, C_sensor constitute a LC parallel circuit. FDC2214 calculates the C_sensor by measuring the resonant frequency f of the LC parallel circuit. Assuming that the resonant frequency is f and the total capacitance of the parallel circuit is C, then C satisfies Eq. (2). Since L ₀ and C ₀ are known, the capacitance C_sensor of the external parallel plate capacitor is shown in Eq. (3).

(2)${\displaystyle C=\frac{1}{L_0\cdot {\left(2\pi \cdot f\right)}^2}}$ (3)${\displaystyle C_{sensor}=C-C_0}$

When the EVM board leaves the factory, the values of welded L₀ and C₀ are 18 µH and 33pF, respectively. The frequency is about 6.5 MHz when there is no load (the parallel-plate capacitor is not connected). The resonant frequency range supported by FDC2214 is 10 kHz–10 MHz. The capacitance measurement accuracy of FDC2214 is about 10 fFfor the resonance frequency. The measurement speed of FDC2214 is related to the internal sampling time setting, which is about 15 times per second in this paper. The measurement system of physical experiment and animal experiment is shown in Figs. 2B and 2C. The size of the parallel plate used in physical experiment is 60 mm * 60 mm, and the distance between the two plates is 120 mm. The size of the parallel plate for animal experiment is 100 mm * 50 mm, and the distance between the two plates is 70 mm. The area and spacing of parallel plate capacitors have great influence on the measurement sensitivity. The larger the area of the parallel plate capacitor, the higher the sensitivity, and the smaller the spacing, the higher the sensitivity. In the physical experiment, because the sensitivity of different positions between the two plates is to be measured, and the height of the measured object is 30 mm, the distance between the two plates needs to be larger, and the final setting is 120 mm. According to the values of L ₀ and C ₀, plus the parallel plate capacitance and stray capacitance caused by wire, the measured resonance frequency of physical experiment system is about 5.2 MHz. In animal experiments, in order to improve the measurement sensitivity, the distance between the two plates should be as small as possible. In this paper, experimental animal is the rabbit. Considering that the height of rabbit’s head is close to 60 mm, the distance between the two plates is set as 70 mm. The area of the plate is just the area covering the rabbit’s head. In addition, the higher the resonant frequency, the higher the sensitivity. Therefore, in order to improve the sensitivity of intracerebral hemorrhage measurement, the original capacitance C₀ of 33pF on the EVM board was replaced by a capacitance of 10pF, which can improve the resonance frequency. According to the values of L₀ and C₀, plus the parallel plate capacitance and stray capacitance caused by wire, the measured resonance frequency of the animal experiment system is about 9.2 MHz. The capacitance C₀ for physical experiment is still 33pF.

Physical experiment

The physical experiment is divided into the following three parts: 1. Sensitivity distribution of different positions in horizontal and vertical directions in two plates. 2. Measurement of different permittivity solutions. 3. Continuous measurement during volume increase of physiological saline. The schematic diagram of physical measurement is shown in Fig. 3A. The center of the plate is the coordinate origin O (0,0,0), the XOY plane is parallel to the plate, and the XOZ plane is perpendicular to the plate. All the test solutions were put into 3D printing cylindrical vessels separately. The Cylindrical vessel is shown in Fig. 2B, and is shown in blue in the schematic diagram. The height of the vessel is 30 mm, the inner diameter is 22 mm, and the material is resin. The distance between the bottom of the vessel and the lower plate is h.

Experiment 1: 9ml of physiological saline (0.9%) and vegetable oil solution were put into two identical cylindrical vessels described above, separately. One by one, put two vessels containing the tested solution into the same position between two plates to measure the capacitance, and calculated the difference of capacitances of the two solutions at that position. For each position, the measurement was repeated four times and the data was averaged. First, measured the capacitance difference of two solutions at five positions (h = 10 mm, 25 mm, 45 mm, 65 mm, 80 mm) along the Z-axis. When measuring, the vessel was coaxial to the Z axis. Secondly, measured the capacitance difference of two solutions at four positions (x = 0 mm, 10 mm, 20 mm, 30 mm; Z = 10mm) along the X-axis. Experiment 2: 9 ml of physiological saline, glycerin and vegetable oil were respectively put into three identical cylindrical vessels. Another same vessel was used for empty measurement. The four vessels are identical in size and material. The three vessels with solution and another empty vessel were measured at the same position. The measured capacitance value of the vessel with each solution was subtracted by the empty vessel value to obtain the capacitance change caused by each solution. Two positions (h = 10 mm (near the plate) and h = 45 mm (in the middle between two plates)) on the Z-axis were measured. The measurement was repeated four times for each position and the average capacitance change for each solution was calculated. Experiment 3: put an empty vessel coaxially to the Z-axis and placed it in the middle position between the two plates (h = 45 mm). Injected 9ml of physiological saline into the empty vessel at a constant speed, and measured the capacitance continuously. The injection time was 1 min. Before injection, the empty vessel was measured at rest for 1 min. After injection, the vessel was measured at rest for another 1 min. The total measurement time was 3 min together. The relationship between the measured capacitance and the volume of the solution injected was obtained. The permittivity of three solutions of physiological saline (0.9%), glycerin and vegetable oil are 80, 37, 2–4 respectively, according to relevant literatures.

Animal experiments

Fifteen New Zealand white rabbits (2.0–2.5 kg in weight) were purchased from the animal center of the Third Military Medical University. Rabbits were arrived one day before experiments and housed under ambient conditions (22 °C, 50% relative humidity, and a 12-h light/dark cycle), with free access to water and chow. These experiments were conducted under the guidance of the Administration of Animal Experiments for Medical Research Purpose issued by the Ministry of Health of China. The protocol was reviewed and approved by the Animal Experiments and Ethical Committee of Army Medical University (AMU, Chongqing, China). All procedures were conducted while minimizing the suffering of rabbits. A model of intracerebral hemorrhage was established by injecting autologous blood into the rabbit brain. The capacitance of the rabbit’s head was measured by the above capacitance measurement method. The data of each rabbit before and after blood injection were the data of control group. The experimental steps are as follows:

1. Rabbits were anesthetized with pentobarbital (2%, 1 ml/kg) via ear vein.

2. After anesthesia, 3 ml blood was drawn from the vein of the hind leg.

3. A hole (d = 1 mm) was drilled one mm in front of the coronal suture and six mm from the midline. In the head of the rabbit, a tube with a diameter of one mm was inserted into the basal ganglia (the depth of insertion was 13 mm).

4. The blood injection tube and the syringe containing three ml blood was installed on the micro injection pump, ready for blood injection at any time.

5. Placed the rabbit head between the two parallel plates, made the blood injection point at the center of the plate as far as possible, and tried to be close to the plate, but the rabbit head did not contact with the two plates. After half an hour of stabilization, FDC2214 measurement started.

6. Measurement process: static measurement for 9 min before blood injection, then measurement of blood injection process for 9 min, and then static measurement for 9 min after blood injection. Injection blood volume was 2 ml, injection speed was 2 ml/9 min.

The injection points of each rabbit should be consistent as much as possible. Each rabbit was measured for 27 min. The first 9 min data was static measurement without blood injection, the last 9 min data was static measurement after blood injection, and the middle 9 min data was blood injection measurement. In this paper, the capacitance measurement rate is about 15 times per second. Rabbits were euthanized via IV pentobarbital overdose at the end of monitoring.

Ethics statement of animal experiments

All experimental protocols were approved by the Animal Experiments and Ethics Committee of the Third Military Medical University, the approval number is AMUWEC20201303.

Signal processing and statistical analyses

In animal experiments, considering that the original signal was affected by respiratory movements plus external interference, a wavelet transform was used to reduce noise. Raw data processing was performed by MATLAB R2015a (Math Works, Inc., USA). Data were presented as mean ±  SD. The Wilcox rank sum test was applied to test the difference in the capacitance value between the injection group data and the control group data in SPSS (SPSS Inc., Chicago, IL, USA). A value of P < 0.05 was considered statistically significant.

Physical experiment results

The results of Experiment 1 are shown in Figs. 3B and 3C, and the capacitance difference of two solutions at five positions on the Z-axis is shown in Fig. 3B. At the position of h = 45 mm, the cylindrical vessel was just in the middle position between the two plates. The experimental results show that the closer the vessel is to the two plates, the greater the capacitance difference, the stronger the ability to distinguish the two solutions, and the higher the sensitivity. The sensitivity is the lowest at the midpoint of the distance between the two plates, and the ability to distinguish the two solutions is the weakest. Since the vessel was not filled in by the 9 ml solution, the surface of the solution is about four mm away from the surface of the vessel. When the vessel was placed at two positions (h = 10 mm and h = 80 mm) close to the upper and lower plate, it is not strictly symmetrical about the middle position between the two plates, so the curve in Fig. 3B are not exactly symmetrically.

The results of the four positions moved along the X-axis are shown in Fig. 3C, and x = 0 mm corresponds to the center position of the plate. The results show that the capacitance difference of the two solutions decreases and the sensitivity to distinguish the two solutions reduces as the measured position is far away from the center. And the closer to the edge of the plate, the faster the sensitivity decreases. Therefore, the results of Experiment 1 show that for a parallel-plate capacitor, the closer the position is to the plates on both sides, the higher the sensitivity is, and the closer it is to the center of the plate, the higher the sensitivity is.

The results of Experiment 2 are shown in Figs. 3D and 3E. The results are the capacitance changes caused by three different solutions of 9 ml. The results of two positions all shows that the capacitance change of physiological saline is greater than that of glycerin, and glycerin is greater than that of vegetable oil.

The results of Experiment 3 are shown in Fig. 3F, and the measured capacitance is normalized with respect to the initial value. The results show that the capacitance is almost constant before and after injection. With the increase of the injection amount, the capacitance also increases linearly.

Animal experiments

A total of 27 min of data were measured for each rabbit. The data of the first 9 min belongs to the static measurement without injection, the data of the last 9 min belongs to the static measurement after blood injection, and the data of the middle 9 min belongs to the measurement of continuous blood injection. Average the data of each rabbit per second to get the average capacitance value per second in 27 min. Then the data is normalized relative to the initial value, and a wavelet transform is used to remove the heartbeat and respiratory signals and reduce the noise. Finally, the mean value and standard deviation of the data of 15 rabbits at the same time point are calculated, and the results are shown in Fig. 4. Figure 5 displays the raw data of four rabbits. From Figs. 4 and 5, it can be seen that the data of static measurement have little change. In the middle 9 min, the capacitance increases with the increase of blood volume. The statistics indicate that the capacitance increase of blood injection process is much greater than the capacitance changes in anterior non-injection process and the posterior non-injection process (P < 0.01), with significant statistical difference. The experimental results are in good agreement with the theoretical predictions. Therefore, it can be proved that the increase of capacitance in the process of injection is really caused by the injected blood.

Secondly, the capacitance increase of each animal is in the 10⁻¹pF order of magnitude, so the change of the corresponding resonance frequency of LC circuit is very small. Accordingly, the change of the permittivity of brain tissues caused by such a small frequency change of excitation signal can be ignored. However, the permittivity of blood is always greater than that of other brain tissues at low frequency (<10 MHz) (Gabriel, Lau & Gabriel, 1996), so the increase of capacitance is caused by the increase of blood volume which leads to the increase of the permittivity of the whole brain. So the change of capacitance can reflect the change of hemorrhage volume.