Waveform analysis of differential graphs of reconstructed impedance cardiography from healthy individuals

Abstract Purpose The aim is to measure and analyze the wave amplitudes and time intervals of differential graphs of reconstructed impedance cardiography (RICG). Methods 180 adults with normal cardiac function between the ages of 18–78 were included in the study. Six mingled impedance changes on chest surface were simultaneously detected for each subject. The differential graphs of five impedance change components of RICG were obtained through waveform separation and software differentiation. The amplitudes of C, X, O, b waves and time intervals of Q‐b and Q‐C were measured and statistically analyzed. Results The amplitudes of C and X waves in PL, PR, AO, and that of C, O, b waves in LV and RV, all decrease as age increases. Wave amplitudes of the female group were bigger than those of the male group (p < .01), while the Q‐C intervals of the female group were shorter than that of the male group (p < .01). Among five impedance change components, the wave amplitude of AO was larger than those of PL and PR (p < .01), and wave amplitudes of PL and PR were bigger than those of LV and RV (p < .01). Q‐C intervals of LV and RV were longer than those of AO, PL and PR (p < .01), while the Q‐b intervals of LV and RV were shorter than the Q‐C intervals of AO, PL, and PR. Conclusions The differential graphs of RICG could reflect indirectly the physiological activities and pathological changes of the heart and of the large blood vessels in thorax.


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HE Et al. in at-risk patients also can be continuously monitored (D'Ambrosio et al., 2018;DeMarzo, 2013;Ebrahim et al., 2016;Heinink, Lund, & Williams, 2015;Rada, Cuffaro, & Galarza, 2014;Wang et al., 2017). Many studies have confirmed that the ICG measured using the above methods is a thoracic mingled impedance change, which mainly derives from volume changes in the aorta, blood vessels in lungs, and ventricles (Baker & Mistry, 1981;Patterson, 1985;Wang & Patterson, 1995). Obviously, the results measured with traditional ICG lack the specificity for cardiac functional assessment of left ventricle.
In order to solve this problem, we have derived five impedance change components corresponding to aorta (AO), left lung vasculature (PL), right lung vasculature (PR), left ventricle (LV), and right ventricle (RV) from six mingled impedance changes measured on the chest surface through waveform separation (Kuang et al., 2010; Ming-Xing, Qiu-Jin, Nan-Zhen, Chao-Ying, & Ai-Rong, 2011). The waveform graphs of these components are collectively referred to as reconstructed impedance cardiography (RICG). The differential graphs of the RICG for 180 normal adults were measured in this paper, and the wave amplitudes and time intervals of the differential graphs of RICG were statistically analyzed.

| Placement method of impedance detected electrodes
The thoracic mixed impedance changes and basic impedances were measured using six leads consisting of 15 electrodes (Kuang, Xiao, He, Jing-Juon, & Kuang, 2014;Ming-Xing et al., 2011). The placement method of each electrode is shown in Figure 1. In which, I 1 , I 2 , and I 2 ' are current electrodes dedicated to injecting a current. I 1 is a semi-ring strip silvered copper electrode which covers the subject's forehead, while I 2 and I 2 ' are silvered copper rectangle electrodes attached the left and right lower legs. 12 black circular dots indicate disposable Ag/AgCl voltage electrodes. E 1 , E 2 , E 3 , E 4 , E 5 , and E 6 are the neck voltage electrodes applied to the neck root, and E 1 ', E 2 ', E 3 ', E 4 ', E 5 ', and E 6 ' are the chest voltage electrodes applied to the chest surface at xiphoid level.

| Basic composition of the measurement instrument
Our research group developed the measurement instrument used in the present study. As shown in Figure 2, the hardware included a crystal oscillation circuit, an alternating current source circuit, six impedance detection circuits with same structure and properties, an amplifier for the electrocardiogram (ECG), an amplifier for the phonocardiogram (PCG), an A/D transform circuit, an isolated direct current source, a computer, an impedance lead wire, and an ECG lead wire.
Operation of the support software consisted of the following: Input information regarding the human body, observe and record six thoracic mixed impedance changes and six basic impedances as well as the ECG and PCG, mark the starting point of ECG's Q wave and second heart sound (S 2 ) for four consecutive cardiac cycles by artificial operation, correct the basic lines of thoracic mixed impedance changes, separate five impedance change components of AO, PL, PR, LV, and RV of RICG from six mingled impedance changes measured on chest surface through establishing and solving the thoracic impedance equations, make the differential treatment for each component, measure the waveform parameters of each differential graph, display, and print the waveform graphs and parameters.

| Measurement of RICG's differential graphs
Height, weight, chest circumference, blood pressure, as well as name, sex, age, and other relevant information were entered into the instrument prior to the measurement. The chest circumference was measured on the chest surface at the xiphoid level. A supine position was adopted for the measurement. The electrodes for sensing the ECG were attached to the right upper arm and left and right lower legs (i.e., Ⅱ lead mode). The transducer for sensing the PCG was placed at the cardiac apex on chest surface. The subject was asked to hold his/her breath for the duration of recording the waveform graphs. Thoracic mixed impedance changes (ΔZ s1 , ΔZ s2 , ΔZ s3 , ΔZ s4 , ΔZ s5 , and ΔZ s6 ) and basal impedances (Z 0s1 , Z 0s2 , Z 0s3 , Z 0s4 , Z 0s5 , and Z 0s6 ) of all six leads, as well as the ECG and PCG, were detected and displayed simultaneously.
The starting point of the Q wave and S 2 of the corresponding cycle were marked for four consecutive cardiac cycles in the waveform graphs by the artificial operation (Ming-Xing et al., 2011).
According to the mathematical methods in reference (Ming-Xing et al., 2011), five impedance change components of AO, PL, PR, LV, and RV of RICG were separated from six mixed impedance changes measured on chest surface (see Figure 3). The differential graphs of each impedance change component of RICG could be further obtained through software differentiation (see Figure 4). The waveform graphs of impedance change components in Figure 3 were only a transition waveform in the measurement, and their differential graphs were usually applied in the measurement of cardiac function.
Thus, only the waveform parameters of RICG's differential graphs were measured and analyzed in this paper.
As shown in Figure 4, lines 2, 3, and 4 are the differential graphs corresponding to the AO, PL, and PR components of RICG.
They all have a high positive C wave in systolic phase, a negative X wave that appears after C wave, and a positive or negative O wave appears in diastolic prophase. Lines 6 and 7 are the differential graphs of LV and RV components, respectively. A small positive b wave appears in initial systolic stage; then, a larger negative C wave appears that is essentially in opposite phase of C wave of AO, PL, and PR. After the negative C wave, a positive O wave appears, and its amplitude is larger. There is no X wave in differential graphs of LV and RV. Lines 1 and 5 were the ECG and PCG, respectively, and they were used to measure the relative time intervals.
As shown in Figure 4, the time interval from the initial point of the Q wave to C wave peak of various components is referred to as the Q-C interval, and that from the initial point of ECG's Q wave to b wave peak of LV and RV is referred to as the Q-b interval. The  Tables 1, 2, 3, and 4.

| Participants
The participants were 180 normal healthy adults. Their ages ranged from 18 to 78 years, and their average age was 50.4 ± 15.4 years. The systolic pressure of the participants was between 95 to 138 mmHg, and diastolic pressure was between 65 and 89 mmHg. All subjects were asked about their medical history, and their ECG, blood pressure, heart rate, and physical examination were all normal. The participants were divided into three age groups according to WTO rules: younger (18-44 year), middle (45-59 year), and elder (60-78 year).
30 males and 30 females were included in each age group.

| Statistical analysis
Statistical analysis was performed by means of SPSS12.0 software.
The measurement results of C, X, O, b wave amplitudes, as well as the Q-b and Q-C time intervals, were all expressed with the average value and standard deviation. The difference level between two averages was judged by t test. If p-value < .05, there was a significant difference between two averages.

| RE SULTS
The measurement results of C, X, O, and b wave amplitudes, as well as Q-C intervals of differential graphs of RICG, are listed in Tables 1,   2, 3, and 4, respectively. Q-b intervals of LV and RV can be found in the footnote of Table 4. It can be seen from the measured data in the four tables and waveform graphs in Figure 4 that: 1. The waveform of PL, PR, and AO was upward in systolic phase, but that of LV and RV was downward. This shows that the waveforms of both were in opposite phases.
2. The waveform amplitudes of C and X waves of various components, as well as that of b and O waves of LV and RV, all decreased as age increased (Tables 1, 2, and 3), and there were significant differences between the younger and elder groups (p < .05), except for X wave of PR (p > .40). The waveform amplitudes of the female group were larger than those of the male group, p < .05.
3. Among the five components, the C wave amplitude of AO was largest, that of PL and PR was next, while that of LV and RV was smallest (See Table 1). The O wave amplitudes of LV and RV were larger than those of AO, PL, and PR, p < .01 (Table 3).
4. The Q-C intervals of AO, PL, and LV increased as age increased (Table 4). The Q-C intervals of AO, PL, and PR of the male group were bigger than those of the female group, p < .05. The Q-C intervals of LV and RV were longer than those of AO, PL, and PR, TA B L E 1 C wave amplitudes of AO, PL, PR, LV, and RV. Symbols C AO , C PL , C PR , C LV , and C RV denote C wave amplitudes of AO, PL, PR, LV, and RV, respectively. Symbol n is number of subjects in each group. Symbol "M + F" denotes "male and female." The "30 + 30" denotes 30 males and 30 females. The "90 + 90" denotes 90 males and 90 females  Table 4). The Q-b intervals of LV and RV were smaller than the Q-C intervals of AO, PL, and PR (Table 4 footnote).

| Impedance change component AO
As shown in Figure 4, the C wave of the differential graph of AO appears after ECG QRS waves, and it is a high positive wave. Its starting point corresponds to the first cardiac sound (S1). The semilunar  Table 1).
C wave amplitude of AO is related to the contractile force and stroke volume of the left ventricle. If C wave amplitude is larger, it suggests that the myocardial contractility of the subject is stronger and that stroke volume is larger. Thus, C wave amplitude of AO is an important parameter reflecting the contractile function of the left ventricle. The contractile function of left ventricle generally decreases as age increases. The C wave amplitude of AO also decreases as age increases (see Table1), and there is a significant difference between C wave amplitudes of the younger and elder groups (p < .001).
In addition, the C wave amplitudes of 196 patients were also 3.029 ± 1.139 Ω/s. These data show that the contractile function of patients in the first, second, and third groups is remarkably decreased, while that of the fourth group is abnormally strengthened.
Thus, C wave amplitude of AO can reflect the pathological changes of patients.
The X wave of AO is a negative wave after the C wave and is in the later stage of left ventricle contraction. Its negative peak point X is in the vicinity of S 2 . The X wave is caused by the recovery of aortal volume, and it reflects indirectly the speed change of aortal recovery. The mean of X wave amplitude in 180 normal adults was −0.882 ± 0.294 Ω/s (see Table 2). The O wave of AO is a positive or negative wave in its initial diastolic stage, and its amplitude is smaller.
The O wave mean of 180 normal adults is −0.036 ± 0.191 Ω/s (see Table 3).  Table1). The amplitude of PL is significantly bigger than that of PR (p < .001).

| Impedance change components PL and PR
There is also a negative X wave in PL and PR, and it is approximately in time phase of the X wave of AO. The X waves of PL and PR are a result of volume recovery of the pulmonary arteries and reflect indirectly the speed change of volume recovery of pulmonary arteries. The average X wave amplitudes of PL and PR are 0.413 ± 0.138 Ω/s and 0.299 ± 0.111 Ω/s, respectively (see Table 2).
The amplitude of PL was significantly larger than that of PR (p < .001).
The positive or negative O wave appears in PL and PR after the X wave. The average O wave amplitudes of PL and PR are 0.049 ± 0.119 Ω/s and −0.032 ± 0.094 Ω/s, respectively (see Table 3). O wave amplitude of PL is bigger than that of PR, p < .001.

The ratio O/C of O wave average to C wave average for PL and PR
is usually smaller for healthy individuals, and the mean of O/C was 0.011 ± 0.138. Large O waves and small C waves appear often in PL and PR for patients with cardiac insufficiency; thus, the ratio O/C in these patients is larger (Kuang et al., 2014).

| Impedance change components LV and RV
As shown in Figure 4, there are b, C, and O waves in LV and RV. The b wave appears in initial systolic stage, and it is a small positive wave.
The b wave amplitudes of 180 normal adults are 0.244 ± 0.110 Ω/s and 0.294 ± 0.122 Ω/s for LV and RV, respectively (see Table 2), and b wave amplitude of RV is bigger than that of LV, p < .001. Q-b TA B L E 4 Q-C intervals of various impedance change components. Symbols Q-C AO , Q-C PL , Q-C PR , Q-C LV , and Q-C RV denote the Q-C intervals of AO, PL, PR, LV, and RV, respectively interval of LV and RV is shorter than Q-C interval of AO, PL, and PR (p < .001), because b wave peak point of LV and RV is in front of C wave peak point of AO, PL, and PR in time phase. On the basis of physiological principles and resistance law, if the ventricle volume diminishes, its impedance should increase as the ventricle ejects the blood. However, the positive b wave in Figure 4 shows that the impedance of the ventricle diminishes in initial systolic stage. It is likely that shortening of the ventricle length is earlier than the contraction of ventricular sectional area in the initial systolic stage (Brecker & Stephen, 2000), and the impedance of ventricle is reduced as a result.

Groups Sex n Q-C AO (s) Q-C PL (s) Q-C PR (s) Q-C LV (s) Q-C RV (s)
After the b wave, a negative C wave appears in LV and RV, which is the main wave of LV and RV. These C waves are caused by rapid contraction of the ventricles. Since the C wave peak points of LV and RV are after the C wave point of AO, PL, and PR, the Q-C intervals of LV and RV are longer than that of AO, PL, and PR (see Table 4), p < .001. C wave amplitudes of LV and RV are −0.545 ± 0.194 Ω/s and −0.455 ± 0.168 Ω/s in 180 normal adults, respectively (see Table 1).
The amplitude of LV is significantly larger than that of RV, p < .001.
The O wave of RV and LV appears after S 2 and is caused due to rapid engorgement of the ventricles in the initial diastolic stage. O wave amplitudes of LV and RV are 0.320 ± 0.119 Ω/s and 0.199 ± 0.086 Ω/s in 180 normal adults, respectively (see Table 3), and the amplitude of LV is significantly larger than that of RV (p < .001).
The O wave amplitudes in RV and LV decrease as the age increases, and there is a significant difference between the measured data of the younger and elder groups (p < .01). O wave amplitudes of RV and LV for patients with cardiac insufficiency are remarkably decreased. For instance, the O wave amplitudes of RV and LV for 72 patients with cardiac insufficiency are −0.130 ± 0.090 Ω/s and −0.109 ± 0.105 Ω/s, respectively, and they are smaller than that of the adults with normal function (see Table. 3, p < .001). It could be proven theoretically that the impedance change on chest surface caused by blood vessels is larger when the included angle between the blood vessels and human body axis (i.e., electrical current line) is smaller (Qiu-Jin et al., 2012). Conversely, the impedance change caused on the chest surface is smaller when the included angle is larger. This is precisely a parallel effect in the measurement of the electrical impedance graph. It can be known from physiology that the blood volume discharged by the left ventricle is in concordance with that of the right ventricle. The measurement results show that the C wave amplitude (1.792 ± 0.557 Ω/s) of AO was significantly bigger than the sum (1.527 ± 0.382 Ω/s) of C wave amplitudes of PL and PR. This difference is related to the strike of blood vessels in thorax.

| Analysis of measurement results
Anatomically, the aorta in the thorax is basically parallel with the human body axis. Thus, it can be expected that the impedance change that the aorta induces on the chest surface would be larger.
But the distribution of the large blood vessels in the lung is more complex. The included angle between a part of pulmonary arteries and the human body axis is larger, and these blood vessels induce only smaller impedance change on chest surface. The included angle between other part of pulmonary arteries and human body axis is smaller, and they can induce bigger impedance changes on the chest surface. It is known from the anatomy that the volume of the right lung is bigger than that of the left lung, and the blood volume of the right lung is larger than that of the left lung. Accordingly, the C wave amplitude of PR should be bigger than that of PL, but the results in In order to obtain the impedance change components that reflect the physiological activity of the heart and large blood vessels in thorax, many interventions were performed in our study.
In the measurement circuit, the isolated direct current source was induced to ensure the safe measurement of human body, and the synchronization detection circuit was applied to elevate the property of opposing the interference. The five impedance change components of RICG were obtained through establishing and solving thoracic impedance equations. Model error and measured error were included in these equations; thus, the thoracic impedance equations were the contradict algebraic equations (Gong-Yan, 2000). If the solutions are computed with usual method, the waveform graphs, which correspond to physiological changes, cannot be obtained. For this reason, the algebraic reconstruction technique, already used in the first X-CT system, was adopted to calculate the solution of the thoracic impedance equations (Gong-Yan, 2000).
Our research has evolved the clinical applications of RICG (for instance, formula of measuring the cardiac output, ejection fraction, and myocardial oxygen consumption), in which, the square root formula for measuring the cardiac output had been published in Med.

| CON CLUS ION
The differential graphs of each impedance change component of RICG for 180 normal adults were measured in this paper, and statistical analysis was performed according to the different age and sex groups. C and X wave amplitudes of various components all decrease as age increases. The wave amplitudes of the male group were smaller than those of the female group, while the Q-C interval of the male group was longer than that of the female group. C wave amplitude of AO was largest, that of PL and PR was next, and that of LV and RV was smallest. The differential waveform graphs of various impedance change components of RICG may reflect indirectly the physiological activity and pathological changes of the heart and of the large blood vessels in thorax.