Development of a real-time, semi-capacitive impedance phlebography device

The proposed semi-capacitive impedance phlebography should apply an alternating current by commercial conductive electrodes, but should provide a contact-less measurement through an isolating material of the corresponding voltage drop. In Figure 1 the systematic concept of the semi-capacitive impedance phlebography device is shown.

Fig. 1

It uses a tetra-polar arrangement of electrodes. The four-electrode technique avoids electrode polarization and minimizes the influence of the skin impedance [10, 11]. The outer pair of conductive electrodes passes a small alternating current I_m of 0_.375 μA_RMS at a frequency f_m into the leg and the inner pair of capacitive electrodes measures the resulting time-depending voltage drop U_m. The inner electrodes should measure the impedance contact-less trough an isolating material, like pressure stockings.

The system samples the corresponding impedance with the sampling-rate f_s and should provide an integrated, real-time peak-detection of the IPG-signal for further analysis. Furthermore, the high sampling rate should provide the recording of a time-resolved IPG-signal.

Two specifications are essential to build the device: the sample rate and the resolution. The minimal sample rate can be estimated based on the results of Soares Filho et al. [12]. They examined the time derivative of ΔZ with respect to the spectral frequency composition of the leg impedances of healthy and arteriosclerotic subjects. The study showed that about 99% of the signal energy in both studied groups was below 32_.7 Hz. Since the derivation of spectral components is amplified proportional to their frequency, it can be concluded that the power of ΔZ is also distributed below this frequency. Therefore, a sample rate of approximately 66 Hz fulfills the Nyquist-Shannon sampling theorem to reconstruct all relevant information of the IPG-signal. Since the normal heart rate at rest is usually between 60 and 100 beats per minute (1 Hz to 1_.67 Hz), 66 Hz provides an oversampling of the heart rate signal [13].

The resolution of the measurement device is an issue since the basal impedance Z is much higher than the amplitude of the pulsatile component ΔZ. For example, a basal impedance of 85Ω but only a pulsatile component of about 35mΩ can be measured in a segment of 20 cm of a lower leg [14]. The high basal impedance Z and the small pulsatile component ΔZ is a challenge for a proper analogue-digital-conversion, unless Z is removed by an analogous filter.

Since the device should measure through an isolating material, a capacitive measurement system was developed. The capacitive measuring was done by active electrodes as an impedance converter, which enables a low-impedance processing of the measured potential φ_G. Figure 2 shows the measurement of a potential φ_G with a capacitive electrode. The lower part of the Figure shows the corresponding equivalent circuit.

Fig. 2

The capacitor C_k represents the capacitive coupling between the electrode and the tissue. It is dependent on the surface of the electrode, the distance between the examined tissue, and the dielectric property of the material between the electrode and the measured object. For example, a 0.5mm thick cotton layer between electrode and measured object with an electrode area of 16_.6 cm² at a measuring frequency of 200 kHz results in a coupling capacitance of 25 pF to 30 pF [15].

In order to ensure a capacitive coupling in the case of a conductive connection between the electrode surface and the tissue, the capacitor C_t was added. The capacitance C_t should be much larger than C_k, so that the latter dominates the resulting capacitance of the series connection of the two capacitors. Static charges that may accumulate on the electrode surface, as well as the bias current of the operational amplifier, are discharged by the resistance R_b. The capacity C_p summarizes the parasitic capacitances. These may arise through the trace routing of the circuit board. Finally, the operation amplifier provides the low impedance potential φ_out.

Eq. (2) describes the Laplace transfer function of the active electrode under the assumption of an ideal operational amplifier.

The active electrodes show high-pass behavior, with a cut-off frequency of

On the one hand, this behavior requires a minimum size of R_b, which is dependent on the frequency of the measurement current I_m and the smallest expected value of C_k. On the other hand, the high-pass behavior can be used to attenuate the common mode noise caused by the power supply lines through the electrode.

This is particularly useful when the operational amplifier is not only connected as an impedance converter, but also as an amplifier. In this case, the amplified common mode noise can drive the operational amplifier into saturation quickly. Nevertheless, by using the high-pass behavior, the attenuation of the lower frequencies is dependent on the coupling capacitance C_k. Eq. (2) also shows that the measured signal is attenuated by the capacitive voltage divider which is formed by Ck'$C_{\text{k}}^{'}$and C_p. This limits the minimum of the coupling capacitance, in which a measurement is possible.

The schematics are shown in Figure 3.

Fig. 3

In this illustration φ_G represents the potential at the tissue and the coupling capacitor between tissue and the electrode is denoted by C_k. The decoupling capacitor C_t, the bias resistor R_b and the parasitic capacitance C_p were described above. The measurement electrodes were made from square, double sided, printed circuit boards with a side length of 3 cm, and a sensitive surface on one side. To guarantee a capacitive coupling, the sensitive area was isolated by polypropylene tape. The discrete components of the circuit board were placed on the opposite side of the electrode as shown in Figure 4. The operational amplifier used in the active electrode was the LMP7721 (Texas Instrument, Dallas, USA), which was supplied by a bipolar supply voltage of ±1.8V. The op-amp was connected in the non-inverting amplifier configuration with a bandwidth limitation effectuated by C_f,_EL and R_f,_EL. Thus, the transfer function of the active electrode is composed by a constant gain, a high-pass and a low-pass, as shown in equation (5).

Fig. 4

with:

To limit the voltage measurement to f_m, the following components were chosen: R_f,_EL = 82kΩ, R_g,_EL = 39kΩ, and C_f,_EL = 10pF. Hence, the cutoff frequency of the low-pass filter was f_g,_TPEL = 194kHz and, with large coupling capacitances, these values resulted in a gain of A_EL≈ 3.1. The remaining components were chosen to C_t = 100nF and R_b = 10MΩ. Both active electrodes were connected to the main board by a four wire cable. Two cables were used for the positive and negative operating voltage, one for the ground connection, and one for the output voltage of the active electrode. A photo of the active electrodes and the electrode position is shown in Figure 4.

The impedance measuring system consisted mainly of the AFE4300 chip (Texas Instruments, Dallas, USA) and active electrodes for capacitive voltage measurement, as mentioned above. To increase the resolution of the impedance measurement the signal was directly amplified at the active electrodes. An additional amplification was done by a differential amplifier between the electrodes and the AFE4300 chip.

The circuit is shown in Figure 5.

Fig. 5

The operational amplifier (TLC252, Texas Instruments, Dallas, USA) and AFE4300 need a supply voltage of 3_.3 V. In the given frequency range, the circuit was independent of the frequency of the input signal and the gain can be calculated as

By selecting R_f,_INA = 10kΩ and R_g,_INA = 892 Ω, the gain was A_INA≈ 23.42. The voltage U_m, which was amplified by the differential amplifier, was used next as measurement voltage of the AFE4300. The full-wave rectification mode of the AFE4300 was used to demodulate the signal. In this paper, a measuring frequency f_m = 24kHz and a sampling rate of f_s = 64Hz was used. The sample rate was slightly below the minimal sampling frequency described above, but in order to achieve a higher oversampling of the Delta-Sigma analog-to-digital converter (ADC) and the reduction of the quantization error, a lower sample rate was selected.

Additionally, the oversampling rate was increased by an increase of the clock frequency f_CLK,_AFE of the AFE4300. Since this oversampling was not intended by the manufacturer, the behavior of the chip was thoroughly tested (the effects of the oversampling on signal quality are given in the appendix) [16]. Due to the change of the clock frequency, the resulting measurement and sampling frequency were changed to

Here, f_s,_AFE denotes the configured sampling rate of the AFE4300 and f_s the resulting operating frequency. k_div,_AFE denotes an integer which controls a clock divider to generate different measurement frequencies. The normal clock frequency of the AFE4300 is f_CLK,_AFE = 1MHz, but in this paper a cycle of f_CLK,_AFE = 4MHz was used. In order to smooth the demodulated signal, the datasheet provides the connection of a 10 μF capacitor. In this paper, a capacitor of 480 nF was chosen to set the cutoff frequency of the low-pass f_g,_demod to 33 Hz.

The aim of the signal processing was the extraction and separation of the beat-to-beat heart interval. The signal processing was implemented on a MSP430F2618 microcontroller. First, the inverted measured signal was filtered with a bandpass filter to separate the physiological frequency components. A real-time beat-to-beat interval detection algorithm was implemented to the recorded regularities in the occurrence of the maxima over time in order to distinguish measurement artifacts from heart related pulsations. If there was a high regularity of the detected maxima, the presence of a heart related pulse signal was assumed and the signal processing detected a heartbeat and used the time between the new and last recognized maximum as one heart cycle.

The process of the signal processing is illustrated in Figure 6.

Fig. 6

For the detection of the maxima, two signals were obtained from the measured signal s_a(n). First, the measured impedance values were inverted and the frequency components components below 0_.6 Hz and above 3 Hz were removed by a second order band-pass. The z-transfer function of the filter and the obtained signal s_f(n) are given by the following equations:

Further, this signal was smoothed by a second order low-pass with cut-off frequency at 0_.6 Hz and subsequently differentiated. These two operations were done by the filter G_df(z). The z-transfer function of the filter and the obtained signal s_df(n) are given by the following equations:

For better illustration, Figure 7 shows an impedance signal measured at the calf as well as the filtered signals s_f(n) and s_df(n).

Fig. 7

The pulsatile component in s_f(n) is obvious, but a simple detection of local maxima would also provide points between beats, for example, at the local maximum near nfs≈$\frac{n}{{{f}_{\text{s}}}}\approx $0.7s. Therefore, s_f(n) was smoothed by a low-pass while the zero crossings of s_df(n) were used to detect the maxima points. Due to the strong smoothing, there was a considerable time delay for the detection of a zero crossing, from positive to negative, in s_df(s). Therefore, the algorithm detected only zero crossings, from negative to positive, in s_df(n). After a zero-crossing was detected, s_f(n) was maintained for the first value, which was smaller than the previous values.

This algorithm showed the best results if flanks rose steadily in s_f(n) and it provided a detection of the maxima with a small and relatively constant delay to s_a(n). The number of samples corresponding to this delay was given by the order of G_BP(z) and one additional sample to detect the decrease in s_f(n). Therefore, the delay time could be calculated to 5fs≈$\frac{5}{{{f}_{\text{s}}}}\approx $78ms, which is small and predictable enough to fulfill the real-time-computing criterion.

For the evaluation, the impedance of the leg was measured and the data were recorded with a PC. In the further analysis, the current I_m was applied to the lower leg by commercial Ag/AgCl ECG-electrodes. The electrodes were placed on the rear side of the lower leg, just below the knee and slightly above the ankle. The distance between the measuring electrodes was about 10 cm and the upper electrode was placed on the calf muscle belly, inclined slightly to the inside of the lower leg. To compare the results with a gold standard, a PPG was measured simultaneously at the second toe of the same leg. For this purpose, a commercially available finger clip device was used (CMS50E, Contec Medical Systems, Qinhuangdao, China). The recordings of the PPG signal were sampled with 60 Hz and the IPG signal with 64 Hz. For the evaluation two experimental setting as validation test were performed.

The first evaluation step was the analysis of the influence of the capacitive measuring method on the signal quality and the detection of the pulse rate. For this, three different configurations were tested: a conductive coupling, a passive capacitive coupling, and an active capacitive coupling. In order to acquire a conductive coupling to the tissue, conventional ECG-adhesive electrodes were used. For passive capacitive coupling, the same electrodes as for the active coupling (described above) were used, but in this case the circuit-boards were unequipped. To provide three comparable conditions, the gain of the active electrode was set to A_EL = 1 by removing the resistor R_g,_EL. Furthermore, the gain resistor of the differential amplifier was raised to R_g,_INA = 470 Ω, resulting in a gain of A_INA≈ 43.6. Hence, the resulting gain of the active electrode and differential amplifier was reduced to 63% of the original value, which should be considered for the comparison to the next results.

In the three configurations, the lower leg was stretched on a chair and the signal was recorded for 95 s. For comparison with the gold standard, the PPG-signal was recorded simultaneously on the second toe. Each peak time t_PPG(i) of the PPG signal was allocated to a peak time t_IPG( j ) in the IPG signal using the rule

The parameter λ_rel was used to adapt the factor to the corresponding heart rate and was chosen as λ_rel = 0.3.

During the next test, the subject sat on a chair while the examined lower leg was bent at an angle of about 90° to the thigh and placed perpendicular to the ground to the ground. Additionally to the second test, the leg was stretched and laid on the seat surface of a second chair. To prevent the occurrence of major motion artifacts during the measurements, the subject tried to move as little as possible and was breathing normally. From these measurements the pulsations were separated in correct and wrong detected beats compared to the control results of the gold standard. The accuracy of the detection algorithm, with respect to the peak time and the heart rate, was analyzed in more detail.

Since the measured PPG signal was artifact free, the beats were identified by the local maxima. From the PPG, the peak time t_PPG(i) and the corresponding heart rate HR_PPG(i) [min⁻¹] were extracted. The number of detected heartbeats, precisely peak times, were denoted as N_PPG. The peak time t_IPG( j) and heart rate HR_IPG, which were extracted by the algorithm, were denoted as N_IPG.