Design and Uncertainty Analysis of a Bioimpedance Measurement Channel

Adalberto Schuck Jr. , Alexandre Balbinot

Electrical Engineering Department UFRGS

Porto Alegre, RS, Brazil schuck@ufrgs.br alexandre.balbinot@ufrgs.br

Rodrigo Wolff Porto Automation and Control Engineering Department

UNIVATES Lajeado, RS, Brazil

wolffporto@univates.br

Abstract—This work presents the design and uncertainty analysis of a bioimpedance measurement channel for use in electrical impedance tomography (EIT). A bioimpedance measurement channel was designed. Then the random error of each stage of the project as well as the entire channel was measured. The loads used were resistive, in the range of 100 Ω -1K Ω. The frequencies of excitation used were 100 kHz and 300 kHz. The errors were calculated through 200 samples of each measure, for each load and frequency. The final uncertainty in the measurement of magnitude and phase was ±0.008% (±3σ) and ±0.05° (±3σ), respectively.

Keywords—Electrical Impedance Tomography; Uncertainty Analysis; Bioimpedance measurement.

I. INTRODUCTION The electrical impedance tomography (EIT) is a medical

imaging modality that allows the visualization of the body’s internal impedance distribution from measures obtained outside the body. Typically, surface electrodes are used to apply an electrical current and to measure the resulting voltages on the subject. After then, based on the data obtained from these measures, computational reconstruction algorithms are used to compute the electrical permittivity and conductivity distribution inside the body. What makes the EIT a promising technique is the possibility of visualize the interior of the body with non-invasive techniques using non-ionizing radiation. Also, the technique provides information about the tissues (its electrical properties) the other methods cannot provide [1].

Although the benefits and low costs and many application of EIT has been developed, like instance, pulmonary imagery, breast tumor detection, gastric function evaluation and cerebral function mapping, still this technique hasn’t a large clinical use, because of its poor spatial resolution in comparison with other medical imaging techniques [1], [2]. Also, the determination of the body’s internal impedance distribution from outside measurements is an ill posed mathematical inverse problem, because small errors in the measures can cause large errors in the reconstructed impedance distribution. So, the literature suggests the maximum accuracy error should be 0.05% for static images and 0.1% dynamic images [3]. These measure errors normally are caused by non-idealities in the electronic circuitry involved, for instance, finite current source’s output impedance, finite Common Mode Rejection Rate (CMRR) of the instrumentation amplifier in the frequencies used and differences of impedances between

electrodes and skin [4]. As the entire measure system is composed by many parts, each one with its own circuitry, it is important to quantify the contributions of each part independently and in the total error of the impedance measure.

The objectives of this work are: (1) design a bioimpedance measurement channel which provides information of its real and imaginary parts, with work frequencies of 100 kHz and 300 kHz and errors in the range suggested by the literature and, (2) evaluate the random error of each stage of the measurement system and of the entire system.

II. BIOIMPEDANCE MEASUREMENT CHANNEL DESIGN The techniques employed to measure bioimpedance usually

involve bridge measuring and quadrature demodulation, for body composition analysis [5] and EIT [3]. However, the need of a balance in a bridge system makes this method slow and unsuitable to measure some changes in the impedance caused by fast physiological changes [5]. Besides, quadrature demodulation use to have a complex realization to reach the specifications pointed in the literature for this kind of measure [1,5]. An alternative solution for bioimpedance measuring was proposed in [5] using gain and phase detection techniques in order to obtain a simpler circuit with lower cost that the traditional techniques, and still reaching all the specifications required for EIT applications, for instance. This philosophy was used here, whose implementation was given by the Analog Devices integrated circuit AD8302. It is important to emphasize that all the integrated circuits and operational amplifiers used in this work were chosen because of their performance in the frequency range proposed as well as easiness to acquire the components in our local market.

The bioimpedance measurement system proposed here is based in a four wire impedance measurement and its diagram can be seen in Fig.1.

Figure 1 Diagram of the bioimpedance measurement channel proposed.

A. Oscillator The oscillator stage was based on the integrated circuit (IC)

AD9834 from Analog Devices which uses a Direct Digital Synthesis (DDS) to generate a sine wave shape with 10 bits resolution. This technique allows a phase and frequency adjustment related with a precise clock source and eliminates drifts caused by the aging process, as in analogical solutions. The sine frequency control was made through its Serial Peripheral Interface (SPI) port with a PIC18F4550 microcontroller system. The frequencies used in this work were 100 kHz and 300 kHz.

B. Voltage controled current source The current source topology chosen for this work was the

modified monopolar Howland current source [4], [6] and its implementation uses operational amplifiers (OPAMP) AD8620. The AD8620 was chosen here because it has an elevated differential gain Ad and a low common mode gain Acm , in the frequency range proposed for this work The electrical diagram of this source can be seen in Fig.2.

Figure 2 Electrical diagram of the current source.

The output current Il as a function of oscillator voltage V0 and OPAMP limitations can be modeled by:

( )⎟⎟⎠

⎞⎜⎜⎝

⎛

++

−⎟⎟⎠

⎞⎜⎜⎝

⎛+

++++⎟

⎠⎞

⎜⎝⎛ +

+−

=

a

cm

a

baLb

ccOsc

L

RRAAR

RRZRR

GAZ

GAZ

PSRRvGAGV

I

43

3

34

4434 11

.

(1)

where Ad and Acm are the OPAMP differential gain and common mode gain, respectively, vcc is any signal or noise present in the power source , PSRR is the Power Source Rejection Ratio, 121 RRG += , cmd AAA 5.0−= ,

bbb CjRZ 444 .1 ω+= and LLL CjRZ ω1//= .

The finite output impedance Zo of the current source causes a dependency of IL with the load ZL , so much care were taken in this Project to maximize Zo in order to minimize variations in current IL as a function of load ZL. The current source output impedance Zo can be expressed by:

( )

( ) ( ) ( )( ) ( )⎥⎦

⎤⎢⎣

⎡+⋅−⋅++⋅−

+⋅⋅+⋅+++

+⋅=

cmd

cmdba

abo

AARRRAARRR

ZRR

RRRZ

222

121

213443

434. (2)

Therefore, respecting the relation given by [6]

( ) 32441 RRZRR ba ⋅=+⋅ , (3)

it is possible to maximize Zo .

C. Instrumentation Amplifier The amplification section chosen use a differential

amplification, due to its capability of amplifying signals in the range of 100µV to 10mV with CMRR above 100dB. This CMRR is necessary to the project reach the requirement of 0.1% of accuracy [1,2]. The instrumentation amplifier was implemented using the IC AD8130 This amplifier has active feedback and unitary differential mode gain, with a typical common mode rejection rate (CMRR) of 105 dB for frequencies up to 100 kHz. However, with work frequencies from 100 kHz to 2 MHz, the CMRR degrades from 105dB to greater than 80 dB and this has to be taken into account [6]. The amplification section representation is shown in Fig.3. Its output was named Vina .

Figure 3 Instrumentation Amplifier used showing its inputs and output

D. Gain and Phase detector The detection of Gain and Phase between the tension

signals originated from the load and the oscillator is performed by the IC AD8302. This IC has a matched pair of logarithmic amplifiers in the input and can deal with signals from -60 dBm to 0 dBm with frequencies up to 2 GHz. The Fig.4 shows the IC diagram.

Figure 4 Diagrama de blocos simplificado do CI AD8302.

It can be seen that the IC AD8302 provides two continuous voltage outputs representing the voltage gain (VMAG) and phase difference (VPHS). These voltages are related with inputs VA and VB by [5]:

9,0log +⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

B

AslpMAG V

VVV , (4)

where VA and VB are the input signals, Vslp is the gain scale factor, and

( )baPHS VV θθϕ −⋅−= 8,1 , (5)

where θa and θb are são the VA and VB phases, respectively, and Vφ is the phase scale factor.

The implementation of Gain and Phase detection is shown in Fig.5. The tension divisor in the inputs is necessary to adequate the signal’s levels to IC inputs VA and VB .

Figure 5 Implementation of gain and phase detection section with AD8302.

III. MEASUREMENT CHANNEL EVALUATION Each block of the system was analyzed individually in

order to assess the random errors whose correction cannot be performed [7]. A set of seven resistive loads was used with values between 100 Ω and 1000 Ω for frequencies of 100 kHz, 300 kHz and 1 MHz. For each load condition and frequency, 200 samples of the measured variables were acquired with the Agilent 34410A multimeter connected to a laptop computer with a sampling period of two seconds. It is important to remark that for AC voltages or current measures, the multimeter provided a true root mean square (RMS) measure. The degree of inaccuracy of the system can be estimated by the standard deviation σ of the measures or standard measurement uncertainty.

For variables IL and VOsc, it was adopted the experimental uncertainty in percent, expanded to three standard deviations UV (%) [7], according to the equation:

( ) 1003% x

VU V

V

σ±=

, (6)

where σV is the standard deviation of the variable V measures and V is the mean value of these measures.

For the variables VMAG and VPHS, it was adopted the relative standard uncertainty (related to the full scale value) uv(%), again expanded to three standard deviations [7], according to

( ) 1003

%v

vv Fs

uσ

±= (7)

where σv is the standard deviation of the measures and Fsv is the full scale value of the variable V.

The calculation of the phase difference between the signals θa and θb, ∆θ, was performed using a Tektronics TDS2014 oscilloscope, and its uncertainty is calculated by the expression for combined standard uncertainty Uc∆θ ,[7], [8], given by:

( )FVF

F

UVV

Uc .⎥⎦

⎤⎢⎣

⎡∆

∂∂

=∆ θθ (8)

where ∆θ(VF) is the phase difference between the signals θA and θOsc as a function of the voltage Vphase , and UVF is the absolute uncertainty of the VPHS measures.

The oscillator amplitude uncertainty was evaluated through its RMS voltage output measure and it was calculated using (6). The current source was evaluated by measures of the output current and its uncertainty was calculated by (6), as well. Also, using the Tektronics TDS2014 oscilloscope, it was measured the phase difference ∆φ between the current IL (indirectly over input load) and oscillator output VOsc. The instrumentation amplifier was evaluated comparing its output voltage (amplitude and RMS value) with its input voltages and the uncertainty was calculated using (7). Its CMRR was determined applying VOsc to both inputs V1 e V2 simultaneously and measuring the amplitude of all signals involved. Finally, the demodulator outputs VMAG and VPHS were measured (RMS values) and the uncertainties were calculated by (7) and (8), respectively. All the measures were made in a room with temperatures controlled in the range of 20o to 30o Celsius (the uncertainty range of the room air conditioning, adjusted to 25o Celsius).

IV. RESULTS Using the methodology described in Section III, the RMS

value of VOsc was 0.704273 V±0.013%, for ±3σ, for the frequency of 100 kHz. For 300 kHz, its RMS value was 0.706279 V ±0.015%, for ±3σ.

The mean values for ∆φ and IL and its uncertainties in percentage, for 100 kHz and 300kHz are presented in Table 1.

TABLE I. EVALUATION OF CURRENT SOURCE UNCERTAINTIES

Load RL (Ω)

IL

(mArms) @ 100 kHz

UIL(%) @ 100 kHz

∆φ @100 kHz

IL

(mArms) @300 kHz

UIL (%) @300 kHz

∆φ @300 kHz

100 0.7019 0.0256 1.80° 0.7030 0.0450 8.1°

220 0.7017 0.0270 1.80° 0.7010 0.0429 8.1°

470 0.7010 0.0326 3.60° 0.6956 0.0462 10.8°

560 0.7010 0.0290 3.60° 0.6937 0.0573 10.8°

680 0.7007 0.0366 3.60° 0.6956 0.0671 13.5°

820 0.7003 0.0502 3.60° 0.6935 0.0846 10.5°

1000 0.6996 0.0573 5.40° 0.6804 0.1406 16.2°

For the instrumentation amplifier, its output relative uncertainty (related to the full scale value) uVina(%) obtained was ±0.03%, for ±3σ. The CMRR of this stage measured was 44 dB.

The expressions for linear regression equation obtained from the observed measures for the instrumentation amplifier, relating its output as function of its inputs, for 100 kHz is

512 107)(0057.1 −+−= xVVVina (9)

and for 300 kHz is

0043.0)(0307.1 12 +−= VVVina (10)

The mean values of the demodulator output voltage VMAG with its respective relative standard uncertainties (related to full scale value) in percent uVG (%), for 100 kHz and 300 kHz are presented in Table 2.

The expressions for the regression logarithmic curves obtained for those measures, for 100 kHz and 300 kHz are, respectively

( ) 8285,0log5876,0 −= LMAG RV (11)

and

( ) 8273,0log5860,0 −= LMAG RV (12)

with correlation coefficients r2=0.9982 for 100 kHz and r2=0.9979 for 300 kHz .

TABLE II. DEMODULATOR OUTPUT MEAN VOLTAGE VMAG AS FUNCTION OF LOAD AND FREQUENCY AND ITS RELATIVE UNCERTAINTY.

Load RL (Ω)

VMAG (VDC) @ 100 kHz

uVG (%) @ 100 kHZ

VMAG (VDC) @ 300 kHz

uVG (%) @ 300 kHz

100 0.3371 0.0050 0.3346 0.0087

220 0.5481 0.0054 0.5462 0.0056

470 0.7466 0.0048 0.7437 0.0054

560 0.7923 0.0047 0.7891 0.0063

680 0.8390 0.0065 0.8367 0.0066

820 0.8799 0.0064 0.8774 0.0048

1000 0.9158 0.0048 0.9107 0.0087

Finally, in Table 3 are presented the mean values for phase difference ∆θ as function of load RL for each working frequency, and their combined uncertainty Uc∆θ , for ±3σ.

TABLE III. PHASE DIFERENCE ∆Θ BETWEEN THE SIGNALS ΘA AND ΘB, AS FUNTION OF LOAD AND FREQUENCY.

Load RL (Ω)

∆θ @ 100 kHz

Uc∆θ @ 100 Hz

∆θ @ 300 kHz

Uc∆θ @ 300 kHz

100 1.2483° 0.0269° 1.6260° 0.0318°

220 1.1267° 0.0158° 1.2326° 0.0242°

470 1.6837° 0.0120° 0.8338° 0.0062°

560 3.1882° 0.0202° 1.7965° 0.0064°

680 4.7581° 0.0112° 3.4085° 0.0060°

820 4.1569° 0.0108° 5.0966° 0.0052°

1000 3.3048° 0.0527° 6.9671° 0.0062°

V. DISCUSSION The literature comments with little frequency about the

oscillator performance. Nevertheless, its role is very important, once it is connected with the current source performance. The uncertainty associated to the oscillator output voltage here implemented was 0.015%. Once this uncertainty propagates to the next section and the current is directly proportional to the oscillator output voltage, then the current source uncertainty is directly affected by the oscillator uncertainty.

The systematic errors of the Howland current source have many well described solutions to correct them, as the use of digital potentiometers and use of negative impedance converters [1]-[4]. But looking to expression (1), it can be concluded that it’s necessary compensate the errors introduced by the OPAMPs used, as well.

The instrumentation amplifier used introduced some systematic errors, but with the knowledge of expressions (9) and (10), these errors can be compensated. The great problem found here was the CMRR measured, that was below the values recommended by literature [1]–[3]. The unbalance in input impedances, as problems in circuit guarding were the factors that contributed to the CMRR degradation and this is in accordance with literature [3].

The mean values of the phase difference ∆θ presented in Table 3 indicate the phase systematic errors in the measure channel. Once it was used resistive loads in the measures, the phase measured by the system should be zero. But the existence of parasitic capacitances in the current source output, the phase of the amplifiers used and the intrinsic uncertainty of the oscilloscope measures lead to a presence of the error in the angle measures.

The block with greatest uncertainty was the current source section and this result is in accordance with literature. But it is important to remark that, even though there are uncertainties around ±0.1% (±3σ) in current source section and around ±0.03% (±3σ) in the instrumentation amplifier section, the total (or final) uncertainty of the entire measurement channel reach around ±0.008% (±3σ) for amplitude measures and ±0.05% (±3σ) for phase measures. This improvement is due to the AD8302 demodulation mode, once it reduced the dispersion of the measures.

VI. CONCLUSIONS This work proposed the design and evaluation of a

bioimpedance measurement channel.

It was confirmed that the current source is the block with greatest uncertainty.

Also, looking to the uncertainties obtained, it can be concluded that the instrument proposed reach the specifications suggested by literature and have a potentiality for its use in bioimpedance measures and in electrical impedance tomography.

As suggestions for the continuity of this work, it is interesting to broad the characterization up to 1 MHz, as well as to find the theoretical transfer functions of each section verifying the theoretic propagation error and comparing with those obtained experimentally. This is being done and the results will be shown in a future work.

Although the power source used is highly regulated and locally filtered in each section, it is possible to foresee its influence in the channel performance using the Power Supply Rejection Ration (PSRR) IC information.

Also a change in the circuit board layout and better choice of components is necessary in order to improve the CMRR of the instrumentation amplifier used. Besides, to improve the channel performance, it is recommended to obtain an instrumentation amplifier with higher input resistance and lower input capacitance than the AD8130.

Finally, it is suggested to evaluate the channel behavior as function of aging and temperature, using a Burning Chamber, for instance. This can improve the channel characterization.

REFERENCES

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[7] F. S. Tse and I. E. Morse, Measurement and Instrumentation in Engineering – Principles and basic laboratory experients. Marcel Dekker, Inc. NY, 1989.

[8] E. O. Doebelin. Measurement Systems Application and Design. McGraw-Hill, New York, 1983.