Assessment of the unilateral pulmonary function by means of electrical ...

INSTITUTE OF PHYSICS PUBLISHING Physiol. Meas. 25 (2004) 803–813

PHYSIOLOGICAL MEASUREMENT PII: S0967-3334(04)74621-3

Assessment of the unilateral pulmonary function by means of electrical impedance tomography using a reduced electrode set Roberto E Serrano1, Pere J Riu1, Bruno de Lema2 and Pere Casan2 1

Center for Research in Biomedical Engineering (CREB), Technical University of Catalonia (UPC), 08034 Barcelona, Spain 2 Departament de Funci´ o Pulmonar, Hospital de la Santa Creu i Sant Pau, Barcelona, Spain E-mail: [email protected]

Received 15 January 2004, accepted for publication 28 April 2004 Published 22 July 2004 Online at stacks.iop.org/PM/25/803 doi:10.1088/0967-3334/25/4/002

Abstract The usefulness of electrical impedance tomography (EIT) to assess ventilationrelated phenomena in the thorax has already been demonstrated, especially in controlled environments. We focus on our developments in the assessment of the unilateral pulmonary function (UPF) in real clinical environments. The impact of the reduction of the number of electrodes used is analysed theoretically and experimentally with different approaches. Sixteen-electrode EIT measurements were performed on a group of lung cancer patients (19 M, 2 F, ages 25–77 years). Results are compared with those obtained from ventilation scintigraphy. Eight-electrode measurements were synthesized from the 16-electrode ones. The Bland and Altman analysis indicates an agreement of about ±1 percent points in the estimation of UPF. On five of these patients real 8-electrode measurements were performed, obtaining differences from 0.2 percent to 6 percent points. It is concluded that reducing the number of electrodes does not adversely affect the assessment of UPF, but there is a reproducibility issue affecting all the techniques which needs further study. Keywords: electrical impedance tomography, functional imaging, unilateral pulmonary function, reduced electrode set (Some figures in this article are in colour only in the electronic version)

0967-3334/04/040803+11$30.00 © 2004 IOP Publishing Ltd Printed in the UK

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1. Introduction The assessment of the unilateral pulmonary function (UPF) is of major interest for those patients scheduled for lung resection because it is necessary to predict the vital capacity of these patients after the operation. The most accurate technique for UPF assessment is bronchospirometry, a highly invasive method. The currently accepted clinical protocol for UPF estimations uses radionuclide-based perfusion scans as the gold standard technique to assess unilateral lung ventilation because of its easy application and the significance of the information obtained (Baier 1980, British Thoracic Society 2001). There is a large number of works that apply EIT techniques to the study of pulmonary function, either ventilation or perfusion, or both. Frerichs (2000) reviews many of these works and comments on the suitability of EIT to assess regional ventilation distributions. Some previous works, such as Kunst et al (1998), have already concluded that it is feasible to assess the unilateral pulmonary function (UPF) from a time series of ventilation images. Hinz et al (2003) compare EIT and SPECT to evaluate regional ventilation in pigs with different degrees of induced lung injury, finding a good agreement between these techniques and Brown et al (2003) introduce the possibility of estimating absolute lung resistivity with the aid of computer models adapted to each individual. Serrano et al (2002) established a protocol aimed at the clinical standardization of EIT by using functional images to separate ventilation-related changes from other effects. The conclusions of this later work were that EIT might be effective to assess UPF as it was demonstrated in healthy subjects and a reduced number of actual patients. This work was later extended to a larger number of patients (Serrano 2003), showing that an acceptable agreement between ventilation scintigraphy and EIT can be reached. However, the application of the method is limited mainly because of electrode artefacts likely to appear due to patient’s involuntary movements that alter the electrode/skin impedance, which is known to distort reconstructed impedance images (Boone et al 1996). In this paper, we study the feasibility of reducing the number of electrodes used in the measurements. Most of the works done so far (Frerichs 2000) use 16 electrodes to acquire information from the body. This was also our initial choice, mainly for historical reasons (Casas et al 1996). By reducing this number from 16 to 8 there are several advantages, most of them related to practical aspects such as the electrode positioning, the cabling, the reduction of movement artefacts or the increase of the signal-to-noise ratio in the measurements; and one main drawback—the reduction of the spatial resolution. Other authors have used 8-electrode approaches in the past, but mainly because of the physical impossibility of applying 16, for instance when working with neonates (Brown et al 2003). In the next sections, we discuss the feasibility and theoretical implications of reducing the number of electrodes and compare the results obtained in a limited number of actual patients. 2. Materials and methods 2.1. Patients For this investigation we selected a group of 21 patients (19 M, 2 F, ages 25–77 years), diagnosed with different types of lung cancer, and scheduled for pulmonary resection surgery in the Hospital de la Santa Creu i Sant Pau (Barcelona, Spain). The research was approved by the Ethics Committee of the hospital and all patients gave informed consent. Table 1 displays some characteristics of the diagnosed lung cancer for each patient.

UPF assessment by EIT with fewer electrodes

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Table 1. List of patients used in the experiment, showing the type of disease and its localization. Patient

Etiology

Localization

AA AL AM CG EN FC FR JC JS LM MC PP RP SA TH TZ

Mesothelioma Large cell carcinoma Small cell carcinoma Small cell carcinoma Large cell carcinoma Small cell carcinoma Large cell carcinoma Large cell carcinoma Large cell carcinoma Small cell carcinoma Small cell carcinoma Small cell carcinoma Mesothelioma Large cell carcinoma Squamous carcinoma Large cell carcinoma

RLL RUL Lingula RUL RML RUL Lingula RUL RUL RML RUL RUL Left mediastinum RUL RML RUL

AG BC JM PM RG

Small cell carcinoma Large cell carcinoma Large cell carcinoma Large cell carcinoma Asthma patient

RUL RML Lingula LUL –

(RUL: right upper lobe; RML: right middle lobe; RLL: right lower lobe; LUL: left upper lobe).

2.2. Measurement protocols The details of the measurement protocol, using 16 electrodes (numbered from 0 to 15), and signal processing can be found in Serrano et al (2002). The most relevant aspects are summarized below: • Fourth and sixth intercostal spaces (IS) were identified • Four electrodes were first attached in the fourth IS following anatomical lines: sternum (electrode 0), left mid-axillary line (electrode 4), column (electrode 8) and right midaxillary line (electrode 12). • Three more electrodes were attached, equidistant, between each pair of the previously attached 4 electrodes. • Measurements were performed with the patient sitting, holding the arms elevated at 90◦ and breathing spontaneously, as shown in figure 1. Two series of measurements lasting 30 s each were acquired. • New electrodes were attached at the sixth IS and the entire protocol above was repeated. The EIT system used was TIE-4sys (Casas et al 1996), a 16-electrode impedance imaging system designed and constructed in the research facilities of the Technical University of Catalonia. For five of the patients (listed at the end of table 1), actual 8-electrode measurements were performed. In this case, electrodes 0, 2, 4, 6, 8, 10, 12 and 14 remained at their locations while the rest were removed. The same acquisition system with the same acquisition algorithm was used. Cables 0–7 were connected to those remaining electrodes, leaving cables 8–14 unconnected and short-circuiting cables 0 and 15, to prevent the saturation of the current

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Figure 1. Collocation of electrodes (left) and position of the patient during the measurements (right).

source just before a new data frame was collected. This arrangement was necessary as the equipment was not originally designed to work with 8 electrodes. A weighted back-projection algorithm was used to reconstruct the images from the impedance data collected. This algorithm was modified to handle 8-electrode data sets. Because the goal was to obtain a functional EIT image relative only to ventilation, the following steps were performed for each impedance data set corresponding to each intercostal space (IS): • Calculate a reference frame by averaging all frames in the data set. • Obtain a synthetic signal representing the change as a function of time for each measured transimpedance. • Apply a filter to this signal in order to extract the information related to ventilation. • Locate maxima and minima on the filtered transimpedance signal and calculate the averaged maximum and minimum. Assemble two data frames with the averaged maximum and minimum. • Reconstruction of both frames over the calculated reference, obtaining two images, which were then subtracted to finally obtain the ventilation EIT image. The ventilation EIT images of each IS were then segmented and the resulting left and right regions of interest (ROI) were quantified as in Serrano et al (2002). The final estimate of UPF for the right lung (RL) considers the impedance changes (IC) from both IS and is calculated as ICRL,4th + ICRL,6th × 100% (1) UPFRL = ICRL,4th + ICLL,4th + ICRL,6th + ICLL,6th where 4th and 6th indicate the intercostal spaces considered. UPF for the left lung (LL) was calculated in the same way. The procedure is the same for both 16-electrode and 8-electrode images. Because electric current flow is not restricted to the plane defined by the electrodes, but is distributed in the three-dimensional space, the estimation using one electrode set will actually have contributions from some volume above and below the electrode plane. By further averaging the 4th and 6th IS we expect to have a good estimate of an ‘average’ ventilation distribution for each lung. R gamma-camera was used. The patient For ventilation radionuclide scanning, a Siemens was asked to sit and hold a mouthpiece connected to the radioisotope dispenser, which


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contained a 74 mbq (2 mCi) equivalent load of 99mTc marked graphite particles. To obtain a homogeneous distribution of the tracer, the patient was asked to perform a set of inhalations in closed circuit. Posterior projection image acquisition (byte mode, 256 × 256 matrix) began after reaching 300 000 counts. These measurements were not necessarily performed on the same day as the EIT measurements. 2.3. Synthetic 8-electrode measurements Eight-electrode equivalent data sets were obtained for all the patients. These synthetic measurements were made from the 16-electrode actual data sets by using the reciprocity theorem and the superposition theorem, with the following expression, V 8 (i, j ) =

2i

2j

V 16 (k, l)

(2)

k=2i−1 l=2j −1

where V 16 (k, l) represents the actual 16-electrode data for injection k and detection l (k, l ∈ [0, 15]) and V 8 (i, j ) is the calculated 8-electrode data for injection i and detection j (i, j ∈ [0, 7]). Injection or detection n means that electrodes n and n + 1 are used to apply current or detect voltage. The use of this expression makes sense only if it can be assumed that there are no changes in the impedance distribution during the acquisition of a data frame, which takes about 50 ms in our case. 2.4. Statistical analysis In order to compare the results on the estimation of the UPF obtained from the actual 16electrode measurements and the synthetic 8-electrode measurements in the 20 patients, a Bland and Altman test is used. For the five patients in whom actual 8-electrode measurements were performed no Bland and Altman test was applied, and the UPF results for each patient are displayed in table 2. Repeatability between 16-electrode measurements was assessed by the standard deviation of the differences between series for each patient. 3. Theoretical analysis of the sensitivity change reducing the number of electrodes Seagar et al (1987) defined the relative sensitivity of the measured voltage (V ) to a change in the conductivity contrast (α) within the region of interest as Sr =

dV /V . dα/α

(3)

In two dimensions, for a circular region containing a circular coaxial perturbation and assuming adjacent current injection, the profile of injected current can be expressed as a Fourier series of trigonometric function and the relative sensitivity takes the following form: π ∞ 4αR 2n 1 dV /V n=1 [(α+1) + (α−1)R 2n ]2 n sin n Nelec sin(nθ ) = ∞ (α+1) − (α−1)R2n 1 Sr = . (4) π dα/α n=1 [(α+1) + (α−1)R 2n ] n sin n Nelec sin(nθ ) Here R = R1 /R0 is the ratio of the perturbation size to the object size, thus representing the spatial resolution; θ is the angle between the injection electrodes and the most sensitive detection pair, which is the one opposite to the injector pair for that type of current injection. Because the smallest detectable change in voltage is limited by the electronic noise of the acquisition system, the above expression relates noise (dV /V ), contrast (α), spatial resolution

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R E Serrano et al Table 2. Estimation of the right lung ventilation (in per cent of the total ventilation), for the 16-electrode actual measurements (RL16), the 8-electrode synthetic measurements (SRL8) and the 8-electrode actual measurements (ARL8). The result of ventilation scintigraphy is also shown where it was available. Patient

16-electrode (RL16)

8-electrode synthetic (SRL8)

AA AL AM CG EN FC FR JC JS LM MC PP RP SA TH TZ

37.5 51.7 58.1 34.4 57.2 51.6 60.9 53.5 48.2 51.5 63.3 50.7 79.3 62.6 57.7 73.8

42.6 50.0 57.7 31.2 56.7 51.8 59.9 52.9 48.7 49.1 65.6 52.0 77.8 61.8 61.0 74.5

AG BC JM PM RG

43.0 52.8 72.8 60.7 55.8

42.8 53.4 72.1 60.4 56.7

8-electrode real (ARL8)

Ventilation scintigraphy 38.4 50.9 – 31.0 53.1 53.8 63.6 47.8 – 49.3 52.0 53.4 80.1 52.1 48.6 70.5

48.8 52.7 68.4 59.4 61.7

43.5 44.2 – 55.8 –

(R) and resolution of the impedance change estimation (dα/α), for a particular electrode arrangement (Nelec , θ ). To estimate the variation in sensitivity between the 16-electrode and 8-electrode arrangements we define the ratio of sensitivities as 816

Sr,8 = = Sr,16

(dV /V )8 (dα/α)8 (dV /V )16 (dα/α)16

.

(5)

The smallest detectable change in voltage will be the same for both arrangements because the measurement system used is the same. If the noise of the system is dominated by the noise of the current source then the signal/noise ratio is independent of the absolute voltage measured, thus (dV /V )8 = (dV /V )16

(6)

and the ratio of sensitivities reduces to 816 =

Sr,8 (dα/α)16 = . Sr,16 (dα/α)8

(7)

If the noise of the system is dominated by the noise in the voltage detection channel, then this noise will be of additive nature, so dV8 = dV16

(8)


809

1

0.99

Sr,8 / Sr,16

0.98

0.97

α =0.25 0.96

α =0.5 α =1 α =2

0.95

0.94 -2 10

-1

10

α =4 0

10

Spatial Resolution (R)

Figure 2. Sensitivity ratio 816 as a function of the spatial resolution (R) for different values of contrast (α).

and the ratio of sensitivities in that case can be expressed as 816 =

Sr,8 (dα/α)16 V16 = . Sr,16 (dα/α)8 V8

(9)

Figure 2 shows the change in 816 as a function of the spatial resolution for different values of the contrast and for the electrode pair opposite to the current injection. For adjacent injection strategies in two-dimensional circular objects, with coaxial perturbations, the electrode pair opposite to the injection pair is the one that displays the highest relative sensitivity. This will also be true for three-dimensional objects with centred perturbations but may be different for non-centred perturbations. For small perturbation sizes (area of the perturbation smaller than 5% of that of the object) the sensitivity for the 8-electrode arrangement is about 94% of that of the 16-electrode arrangement, irrespective of the value of the contrast. As the normalized size of the perturbation increases to 1, 816 also increases to 1, with a slope that is a function of the conductivity contrast. If the noise of the system is dominated by the current source (equation (7)) then this reduction in sensitivity will be directly translated to a reduction in the ability to detect small conductivity changes. However, this reduction will be small (0.94) even in the worst case. In the case of a system with the noise dominated by the voltage detection 816 will be multiplied by V8 /V16 (equation (9)) which is always larger than 1, so the ability to detect small conductivity changes may be increased. The reduction in the number of electrodes will also produce a reduction in the ability of locating small objects. This reduction depends on the reconstruction algorithm being used and a detailed analysis is out of the scope of this work. To have an idea of the order of magnitude of such a reduction we may consider that the number of independent measurements that can be collected with N electrodes (once the three-wire measurements have been eliminated) is N (N − 3) . (10) 2 For a 16-electrode system this gives 104 independent measurements and for an 8-electrode system this gives 20 independent measurements. If there is no a priori information about the conductivity distribution, then the number of independent measurements is directly related to the number of independent pixels that can be reconstructed. If those pixels were of the

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Difference (VS - RL16)

5

0 Mean -5

-10 -95% Confidence Interval

-15 30

40

50

60

70

80

90

Mean (VS+RL16)/2

Figure 3. Bland and Altman test for the estimation of the right lung (RL) ventilation (in per cent) comparing ventilation scintigraphy and EIT measurements with 16 electrodes.

same size and uniformly distributed within the object (this is not true for most reconstruction algorithms), a 16-electrode system would be able to resolve perturbations as small as 1% of the area of the object (10% of the diameter). For an 8-electrode system the smallest perturbation would be about 5% of the area of the object, that is 22% of the diameter. The conclusion from this theoretical analysis is that a reduction in the number of electrodes from 16 to 8 should have a small impact in the estimation of impedance changes related to the ventilation of a whole lung, because the size of the perturbation (lung) is quite large compared to that of the object (thorax) and the change in conductivity induced by ventilation is also large. 4. Results Table 2 displays the results for the estimation of the contribution of the right lung to the total ventilation, expressed in percentage, for the 16-electrode arrangement, the 8-electrode synthetic measurements for all the patients, the 8-electrode actual measurements for the last five patients in the table, and the result of the estimation of the UPF made out of ventilation scintigraphy scans, which was not available for all the patients (Serrano 2003). The Bland and Altman test displayed in figure 3 relates ventilation scintigraphy and EIT performed with 16 electrodes. There is a bias of −3.2 percent points and a standard deviation of ±4.7 percent points. There is no clear relationship between the value of the mean and the differences, so they are mostly of random nature. The correlation coefficient is r = 0.89. The Bland and Altman analysis shown in figure 4 compares the estimation with the 16electrode measurements to the estimation with the 8-electrode synthetic measurements. It reveals that there is a slight bias, of about −0.1 percent points, and the 95% confidence limits are smaller than ±3.8 percent points, while most of the subjects lie within the ±1% difference. The correlation coefficient is r = 0.985. For the actual 8-electrode measurements, performed only in five patients, the differences obtained are larger. The differences range from 0.1 percent to about 6 percent points, with a standard deviation of 4.4 percent points. The Bland and Altman test for this case is not


811

5 4

+95% Confidence Interval

Difference (RL16 -SRL8)

3 2 1

Mean of differences

0 -1 -2

-95% Confidence Interval

-3 -4 -5 30

40

50

60

70

80

90

Mean (RL16+SRL8)/2

Figure 4. Bland and Altman test for the estimation of the right lung ventilation (in per cent) comparing the actual measurements with 16 electrodes (RL16) and the synthetic measurements of 8 electrodes (SRL8). %Z

%Z

%Z

A

5

A

7 6

A 4

4

5

R

L

4 3

3

3

R

R

L

L

2

2

1

1

2

P (a)

1 0

P (b)

P (c)

Figure 5. Ventilation EIT images corresponding to the 6th IS obtained on patient RG for: (a) the 16-electrode arrangement, (b) the 8-electrode synthetic measurements and (c) the actual 8-electrode measurements (see text for the details of the procedure used to obtain the images).

presented because the reduced number of patients makes it difficult to draw any conclusions. The correlation coefficient here is r = 0.94. The images obtained in the reconstruction process are, by themselves, of little interest for the estimation of the UPF. However, for the sake of completeness we present in figure 5 a series of images for the same patient obtained from the three procedures described above, corresponding to the 6th IS. In short, these images are a representation of the difference between the reconstructed conductivity changes corresponding to the averaged (over time) maximum and minimum transimpedance variations related to ventilation. As expected, the images for the 8-electrode arrangements are much rougher than the image for the 16-electrode arrangement. 5. Discussion EIT can be regarded as a substitute for other techniques, mainly perfusion scintigraphy which is currently considered the gold standard for UPF estimation. However, to draw such a replacement in practice, clear advantages of EIT must be shown. Other authors (Frerichs 2000, Kunst et al 1998) as well as our own work have demonstrated that EIT can estimate

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regional ventilation in general, and unilateral ventilation in particular, either in healthy subjects or in patients, and mainly in controlled environments. We regard the ability to reduce the number of electrodes used in the measurements as a substantial requirement to be able to apply EIT in routine clinic procedures. Results displayed in table 2 and figure 3 show that EIT and ventilation scintigraphy do, generally, agree in the estimation of UPF. A detailed discussion on the goodness of this agreement and the differences between perfusion and ventilation scintigraphy and EIT is out of the scope of this paper. But assuming that this agreement allows for the replacement of the radionuclide techniques, we show that a reduction in the number of electrodes preserves the essential information for this application. The results obtained for the synthetic data sets (table 2, figure 4) show that there is a very small change in the estimation of UPF, even in patients displaying a very wide range of values for the ventilation of the right lung (30% up to 80%). The largest differences are about 3 percent points, while for most of the patients the agreement is within ±1 percent point. The Bland and Altman test in figure 4 shows that the differences are of random nature and can be attributed to the diminution in the spatial resolution expected from the reduction in the number of electrodes. This result agrees with what was concluded in section 3. Moreover, these differences are insignificant from a diagnosis point of view for the intended application. The situation seems to be a little worse for the actual 8-electrode measurements. Differences of about ±6 percent points are found. Because the number of patients is much reduced, it is difficult to draw statistical conclusions. It is important to note that there is a significant change in the methodology that may explain the spread of the data. The data for the 16-electrode and the synthetic 8-electrode measurements correspond to the same acquisition, so differences can only be attributed to the performance of the reconstruction algorithms estimators and loss of resolution (compare figures 5(a) and 5(b)). However, the data for the 8-electrode actual measurements were obtained at a different time from the data for the 16-electrode arrangement. There is a slight difference between their maximum reconstructed IC (see figures 5(b) and (c)) of about 0.2 percent points. The repeatability and reproducibility in vivo of those kinds of measurements, both EIT and scintigraphy, are poorly known. Even the parameter that is estimated, the distribution of ventilation between lungs, may suffer changes at short and medium term or with small postural changes, which happens when changing the electrode arrangement to perform the actual 8-electrode measurements. The differences between the two measurement series performed for the 16-electrode data showed a standard deviation of 1.6 percent points, which is acceptable for this application. The off-plane conductivity changes are known to have an effect on the reconstructed impedance changes. Rabbani et al (1991) and Avis (1993) have determined that, for saline tanks, perturbations occurring up to a distance from the electrode plane equal to the radius of the tank contribute to reconstructed images. In the case of the human thorax, the complexity of the geometry makes it difficult to quantify off-plane contributions, but these happen without doubt. Thus, it is reasonable to estimate UPF from measurements performed at the 4th and 6th IS, as most of the lung activity will be detected. The differences of ±6 percent points for the latter case are in the range of the differences found when comparing different methods applied to the estimation of pulmonary function. Victorino et al (2004) found differences of ±10% when comparing estimations of ventilation imbalance made using Dynamic CT and EIT but still consider that EIT can reliably assess ventilation distribution. Our own results show that there are differences between ventilation and perfusion scintigraphy that can reach ± 10 percent points in the estimation of UPF (Serrano 2003).


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6. Conclusions It is necessary to minimize the complexity and sources of artefacts in EIT measurements if this technique has to be used in routine clinic procedures. The reduction from 16 to 8 electrodes achieves this goal. The results demonstrate that the loss in spatial resolution associated with a reduced number of electrodes does not influence the estimation of UPF, from a diagnosis point of view. However, there is still an issue of reproducibility that deserves future work, not only for the EIT technique but also for the radionuclide techniques and for the estimated parameter itself. Acknowledgments This work was partially supported by project FIS PI020387 from the ‘Carlos III’ Health Institute (ISCIII) of the Spanish Government and the Spanish SEPAR-ISCIII-FIS-Red Respira. References Avis N J 1993 Image reconstruction in electrical impedance tomography PhD Thesis University of Sheffield Baier H 1980 Assessment of unilateral lung function Anesthesiology 52 240–7 Boone K G and Holder D S 1996 Effect of skin impedance on image quality and variability in electrical impedance tomography: a model study Med. Biol. Eng. Comput. 34 351–4 British Thoracic Society and Society of Cardiothoracic Surgeons of Great Britain and Ireland Working Party 2001 Guidelines on the selection of patients with lung cancer for surgery Thorax 56 89–108 Brown B H, Primhak R A, Smallwood R H, Milnes P, Narracott A J and Jackson M J 2003 Neonatal lungs—can absolute lung resistivity be determined non-invasively? Med. Biol. Eng. Comput. 40 388–94 Casas O, Rosell J, Bragós R, Lozano A and Riu P J 1996 A parallel broadband real-time system for electrical impedance tomography Physiol. Meas. 17 57–68 Frerichs I 2000 Electrical impedance tomography (EIT) in applications related to lung and ventilation: a review of experimental and clinical activities Physiol. Meas. 21 R1–21 Hinz J, Neumann P, Dudykevych T, Andersson L G, Wrigge H, Burchardi H and Hedenstierna G 2003 Regional ventilation by electrical impedance tomography: a comparison with ventilation scintigraphy in pigs Chest 124 314–22 Kunst P W A, Vonk Noordegraaf A, Hoekstra O S and Postmus P E 1998 Ventilations and perfusion imaging by electrical impedance tomography: a comparison with radionuclide scanning Physiol. Meas. 19 481–90 Rabbani K S and Kabir A M B H 1991 Studies on the effect of the third dimension on a two-dimensional electrical impedance tomography system Clin. Phys. Physiol. Meas. 12 393–402 Seagar A D, Barber D C and Brown B H 1987 Theoretical limits to sensitivity and resolution in impedance imaging Clin. Phys. Physiol. Meas. 8 issue 4A, 13–31 Serrano R E, de Lema B, Casas O, Feixas T, Calaf N, Camacho V, Carrió I, Casan P, Sanchis J and Riu P J 2002 Use of electrical impedance tomography (EIT) for the assessment of unilateral pulmonary function Physiol. Meas. 23 211–20 Serrano R E 2003 Estudio de la función pulmonar mediante tomograf´ıa de impedancia electrica PhD Thesis Technical University of Catalonia (in Spanish) Victorino J A et al 2004 Imbalances in regional lung ventilation: a validation study on electrical impedance tomography Am. J. Respir. Crit. Care. Med. 169 791–800