Improvement of cardiac imaging in electrical impedance tomography ...

4 downloads 0 Views 586KB Size Report
Feb 22, 2016 - tomography by means of a new electrode configuration ... Until now, electrical impedance tomography (EIT) has been used for cardiac imaging.
Home

Search

Collections

Journals

About

Contact us

My IOPscience

Improvement of cardiac imaging in electrical impedance tomography by means of a new electrode configuration

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1996 Physiol. Meas. 17 179 (http://iopscience.iop.org/0967-3334/17/3/004) View the table of contents for this issue, or go to the journal homepage for more

Download details: IP Address: 163.117.11.96 This content was downloaded on 22/02/2016 at 03:27

Please note that terms and conditions apply.

Physiol. Meas. 17 (1996) 179–188. Printed in the UK

Improvement of cardiac imaging in electrical impedance tomography by means of a new electrode configuration A Vonk Noordegraaf†, T J C Faes‡, A Janse†, J T Marcus‡, R M Heethaar‡, P E Postmus† and P M J M de Vries† † Department of Pulmonary Medicine and ‡ Department of Medical Physics and Informatics, University Hospital Vrije Universiteit, Amsterdam, The Netherlands Received 2 February 1996 Abstract. Until now, electrical impedance tomography (EIT) has been used for cardiac imaging with the electrodes attached transversally at the level of the fourth intercostal space at the anterior side. However, the results obtained with this electrode configuration have been disappointing. The aim of the present study was to improve the measurement design of EIT for cardiac imaging. Therefore, magnetic resonance imaging (MRI) scans were analysed in two healthy subjects to determine the optimum anatomical plane in which atria and ventricles are clearly visually separated. From these findings, we proposed a new oblique plane at the level of the ictus cordis anteriorly and 10 cm higher posteriorly. EIT pictures obtained in the oblique plane revealed a better visual separation between the ventricles and atria than with the electrodes attached in the transverse plane. Comparison between volume changes measured by means of MRI and impedance changes in different regions of interest measured with EIT were performed with the electrodes in the proposed oblique plane. Ventricular and atrial volume changes measured by MRI show the same pattern as do impedance changes measured by EIT. Furthermore, we assessed the reproducibility and validity of the oblique electrode configuration in ten healthy male volunteers during rest and during exercise compared with the currently used transverse electrode configuration. The reproducibility coefficient assessed from repeated measurements with the electrodes attached in the oblique plane was 0.98 at rest and 0.85 during exercise. For the transverse plane the reproducibility coefficient was 0.96 at rest and 0.66 during exercise. The well-known increase in stroke volume during exercise is 40% in healthy subjects. The increase in impedance change during exercise compared with rest was 34 ± 13% (20–59%) for the oblique plane and 68 ± 57% (13–140%) for the transverse plane. From these results we infer that the stroke volume is assessed more accurately by using the oblique plane. From these findings, we conclude that the oblique plane improved the cardiac measurements, because (i) a better spatial separation of the heart compartments is obtained, (ii) the results are more reliable and (iii) measurements during exercise are more accurate with the electrodes attached in an oblique plane. Keywords: electrical impedance, tomography, stroke volume, magnetic resonance imaging

1. Introduction There is a need in clinical medicine and research for non-invasive continuous cardiopulmonary monitoring techniques. One of the non-invasive methods to measure stroke volume is electrical impedance cardiography (Bernstein 1986). This technique relates changes in thoracic impedance to changes in thoracic blood volume. However, the validity of electrical impedance cardiography remains controversial (Sakamoto et al 1979). The c 1996 IOP Publishing Ltd 0967-3334/96/030179+10$19.50

179

180

A Vonk Noordegraaf et al

signal is simultaneously influenced by the widespread impedance changes produced by the blood flow in the ventricles, atria thoracic arteries and veins. A disadvantage of electrical impedance cardiography is the inability to localize impedance changes (Bonjer et al 1952, Wang and Patterson 1995). ECG-gated electrical impedance tomography (EIT) is able to localize the impedance variations occurring during the cardiac cycle (Ey¨uboˇglu et al 1989, Brown et al 1992). EIT constructs cross sectional images of the electrical impedance changes during the cardiac cycle. The impedance change, measured by EIT, is caused by changes in blood volume (Brown et al 1994). In contrast with other impedance techniques, this technique makes it possible to discriminate between ventricular and atrial impedance changes (Ey¨uboˇglu et al 1989, McArdle 1992). Although a lot of effort has been devoted to the development of this technique, only a few studies describing the cardiac-related impedance changes exist (Ey¨uboˇglu et al 1989, McArdle 1992, Brown et al 1994). The results of these studies have been disappointing. Only a poor correlation was found between stroke volume and impedance changes (McArdle 1992). All of these studies were performed with the electrodes spaced around the thorax at the level of the fourth or fifth intercostal space at the anterior side of the thorax in a transverse plane. Two possible explanations for the poor results can be given. First, the transverse plane does not intersect the heart through its long axis. Therefore, ventricles and atria are partially overlapping on the EIT image due to poor spatial resolution (Ey¨uboˇglu et al 1988, McArdle 1992). As a result, ventricular and atrial impedance changes interfere to a great extent. Second, the contraction of the heart is directed along the long axis of the left ventricle. Therefore, the ventricles will move through the transverse electrode plane during the cardiac cycle. The aim of the present study was to improve the application of EIT to cardiology by developing a new electrode configuration. Therefore, magnetic resonance imaging (MRI) scans were analysed to determine an optimum anatomical plane, in which the visual separation of the ventricular and atrial regions is maximal. From these findings, we propose a new oblique electrode configuration to be used in EIT. After that, the interpretation of oblique EIT images was investigated by means of MRI scans that were produced to determine area changes of the ventricles and atria during the cardiac cycle. These area changes were compared with EIT results obtained from the corresponding areas. Finally, EIT results obtained with the oblique electrode configuration were investigated. The reproducibility was assessed in a duplicate measurement design, comparing the oblique and transverse planes. A first investigation into the assessment of ventricular volume changes (stroke volume) by measuring impedance changes was accomplished by comparing measured impedance changes during exercise with values of stroke volume changes known from the literature.

2. Methods 2.1. Subjects Ten healthy male volunteers aged 26 ± 3 years were studied. None of them had a cardiovascular or neurological history. MRI scans were obtained from two of the ten subjects. The research was approved by the Ethical Committee of the University Hospital Vrije Universiteit. All of the subjects gave their informed consent to participate in the study.

Improvement of cardiosynchronous EIT imaging

181

2.2. MRI This research is performed on a 1 T whole body MRI system (Impact Expert,Siemens, Erlangen, Germany), with a phased-array body coil installed. The subjects were made to lie in the supine position. Using end-diastolic scout images, the following image planes were defined for the heart: (i) a transverse plane at the level of the fourth intercostal space at the anterior side of the thorax and (ii) an oblique plane, rotated from transverse to coronal over 25◦ , passing through the apex cordis and the mitral valve. MR image acquisition of the heart was triggered on the R-wave in the ECG. A 2D gradient echo pulse-sequence (’FLASH’) was applied, at excitation angle 20◦ and with segmented k-space with seven ky lines per heart beat. The matrix size was 140 × 256, thus 20 consecutive heart beats were needed to obtain one image. During this time period the subject held his breath during end expiration. The echo time was 6.1 ms, the receiver bandwidth was 195 Hz and flow compensation was implemented. The temporal resolution within the cardiac cycle was 80 ms, allowing for ten phases per cardiac cycle. The slice thickness was 8 mm. The field of view was 300 mm × 300 mm for the transverse images of the heart and 350 mm × 350 mm for the oblique images. The cross section of the aorta was imaged in a transverse plane through the ascending aorta, at the level of the right pulmonary artery applying a 2D ‘FLASH’ sequence with a matrix size of 168 × 256, field of view 263 mm × 300 mm, and slice thickness 6 mm. Temporal resolution was 31 ms; the total scan time was determined by the duration of 168 consecutive heart beats. Surface areas of different regions of interest were calculated by drawing a contour along the endocardial contour.

2.3. EIT In this study, EIT measurements were performed with the Sheffield Applied Potential Tomograph (DAS-01P Portable Data Acquisition System, Mark I, IBEES, Sheffield, UK), which has been extensively described before (Brown and Seagar 1987, Smith et al 1995). In short, EIT is a technique by which to produce images of the changes in distribution of electrical impedance in a 2D slice through a conducting medium by means of impedance measurements performed at the surface of the medium. A set of 104 independent impedance measurements were performed using an array of 16 equidistantly spaced electrodes around the part of the body under study. A current source, which generates a harmonic current (50 kHz, 5 mA peak–peak), was used to measure impedance. In ECG-gated EIT, a sequence of images is constructed to visualize the impedance changes during the cardiac cycle. Data collection is synchronized with the R-wave of the electrocardiogram. Starting at the R-wave, a data set is recorded each 40 ms. Experience has shown that averaging over at least 100 cardiac cycles is needed in order to attenuate the respiratory component (Ey¨uboˇglu et al 1989). For reasons of safety, 200 cardiac cycles were averaged in this study to obtain one complete cardiac cycle, containing 30 data sets spaced 40 ms apart. Difference images compared to a reference set were generated with the Sheffield tomograph. The reference set was chosen over the first five frames (end diastole). The normalized difference between the reference set and each data set was passed to a reconstruction algorithm to produce images. In each reconstructed image, pixel values are

182

A Vonk Noordegraaf et al

Figure 1. Variations in the course of time in cross sectional areas in the MRI images (upper curves) and in impedance in the EIT images (lower curves) for the ventricles (first column) and atria (second column). EIT measurements were performed with the subject in the supine position. The oblique plane was used to image the ventricles and atria. The results for the cross sectional area (MRI) and impedance (EIT) are inversely proportionally related to each other. The value of A was used as a measure of stroke volume.

related to the impedance changes. Changes in the impedance distribution due to volume changes during the cardiac cycle are imaged. The dynamics of the volume changes can be studied in the sequence of images (film). Impedance changes in specific areas of the images were studied by defining a region of interest (ROI). In this study, we defined the ROI by drawing a boundary around the ventricular and atrial features during systole. At that moment both ventricles and the right atrium are clearly distinguished from the other features. After defining a ROI around the area to be investigated, the average pixel value in that area was plotted as a function of time, to show the impedance change during the cardiac cycle. The average pixel value has no unit because it is dimensionless as a consequence of the reconstruction algorithm being based on normalized differences. Therefore, the change in the average pixel value in the sequence during the cardiac cycle relative to end diastole is expressed as an arbitrary unit (AU). For the measurement of impedance changes over the ventricles we include all pixels in the ventricular region, with positive impedance changes (image pixel value of 0.001 or

Improvement of cardiosynchronous EIT imaging

183

Figure 2. Sequences of images recorded with EIT and MRI techniques in the oblique plane (columns 1 and 2) and in the transverse plane (columns 3 and 4) during a cardiac cycle; from top to bottom, images are shown at a time interval of 80 ms, starting from end diastole (first row). The oblique MRI images at end diastole clearly visualize different thoracic structures: the left ventricle (LV), the right ventricle (RV), the left atrium (LA), the right atrium (RA), the left lung (LL), the right lung (RL), the descending aorta (the circular white spot below the left atrium), the spinal cord and the thorax wall. The EIT images were reconstructed with the reference at end diastole (black images on top). In the oblique plane during systole (rows 2–5), blood volume decreases in the ventricles, appearing as an increase in impedance (blue colour) and blood volume increases in the atria, appearing as a decrease in impedance (red colour). Interpretation of both sequences in the transverse plane is more difficult due to ‘through-plane motion’.

184

A Vonk Noordegraaf et al

more). Multiplication of the number of pixels by the average pixel value at end systole (see figure 1, amplitude A) gives the total impedance change in the ventricular region. We used the total value of the impedance change over the ventricles between systole and diastole as a measure of stroke volume. 2.4. Experimental protocol First, MRI scans were performed in two subjects from different angles, to determine the optimal cross section for visual inspection through the heart. The imaging strategy was optimized using oblique planes aligned with the long axis of the heart. Ventricles, atria and aorta are most clearly distinguished in these images (figure 2, top row, second column). From these findings, the optimal cross-sectional plane was determined at the level of the ictus cordis anteriorly and 10 cm higher posteriorly. Next, EIT measurements were performed in two subjects before and after the MRI session with the 16 electrodes (Red Dot, 3M, St Paul, USA) equidistantly attached in the proposed oblique plane as well as transversally at the level of the fourth intercostal space at the anterior side of the thorax. The heart rate was approximate constant during the measurements. EIT images were visually compared with the MRI images obtained in the same plane. Furthermore, curves from the volume changes in the atria, ventricles and aorta were obtained and compared with the impedance changes registered with EIT. Finally, the validity and reproducibility of both electrode configurations were assessed during a period of rest and exercise on ten healthy volunteers. On the first day we tested the transverse electrode plane. All measurements were performed with subjects upright on a bicycle ergometer (KEM-3, Mijnhardt, Bunnik, The Netherlands). Repeated resting measurements were carried out after a 15 min equilibration. The measurements during exercise started after 5 min cycling with a continuous load of 60 W; at that moment, the person was supposed to be in a steady state, which was confirmed by registration of their heart rate. During the next 5 min, repeated measurements were performed while the subject cycled. From these measurements, the impedance change of the heart during exercise compared with during rest was calculated. We repeated the whole procedure on the next day with the electrodes attached in the oblique plane. The validity of both electrode configurations was assessed by calculating the increase in impedance change during exercise compared with during rest. The results were compared with normal stroke volume values known from the literature. 2.5. Statistical analysis All results are reported as mean ± sd (ranges). The reproducibility of the EIT results was estimated from the repeated measurements during rest and exercise. In a duplicate measurement design, the reproducibility coefficient equals the correlation coefficient (Pearson) between the results measured the first and second time (Snedecor et al 1989).

3. Results Figure 2 shows a sequence of images recorded with EIT and MRI techniques in the oblique and transverse planes during the cardiac cycle. Images obtained in the oblique plane are shown in columns one and two for EIT and MRI respectively, whereas the EIT and MRI

Improvement of cardiosynchronous EIT imaging

185

results for the transverse plane are shown in columns three and four, respectively. Going from top to bottom, sequences of images are shown with a time interval of 80 ms between the successive rows. The first row shows MRI images during end diastole. At that moment the EIT images are black, because the reference image was chosen at end diastole. Note that the left-hand side of the thorax is shown on the right-hand side of the EIT and MRI images, due to conventions in radiology. The colours blue and red are respectively used to visualize increases and decreases in impedance, relative to the reference image. In the MRI images made in the oblique plane (second column) the following anatomical structures are clearly identifiable: the left ventricle (LV), the right ventricle (RV), the left atrium (LA), the right atrium (RA), the left lung (LL), the right lung (RL) and the descending aorta (the circular white spot below the left atrium). As a consequence of the anatomical position, the left atrium is largely outside the oblique plane. In the systolic phase of the cardiac cycle the cross sectional area of both ventricles decreases, whereas the cross sectional area of the atria increases (rows 2, 3, 4 and 5); in diastole these changes are in the opposite direction, namely the ventricular area increases and the atrial areas decrease (rows 6, 7 and 1). In the transverse MRI images (column 4) at end diastole (first row) the same anatomical structures are recognizable. However, in the following sequence of the images, separation of the atria and ventricles becomes more difficult. In particular, the area of the two ventricles becomes more difficult to identify, because the pulmonary artery (the bright white spot in the RV, rows 2–6) and the ascending aorta (the circular spot at the centre of the heart, row 2–5) dominate the MRI images (through plane motion). The EIT images show temporal changes of the impedance distribution relative to end diastole (blue for an increased impedance and red for a decreased impedance). Since the blood volume in the ventricles decreases while atrial volume increases during systole (column 2), the impedance of the ventricles increases and the impedance of the atria decreases. This might indicate that the large bilobular blue and red regions in the oblique plane images (column 1) could possibly correspond to the ventricles and atria respectively. The sequence of the transverse EIT images is more complicated to interpret. For example, the colour intensities of atrial and pulmonary regions in the transverse plane are equal, making it impossible to separate atria and lungs visually. Figure 1 shows variations in the course of time of the cross sectional areas in the MRI images (upper curves) and the impedance in the EIT images (lower curves) for the ventricles (first column) and atria (second column). The oblique plane was used to image the ventricles and atria. The ventricles show a decrease in cross sectional area and an increase in impedance during systole (0–0.35 ms), and vice versa during diastole (0.35–0.80 ms). The cross sectional area and impedance changes in the atria during the cardiac cycle are in the opposite direction compared with those in the ventricles. Notice the strong inversely proportional relationship between the cross sectional area (MRI) and impedance (EIT) for the ventricles and the atria. Similar results were found in the second subject, who underwent MRI scanning. The reproducibility of EIT was determined by repeated measurements of the impedance changes in the ventricular region during rest and exercise for both electrode configurations. During rest the reproducibility coefficient was 0.98 in the oblique plane and 0.96 in the transverse plane, whereas during exercise this coefficient was 0.85 in the oblique plane but only 0.66 in the transverse plane. For both electrode configurations the impedance change of both ventricles during exercise was determined relative to the impedance change during rest. For the oblique plane, the group average increase was 34 ± 13% (20–59%), for the transverse plane, the group average increase was 68 ± 57% (13–140%).

186

A Vonk Noordegraaf et al

4. Discussion By comparing the MRI results, it is clear that the ventricles and atria are better spatially separated during the whole cardiac cycle in the oblique plane than they are in the transverse plane. The transverse images are seriously distorted by the phenomenon of the motion of the heart through the transverse plane during the cardiac cycle. This ‘through-plane motion’ is demonstrated in the sequence of images, because the pulmonary artery and ascending aorta are only visible during systole. In the oblique plane, the movement of the heart during the cardiac contraction is parallel to the oblique plane, causing an ‘in-plane motion’. Thus, to study the changes of the ventricle and atria during the cardiac cycle, the oblique plane is to be preferred in MRI images. The EIT results in the oblique plane (figure 2, column 1) indicate that the blue and red regions in the oblique plane images might be interpreted as the ventricles and atria respectively. To investigate this interpretation, ventricular and atrial changes in cross sectional area measured by MRI were compared to the impedance changes measured by EIT (figure 1). The results show a strong inversely proportional relationship between the cross sectional area (MRI) and impedance (EIT) for the ventricles and the atria. During systole, the impedance of both ventricles increases with outflow of blood, whereas the impedance of the right atrium decreases due to inflow of blood. During diastole the opposite results are found. The inverse proportionality in the relationship between MRI and EIT results is easily explained; an increase in area filled with blood (low specific resistivity) surrounded by an area of tissue (high specific resistivity) corresponds to a decrease in impedance in that region. Thus, the strong inversely proportional relationship between experimental MRI and EIT results provides a firm basis for our interpretation of the EIT images. Moreover, the MRI and EIT curves demonstrate the same details. For instance, the three phases of diastole are clearly visible in the ventricular and atrial EIT curves (Guyton 1991). In particular: (i) the period of the rapid filling of the ventricles lasts for approximately the first third of diastole (0.35–0.55 s), (ii) during the middle third of diastole (0.55–0.65 s) the inflow of blood in the ventricles is almost at a standstill and (iii) during the final third of diastole (0.65–0.80 s) the atria contract, causing a rapid decline in volume and increase in impedance at the end of diastole. Thus, our interpretation of the blue and red regions in the EIT image (figure 2, row 1) as ventricular and atrial regions, was confirmed by the close correspondence between the MRI and EIT results (figure 1). Analysing the oblique EIT images in terms of left and right sides of the heart is, in our opinion difficult. Due to the limited spatial resolution of EIT, both ventricles appear as a bilobular blue region which makes it impossible to separate left and right ventricular regions. In contrast to the right atrium area, only a small part of the left atrium is visible on the oblique MRI images. Therefore, the impedance changes measured in the red region will be mainly caused by blood volume changes in the right atrium. In contrast with earlier studies using a transverse plane at the level of the fourth intercostal space (Ey¨uboˇglu et al 1989, McArdle 1992), we could not find the ascending aorta in the EIT image. This could be explained by the fact that the cardiac-related volume changes of both atria exceed the volume changes of the aorta. Although the impedance changes in the aorta and atrium are in the same direction during the cardiac cycle, the aorta is overshadowed by the atria. The difference in body position between the MRI and exercise measurements will cause changes in the anatomical position of the heart. The influence of changes in the position of the heart on the EIT signal was reduced by choosing the ictus cordis as the reference point. For both electrode planes, we determined the reproducibility of the ROI analysis of the ventricular region in the EIT images during periods of rest and exercise. The

Improvement of cardiosynchronous EIT imaging

187

reproducibility coefficient was high for the two configurations during rest. During exercise, however, the reproducibility coefficient was significantly lower for the transverse plane, but still high for the oblique plane. An explanation for the lower reproducibility in the transverse plane during exercise might be the increased cardiac movements during exercise compared with during rest, causing an increased through-plane motion. Thus, from the viewpoint of reproducibility, the oblique plane is to be preferred. Since the volume conduction of electric current extends to the dimension perpendicular to the plane, the EIT images contain significant information on volume changes of cavities located a few centimetres above and below the electrode plane (Rabbani and Kabir 1991). Therefore, volume changes can probably be assessed from a two-dimensional EIT image. A first indication that ventricular volume changes might be validly estimated by measuring impedance changes was found by comparing our experimental impedance changes with the known stroke volume changes during exercise. During steady state exercise in healthy young male subjects, stroke volume increases by 40% (Higginbotham et al 1986). Therefore, the impedance should increase by 40% during exercise. For the oblique plane our results show an increase of 35% for the group mean, while the interindividual variation is within the physiological range. The results in the transverse plane, however, show an unlikely large interindividual range of variation. Thus, these results might indicate that stroke volume can be assessed from EIT measurements performed in the oblique plane. Some advantages of the oblique electrode configuration can be summarized. First, the orientation of the oblique electrode plane is parallel to the long axis of the ventricles in contrast to the transverse plane. Therefore, both ventricles are more clearly visually separated in the oblique plane (see figure 2). Second, whereas the major movement of the heart is in the direction of the long axis, through-plane movements of the heart during the cardiac cycle are reduced, using an oblique plane. This might explain the highly reproducible results obtained in the oblique plane during exercise. Third, the oblique plane makes it possible to measure females in the same plane as males. Fourth, the oblique configuration comes closer to a circular boundary, which is a basic assumption in the reconstruction algorithm used in the Sheffield tomograph (Brown et al 1987). Fifth, the influence of the interindividual anatomical variation of the position of the heart in the thorax cavity is reduced, because the level of the ictus cordis anteriorly is easily established individually. 5. Conclusion This study demonstrates that a better spatial separation of atrial and ventricular areas, as well as an increased accuracy of the EIT method in measuring stroke volume, can be obtained by means of a new oblique electrode configuration. Further clinical research is necessary to validate the EIT method suitable for assessment of stroke volume. Acknowledgment This study was supported by Glaxo Wellcome plc, The Netherlands. References Bernstein D P 1986 Continuous non invasive real-time monitoring of stroke volume and cardiac output by thoracic electrical bioimpedance Crit. Care Med. 14 898–901 Bonjer F H, van den Berg J and Dirken M N J 1952 The origin of the variations of body impedance occurring during the cardiac cycle Circulation 6 415–20

188

A Vonk Noordegraaf et al

Brown B H, Barber D C, Morice A H and Leathard A D 1994 Cardiac and respiratory related electrical impedance changes in the human thorax IEEE Biomed. 41 729–34 Brown B H, Leathard A D, Sinton A M, McArdle F J, Smith R W M and Barber D C 1992 Blood flow imaging using electrical impedance tomography Clin. Phys. Physiol. Meas. A 13 175–9 Brown B H and Seagar A D 1987 The Sheffield data collection system Clin. Phys. Physiol. Meas. 8A 91–7 Ey¨uboˇglu B M, Brown B H and Barber D C 1988 Problems of cardiac output determination from electrical impedance tomography scans Clin. Phys. Physiol. Meas. A 9 71–7 ——1989 In vivo imaging of cardiac related impedance changes IEEE Eng. Med. Biol. Mag. 39–45. Guyton A C 1991 Textbook of Medical Physiology (Philadelphia, PA: Saunders) pp 170–83 Higginbotham M B, Morris K G, Williams R S, McHale P A, Coleman R E and Cobb F R 1986 Regulation of stroke volume during submaximal an maximal upright exercise in normal man Circ. Res. 58 231–91 McArdle F J 1992 Investigation on cardiosynchronous images of the heart and head using applied potential tomography Thesis University of Sheffield pp 70–82 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. Physiol. Meas. 12 393–402 Sakamoto K, Muto K, Kanai H and Lizuka M 1979 Problems of impedance cardiography Med. Biol. Eng. Comput. 17 697–709 Smith R W M, Freeston I L and Brown B H 1995 A real time electrical impedance tomography system for clinical use – design and preliminary results IEEE Trans. Biomed. Eng. 31 133–40 Snedecor G W and Cochran W G 1989 Statistical Methods (Iowa: Iowa State University Press) pp 183–6 Wang L and Patterson R 1995 Multiple sources of the impedance cardiogram based on a 3-D finite difference human thorax model IEEE Trans. Biomed. Eng. 42 141–8