Electrical impedance tomography

To improve the reliability of the image or to selectively enhance parts of the image produced by way of a tomographic technique such as electrical impedance tomography (EIT), also known as applied potential tomography (APT), the method and apparatus of the invention provides that the electrical signal measurements be made over varying periods of time. The manner of variation can be related to the relative positions of drive and receive electrode pairs or to the output signal size, either as theoretically expected or as actually measured. The invention can be applied to serial or to parallel data collection techniques.

BACKGROUND TO THE INVENTION 
This invention relates to tomography and more particularly to the technique 
known variously as electrical impedance tomography or applied potential 
tomography referred to hereinafter as EIT. 
EIT involves the production of images representing the distribution of an 
electrical characteristic, such as electrical conductivity or resistivity, 
across a sectional plane of a body under investigation from measurements 
made on the periphery of the sectional plane. The technique finds 
application in non-invasive investigation of human patients, but may be 
applied to investigation of animals or of other bodies, such as geological 
masses. It is a relatively inexpensive method of tomography, allows 
continuous monitoring, and does not suffer from the biological hazards 
implicit in other procedures such as X-ray computed tomography. The 
technique is described in, for example, a paper entitled "Applied 
potential tomography" by D. C. Barber and B. H. Brown published in 
J.Phys.E: Sci.Instrum., Vol.17 (1984), pages 723-733, and in other papers 
referred to therein or published subsequently. 
In a typical application of EIT to a body an array of, say, sixteen 
electrodes is placed around the periphery of a body section such as the 
thorax. Electrical currents, from a constant current source of a few 
milliamps at a fixed frequency, are applied in turn to adjacent pairs of 
the electrodes (known as `drive pairs`) and for each applied current the 
real component of the potential difference is measured between the 
thirteen adjacent pairs of the fourteen other electrodes (known as 
`receive pairs`). Further measurements between non-adjacent electrode 
pairs are not required, as they would not represent independent data but 
could be obtained by linear combinations of the adjacent measurements. It 
is of course to be noted that drive pairs and receive pairs need not 
necessarily be made up of adjacent electrodes and that other combinations 
of electrodes can be used to gather the set of independent data. The 
resulting set of voltages from all thirteen receive pairs is referred to 
as a `data profile`. The measured values from all such data profiles are 
stored and processed to create a two-dimensional image of the resistivity 
distribution within the body. A static image may be created, showing the 
absolute value of tissue resistivity, or a dynamic image may be produced, 
displaying the changes in resistivity from a reference. The latter is the 
more clinically useful as changing features of the body such as cardiac 
activity and lung activity can be monitored. 
The EIT image is reconstructed by assuming the measurements have been taken 
around the periphery of a two dimensional homogenous circular conducting 
plane. The measured values are filtered to correct for blurring inherent 
in the imaging process and then backprojected along lines of 
backprojection to allow determination of the resistivity values within the 
conducting image plane. The final reconstructed image can then be 
displayed, the speed of image production depending on the data handling 
capacity of the image reconstruction system. The technique of 
backprojection is described more fully in U.S. Pat. No. 4,617,939, to 
which reference can be made for further details. 
The resolution of the image is restricted by the number of independent 
measurements available, in other words, by the number of electrodes 
employed. To improve image reconstruction speed, transputers are used for 
digital signal processing. In addition, the measurements of the voltages 
in all receive pairs can be made in parallel. Such parallel data 
collection allows each measurement to be made over a longer period and 
hence to a higher accuracy. Further details of this system can be found in 
WO91/19454. 
The image reconstruction technique briefly described above produces 
clinically valuable images. However, it is widely recognised that the 
reliability of the image is not constant over the entirety of the image 
plane because of the remoteness of the measuring points from the centre of 
the body section. The greatest uncertainty is found in the centre of the 
reconstructed image, since small errors in boundary measurements cause 
large errors in the reconstructed image data in that central area. In 
consequence, the signal-to-noise ratio (SNR) of the image is relatively 
high adjacent to the periphery and decreases towards the centre of the 
image. As a result, it is difficult to reliably detect small changes in 
the centre of the image. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to reduce the above-mentioned 
problem and to selectively enhance the image quality of part of an image 
and to this end there is provided according to one aspect of the invention 
a method of data collection for use in the construction of a tomographic 
image of a body comprising: 
placing a plurality of electrodes adjacent the surface of the body at 
spaced intervals on the body: 
applying, in successive manner through the electrodes, an electrical input 
signal to at least one electrode pair to generate a potential difference 
between other electrode pairs, and measuring at the said other electrode 
pairs; and 
measuring, at the said other electrode pairs and at each stage of the 
successive application of input signal, output signals representing an 
electrical characteristic of that body subjected to each applied input 
signal, wherein the measurements are made over varying periods of time. 
In one embodiment, the period of time over which each measurement is made 
is selected according to the relative positions of the electrode pair at 
which the signal is measured and the electrode pair at which the 
electrical input signal is applied. Preferably, for the purposes of time 
weighting, the period of time over which each measurement is made is 
selected according to a theoretically expected signal size based on said 
relative positions. 
Alternatively, the period of time over which each measurement is made is 
selected according to the size of the measured output signal. 
The manner of variation of the measurement time periods is chosen to 
improve image quality in a preselected part of the image. 
For each stage of the successive application of input signal the output 
signals at the other electrode pairs may be measured in parallel. 
In the case of parallel data collection, it is preferred that the applied 
input signals are applied simultaneously at different electrode pairs at 
different frequencies, whilst the output signals are measured 
simultaneously at selected other electrode pairs at corresponding 
frequencies. 
According to another aspect of the invention there is provided apparatus 
for data collection for use in the construction of a tomographic image of 
a body comprising: 
a plurality of electrodes applicable adjacent the surface of the body at 
spaced intervals on the body; 
means for applying, in successive manner through the electrodes, an 
electrical input signal to at least one electrode pair to generate a 
potential difference between the other electrode pairs; and 
means for measuring, at the other electrode pairs and at each stage of the 
successive application of the input signal, output signals representing an 
electrical characteristic of the body subjected to each respective applied 
input signal, wherein said means for measuring comprises means for varying 
the periods of time over which the measurements are made. 
A longer period of measurement can therefore be used for the smaller 
signals, and this results in the noise element of the signal, which is a 
random fluctuation, being reduced, as the measurement recorded represents 
an average over that period. If the noise is Gaussian then the SNR will 
improve in proportion to the square root of the integration time. For 
small signals, lower noise levels are obtained and thus, in the case of a 
substantially circular body section, say, more accurate measurements 
representing information about the centre of the image are made.

FIG. 1 illustrates the technique of back projection as applied to a 
circular plane of uniform conductivity with 16 electrodes regularly spaced 
around its periphery. The curved lines represent isopotentials for the 
electrode drive pair 1/2, shown as a dipole D, and it is along such lines 
that actual measured signals can be backprojected to locate the 
resistivity values at points within the plane. Once all the measurements 
have been made for all the alternative drive pairs, and the data filtered, 
the resistivity images from each data profile are produced and 
superimposed in a weighted manner to create the image data. 
Of course, other methods of image reconstruction other than that referred 
to above and illustrated in FIG. 1 are possible, and it is to be 
understood that the applicability of the present invention is in no way 
limited to any particular technique of reconstruction that may be used. 
Clearly when the uniform circular plane of FIG. 1 is considered the signal 
amplitude measured at the different electrodes will be a function of the 
distance from the drive pair, the weakest signal being that detected at 
the electrodes on the opposite side of the circular plane. This 
distribution of signal amplitudes is represented in the graph of FIG. 2, 
the signal amplitude being shown on the vertical axis and the electrode 
position around the circumference of the circular plane being shown on the 
horizontal axis, channel number 1 representing the receive pair 1/2, and 
so on. 
As a result of this uneven distribution of signal amplitudes, and assuming 
uniform noise from the different measurements, the signal-to-noise ratio 
(SNR) is correspondingly lower for those measurements made on the opposite 
side of the circular plane from the drive pair, such as electrodes 9 and 
10 in this example. Actual measured signals representing resistivity 
information about points within the body plane in the area shown shaded in 
FIG. 1 will have the lowest SNR. As can be seen this area includes the 
central region of the plane and more peripheral parts of this shaded area. 
As the other adjacent pairs of electrodes are subsequently used as drive 
pairs more information is gathered about the more peripheral areas of the 
plane, but points within the more central region of the body plane always 
result in detected signals having the lowest SNR. This is the reason for 
high noise and hence low signal reliability for pixels within the central 
region of the image. 
By making use of the method of the invention the SNR can be increased for 
this central region by spending a longer period of time making each 
measurement if that measurement contains information about the central 
region. In other words, within each data profile the period of time over 
which each measurement is made, or dwell time, is dependent on the 
electrode pair position where the measurement is made. The total time for 
gathering the data profile is maintained by correspondingly reducing the 
dwell time for receive pairs close to the drive pair, and therefore at 
least partially balancing the SNR across the image. 
The most basic EIT data collection system involves serial data collection, 
whereby, for each data profile, measurements are made from the receive 
pairs in a sequence progressing around the circumference. This is 
accomplished by switching the inputs to amplifiers of the data acquisition 
system according to a stored switching sequence. Using such a system the 
invention is utilised by programming a new switching sequence, the dwell 
times being determined from, say, the theoretical signal amplitude 
distribution of FIG. 2, such that the data collection interval is 
proportional to the inverse of the theoretical signal amplitude and the 
total data collection time is substantially unchanged. The technique 
requires no new equipment over that conventionally used for EIT systems, 
but simply requires a modified switching sequence. 
In actual fact, two factors dominate the unequal SNR across an EIT image. 
The dynamic range of the signals is one factor, and the other is the 
weighting process implicit in the reconstruction algorithm. Modifying the 
dwell times according to the theoretical signal amplitudes will not in 
fact equalise the noise distribution across the image, due to this second 
factor. However in practice modifying the dwell times even in this simple 
manner does produce a considerable improvement in image quality in the 
central region of the image. 
As an example, a 50 kHz signal is supplied from a controlled current source 
with a constant peak-to-peak amplitude of 5 mA. To achieve a image display 
speed of 25 frames per second a frame interval of 40 ms is required. For a 
sixteen electrode system each data profile must therefore be collected in 
2.5 ms, allowing an average dwell time of 192 .mu.s for each measurement. 
By modifying this dwell time depending on the position of the receive pair 
relative to the drive pair by a factor determined by, say, the theoretical 
signal amplitude as explained above, the equalisation of the noise 
elements of each data profile can be significantly improved. 
More recent EIT data collection systems involve parallel data collection to 
increase the speed of data acquisition. In such systems a constant current 
generator is multiplexed between adjacent electrode pairs and differential 
amplifiers are placed between all such electrode pairs, allowing 
simultaneous collection of data from each data profile. In this way, for a 
certain frame interval, a longer dwell time is available for each voltage 
measurement. 
Using such a system the invention can be utilised by successively 
reallocating amplifiers to more remote pairs as they are switched out from 
the more adjacent ones, in a sequence selected to collect the data in the 
most efficient way whilst ensuring the desired dwell times are maintained 
for each measurement. In this way two or more amplifiers are used to make 
measurements of the smaller signals, whereas only one would be used to 
measure the largest signals. When the entire image set is collected, the 
SNR of the data containing information about the more central regions of 
the body will therefore be higher. 
Alternatively a multifrequency system is employed using interleaved drive 
and receive pairs. With this system, each drive pair and each receive pair 
is operable at any one of a number of frequencies. Measurements can 
therefore be made in parallel between different drive and receive pairs by 
operating simultaneously at the different frequencies. 
For example, in a 16 electrode system electrode pairs 1/3, 3/5, 5/7 etc. 
can each be arranged to be driven at any one of a number of eight 
frequencies f1 to f8. Electrode pairs 2/4, 4/6, 6/8 etc. can be used as 
receive pairs each at any one of frequencies f1 to f8. The data collection 
is made as follows: 
______________________________________ 
Drive Receive 
______________________________________ 
1/3 at f1 4/6 at f1 
3/5 at f2 6/8 at f2 
5/7 at f3 8/10 at f3 
.dwnarw. .dwnarw. 
15/1 at f8 2/4 at f8 
______________________________________ 
The above represents a single period of measurement, and since all the 
corresponding drive and receive pairs are separated by a relatively short 
peripheral distance the signals will be large and a short dwell time can 
be selected. The next data collection set is made as follows: 
______________________________________ 
Drive Receive 
______________________________________ 
1/3 at f1 6/8 at f1 
3/5 at f2 8/10 at f2 
5/7 at f3 10/12 at f3 
.dwnarw. .dwnarw. 
15/1 at f8 4/6 at f8 
______________________________________ 
These will be smaller signals so a longer dwell time is selected. The 
process is continued, each data collection period being used to measure 
signals in parallel from drive pairs and receive pairs separated by the 
same peripheral distance, and the dwell time for each collection period 
being predetermined according to this distance. The final data collection 
set of the above sequence will be as follows: 
______________________________________ 
Drive Receive 
______________________________________ 
1/3 at f1 14/16 at f1 
3/5 at f2 16/2 at f2 
5/7 at f3 2/4 at f3 
.dwnarw. .dwnarw. 
15/1 at f8 12/14 at f8 
______________________________________ 
The data collection time for this final set will be the same as that for 
the first set of the sequence as the drive pair-receive pair separation is 
identical. 
This technique gives a complete data set of 384 (8*8*6) measurements. 
Separate generators are required for each of the drive pairs, but the 
system does not involve the switching of amplifiers from one electrode 
pair to another, merely the switching of frequencies received at different 
times. 
The methods of data collection described above suggest modifying the dwell 
time for each measurement, according to the position of the receive pair 
relative to the drive pair, by an amount determined by the theoretical 
signal size. Alternatively, the dwell time for each measurement can be 
controlled on the basis of the amplitude of each signal as measured, as it 
has been observed that theoretical and measured signals can differ, 
especially where the expected signal is large. 
A series of experiments was conducted by the inventors to investigate the 
spatial distribution of noise in images from a saline-filled tank and to 
test a noise equalisation method according to the invention, such method 
depending on choosing a longer dwell time for smaller signals. 
Test data was collected from a circular cylindrical saline filled tank with 
16 brass electrodes equally spaced around its circumference, The tank 
diameter was approximately 152 mm. The saline solution extended 155 mm 
above and 90 mm below the electrode plane with 2 mS/cm conductivity at 
25C. 
Two groups of tank data were collected for both the noise distribution 
study and the equalisation experiments. Each group of data contained 6000 
frames of 104 measurements collected at 25 frames per second. The first 
group of data was collected from the saline filled tank without any object 
and the second data set with a plastic rod (10 mm diameter) introduced at 
38 mm from the edge of the tank. 
The noise distribution of both the measured voltages and the reconstructed 
image pixels was determined by calculating the root-mean-square (RMS) 
noise and the signal-to-noise ratio. 
The noise distribution of the measurements of voltage between the 
electrodes around the tank was calculated as the ratio of the standard 
deviation to the mean of the measurements of each voltage difference over 
the 6000 frames of the first group of data. It was found that the SNR on 
the smallest voltage measurements was about 10 dB worse than that of the 
largest voltage measurements. The largest voltages are those recorded 
close to the electrodes through which current is being injected and the 
smallest are those on the other side of the tank. 
Having reconstructed the frames as images, using the first frame as a 
reference, the RMS noise at each of the 16 pixels across a diameter of the 
images was computed as the standard deviation of the pixel value over the 
6000 images. Two image reconstruction algorithms were used, referred to 
henceforth as the Mk 1 and the Mk 2 algorithms. The Mk. 1 algorithm is 
described in Barber D C and Brown B H, 1986, Recent developments in 
applied potential tomography, information Processing in Medical Imaging, 
ed. S Bacharach (Dordrecht: Martinus Nijhoff), pp 106-21, whilst the Mk 2 
algorithm is described in Barber D C and Brown B H, 1990, Progress in 
electrical Impedance tomography, Inverse Problems in Partial Differential 
Equations, ed. D Colton, R Ewing and W Rundell (Philadelphia: SIAM), pp 
151-64, and in Barber D C and Brown B H, 1990, Reconstruction of impedance 
images using filtered back projection, Proc. CAIT Meeting on Electrical 
Impedance Tomography (Copenhagen), pp 108. These two reconstruction 
algorithms differ in that the second gives a better and more uniform point 
response function than the first. Results showed that the RMS noise at the 
centre was about 20.4 dB and 29.5 dB worse than at the edge when using the 
Mk 1 and Mk 2 reconstruction algorithms respectively. 
In order to find out how uniform the image noise would be with perfect 
data, 6000 frames with added noise to give a standard deviation of 0.1 on 
all voltages were simulated. These frames were reconstructed to produce 
6000 images using both the Mk 1 and Mk2 reconstruction algorithms. By 
measuring the RMS noise on the 16 pixels crossing the diameter, it was 
seen that the noise on the central pixels was about 3 times and 10 times 
higher than on the edge pixels, when using the Mk 1 and Mk 2 
reconstruction algorithms respectively. It was concluded that the unequal 
distribution of noise in images from the tank is caused both by variations 
in SNR on the measured voltages and on the image reconstruction algorithm 
used. It might also be inferred that there is a distribution of signal to 
noise ratios on the measured voltages which would give rise to uniform 
noise in the reconstructed images. 
Various ways of implementing noise equalisation were then tried and the 
results compared. It was found that a ratio of 49 to 1 (Table 1) between 
the dwell times for the smallest and largest signals respectively gives a 
large improvement in the image noise uniformity but the noise is still 
worse in the middle than at the edge of the image. Larger ratios could be 
used but these may not be practical. A ratio of about 49 to 1 is a 
realistic ratio that could be implemented on a serial data collection 
system running at 10 frames per second by spending about 30 .mu.s on the 
large measurements and 1500 .mu.s on the small ones. As most EIT systems 
use frequencies of about 50 kHz with a period of 20 .mu.s, larger ratios 
would not give enough time to make the larger measurements. Also, for a 49 
to 1 ratio, it was found that the SNR improvement was almost linearly 
proportional to the square root of the collection time, but for much 
larger ratios this was not the case because the noise is not strictly 
Gaussian. 
TABLE 1 
______________________________________ 
RESULTS OF NOISE EQUALISATION SCHEME 
IMAGE SNR IMAGE SNR 
DATA SET Improvement Improvement 
Y Dwell Time (Theoretical) 
(Measured) 
______________________________________ 
1 largest 
1 0 dB edge 0 dB edge 
2 4 6.0 dB 5.9 dB 
3 9 9.5 dB 9.5 dB 
4 16 12.0 dB 11.9 dB 
5 25 14.0 dB 13.8 dB 
6 36 15.6 dB 15.4 dB 
7 smallest 
49 16.9 dB centre 
16.5 dB centre 
______________________________________ 
This shows the results of applying noise equalisation to images 
reconstructed using the Mk 1 algorithm. Y lists the measurements from the 
largest (adjacent to the current injection pair) to the smallest (on the 
opposite side of the tank). The system uses 16 electrodes such that one 
profile is of 13 measurements. By varying the dwell times as shown an 
increasing improvement in SNR is obtained from the edge to the centre of 
the image. 
Using a ratio of 49 to 1 the improvement in central noise is 16.5.+-.0.3 dB 
and 15.6.+-.0.4 dB using the Mk 1 and Mk 2 reconstruction algorithms 
respectively. After noise equalisation, the RMS noise at the image centre 
relative to that at the edge drops from 15 to 2.2 times and from 30 to 5.0 
times when using the Mk 1 and Mk 2 reconstruction algorithms respectively. 
It is difficult to produce a completely uniform noise distribution but it 
is possible to make a very significant improvement in the noise 
uniformity. 
FIGS. 3 and 4 show the results of noise equalisation on the images of the 
plastic rod in the tank, using the equalisation scheme shown in Table 1, 
with Mk 1 and Mk 2 reconstruction algorithms respectively. 
FIG. 3a shows the standard deviation over the images before the 
equalisation, whilst FIG. 3(b) shows that after the equalisation. FIG. 
3(c) shows the SNR before the equalisation whilst FIG. 3(d) shows that 
after the equalisation For a particular pixel, the SNR is given by the 
mean signal value divided by the standard deviation. The improvement in 
the SNR over the central region is very clear. FIGS. 4(a) to 4(d) show 
equivalent spatial plots for images reconstructed using the Mk 2 
algorithm. Again, the improvement in the SNR is clear, but the noise 
distribution is in fact less uniform than in FIG. 3. These figures 
illustrate the significance of the reconstruction algorithm and show how 
the weighting implicit in the algorithm can affect the uniformity of noise 
across the image. 
It is further possible using the method of the invention to specifically 
alter the dwell times in order to target selected areas of the image and 
thereby increase the SNR and enhance the image in that selected area. For 
example, at the expense of image quality in other parts of the image, the 
distribution of dwell times can be computed to specifically target the 
lungs. 
The embodiments of the invention described above are given by way of 
example only and it should be understood that these are not intended in 
any way to limit the scope of the invention.