Modified Spectral Expansion Images
Both images and quantitative measurements made on the images will be affected by errors associated with the electrode positions. A modified reconstruction that minimises the effect of the electrode positions should produce the most reliable clinical results. To establish if a modified spectral expansion reconstruction is more robust than the standard reconstruction algorithm, a number of clinical applications were investigated using the two spectral expansions.
For cardio-pulmonary investigations the electrodes were placed in a transverse ring around the normal test subject, at the level of the base of the sternum, and a maximum frame rate of ten frames per second was used.
Measurements made on the thorax contain information about ventilation, perfusion and other physiological processes that cause responses which can be measured as changes in conductivity. Fortunately these processes occur at different frequencies. Therefore by applying frequency filters, much of the unwanted signal can be removed. To do this the data are first converted to the frequency domain by a Fast Fourier Transform (FFT). Band pass filters, whose ends are smoothed by half periods of a sine wave, are used to filter the data in order to reduce the corruption of the data that would otherwise be created by using a simple straight edged band pass filter. After filtering the data are converted back to the temporal domain. Data are then averaged over a number of cardiac cycles, measured using an ECG R-wave trigger that records the R-wave activity during clinical studies. The cardiac cycle image sequences are produced by averaging the data into 10 bin vectors, each 0.1 seconds long with the R-waves occurring at me index zero seconds. With the reference frame set as the R-wave frame, perfusion image sequences starting from the R-wave are created.
The effect of switching to the modified spectral expansion is to generate images of the heart with smaller changes in resistivity, larger FAHM (full image area at half maximum change in resistivity), and improved separation of the two lungs (see pdf image sequence - data from a normal). In the standard spectral expansion images the two lungs can only be differentiated from time index 0.3 seconds onwards, but in the modified spectral expansion the two lungs can be differentiated virtually throughout the perfusion cycle. Furthermore the magnitude of the changes in impedance are closer in the two lungs in the modified spectral expansion image sequences. Some improvements in artefact size and quantity were also observed.
The ventilation data is obtained by filtering, in a similar manner to the way the perfusion data was extracted from the whole data set. Data were recorded from a normal who was standing. Breathing was normal tidal flow; the reference frame was that taken from the start of the data acquisition. Increases in lung resistivity due to the more resistive air entering the lungs during one ventilation cycle are shown in this pdf file. The changes observed are those from residual volume to full inhalation and back to residual volume again. The left lung FAHM is not as large as that for the right lung, because the heart has displaced the lung at this level in the body. This is confirmed by the position of the heart in the perfusion images (pdf perfusion image sequence). The modified spectral expansion ventilation images show relative changes of smaller magnitude, but the FAHM of the lungs are greater than for the standard spectral expansion images. Furthermore the artefacts are less well defined and the left lung is less fragmented in the modified spectral expansionimages.
For gastric studies the electrodes were arranged in a transverse plane mid way between the umbilicus and the base of the sternum (level of the xiphoid process), and the data collection rate was set at one frame every two seconds. Subjects were seated, breathing was normal tidal flow. No acid suppression was used. A baseline set of data were recorded before the start of the clinical test, and this data was averaged to produce a mean reference frame. The clinical test involved the patient ingesting a conductive meal and remaining seated and static for the whole data acquisition period. Since the physiological processes being studied are slow, data were averaged over every five frames of data to increase the signal to noise ratios.
Sequences of images were used to determine the length of the data baseline period, therefore without averaging. An example image sequence generated using the modified spectral expansion is included as a pdf file. The first image, time index 560.0 seconds , shows the fluctuations that occur in a fasted stomach before the start of the test and the final image, time index 760.0 seconds, shows the changes in resistivity associated with a conductive meal in the stomach. As seen in the previous results the effects of switching to the modified spectral expansion were a lower peak resistivity change, and larger FAHM. These images generally contain fewer and less intense artefacts than the standard spectral expansion images.
The Sheffield algorithm reduces the dependence of the reconstructed images on the electrode positions, provided the reference and measurement data set are recorded with the electrodes in the same positions. However small errors will still be introduced due to the non-uniform placement of the electrodes around the periphery of the conductivity distribution. The errors will be larger when the electrodes are allowed to move between measurements, for example when EIT is used to monitor patients for long periods. A modification to the Sheffield approximation has been suggested to further reduce the sensitivity of the reconstruction process to the electrode positions. The inverse eigenvalues used in the reconstruction process, calculated using the singular value decomposition of the Jacobian matrix, were replaced by a new set of values derived by minimising the changes in the Jacobian due to non-uniform placement of the measurement electrodes. A major advantage of using these new values is that there is no need foa regularisation filter, to control noise in the images, since the new values were designed to preferentially select those basis images that are least sensitive to electrode positions and are already constrained by the minimisation process. The main consequences of this change are that images with reduced dynamic range are produced, the number of artefacts and their magnitude are generally reduced, and the FAHM of the images are larger. Therefore there appears to be a trade off between image dynamic range and the sensitivity of the reconstruction to the electrode positions. The increased FAHM lead to smaller errors in region of interest measurements, because a larger area is used, reducing the finite element discretisation errors caused by including border line pixels. This is confirmed by increased signal to noise ratios for region of interest integral measurements made on perfusion images.
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Last modified 11th November 2009