Image Reconstruction for 3D Lung Imaging - Department of Systems ...

is selected, measurements are taken using only the remaining N − 2 electrodes. This allows
N −3 possible voltage measurements to be made using a single reference. The total number
of measurements possible is therefore N(N −1)(N −3)/2. For n = 16 this is 1560 individual
measurements. Any combination of electrode pair voltages can be reconstructed from this
basic set. This number of measurements is valid for any electrode spatial arrangement such
as 2D tomographic, 3D, and planar. Of these possible pairs only a subset are typically used.
The typical subsets used have been dictated in the past more by timing and system design
configurations more than anything else.
The next sections discuss the most well known current injection patterns for 2D configurations.
In 2D configurations the electrodes define a boundary encompassing the domain of
interest. Here there are as many electrodes as there are electrode pairs, with each pair defined
as being the neighbours along the boundary path. The electrodes in this configuration
also define a plane of intersection with the object being imaged.
2.5.1.1 Adjacent Pattern
The adjacent drive method [16], also known as the neighbouring method, is the most common
pair drive protocol. As can be seen in figure 2.2, current is applied through two
adjacent electrodes and the voltages measured from successive pairs of adjacent electrodes.
Current is then applied through the next pair of electrodes and the voltage measurements
repeated. The procedure is repeated until each possible pair of adjacent electrodes has been
used to inject current.
The adjacent measurement strategy provides N 2 measurements, where N is the number
of electrodes. However to avoid the problem of unknown contact impedance, the voltage is
not measured at a current injecting electrode thus the number of measurements is reduced to
N(N − 3). The four-electrode reciprocity theorem [38][55] states that for any measurement
set the mutual impedance is preserved under an interchange of injection and measurement
pairs. Therefore only N(N − 1)/2 of the measurements are independent. However, it is
common to use all N(N − 3) measurements in most reconstruction algorithms. Thus a 16
electrode system will produce 208 measurements of which 104 are independent but all 208
are used in the reconstruction algorithm.
The adjacent strategy requires minimal hardware to implement. With the adjacent
strategy current is driven mainly in the outer region of the imaged object. The current
density is highest between the injecting electrodes, and decreases rapidly as a function of
distance. The method is therefore very sensitive to conductivity contrasts near the boundary
and insensitive to central contrasts. It is also sensitive to perturbations in the boundary
shape of the object, in the positioning of the electrodes and is quite sensitive to measurement
error and noise [43].
A feature of adjacent drive protocol is that on a two dimensional domain the adjacent
voltage measurements are all positive. This can be seen in figure 2.8(a) which shows that
the potential is monotonically decreasing from source to sink. The resulting measurements
will have a ‘U’ shaped graph for each drive as shown in figure 2.8(b).
2.5.1.2 Opposite Pattern
The opposite or polar drive pattern [14], which is commonly used in brain EIT [20], applies
current through electrodes that are 180 ◦ apart while voltage differences are measured on
the remaining electrodes. There are various ways to collect the voltage measurements. The
most common appears to be to use the electrode adjacent to the current-injecting electrode
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