3.1
In t r o d u c t io n
3.1.1
The need for a new reconstruction algorithm
Most EIT reconstruction algorithms, as reviewed in section 1.4, are intended to be used for imaging the thorax or abdomen. For example, it is justifiable to model the torso as a circular plane through a homogeneous cylinder. Such an approximation cannot be made for the head, which is inherently spherical and highly inhomogeneous. Any technique used for imaging impedance changes in the head should allow for the additional difficulties which arise, some o f which are listed below:
• The impedance changes are small - less than 5 % for evoked responses (Holder et al.
1996b) and 15 % in epilepsy in experimental rabbits (Rao 2000).
• This impedance change occurs in the brain, but the brain is surrounded by the skull and the scalp. The skull acts as a high resistance shell approximately 30 times as resistive as the scalp and brain (Geddes and Baker 1967), and the scalp acts a low resistance shunt path. Together, they have been shown to reduce the current density, and therefore sensitivity, in the neonatal brain by a third using adjacent current drive (McArdle et al. 1988).
• The geometry o f the head is inherently 3D - unlike other parts o f the body, it cannot be modelled as a 2D slice through a translationally invariant cylinder.
• The shape o f the head and the internal boundaries within it are complex. The skull has holes through it {e.g. the eye sockets, and the foramen magnum, through which the spinal cord passes) and the cortex is convoluted.
• There are practical problems in attaching electrodes to the head - adhesive electrodes cannot be used and contact must be made through the hair. This means that the data may be noisier than equivalent data obtained from elsewhere in the body
For the brain to be imaged successfully, a new reconstruction algorithm was required which was optimised for imaging through the skull and designed for imaging from a 3D sphere. Both o f these criteria had been realised previously, but no reconstruction technique had combined the two. The methods o f Bayford et al. (1996) and Morucci et al. (1995), described in section 1.4, were intended for imaging through the skull and imaging a 3D hemisphere, respectively.
3.1.2
Requirements for brain imaging
A reconstruction algorithm was therefore needed which was capable o f three-dimensional real-time imaging through the skull. The intended application was the imaging o f short-term functional brain activity, such as evoked responses and epilepsy. Both o f these consist o f a baseline resting period with no stimulus, followed by a localised impedance change o f less than 20 %, then recovery and more baseline. Hence, this application is ideally suited to linearised, dynamic imaging. The relative merits o f dynamic, linear algorithms and absolute, non-linear algorithms were discussed in section 1.3 but, briefly, non-linear algorithms can give images o f absolute impedance if the electrode positions and the geometry are known and the noise is low. Linear algorithms, used to acquire a dynamic image o f impedance change, are far more robust to measurement and modelling errors. Here, the impedance changes are expected to be 10 % or less, meaning that the signal-to-noise ratio is likely to be poor but also that the impedance change is likely to be within the linear range.
The head is inherently three-dimensional and a reconstruction method optimised for it must therefore take into account the three dimensional nature o f current flow. In this work, the head was modelled as a sphere with electrodes placed on the upper hemisphere. The optimum electrode positions and measurement combinations on a sphere are not known. In 2D, the sensitivity to a central impedance change is maximised when current is injected on opposite electrodes (Tarassenko 1985, Bayford et al. 1996). When electrodes are placed on the surface o f a hemisphere, where polar electrodes may not exist, the optimum measurement combinations are less easy to define.
3.1.3
Overview of this section
S. 1.3.1 C om parison o f three im aging techniques
The main aim o f this work was to design, implement and test a method for reconstructing images o f an impedance change within a sphere from measurements made on the sphere’s surface. The first step was to devise a system for placing and recording from scalp electrodes. Based on these electrode combinations and positions, a sensitivity matrix was calculated analytically using the solution to Poisson’s Equation for a homogeneous sphere. This matrix was then inverted using three different techniques - iterative inversion, singular value decomposition, and using the transpose o f the sensitivity matrix as an approximation to its inverse. These three techniques were compared by reconstructing images from simulated data
and from a hemispherical saline-filled tank. One technique was to be selected for extension to human imaging.
3.1 .3 .2 E ffect o f sku ll on im age q u ality
The brain is surrounded by the skull, which has a resistivity around 30 times that o f the brain and scalp (Table 1.1). In addition, the thickness and resistance o f the skull varies considerably between sites (Law 1993). Various studies have shown that the skull’s effect on current flow leads to a reduction in sensitivity and distortions in localisation. These effects were examined in this work using two saline-filled tanks: a hemispherical saline-filled tank with a shell o f plaster o f Paris was used to examine the effect o f a uniform, highly resistive barrier; whilst a head-shaped saline-filled tank, incorporating a real human skull, was used to investigate the effect o f the complex shape o f the head and skull on image quality.
3.1.3.3 Im plication s f o r human im aging
The reconstruction algorithm produced in this chapter was designed for imaging impedance changes in a sphere. This chapter concludes with some recommendations about extending this algorithm for human imaging, which is the subject o f Chapter 4.