ELECTRICAL IMPEDANCE TOMOGRAPHY
CHAPTER 1: PRINCIPLES OF ELECTRICAL IMPEDANCE
Bioimpedance: Principles
The concept of electrical impedance is a generalization of the concept of
electrical resistance, useful to describe the laws that govern the passage of
alternating current through a structure or tissue. Besides the intuitive concept of
resistors (essential to describe the behavior of current), it is necessary to grasp
the concept of capacitors (structures that act as temporary storage of electrical
charge) to understand the behavior of alternating currents.
Any structure or biological tissue is a composition of resistors and capacitors.
This composition is related to the tissue architecture, which determines the
greater or lesser difficulty for the passage of current. For the same intensity of
current applied, the greater the difficulty (impedance) to the passage of current,
the greater is the voltage gradient through the structure. Numerically, electrical
impedance is the difference in voltage between two points of injection, divided
by the intensity of the resulting current between these two points. It is
expressed by a complex number, the real part of which corresponds to the
electrical resistance, and the imaginary part, to the reactance (= inverse of
capacitance).
All devices that use the principle of electrical impedance - from body fat meters
to the impedance tomography - use the measurements of voltages or voltage
gradients which result from the injection of low-amplitude alternating currents.
During the measurement of body fat, or for the detection of tumors, for example,
it may be interesting to estimate the contribution of the impedance components
(resistance and reactance) in order to estimate the greater or lesser presence of
cells in tissues (the cell membranes act as capacitors). Therefore, for these
purposes, a system able to inject current and measure the voltages in a wide
range of frequencies (5 to 1000 kHz) is generally used. A sharp fall of total
impedance with increasing frequency suggests a higher capacitance and
therefore a higher cellular content.
TIMPEL: PRINCIPLES OF EIT 1 For applications in respiratory medicine, we usually measure total impedance,
without concern for its components, assuming that the entry of the air into the
lungs causes mainly a change in the resistance of the lung. Thus, these devices
usually work at a pre-determined and fixed frequency, usually around 50-100
kHz.
With very high frequencies of the injected current, there is virtually no damage
to biological tissues and little interference with the cardiac electrical activity.
How EIT works
EIT commonly uses the injection of high-frequency (> 10 kHz) and low
amplitude (< 12 mAmp) currents applied to the thorax through 8 to 32
electrodes. The electrodes are arranged circumferentially around the chest
delimiting a transverse or axial plane that is represented in the image
reconstruction of the lungs. The electric currents injected on the thoracic
surface follow paths that vary according to the distribution of the tissue inside
the thorax as well to the conformation of the chest. In general, multiple points of
injection are used simultaneously or sequentially in order to generate multiple
perspectives. The most common configuration uses only two electrodes at a
time to inject the currents (one electrode for injection and one for current
drainage). However, there are devices that inject current through several
electrodes simultaneously. The voltages measured in the other (non-injecting)
electrodes on the surface of the chest are used to feed an image reconstruction
algorithm that solves a mathematical inverse problem, nonlinear and ill-posed.
Ill-posedness translates a situation on which the solution (the estimated image)
for the distribution of impedances may not be unique, and may be unstable:
small errors in voltage measurement can result in significantly different
solutions. This problem is compounded by the relatively small number of
independent measures on the surface of the chest (usually 104 to 464,
depending on the number of electrodes), a number well below the number of
pixels in the reconstructed image. The only present limitation to obtain a larger
number of independent measures is the technical difficulty to reduce the size of
the electrode: the “amount” of currents injected through small electrodes is
limited and leads to worse signal-to-noise ratios. With improvements in the
technology of the electrodes, it will soon be possible to have a greater number
of electrodes, possibly in multiple planes, allowing a greater number of
perspectives and image reconstructions with higher spatial resolution. In order
to overcome the ill-posed nature of impedance estimation, most EIT imaging
algorithms make use of additional assumptions, known as regularizations, such
as
smoothness
of
the
intrathoracic
impedance
distribution.
These
regularizations help the estimation algorithm to decide between competing
solutions, producing an image that is a reasonable estimation of the true
impedance distribution within the thorax, at the expense of degraded spatial
resolution or attenuation of maximum perturbations
TIMPEL: PRINCIPLES OF EIT 3