electrical impedance tomography by yubenjoseph@gmail.com

VIEWS: 180 PAGES: 15

									Electrical Impedance Tomography                                                 Seminar’04




                                INTRODUCTION

To begin with, the word tomography can be explained with reference to ‘tomo’ and
‘graphy’; ‘tomo’ originates from the Greek word ‘tomos’ which means section or slice,
and ‘graphy’ refers to representation. Hence tomography refers to any method which
involves reconstruction of the internal structural information within an object
mathematically from a series of projections. The projection here is the visual information
probed using an emanation which are physical processes involved. These include
physical processes such as radiation, wave motion, static field, electric current etc. which
are used to study an object from outside.


Medical tomography primarily uses X-ray absorption, magnetic resonance, positron
emission, and sound waves (ultrasound) as the emanation.              Nonmedical area of
application and research use ultrasound and many different frequencies of
electromagnetic spectrum such as microwaves, gamma rays etc. for probing the visual
information. Besides photons, tomography is regularly performed using electrons and
neutrons. In addition to absorption of the particles or radiation, tomography can be based
on the scattering or emission of radiation or even using electric current as well.


When electric current is consecutively fed through different available electrode pairs and
the corresponding voltage, measured consecutively by all remaining electrode pairs, it is
possible to create an image of the impedance of different regions of the volume conductor
by using certain reconstruction algorithms. This imaging method is called impedance
imaging. Because the image is usually constructed in two dimensions from a slice of the
volume conductor, the method is also called impedance tomography and ECCT (electric
current computed tomography), or simply, electrical impedance tomography or EIT.




Dept. of EEE                                  1                      MESCE Kuttippuram
Electrical Impedance Tomography                                               Seminar’04




Electrical Impedance Tomography (EIT) is an imaging technology that applies time-
varying currents to the surface of a body and records the resulting voltages in order to
reconstruct and display the electrical conductivity and permittivity in the interior of the
body. This technique exploits the electrical properties of tissues such as resistance and
capacitance. It aims at exploiting the differences in the passive electrical properties of
tissues in order to generate a tomographic image.


Human tissue is not simply conductive. There is evidence that many tissues also
demonstrate a capacitive component of current flow, and therefore, it is appropriate to
speak of the specific admittance (admittivity) or specific impedance (impedivity) of
tissue rather than the conductivity; hence, electric impedance tomography. Thus, EIT is
an imaging method which maybe used to complement X-ray tomography (computer
tomography, CT), ultrasound imaging, positron emission tomography (PET), and others.




Dept. of EEE                                2                      MESCE Kuttippuram
Electrical Impedance Tomography                                                  Seminar’04




                 X-RAY COMPUTED TOMOGRAPHY

Projection radiography suffers from the loss of depth information and the difficulties of
detecting structural details that are partly hidden by overlying images of body areas that
are not of interest. This problem is solved by selectively recording an image of a single
plane in the body; the result is called a tomogram. An early technique of producing
sectional views is motion tomography. By defined motions of the X-ray tube and the film
during exposure, images are produced in which all but one predetermined plane are
blurred. Thus, the projection shows a single plane with an added, approximately constant
background intensity caused by the other planes. Contrast enhancement is not possible
with this technique.


X-ray computerized tomography is a scheme for imaging human body cross-sections
with very high resolution, so that the physician can view the structure of internal organs
for diagnostic purpose. The cross-section to be imaged is illuminated using a source of X-
rays. As the X-rays propagates through the tissues photons are continually lost from the
beam either due to absorption or due to scattering which accounts for a constant at each
point called the linear attenuation coefficient μ(x,y) of the tissues. The intensity of the
exciting X-rays are collected using a ring of detectors placed at the opposite side of the
X-ray source. The source detector arrangement is then rapidly rotated around the body
and data for various angles are taken. This probed visual information is called the
projection data which are actually the line integral of the attenuation coefficient of the
tissues. The problem here is to mathematically reconstruct the image function μ(x,y) from
the measured projection data. Drawbacks of this method are radiation hazards,
comparatively costly, only transverse sections can be imaged and a single parameter is
available for imaging.




Dept. of EEE                                  3                       MESCE Kuttippuram
Electrical Impedance Tomography                                                 Seminar’04




                MAGNETIC RESONANCE IMAGING

MRI is a clinically important medical imaging modality due to its’ exceptional soft tissue
contrast. This technique is based on the fundamental property that protons inherently
possess a magnetic moment and spin. When placed in a magnetic field the protons align
either parallel or anti-parallel to the magnetic field. In MRI, also referred to as Nuclear
Magnetic Resonance (NMR), the patient is placed inside a strong magnetic field that is
usually generated by a large bore superconducting magnet. Nuclear Magnetic Resonance
is utilized to obtain images as a function of proton spin density and relaxation times.


Application of a short pulse of circularly polarized radio frequency radiation, whose
magnetic field vector is perpendicular to the applied magnetic field of flux density B0,
causes the net magnetic component M to tilt away from the z-axis and rotate in the xy
plane at frequency ω0, called Larmour frequency. This represents a source of detectable
radiation at the frequency ω0. The recovery of the z-component gives rise to a signal,
which is characterized by two decay mechanisms that are represented by the longitudinal
and transverse relaxation times, T1 and T2 respectively. T2 relaxation, which is usually
considerably faster than T1 relaxation, is due to a loss in phase coherence between
neighbouring nuclei, caused by the local variations in the magnetic field, which arise
from a local, tissue dependent, variation in magnetic susceptibility as well as a non-
uniform magnetic field.


T1 relaxation is a result of the precessing nuclei losing their associated potential energy
due to the coupling with the magnetic moments of the surrounding nuclei. Because of the
nature of interaction, T1 provides information about vibrational motion in the lattice,
which in biological tissues is usually water. These relaxation times are characteristic of
different tissue types and can be measured by applying suitable sequences of RF pulses
and measuring the radio frequency NMR signals with a receiver coil.




Dept. of EEE                                 4                       MESCE Kuttippuram
Electrical Impedance Tomography                                                Seminar’04




Spatially resolved anatomical data sets are acquired by applying magnetic field gradients
across the patient that result in a measurable gradient in the Larmour frequency in one
plane, and a phase encoding gradient in the orthogonal plane. 2D Fourier transformation
yields a slice image of the plane of interest.


Among the reasons for the success of MRI as a diagnostic imaging tool are the high
resolution (sub mm.), complete non-invasiveness and very low risk. Disadvantages are
the high costs, bulkiness of the equipment, the requirement for the patient to stay still in
the magnetic field for up to half an hour and the problems associated with the presence of
high magnetic fields.




Dept. of EEE                                     5                  MESCE Kuttippuram
Electrical Impedance Tomography                                                 Seminar’04




                             DATA COLLECTION

Data are collected by applying a current to the object through electrodes connected to the
surface of the object and then making measurements of the voltage on the object surface
through the same or other electrodes. Although conceptually simple, technically this can
be difficult. Great attention must be paid to the reduction of noise and the elimination of
any voltage offsets on the measurements. The currents applied are alternating currents
usually in the range 10 KHz to 1 MHz. Since, tissue has a complex impedance; the
voltage signals will contain in-phase and out-of-phase components. In principle, both of
these can be measured. In practice, measurement of the out-of-phase (capacitive)
component is significantly more difficult because of the presence of the unwanted (stray
capacitance between various parts of the voltage measurement system, including the
leads from the data collection apparatus to the electrodes. These stray capacitances can
lead to appreciable leakage currents, especially at the higher frequencies, which translate
into systematic errors no the voltage measurements. The signal measured on an electrode,
or between a pair of electrodes, oscillates at the same frequency as the applied current.


Various data collection schemes have been proposed. Most data are collected from a two-
dimensional (2D) configuration of electrodes. The simplest data-collection electrodes
(often an adjacent pair) and measure the voltage difference between other adjacent pairs.
Although in principle voltage could be measured on electrodes through which current is
simultaneously flowing, the presence of an electrode impedance generally unknown,
between the electrode and the body surface means that the voltage measured is not
actually that on the body surface. However, in many systems, measurements from
electrodes through which current is flowing are simply ignored. Electrode impedance is
generally not considered to be a problem when making voltage measurements on
electrodes through which current is not flowing, provided a voltmeter with sufficiently
high input impedance is used, although since the input impedance is always finite, every
attempt should be made to keep the electrode impedance as low as possible. Using the



Dept. of EEE                                 6                      MESCE Kuttippuram
Electrical Impedance Tomography                                             Seminar’04




same electrode for driving current and making voltage measurements even at different
times in the data collection cycle, means that at some point in the data-collection
apparatus wires carrying current and wires carrying voltage signals will be brought close
together in a switching system, leading to the possibility of leakage currents. Thus,
separate sets of electrodes are used for driving and measuring in order to reduce this
problem.


Clearly, the magnitude of the voltage measured will depend upon the magnitude of the
current applied. If a constant current drive is used this must be able to deliver a known
current to a variety of input impedances with a stability of better than 0.1%. This is
technically demanding. The best approach to this problem is to measure the current being
applied, which can easily be done to this accuracy. These measurements are then used to
normalize the voltage data.




Dept. of EEE                               7                      MESCE Kuttippuram
Electrical Impedance Tomography                                               Seminar’04




            IMPEDANCE MEASUREMENT METHODS


The electric impedance may be measured either traditionally by pure electric methods or
by electromagnetic methods. In impedance tomography the current is fed and the voltage
is measured through different electrode pairs to avoid the error due to the contact
impedance. In spite of the problem of skin impedance, to obtain the greatest sensitivity to
changes in resistivity of the body, voltages from current carrying electrodes should also
be included. In the following, some of the measurement methods used are described.



A] NEIGHBOURING METHOD




Dept. of EEE                                8                      MESCE Kuttippuram
Electrical Impedance Tomography                                                Seminar’04




In this method, the current is applied through neighbouring electrodes and the voltage is
measured successively from all other adjacent electrode pairs. The above figure illustrates
the application of this method for a cylindrical volume conductor with 16 equally spaced
electrodes.


The current is first applied through electrodes 1 and 2, and, the current density is, of
course, highest between these electrodes, and decreases, and decrease rapidly as a
function of distance. The voltage is measured successively with electrode pairs 3-4,4-5,…
15-16. From these 13 voltage measurements the first four measurements are independent,
such that, the electrode used as driving electrode is not used for measuring the voltage.
Each of them is assumed to represent the impedance between the equipotential lines
intersecting the measurement electrodes. This is indicated by the shading, for the voltage
measurement between the electrodes 6 and 7. The next set of 13 voltage measurements is
obtained by feeding the current through the electrodes 2 and 3, as shown in figure 1(B).
For a 16-electrode system, 16*13=208 voltage measurements are obtained. Because of
the reciprocity, those measurements in which current electrodes and voltage electrodes
are interchanged yield identical measurement results. Therefore, only 104 measurements
are independent. In the neighbouring method, the measured voltage is at maximum with
adjacent electrode pairs, and is only about 2.5% of that, with opposite electrode pairs.




Dept. of EEE                                 9                      MESCE Kuttippuram
Electrical Impedance Tomography                                                Seminar’04




B] CROSS METHOD




A more uniform current distribution is obtained when the current is injected between a
pair of more distant electrodes. In the cross method, adjacent electrodes – for instance 16
and 1, as shown in figure 2(A) – are first selected for current and voltage reference
electrodes, respectively. The other current electrode, 2 is first used. The voltage is
measured successively for all other 13 electrodes with the aforementioned electrode 1 as
reference. The current is then applied through electrode 4 and the voltage is then


Dept. of EEE                                10                      MESCE Kuttippuram
Electrical Impedance Tomography                                             Seminar’04




measured successively for all the other 13 electrodes with electrode1 as a reference, as
shown in figure 2(B). One repeats this procedure using electrodes 6, 8,……14; the entire
procedure thus includes 7*13=91 measurements.


The measurement sequence is then repeated using 3 and 2 as the current and voltage
reference electrodes, respectively. Applying current first to electrode 5, one then
measures the voltage successively for all other 13 electrodes with electrode 2 as the
voltage reference. One repeats this procedure again by applying current to electrode 7.
Applying current successively to electrodes 9, 11,……1 and measuring the voltage for all
the other 13 electrodes with the aforementioned electrode 2 as a reference, one makes 91
measurements.


From these 182 measurements, only 104 are independent. The cross method does not
have as good sensitivity in the periphery as does the neighbouring method, but has better
sensitivity over the entire region.




Dept. of EEE                               11                     MESCE Kuttippuram
Electrical Impedance Tomography                                             Seminar’04




C] OPPOSITE METHOD




Another alternative for the impedance measurement is the opposite method. In this
method, current is injected through two diametrically opposite electrodes. The electrode
adjacent to the current-injecting electrode is used as the voltage reference. Voltage is
measured from all other electrodes except from the current electrodes, yielding 13
voltage measurements. The next set of 13 voltage measurements is obtained by selecting
electrodes 1 and 9 for the current electrodes. When 16 electrodes are used, the opposite
method yields 8*13=104 data points. The current distribution in this method is more
uniform and, therefore, has a good sensitivity.




Dept. of EEE                                12                   MESCE Kuttippuram
Electrical Impedance Tomography                                                Seminar’04




D] ADAPTIVE METHOD




In the aforementioned methods, current has been injected with a pair of electrodes and
voltage has been measured similarly. In the adaptive method, current is injected through
all the electrodes. Because current flows through all the electrodes simultaneously, as
many independent current generators are required, are the number of electrodes used. The
electrodes can feed a current -5 to +5 mA, allowing different current distributions.
Homogenous current distribution may be obtained only in a homogenous volume
conductor. If the volume conductor is cylindrical with circular cross-section, the injected
current must be proportional to Cosθ to obtain a homogenous current distribution. The
voltages are measured with respect to single grounded electrode. When 16 electrodes are
used the number of voltage measurements for a certain current distribution is 15. The
desired current distribution is then rotated one electrode increment. Thus, 8 different
current distributions are obtained, yielding 8*15=120 independent voltage measurements.


Several EIT systems apply current in a distributed manner, with currents of various
magnitudes being applied to several or all of the electrodes. These optimal currents must
be specified accurately, and again, it is technically difficult to ensure that the correct
current is applied at each electrode. Although there are significant theoretical advantages


Dept. of EEE                                13                      MESCE Kuttippuram
Electrical Impedance Tomography                                                Seminar’04




to using distributed current patterns, the increased technical problems associated with this
approach, and the higher noise levels associated with the increased electronic complexity,
may outweigh these advantages.


E] ELECTROMAGNETIC MEASUREMENT OF THE ELECTRIC
IMPEDANCE




Maxwell’s equations tie the time-varying electric and magnetic fields together so that
when there is an electric field, there is also a magnetic field and vice-versa. In the
electromagnetic measurement of the electric impedance, as in pure measurement, the
sensitivity distribution of the measurement is proportional to the dot product between the
electric current field in the volume conductor and the lead field of the voltage
measurement. This holds true irrespective of whether or not the electric current in the
volume conductor is generated through direct application of electric fields or is induced




Dept. of EEE                                14                      MESCE Kuttippuram
Electrical Impedance Tomography                                                 Seminar’04


by a time-varying magnetic field, and whether the detector is a magnetometer or a
voltmeter respectively.


One way to utilize the electromagnetic connection in the electric impedance
measurement is to feed the electric current to the volume conductor by means of
electrodes on its’ surface, but instead of detecting the generated voltage with a pair of
electrodes, the induced magnetic field is detected with a magnetometer. In this method,
the electric current distribution id irrotational (zero curl). The electromagnetic connection
may also be used the other way around in the measurement of the electric impedance of
the volume conductor. Due to the electromagnetic connection, the electric current may
also be induced to the volume conductor by a time-varying magnetic field generated by a
coil or a set of coils around the volume conductor.




Dept. of EEE                                 15                      MESCE Kuttippuram

								
To top