coefficient. That is, if N0(y, z) monoenergetic
x-ray photons traverse the body along a line in the x
direction after entering the body at coordinates (y, z),
the number emerging without interaction is N(y, z) =
N0(y, z)e−α(y,z), where
α(y, z) = _ μ(x, y, z) dx.
The radiograph measures N(y, z) or α(y, z). The desiredinformation is μ(x, y, z). The radiographic image is often
difficult to interpret because of this integration along x.
For example, it may be difficult to visualize the kidneys
because of the overlying intestines.
Several types of computed tomography (tomos means
slice) have been developed in the last few decades. They
include transmission computed tomography (CT), singlephoton
emissioncomputed tomography (SPECT), and
positron emission tomography (PET). They all involve reconstructing,
for fixed z, a map of some function f(x, y)
from a set of projections F(θ, x), as described in Secs.
12.4 and 12.5. For CT the function f is the attenuation
coefficient μ(x, y). For SPECT and PET it is the concentration
of a radioactive tracer within the body, as will be
described in Chapter 17.The history of the development of computed tomography
is quite interesting [DiChiro and Brooks (1979)]. The
Nobel Prize in Physiology or Medicine was shared in 1979
by a physicist, Allan Cormack, and an engineer, Godfrey
Hounsfield. Cormack had developed a theory for reconstruction
and had performed experiments with a cylindrically
symmetric object that were described in two papers
in theJournal of Applied Physics in 1963 and 1964.
Hounsfield, working independently, built the first clinical
machine, which was installed in 1971. It was described in
1973 in the British Journal of Radiology. The Nobel Prize
acceptance speeches [Cormack (1980); Hounsfield (1980)]
are interesting to read. A neurologist, William Oldendorf,
had been working independently on the problem but did
notshare in the Nobel Prize [See DiChiro and Brooks
(1979), and Broad (1980)].
Early machines had an x-ray tube and detector that
moved in precise alignment on opposite sides of the pa-
FIGURE 16.28. A spiral CT scan of the abdomen. The arrow
points to a biliary cystadenoma, a benign tumor of the liver.
Scan courtesy of E. Russell Ritenour, Ph.D., Department of
Radiology, University ofMinnesota Medical School.
tient to make each pass. The size of these machines allowed
only heads to be scanned. After one pass, the
gantry containing the tube and detector was rotated 1 ◦
and the next pass was taken. After data for 180 passes
were recorded, the image was reconstructed. A complete
scan took about 4 minutes. Modern CT units use an array
of detectors and a fan-shaped beam that coversthe
whole width of the patient. The scan time is reduced to
a few seconds. Figure 16.27 shows the early evolution of
the scanning techniques.
On modern machines all of the electrical connections
are made through slip rings. This allows continuous rotation
of the gantry and scanning in a spiral as the patient
moves through the machine. Interpolation in the direction
of the axis of rotation(the z axis) is used to perform the
reconstruction for a particular value of z. This is called
spiral CT or helical CT. Kalender (2000) discusses the
physical performance of CT machines, particularly the
various forms of spiral machines. Array detectors are now
used to fill in the space between the spirals. Table 16.3
shows how scanners have improved since they were first
introduced.Spiral CT provides μ(x, y, z), and the images
can be displayed in three dimensions.
Figure 16.28 is an abdominal scan showing a benign
tumor in the liver. Computer analysis of μ(x, y, z) data
can be used to display 3-dimensional images of an organ
(Fig.16.29). The surface of an organ is defined by a change
It is often desirable to measure the attenuation coefficient
with an accuracy of...