Biomedical Engineering Reference
In-Depth Information
the image. Thus, three-dimensional information about anatomy is
lost. Computed tomography was an enormous technical breakthrough.
Using X-ray projection measurements taken from all around the
patient's body, CT computes a property of the patient at every point
within 3D space to within a spatial resolution of, typically, a milli-
meter or less. By doing so, CT largely eliminates the confusion of
tissues caused by the unavoidable superposition of information in
radiographs. The property which is measured is the linear X-ray
absorption coefficient of the tissue at a given point relative to the
linear X-ray absorption coefficient of water. This is expressed in so-
called Hounsfield units (HU), named after one of the inventors of CT.
The HU scale is air: -1000, and water: 0. To the extent that the X-ray
absorption coefficients of tissues vary from one another, one can then
identify the extent of a particular tissue in all three dimensions.
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The basis of tomographic reconstruction
How is it possible to reconstruct 3D information from projections?
First, CT uses a trick which immediately reduces the problem by one
dimension. Namely, it makes its measurements in “slices” through
the patient. An X-ray beam is collimated by a slit and the transmitted
X-rays measured by a linear detector (for example, an array of small
1
I made my own entry into medical physics, and became one of the several
“inventors” of CT who solved the problem after it had already been solved
by Hounsfield and Cormack, through being faced with this problem.
While attempting to get a job in Medical Physics I approached Cornelius
Tobias at the Lawrence Berkeley Laboratory. He told me of his convic-
tion that one could compute the densities within an object by taking
radiographs of it from many different directions. That is, before it was
introduced on the public stage, he felt sure that computed tomography was
possible. In my haste to impress, I told him that I thought I knew how to
solve the problem and would come back in a couple of days to show him
the solution. On returning home I realized that I had made a big mistake in
my thinking. I had thought that to reconstruct an 80 x 80 map of the object
I would have to invert an 80 x 80 matrix - which was time-consuming but
do-able. In fact, however, it was a 6400 x 6400 matrix which needed to be
inverted, and in those days this was not practical. Pride then required that I
find a solution that would work, and I came up with an iterative solution
(Goitein, 1972) which I was eventually able to show Dr. Tobias - although
he never offered me that job! I offer this anecdote to underline both how
varied can be the stimuli to invention and how, quite often, conditions are
“ripe” for something to be discovered.
