
14
CT or Hounseld Numbers
by David Goodenough, Ph.D.
Users of CT systems are often surprised when the CT number of a given tissue or
substance is different from what they expect from previous experience. These differences
do not usually indicate problems of a given CT scanner, but more likely arise from the
fact that CT numbers are not universal. They vary depending on the particular energy,
ltration, object size and calibration schemes used in a given scanner. One of the
problems is that we are all taught that the CT number is given by the equation:
CT# = k(µ - µw)/µw,
where k is the weighting constant (1000 is for Hounseld Scale), µ is the linear
attenuation coefcient of the substance of interest, and µwis the linear attenuation
coefcient of water. Close review of the physics reveals that although the above
equation is true to rst order, it is not totally correct for a practical CT scanner. In
practice, µ and µw are functions of energy, typical x-ray spectra are not monoenergetic
but polychromatic, and a given spectrum emitted by the tube is “hardened” as it is
transmitted (passes) through lter(s) and the object, nally reaching the detector. More
accurately, µ=µ(E), a function of energy. Therefore:
CT#(E) = k(µ(E) - µw(E))/µw(E)
Because the spectrum is polychromatic we can at best assign some “effective energy” Ê
to the beam (typically some 50% to 60% of the peak kV or kVp). Additionally, the CT
detector will have some energy dependence, and the scatter contribution (dependent on
beam width and scanned object size, shape, and composition) may further complicate
matters. Although the CT scanner has a built in calibration scheme that tries to correct
for beam hardening and other factors, this is based on models and calibration phantoms
that are usually round and uniformly lled with water, and will not generally match the
body “habitus” (size, shape, etc.).
The situation is really so complicated that it is remarkable that tissue CT numbers are in
some rst order ways “portable”!
In light of the above we can examine a parameter of CT performance, the “linearity
scale”, as required by the FDA for CT manufacturer’s performance specications.
The linearity scale is the best t relationship between the CT numbers and the
corresponding µ values at the effective energy Ê of the x-ray beam.
The effective energy Ê is determined by minimizing the residuals in a best-t straight
line relationship between CT numbers and the corresponding µ values.
In review, we will encounter considerable inter and intra scanner CT number variability.
CT numbers can easily vary by 10 or more based on kVp, slice thickness, and object size,
shape, and composition. There is some possibility of the use of iterative techniques and/
or dual energy approaches that might lessen these effects, but certainly CT numbers are
not strictly portable and vary according to the factors listed above.
More complete scientic references are contained in the bibliography. In particular,
references 2, 13, 14, and 20 are recommended for those with greater interest in the
topic.