Biomedical Engineering Reference
In-Depth Information
effect, but its primary impact is to complicate such things as
presenting a beam's-eye view image of the patient's anatomy and
computing the tapering of beam trimmers, if any.
T
HE
E
LECTRON
'
S
B
RAGG
P
EAK
The depth-dose distributions of electrons in the therapeutic range of
energies, which is generally from 6 to 25 MeV, appear to be smooth,
decreasing monotonically towards the end of range, and peak-free.
Why is it that, if the electron is simply a lighter cousin of the proton
so far as its electromagnetic interactions are concerned, electrons
don't exhibit a Bragg peak?
The answer is, I think, informative. The fact is that electrons do have
a Bragg peak, but it gets blurred out to the point of vanishing. As you
know from Chapter 4, electrons, like protons, gradually lose energy
due to their Coulomb collisions with atomic electrons and, like
protons, their rate of energy loss rises as the electron's energy
decreases. This increase in dose with depth is the necessary condition
for a Bragg peak to appear. Electrons, like protons, also experience
multiple Coulomb scattering. The big difference is that, owing to
their much lighter mass, electrons are scattered, and their path thereby
altered, much more than protons. While protons scatter a few degrees
and follow an only slightly un-straight path, electrons can be scattered
through very large angles so that their path is dramatically modified,
even to the extent that some electrons turn back on themselves.
If one followed an individual electron along its meandering track, and
noted the dose deposited per unit path length, one would indeed
observe a Bragg peak. However, for a beam comprised of very many
electrons, it is their deposition of dose with depth in the medium, as
opposed to path length, that can be measured and that is of therapeutic
interest. Due to their large degree of multiple scattering, electrons
crossing a plane normal to the beam and located at depth, are at a
rather different points
along their paths
and so have quite a wide
range of energies and, hence, of stopping powers. The dose one
would measure at that plane, then, would be the average of the dose
delivered by each of the electrons
and that averaging process blurs
out the Bragg peaks to the point of invisibility.
−
Let us now return to protons, with no more parenthetical side trips.
