Biomedical Engineering Reference
In-Depth Information
Yes, it is so. The interaction probability is so low that the most likely
thing to happen is for the photon to pass through the patient and out
the other side without suffering any interaction at all - and hence
without doing any damage to the patient's tissues whatsoever.
The second most likely event is for the photon to have a single
interaction. As we have seen, it is Compton scattering which
dominates the interactions of photons in the therapeutic range, so that
collision will just about certainly be a Compton interaction. That is,
in the case, for example, of a 4 MeV photon, the scattered photon will
continue on with diminished energy (anywhere from about 0 to
4 MeV), and an electron will be ejected from the target atom with an
energy between ~4 and ~0 MeV. The most probable thing that will
happen to the scattered photon is, again, nothing! It is likely to
escape our patient with no further interactions.
We will come back to the scattered photon's fate in a moment, but let
us now concentrate on the ejected electron - and let us imagine that it
got about half of the available energy, i.e., ~2 MeV. What will it do?
Well, unlike the neutral photon whose interaction probability is small,
a charged particle like the electron has a very high probability of
interacting. As we know, it will either excite or ionize atoms. In the
first case, one, and in the second case, two electrons will emerge, still
carrying a lot of energy - namely the full energy of the incident
electron minus the binding energy of the ejected electron which is of
the order of 10's to a few 100 eV. That is, very little energy will have
been lost. So, the still energetic electron(s) continue on to have yet
other interactions, and their children will have other interactions, and
so on
ad
(nearly)
infinitum
. In the end, since binding energies tend to
be of the order of tens of eV (say, 50 eV), there will typically have
been about 2 MeV divided by 50 eV
≃
40,000 ionizations before the
incident electron and its progeny lose all their energy and come to
rest. This large number of interactions results in the electron loosing
about 2 MeV per centimeter of water path creating a “splash” of dose
in the neighborhood of the interaction of something like 1 cm length
and a few millimeters width.
The upshot of all this is that, while the initial photon interaction will
have ionized a single atom, the ejected electron will go on to ionize
tens of thousands of atoms. That is,
virtually all the damage caused
by a photon is due to damage caused by secondary electrons
.
Let us now return to the scattered photon that emerged from the initial
Compton interaction. I had said that the most likely thing was that it
