Treatment planning with ion beams Page: 3 of 5
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TREATMENT PLANNING WITH ION BtAMS*
H. Foss, AT -6, MS U829
Los Alamos National Laboratory, Los Alamos, NH 87545 USA
Summary
Ions have higher 1 inear energy transfer (LEI) near
the end of their range and lower LEI away from the end
of their range. Mixing radiations of different LEI
complicates treatment planning because radiation kills
cells 1n two statistically Independent ways, In some
cases, cells are killed by a single particle, which
causes a linear decrease In log survival at low dosage,
When the linear decrease Is subtracted from the log
survival curve, the remaining curve has zero slope at
zero dosage. This curve 1s the log survival curve for
cells that are killed only by two or more particles.
These two mechanisms are statistically Independent,
lo calculate survival, these two kinds of doses must
be accumulated separately. The effect of each accumu
lated dosage must be read from Its survival curve, and
the logarithms of the two effects added to get the log
survival. Treatmen’ plans for doses of protons, He3
Ions, and He4 ions suggest that these Ions will be use-
ful therapeutic modalities.
lnt rodu c t Ion
Radiation modifies cells so that they cannot con
tlnue to multiply. Cells not so affected after a rad1
atlon treatment are said to survive. The effect of
radiation 1s often presented as a curve showing ttie
logarithm of the surviving fraction as a function of
physical dose, An Idealized log survival curve 1s
shown 1n F1g. la. No*e that the relationship between
dose and survival 1s not simple. Doubling the dose
does not simply double the decrement 1n log survival.
1:-'"
; U.'eP
i\;’n
I!.in Hg. 'a • fog
survival curves:
it,(«, <" Net survival versus
dose .
i v i1
However, a complicated log survival dors no!
greatly complicate trea.merit planning with < unvrnt Iona 1
modalities. Ihe 1 hape of the curve Is aimed the same
throughout thr tieated volume, If two doses are added
using multiple portals, the same survival curve Is oh
served In the region of overlap. Ireatmerits can be
planned by calculating the total physlial dose at ea>h
point In the treated volume. Ihpn the survival at eath
point can be determined (rom the 'og survival curve,
Ihe plan can he modified until the optimum treatmenl
1s found.
Ions are quite dllfprenl. Although Ihe el In Is ol
conventional dos«s attenuate with depth, ton lieam
effects Increase with depth, Ihe physical dose rale,
or III, Increases to a maximum, then drops rapidly,
lighter ions have no exit el lei t. Ihe shape ol l lie log
survival curve Is dillerenl at eaih point along the
path ol the Ion beam, therapy will, In most lasey,
•Work supported hy the US Dept, ol Inorgy,
require the use of many beams stopping at different
depths and coming from different directions, whlci will
Introduce a host of new survival curves. To find o
procedure simple enough for treatment planning, it s
necessary to study further the therapeutic effects o'
radiation.
Two Therapeutic Effects
Photons, ions, and other pirtlcles have two major
therapeutic effects. In 1959, Puck reported1 that the
inability of cells to replicate can be caused by two
or more particles. He also showed that chromosomal
breaks correlate with decreased survival. Barendsen'
found that Inhibition ov replication by single parti
cles must be included 1n a complete explanation of sur
vlval curves. He also presented results showing that
the single and multiple-particle effects are statisti
cally independent. Statistical Independence of these
two effects means that the net survival is the survival
from one effect multiplied by the survival from the
other effect. That Is, the net log survival is the sum
of the two log survivals.
The single particle effect causes a linear decrease
1n log survival at zero dose and is thus observable.
Ih1s biological effect, which has been called the a
effect, 1s shown 1n Hq. lb. Ihe unit of dose is Un,
the number of particles per square millimeter required
to Inactivate 1/e - 0.37 of the cells. With this unit
of dose, the a curve 1s the same for all radiations.
r .V
i U , M‘
.
, 11 . , ■ I ‘ c
Y |1 11' ' Fly. It), 1 hr «
!,, el effect versus rinse.
! ' "
, U IV
When the a curve Is subtracted Irom I in, 1 a, a curve
with zero slope at zero dose is obtained, as shown In
llg, If. Ih1s i ur ve 's the log survival from thr mill
tlpartlc'e, or f). effeit. Ihe unit dose l)|j is thr num
her ol particles required to Inactivate I/r ot the iclls
Ireatmenc planning is not difficult In prlmlplr.
Ihp dose In eaih beam to be used Is the numhpr o! Ions
In that opam, Ihe Un and Ujj (or all points Iri every
beam are known from previous experiments, ihe inntrl
but Ion ol one beam to the n effect at a part'cular
point Is the dosr in that beam divided by the b lor
that particular point in that beam, Ihe contribution
of ttie same beam to the II ellecl at Ihr same point Is
the dose divided hy l)|) , Ihe total •> pIIpc! at a point
Is the sum ol the rlose/|)(1 for all beams used, anil thr
total (1 el I ect at thr same point Is the sum ol I In-
dose/Dn lor all hpqms used Ihe survival I r om t In- u
ellecl at this point Is obtained hy using Ihe «« sum and
the n survival curve Ihe survival I rom the 11 rlleil
at ttds point Is obtained by using tire II sum and the |i
survival curve. Ihr net sucvlva' at this point Is thr
|> roil in I ol t he it and It survivals.
In oilier words, hei ause thrsr ptleits ate stalls
tlially lodepeiiileo ' , Ihe i on t r I bu t 1 on s lo eai h Hint
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Foss, M.H. Treatment planning with ion beams, article, January 1, 1985; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1093554/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.