Transcript No Slide Title

Optimization of dose delivery with a beam scanning system.
A.V. Trofimov and T.R. Bortfeld
Northeast Proton Therapy Center, Massachusetts General Hospital, Harvard Medical School , Boston MA
Contact e-mail: [email protected]
Abstract
Introduction
The use of highly target-conformal Intensity Modulated Proton Therapy (IMPT) in radiation cancer
treatment offers the possibility of better sparing of the normal tissue. Preliminary tests of IMPT delivery,
using the pencil beam scanning system developed by IBA and the inverse treatment planning system
(TPS) KonRad of the German Cancer Research Center (DKFZ), have been performed at the Northeast
Proton Therapy Center (NPTC) in Boston in May 2002.
Treatment planning and delivery
The treatment planning system KonRad is capable of creating plans suitable for delivery using various
techniques, such as the 3-D intensity modulation, distal edge tracking (DET)1, etc. In 3-D modulation,
individually weighted proton Bragg peaks are distributed throughout the target volume. In DET, Bragg
peaks are matched to the distal edge of the target. Plan optimization is performed for several beam fields
simultaneously. The total dose distribution planned for the target is then the sum of inhomogeneous dose
distributions delivered by each of the beam fields.
In an IMPT treatment plan, using the intensity modulation in 3-D, for each beam field, the target
volume is subdivided into a set of equal-proton-range layers, corresponding to different proton energies.
For each layer, the TPS generates a discrete beam weight map for regularly spaced pencil beam spots (as
shown in Figure 1). The separation (spacing) between the beam spots on the grid, D, is typically of the
order of the beam s in both directions.
The IBA system performs continuous magnetic
FIGURE 1: Treatment planning and
scanning in two dimensions, on a raster pattern. Beam
delivery for a single equal-range slice
fluence variation along the path is achieved by
within the target volume. Different spot
simultaneously varying the beam current and the speed
colors reflect differences in the
2
of scanning . The slowest direction of scanning is in
corresponding beam weights. Also shown is
depth: the transition between the layers is achieved by
a sample pattern of continuous scanning.
changing the energy of the proton beam.
For the purposes of continuous scanning on a
raster pattern, it is necessary to convert the discrete
pencil beam weight map generated by the TPS into a
continuous one. Figure 2 shows two simple ways of
doing that. In the rectangular (d-vector) approximation,
the beam fluence is constant within every scanning path
element (of the length equal to D) and is proportional to
the weight of the corresponding d-function spot. The dvector map is obtained as convolution with a rectangle
(of the width D) of the TPS beam weight map for dfunction spots. With a triangular approximation
(convolution with a triangle of the base length D), the
scanning beam fluence varies linearly from one pointlike spot to the next.
Since, along a scanning path element, delivered
dose has a pseudo-gaussian profile, different from the
planned gaussian spot (Figure 3), such conversion may
produce a significant discrepancy between the planned
and delivered doses. Figure 4 shows the dose
discrepancy for a sample weight map, generated by
KonRad for a 3-D modulation plan using real NPTC
patient data.
The discrepancy is maximal in the regions of
sharp dose gradient (edge of the target, boost volume)
and is generally larger if the triangular approximation is
used. The size of the discrepancy depends on the
relative size of TPS spot spacing and the proton beam
(D/s), range of variation in the weight map, scanning
path. Reducing the spacing between the pencil beams
during the treatment planning would minimize such
discrepancy, but also increase the time required for the
calculation and, eventually, for treatment. Alternatively,
a TPS fluence map may be adjusted for the use by the
delivery system to achieve the desired dose conformity.
FIGURE 2: Conversion from a discrete to a
continuous beam weight spectrum.
c)
DTPS = WTPS  g(s)
At the first step of every iteration (number i), the delivered dose is calculated as convolution of the weight
map with a pseudo-gaussian kernel, which, in turn, is obtained by convolution of a gaussian with either a
rectangular (for d-vector approximation) or triangular distributions:
D(i-1) = W(i-1)  [ g(s)  f(D) ]; with f =
or
(For the first iteration the weight map used is the one generated by the TPS: W0 = WTPS ). Finally, the
optimized beam map is calculated as:
Wi (x,y) = W(i-1)(x,y)*[DTPS(x,y)/D(i-1)(x,y)]
where x and y are the coordinates of optimization points.
The optimization points may be chosen the same as the TPS beam spots, in which case it is the
values of the d-vectors that will be adjusted (d-vector optimization).
The algorithm may be slightly modified, so that the optimization is performed for a larger set of
points along the scanning path, separated by a distance smaller than the grid spacing D used by the TPS
(i.e. the d-vectors are further discretized). The result of this would be similar to using a fine spot spacing
at the treatment planning stage, with the beam fluence varying smoothly along the scanning path (smooth
profile optimization). Compared to the TPS optimization, the calculation time would be reduced
substantially though, since only a small fraction of the grid points (those along the scanning path) need to
be taken into account. In either case, the result of optimization is equivalent to de-convolution of the
planned dose distribution with the interpolation kernel of the dose deposited by the scanning beam.
Results
Figure 5 shows the results of the beam weight map optimization for a sample field, with D=s, for both
the d-vector and smooth profile optimization, obtained after 20 iterations as described above. (The
number of required iterations depends on the tolerated discrepancy value.) For the case shown, calculated
dose discrepancy within the target is reduced more than 3-fold within the target volume. In the penumbra,
the discrepancy persists for the d-vector result, since optimization is not done for the penumbra spots. The
result for smooth profile optimization is similar to the one obtained for d-vector on the target, but better in
the penumbra, since in this case beam fluence can be further reduced along the marginal elements of the
scanning path, thus delivering a smaller dose to the target edges. (Complete removal of the hot spots
would require the unphysical negative fluence in the penumbra). Sample beam fluence profiles along a
single scanning line are shown in Figure 5(d).
Table 1 contains the maximal values of the discrepancy between the planned and delivered doses
for different spot spacing sizes used for the TPS optimization (averaged over a set of beam fields and
slices used in a single patient treatment plan).
FIGURE 5: The results of optimization: discrepancy between the planned and delivered doses (a)
before the optimization; (b) for the d-vector optimization; and (c) for smooth fluence profile optimization. A sample set of fluence profiles along one scanning line for cases (a,b,c) is shown in (d).
a)
FIGURE 3: Dose deposit from a single
scanning path element (top), and the
discrepancy between the planned and
delivered doses (bottom) for a d-function
spot, rectangle (d-vector), and a triangle.
b)
d)
c)
TABLE 1: Results of the optimization for various TPS grid spacings.
Spot
FIGURE 4: (a) A sample TPS beam weight map (pixel color reflects the weight of a point-like
beam spot) and (b) corresponding planned dose distribution. Different directions of scanning (c, d)
produce differing discrepancy patterns between the planned and delivered doses (calculation).
a)
Optimization of the beam weight map
We used the following iterative algorithm for optimization of the TPS beam weight data. The planned
dose distribution (DTPS) is calculated as the convolution of the beam weight map from the previous
iteration,W(i-1), with a gaussian kernel :
b)
d)
spacing (D)
s
0.75 * s
1.0 * s
1.25 * s
1.5 * s
2.0 * s
0.5 *
Before
optimization
Maximal dose difference (%)
Optimized
on target
in penumbra
<1
0.1
0.3
1.5
0.3
0.7
2.5
0.5
1.2
3.5
1
2.5
6
1.5
4
10
4
8
Conclusion
Good conformity between the planned and delivered doses can be achieved by optimizing the beam weight
maps, without reducing the relative TPS pencil beam spacing (D/s). Calculation shows that, for D/s
between 0.75 and 1.5, the dose discrepancy may be reduced 4-fold within the target volume, and 2-fold in
the penumbra. We plan to verify the results of this study during our future proton beam scanning tests.
References
1A. Lomax. Phys. Med. Biol. 44(185), (1999).
2C.Brusasco. Talk at the PTCOG-XXXVI, Catania, Italy, May 2002.