Studies of optimization methods for dose delivery with a beam scanning system Alexei Trofimov,...

Studies of optimization methods for dose delivery

with a beam scanning system

Alexei Trofimov, Thomas BortfeldNortheast Proton Therapy Center

MGH, Boston

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Beam scanning at the NPTC

First tests have been conducted in collaboration with IBA last week

Use the IBA scanning system for delivery

Inverse treatment planning with KonRad (DKFZ)

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Treatment planning and delivery

For each layer w/in target, treatment planning system generates a discrete beam weight map for regularly spaced pencil beam spots Scanning within a layer is continuous Fluence variation along

the path is achieved by simultaneously varying the beam current and scanning speed

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Example: plan for a NPTC patient (medulloblastoma, 3D plan with 2cm-FWHM

beam)

boost

sp.cord

target

hypoth.

cochlea

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Example: plan for a NPTC patient (RPO field, spot spacing = = 8.5 mm)

beam weight map dose distribution at B.p. range

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Converting a discrete spectrum into a continuous one

vector approximation Triangular approximation

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Difference between planned and delivered doses

Along a scanning path element, delivered dose has pseudo-gaussian profile, different from the planned gaussian spot

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Calculated dose difference (vector approximation)

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Difference between the planned and delivered doses

The discrepancy is maximal in the regions of sharp dose gradient

(rim of the target, boost) Size of the discrepancy depends on TPS spot spacing (, range of variation in the weight map, scanning path. Generally, smaller for finer / values

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Spot weight optimizationPlanned dose (conv. of TPS weight map with a gaussian)

DTPS = WTPS g()Iteration #i: Delivered dose (convolution with a pseudo-gaussian)

Di = Wi [ g() f() ]; f= or Optimized beam weight map for spots at (x,y):

Wi+1 (x,y) = Wi(x,y)*[DTPS(x,y)/Di(x,y)]

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Results of the optimizationstart 1 iteration

10 iterations

100 iterations

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Results of the optimization

f(i)= (x,y) [ ( Di - DTPS)2 / DTPS ]

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Optimization for a quasi-continuous path:

W0 = WTPS f(); f = or

Iteration # i:

Delivered dose: Di = Wi g()Optimized beam weight for a quasi-continuous set of

points (x,y) along the scanning path:

Wi+1 (x,y) = Wi(x,y)*[DTPS(x,y)/Di(x,y)]

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Results of the optimization

For a quasi-continuous weight variation along the path

20 iterations

start

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Optimization results for one scanning line

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Another example: PA field

-vector approximation optimized (100 iterations)

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Another example: LPO field

-vector approximation optimized (100 iterations)

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Another example: spacing

1.5*

-vector approximation optimized (100 iterations)

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Results of the optimization

Spot

spacing ()

Maximal dose difference (%)

Before optimization

Optimized

on target penumbra

0.5 * < 1 0.1 0.3

0.75 * 1.5 0.3 0.7

1.0 * 2.5 0.5 1.2

1.25 * 3.5 1 2.5

1.5 * 6 1.5 4

2.0 * 10 4 8

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Summary

Simulation shows that a good dose conformity can be achieved by optimizing the TPS beam weight maps discrepancy reduced 3-fold on the target, 2-

fold in the penumbra (from 1-6%) no need to use finer grid

Plan to verify the results with the beam