Intensity- modulated radiotherapy. Beyond fluence map op.miza.on

Transcription

1 Intensty- modulated radotherapy ì Beyond fluence map op.mza.on

2 Overvew So far: Fluence map op.mza.on Now: - Intensty- modulated proton therapy (IMRT) Extensons n IMRT plannng - leaf sequencng - drect aperture op.mza.on - VMAT op.mza.on

3 Fluence map IMRT / photons (2D) IMPT / protons (3D)

4 Overvew d =! x j D j j Fluence map Dose dstrbu.on

5 Overvew Trad-onal approach to IMRT plannng: Two steps 1. Fluence map op.mza.on 2. Leaf sequencng Thrd component Drect Aperture Op.mza.on (DAO)

6 Beam collmaton usng MLC

7 Beam collmaton usng MLC

8 Leaf sequencng Superpos-on of mul-ple apertures yelds an IMRT feld Leaf sequencng s the nverse problem Fnd a set of MLC apertures that delver an op.mzed fluence map

9 Leaf sequencng does not have a unque solu.on (trval solu.on: delver each beamlet ndvdually) Leaf sequencng Goal: Fnd an effcent solu.on reproduce fluence map fathfully mnmze number of apertures mnmze total number of montor unts Construc-ve method: Sldng wndow (mnmzes total MU) Dscrete op-mza-on methods: am to mnmze number of apertures

10 Sldng wndow sequencng consder dscre.zed fluence map consder one MLC leaf par leaves move un- drec.onally lev leaf pos.ons: determned by pos.ve gradents rght leaf pos.ons: determned by nega.ve gradents total MU = sum of pos.ve gradents

11 Drect aperture optmzaton Lmta-ons of Two- step approach: Poor dose calcula.on accuracy for fluence map op.mza.on (use of pencl beam algorthm for Dose- nfluence matrx) Dscrepancy between op.mzed fluence map and sequenced map (treatment plan wth few apertures) dscrete leaf pos.ons lmted to beamlet boundares (beneft of fne tunng leaf pos.ons at the target edge) Inherent lmta.ons of the dose- nfluence matrx concept (example: tongue & groove effect)

12 Drect aperture optmzaton Tongue & Groove desgn of MLC leaves: dose- nfluence matrx assumes lnearty.e. dose of beamlets delvered ndvdually equals dose delvered by combned aperture not strctly true center s blocked as soon as one leaf s closed è center s underdosed f beamlets are delvered separately

13 Drect aperture optmzaton Drect aperture Op-mza-on (DAO) = drectly op.mze shape and ntensty of apertures leaf par (n) FMO DAO beamlet ndex (j)

14 Drect aperture optmzaton Fluence map op-mza-on: Dose s lnear func.on of beamlet ntens.es è effcent algorthms can fnd the global op.mum

15 Fluence map optmzaton Objec.ves and constrants are nce func.ons of the varables # & mnmze w! T %! x j D j " 70 ( + w!! H x j D j x )T $ j ' )H j 2 subject to x j! 0 "j quadra.c func.on of x j! x j D j " 40 # $ S j lnear func.ons of x j

16 Drect aperture optmzaton Fluence map op-mza-on: Dose s lnear func.on of beamlet ntens.es è effcent algorthms can fnd the global op.mum Drect aperture op-mza-on: Dependence of dose on leaf pos.on s a smoothed step func.on è hghly non- convex op.mza.on problem wth local mnma How many apertures should each beam drec.on get? è combnatoral aspect

17 Drect aperture optmzaton Three common approaches stochas.c search methods (smulated annealng) (commercalzed by Prowess) gradent- based leaf pos.on op.mza.on (RaySta.on, Pnnacle) aperture genera.on methods

18 Gradent based DAO How does dose depend on leaf pos-ons? d = " k " n y k! kn ( L kn, R kn ) dose n voxel sum over apertures k sum over MLC rows n leaf/rght leaf pos.ons dose contrbu.on of MLC row n n aperture k to voxel

19 Dose dependence Assume that leo leaf s at the leo- most pos-on at the edge of the fluence map Determne dose contrbu-on of MLC row as a func-on of the rght leaf pos-on:! nk (R nk )

20 Dose dependence Loca.on of voxel projected onto the MLC row leaf par n beamlet ndex j

21 Dose dependence! nk (R nk ) Dose contrbu.on 5! j=1 D j n 4! j=1 D j n 4!x 5!x Loca.on of voxel projected onto the MLC row beamlet j / pos.on along the MLC row

22 Dose dependence Dose contrbu-on of MLC row n:! nk (R nk ) = pecewse lnear func.on (corners gven by dose- nfluence matrx)! kn ( L kn, R kn ) =! kn ( R kn ) "! kn ( L kn ) contrbu.ons from beamlets that are not blocked by the rght leaf, assumng the lev leaf s at the edge of the feld subtract dose contrbu.ons from beamlets blocked by the lev leaf

23 Treatment plan op.mza.on x Drect aperture optmzaton mnmze w # T d! 70 + w H d "T ( ) 2 # "H mnmze deva.on from 70 Gray n the tumor mnmze dose n healthy.ssues subject to x j! 0 "j fluence cannot be nega.ve

24 Treatment plan op.mza.on x Drect aperture optmzaton mnmze w # T d! 70 + w H d "T ( ) 2 # "H mnmze deva.on from 70 Gray n the tumor mnmze dose n healthy.ssues subject to x j! 0 "j fluence cannot be nega.ve

25 Treatment plan op.mza.on y,l,r Drect aperture optmzaton mnmze w # T d! 70 + w H d d = "T " k ( ) 2 " n y k! kn # "H ( L kn, R kn ) (dose n voxel ) L kn! R kn "n, k (leaves cannot cross) y k! 0 "k (pos.ve aperture weghts)

26 Gradent based optmzaton Derva-ve wth respect to aperture weght: d = " k " n y k! kn ( L kn, R kn )!f!y k =!f!d " =!d!y k " $!f & # kn %!d " n ' ( L kn, R kn )) (

27 Gradent based optmzaton Derva-ve wth respect to leaf pos-ons: d =! kn " k " n y k! kn ( L kn, R kn ) =! kn ( L kn, R kn ) ( R kn ) "! kn ( L kn )!f!r kn =!f!d " =!d!r kn " #!f!! y kn % k $!d ( R kn )!R kn & ( '! D j n j = beamlet ndex where leaf edge s pos.oned

28 VMAT optmzaton Volumetrc modulated arc therapy (VMAT) Con.nuous delvery mode: Rada.on beam s constantly on whle gantry and MLC leaves move Varables (conceptually): leaf pos.ons as a func.on of.me gantry angle as a func.on of.me dose rate as a func.on of.me Varables (n prac.ce): (drven by DICOM specfca.on) Determne one aperture every 2 degrees

29 VMAT optmzaton

30 VMAT optmzaton VMAT op-mza-on methods Ref: Unkelbach et al, Med Phys, 2015, Op.mza.on approaches to volumetrc modulated arc therapy plannng VMAT approaches reuse the concepts from IMRT plannng fluence map op.mza.on (arc) sequencng drect aperture op.mza.on Approaches dffer n the exact mplementa-on of each step, and on the step they rely on most

31 VMAT optmzaton Example: Prostate case treated n a sngle 360 degree arc Goal: dvde arc nto 180 sectors of 2 degree lengths assgn one aperture (control pont) to each sector neghborng apertures should be smlar Raysta-on, Pnnacle, Monaco: Three- step approach (largely rely on DAO step) 1. Fluence map op.mza.on 2. Arc sequencng 3. Drect aperture op.mza.on

32 VMAT optmzaton Step 1: Perform fluence map op.mza.on at 20 equspaced angles Step 2: approxmate each fluence map through 9 apertures (yelds 180 control ponts, one every 2 degrees) typcal approach: sldng wndow sequencng Why?

33 VMAT optmzaton Step 1: Perform fluence map op.mza.on at 20 equspaced angles Step 2: approxmate each fluence map through 9 apertures (yelds 180 control ponts, one every 2 degrees) typcal approach: sldng wndow sequencng Why? Naturally yelds ordered apertures. Undrec.onal leaf mo.on makes subsequent apertures smlar.

34 Sldng wndow sequencng

35 VMAT optmzaton Step 1: Perform fluence map op.mza.on at 20 equspaced angles Step 2: approxmate each fluence map through 9 apertures (yelds 180 control ponts, one every 2 degrees) typcal approach: sldng wndow sequencng Why? Naturally yelds ordered apertures. Undrec.onal leaf mo.on makes subsequent apertures smlar. Step 3: Perform gradent based DAO one aperture at each of 180 gantry angles

36 VMAT optmzaton DAO step yelds a DICOM VMAT plan, specfed by for each control pont: all leaf pos.ons gantry angle (couch and collmator angle) total MU delvered up to ths control pont ths does not contan -me! Lnac machne controller translates DICOM nto trajectores (TPS reles on assump.ons to es.mate treatment.me)

37 VMAT optmzaton How do aperture weghts relate to gantry speed and dose rate? y k =! k! k s k dose rate [MU/s] aperture weght [MU] gantry speed [degree/s] angular dstance between control ponts [degree] large aperture weght realzed by hgh dose rate or low gantry speed

38 VMAT optmzaton Constran maxmum leaf travel for effcency: assumng we want to delver a 360 degree arc n one mnute (maxmum gantry speed) control pont spacng: Δ k = 2 gantry speed: s = 6 / second è ⅓ second per control pont maxmum leaf speed: v = 6 cm / second è maxmum leaf travel between control ponts s Δ = 2 cm

39 Drect aperture optmzaton mnmze w # T d! 70 + w H d y,l,r d = "T " k ( ) 2 " n y k! kn # "H ( L kn, R kn ) (dose n voxel ) L kn! R kn "n, k (leaves cannot cross) y k! 0 "k (pos.ve aperture weghts) R kn! R (k+1)n " # (constran maxmum leaf travel between apertures)