Dose distribution calculations in TPS photon beams Pawe Kukoowicz - PowerPoint PPT Presentation

Dose distribution calculations in TPS photon beams Paweł Kukołowicz Medical l Physics De Department, War arsaw, Pola oland

Delivered dose does matter! NORMAL TISSUE DOSE (Gy) 10 20 40 10 20 30 50 30 40 50 1,0 PROBABILITY OF EFFECT 0,9 TCP 0,8 0,7 3.5% st. dev. 0,6 0,5 0,4 0,3 0,2 NTCP 0,1 0,0 0 20 40 60 80 100 120 TARGET DOSE (Gy) Accuracy required and achievable in radiotherapy dosimetry: Have modern technology and techniques changed our views? Journal of Physics: conference Series 444 (2013) David Thwaites 2/#21

Clinical trials Peters L J et al. JCO 2010;28:2996-3001 Critical Impact of Radiotherapy Protocol Compliance and Quality in the Treatment of Advanced Head and Neck Cancer: Results From TROG 02.02 5/#22

Delivered dose does matter! Measurements of dose Input Callibration of : distributions dosimetry data dosimeters of therapeutic beams Pre-treatment imaging Treatment planning Treatment delivery Quality control of Tumour & OAR Outlining Treatment Planning Systems Courtesy Liz Miles RTTQA 6/#22

Treatment planning system • Accuracy of dose distribution calculation Treatment planning Quality control of Treatment Planning Systems

What are characteristics of a good TPS? Varian - Eclipse Pinnacle • High accuracy of dose distribution calculations • Fast calculations • Should be able to prepare plans Elekta - Monaco for all contemporary techniques • User friendly • Robust RaySearch – RayStation

How to build a good model?

What are characteristics of a good TPS? • High accuracy of dose distribution calculations • Fast calculations • User friendly • Robust Algorithms implemented in TPS

Step 1 - exposure • What radiation is reaching an absorber • fluence and energy fluence • spectrum of energy fluence • We call it: primary radiation

Step 1 - exposure • Fluence – F [1/ m 2 ] • the number dN of particles (photons) incident on a sphere of cross-sectional area da dN • Energy fluence – ψ [ J / m 2 ] F  • the energy dE incident on da a sphere of cross-sectional area da    F E

Energy spectrum • Depends on • effective accelerating potential • target material • flattening filter material and construction • there are flattenning filter free accelerators • head (colimator system) material and construction

Energy spectrum 15 MV 6 MV

Energy spectrum calculations • Reconstruction of spectra by iterative least squares fitting of narrow beam transmission • it requires very precise measurements of attenuation factors • Monte Carlo • precise knowledge of the treatment head design • now this information is usually available • Fiting routine • a given spectrum is used to calculate PDDs (using a database of Monte Carlo generated Kernels) and compared with the measured ones • procedure is repeated until expected compliance is obtained

Energy spectrum calculation Monte Carlo

Step 2 – Energy deposition • Primary and secondary dose • Primary dose • interaction of primary photon • energy transfered to charged particle (mostly to electron) • electron transfered its energy to medium • Secondary dose • interactions of secondary photons (scattered) and so on

Primary and secondary dose Precise modeling of primary dose is the most important! Sontag, Med. Phys. 1995, 22 (6)

Energy transfered from photons to electrons Kerma     F   number of interactions   Δ A r per unit mass Φ = Δ N / Δ A   Δ z      F   energy transferred E   tr r to electrons   r

Energy transferred to electrons        F   E tr r   • KERMA • Kinetic Energy Released per unit mass

Charged particle equilibrium (CPE) E tr,2 E tr,1 Photon interaction Electron enters D m E 2,in Electron leavs D m E 1,in E tr,3 Charged particle equilibrium exists for the volume V E tr,1 if each charged particle of a given type D m and energy leaving V is replaced E 1,out by an identical particle E 2,out of the same energy entering

Kerma Collision versus Absorbed Dose • If CPD exists Kerma col =Kerma·(1 -g) Absorbed Dose = Kerma col g – fraction of energy emmited in the form of Bremstrahlung

CPD never exists • Transient CPD exists D=  ·K col K col z max Absorbed dose is equall to relative energy per unit mass Kerma at a little smaller depth. D D= (1+ f TCPE )· K col  > 1  < 1  = 1 depth in medium

Fluence in air – inverse square low F F isocenter isocenter plane plane F F air + F F f air 2 F + F  F  F f F (  air air + 2 F f

Fluence in water – dose in water F 2 F +    F  F   F f F d e (  d + water air 2 F f f + F F f water Primary dose – dose deposited by electrons    2 F +       F         F f F d D e E g   ( 1 ) (  r + water air tr 2   F f

Fluence – real situation F • Radiological depth r1 h 1   r +  r +  r d rad h 1 1 h 2 2 h 3 3 r2 • In general h 2  h 3  r  Q’ d h r3 rad k k    2   F +       F         F h h F k k k D e E ( 1 g )   (   r Q ' air tr + 2   F h k

radiological depth    2   F +    F h    F   h       F k k k D e   E ( 1 g ) (   r Q air tr ' 2 +   F h k physical distance

Another aproach to dose distribution calculation • Total energy released per unit mass    2 F     F         F d h  TERMA e h   h (   r + h air 2   F f primary energy fluence • What will happen with this released energy? • mostly it will be absorbed as primary and secondary dose • only a little energy will escape (scattered photons, bremstrahlug)

Convolution – monoenergetic case TERMA h  = T h  (  (       ' ' 3 ' D ( r , h ) T r A r r d r hv hv TERMA (  Convolution kernel representing ' r r the relative energy deposited  ' A hv r r per unit volume for photons r of energy hv; integral over whole medium Med.Phys. Papanikolau 1993,5,1327-1336.

Convolution – polyenergetic (real case) • Integral over space and energy spectrum (  (    ' dT r    ' 3 ' hv D ( r , h ) A r r d r dhv hv dhv Mohan, Med.Phys, 1985, 12, 592 – 597.

Kernels – Point Spread Function Anders A. Ahnsjö, Med.Phys. 16 (4), 1989      +    2 h w ( r , ) ( A exp( a r ) B exp( b r )) / r     scattered primary A a B b , , ,     • parameteres generated for beams of spectrum typical for 4Mv, 6MV, 10MV, and 15 MV • Ө angle with respect to the direction of impinging primary photon  • w – stands for water

1,25 MeV 10 MeV Kernels 0,4 MeV   The dash-dotted line first scatter terma, calculated using the Klein-Nishina cross sections and neglecting other process than the Compton interaction. Energy imparted per cm -3 Acta Oncologica, 1987, Ahnesjo

1,25 MeV 10 MeV Kernels 0,4 MeV   The dash-dotted line first scatter terma, calculated using the Klein-Nishina cross sections and neglecting other process than the Compton interaction. Energy imparted per cm -3 Acta Oncologica, 1987, Ahnesjo

Convolution – polyenergetic (real case) • Integral over space and energy spectrum (  (    ' dT r   ' 3 ' hv D ( r , h ) A r r d r dhv hv dhv    2 F     F         d F h  TERMA e h   h (   r + h air 2   F f      +    2 h w ( t , ) ( A exp( a t ) B exp( b t )) / t     (   ' A hv r r Mohan, Med.Phys, 1985, 12, 592 – 597.

Approximations • To allow calculations in a resonable time several approximations are used • treatment planning system dependent • the same model different results • polyenergetic monoenergetic (e.g. for mean energy) • single energy spectrum is used • collapse cone method • Kernels generated for water only • scaling with density

6 MV spectrum polyenergetic : monoenergetic Spectrum 6 MV Mean Energy 1.48 MeV 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0 0 1 2 3 4 5 6 7

Changes of spectrum lateral softenning lower energy higher energy single energy spectrum

Collapsed Cone Convolution speed-up calculations • 30 x 30 x 30 cm 3 water Phantom • 0.3 cm grid size • 100 x 100 x 100 calulations point = 1 000 000 • Convolution: contribution from each voxel to each voxel 1 000 000 x 1000 000 = 1 000 000 000 000

Collapsed Cone Convolution • CCC aproaches assumes that all the energy scattered from one voxel into small cone is absorbed along the line forming the axis of the cone