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Hierarchical Particle Transport
in Radiation Therapy
Applications
Dragan Mirkovic, Ph.D.
Department of Radiation Physics
D. Mirkovic, Rice University Seminar, Spring 2014
Motivation
•  Cancer represents a huge socioeconomical burden in US and the World
•  Cancer treatment
–  Surgery
–  Chemotherapy
–  Radiation therapy
•  Treatment outcomes have improved but
are still far away form the cure
Motivation (cont.)
Motivation (cont.)
Introduction
•  Radiation therapy (RT) has proven to be an
effective form of treatment in many cancer
types
•  The main goal of RT is to maximize tumor
control probability (TCP) while minimizing the
normal tissue complications probability
(NTCP)
–  Most of the biological effects of radiation are
stochastic
–  Biological effects are proportional to the dose
•  1st approximation
Introduction
•  The 1st approximation of the problem
–  Maximize the dose to the tumor while minimizing
the dose to normal tissue
–  Approximate the all other dependencies using a
single fudge factor called RBE
•  Most of the technical innovations so far have
been directed towards improving the dose
conformity in treatment planning
–  More conformal modalities: protons and heavy
ions
Difficulties
•  Problem is very complex
–  Cancer is a cell disease
–  Biological effects of radiation span multiple
time and space scales
–  Accurate solutions based on 1st principles
would be very time consuming if not
impossible
–  Need good models and accurate
approximations
Modeling mantra
•  “Essentially, all models are wrong, but
some are useful.”
–  George E.P. Box, 1987*
*Box, G. E. P., and Draper, N. R., (1987), IN: Empirical Model Building
and Response Surfaces, p. 424, John Wiley & Sons, New York, NY.
Problem complexity
•  A human body of 70 kg is comprised of:
•  ~6.7⋅1027 atoms and ~1014 cells
•  Activity:
•  ~1025-1026 molecular reactions per day in human body
•  ~10,000 DNA single strand breaks/base loss per cell per day
•  Blood and small intestinal cells produced per day: ~1010-1011
•  A human cell is 20µm in diameter and consists of
•  ~65% water, 20% proteins, 12% lipids, ~1% RNA and 0.1–
3% DNA
•  No. of genes in the human body: ~20–25,000
Biological effects of radiation
Physics
Chemistry
Biology
Introduction proton therapy
•  Proton therapy provides a superior dose distribution
–  Better local control of tumors
–  Better sparing of normal tissue
•  It has taken a long time for protons to enter the
mainstream of radiation therapy
–  The idea has been around for more then 50 years
•  Why?
–  Technology is complex, expensive and there are many
challenges
–  Clinical benefits have not yet been proven in randomized
clinical trials (except for ocular treatment)
•  How to bring protons closer to the mainstream of RT
–  Development, research, and implementation
Proton beam physics
•  Proton treatment offers many advantages
over classical photon therapy
–  Finite range - no exit dose
–  Sharp lateral penumbra
–  Bragg peak - localized dose deposition
–  Proton dose distributions can be made to conform
tightly to irregular target shapes in all three
dimensions
–  Clinically, the radiobiology of proton beams is
almost identical to that of photon beams
–  Lower normal tissue dose for the same therapeutic
dose
Physics
Koehler 1972
Radiation beam quality
Ar
Si
C
Pions
250 kV
X-rays
60Co
22 MeV
X-rays
RBE
LET
Ne
He
H
Quality of dose distribution
Based on Fowler (1981)
Energy loss of protons
• 
Interaction with atomic electrons
– 
– 
– 
– 
– 
Almost no deflection
Small energy loss in individual collision
Continuous slowing down approximation
Bethe-Bloch theory (1930-33)
Stopping power:
S/ρ = 1/ρ[dE/dx] ~ 1/v2
–  Results in a narrow Bragg peak “broadened” by
two effects:
1.  The incident beam has a narrow energy spread (not
monoenergetic)
2.  Range straggling caused by statistical differences in
energy losses in individual proton paths.
Energy deposition
•  Energy range:
72 – 221 MeV
•  Monte Carlo
Simulations
using MCNPX
•  Compared to
measurements
•  Useful for
scanning beam
comissioning
Multiple Coulomb Scattering
•  Protons are deflected frequently in the
electric field of the nuclei
–  Small deflection angles
•  Beam broadening can be approximated
by a Gaussian distribution
•  Theory:
–  Moliere, Bethe, Scott (1940-63)
Nuclear interactions of protons
•  A certain fraction of protons undergo nuclear
interactions, mainly on 16O
•  Nuclear interactions lead to secondary particles and
thus to local and non-local (neutron) dose deposition
Pedroni et al PMB 2005, 2007
Beam delivery systems
•  Passive scattering
–  Uses double scattering system with range modulation to
produce distal edge conforming dose in the patient
–  Needs patient specific aperture and range compensator for
each beam
–  Neutrons are produced in the first and second scatterers,
range modulation wheel, aperture, range compensator, and
in the patient
•  Dynamic scanning
–  Uses two magnets to scan a narrow proton beams of
different energies to cover the target volume
–  Scanning beam has almost no neutrons generated outside
of the patient
Passive scattering nozzle
RMW
Brass
aperture
Range
Compensator
Smith, AAPM 2008
Pencil Beam Scanning Nozzle
•  Performance:
•  Range 4–36 g/cm2
•  Adjustability 0.1 g/
cm2
•  Max. field size 30 x
30 cm
•  Beam size in air 6 –
10 mm σ
•  SAD = 2.7 m
MDACC Proton Center
3 Rotating Gantries
1 Fixed Port
1 Eye Port
1 Experimental Port
Accelerator System
(slow cycle synchrotron)
Synchrotron
Beam transport line
Gantry factory tests
13 m diameter
190 tons
SAD ! 2.7 m
Treatment room
Mathematical description
•  Charged particle transport through a
prescribed background medium
–  Described by a linear kinetic or transport
equation
•  Simple particle balance in phase space
(Liouville’s theorem)
–  Assume continuous, isotropic, stationary
medium
–  May need separate solutions on various
length and time scales
Space and Time Scales
Particle interactions
 
(r, v, t)2
Particle
 
(r, v, t)1
θ
Medium
•  Interactions described with a linear integral operator whose  
kernel indicates
 the probability of scattering from the state (r, v, t)1
to the state (r, v, t)2

 

•  It is often more practical to use (r, E, Ω, t) instead of (r, v, t)1
The Transport Equation


•  Let f (r, E, Ω, t) denote the density of particles in
phase space, such that




dn = f (r, E, Ω, t)drdEdΩ
•  Is the number of particles at time t in a six

dimensional infinitesimal volume drdEdΩ .
•  Particle interact by absorption and scattering
specified by the respective cross sections, sa and ss
such that in traveling a distance ds, a particle has a
probability of absorption pa and scattering ps given by


ps = σ s (r, E, t)ds
pa = σ a (r, E, t)ds
•  Assume isotropic medium
–  sa and ss are not functions of W
•  Absorption removes particle from the beam
•  Scattering changes the particle energy and direction

–  Define the scattering kernel as σ s (r, E, E !, Ω! ⋅ Ω, t) ,
such that in traveling a distance ds, the probability ps’s of a
particle with energy E’ and direction W’ before the collision,
scattering to an energy E and direction W after the collision
is given by

ps!s = σ s (r, E, E !, Ω! ⋅ Ω, t)dsdEdΩ
–  W’ . W is the cosine of the scattering angle
Numerical approximations
•  The problem has 7 dimensions
•  Numerical methods
–  based on discretization using FEM and FD
are very rare
–  Monte Carlo very popular
•  Simple modeling of geometry and physics
•  Caveat: may need a large number of events in
order to achieve desired numerical uncertainty
Multiple scales
•  Macroscopic dose calculations
–  Domain size in ~0.5 m
–  Patient discretization in mm (1 – 5 mm
voxel size)
–  Millions of voxels
•  Microscopic effects captured using track
structure simulations and RBE models
–  Domain size in microns
–  Resolution in nm
Monte Carlo for Protons
•  Motivation:
–  Proton treatment planning is usually done using a
simplified, pencil beam (PB) algorithm for dose
calculation
–  PB is inaccurate in some cases
•  High heterogeneities
•  Distal edge degradation
–  Neutrons are neglected completely
–  Are the errors and approximations clinically
significant?
•  Analysis of treatment failures and excessive toxicities
–  Can we improve the treatment?
Monte Carlo Implementation
•  Use in-house made Monte Carlo
Treatment planning systems:
–  MCPRTP (Newhauser et al.), MC2
(Mirkovic & Titt)
•  Monte Carlo (MC) calculations provide
superior accuracy
•  MC requires a detailed, patient specific
geometrical model
•  Use DICOM files exported from TPS to
build the input for MC code
MC model for passive scattering nozzle
c
e
d
a
b
f
(a) range-modulator wheel, (b) scattering foils, (c) range-shifting plates, (d) block (aperture), (e) range compensator, and (f) voxelized
phantom.
Taddei P, Mirkovic D, Fontenot JD, Giebeler A, Zheng Y, Titt U, Woo S, Kornguth, D and Newhauser WD. Estimated risk from stray
neutron dose for proton craniospinal irradiation to a pediatric patient represented by a voxelized phantom. PMB (In press).
Biological effects of protons
•  Biological effects of ionizing radiation
are consequence of a complex
sequence of events
–  Unreparable DNA damage is the most
important
•  Modeled using relative biological
effectiveness (RBE)
–  Depends on many factors
DNA Damage
Low
HighLET
LET
Radiobiological models
•  Need to predict a complex sequence of molecular,
cellular, and tissue responses to initial radiation
damage
–  Relative biological effectiveness (RBE) models
Radia+on RBE Dose • 
• 
• 
• 
• 
energy linear energy transfer (LET) dose per treatment frac+on +ssue type clinical endpoint, … Eﬀect Variable RBE for protons
•  Constant value of 1.1 is used in clinical practice today
•  There is experimental evidence that the RBE is not constant, but
depends on dose and on the LET
–  In vitro experiments confirm the dependence on LET
•  Blakely et al 1984, Belli et al 1993, Wouters et al 1996, Skarsgard 1998
•  In vivo experiments show much smaller variations and confirm
1.1 for clinical use
–  most in vivo studies were done at low LET - entrance region or in mid SOBP
•  Gueulette et al 2001, Paganetti et al 2002, Mason and Gillin 2007.
•  Measured values have insufficient resolution of RBE
dependence on LET
–  Many authors use physics based phenomenological models
(Wilkens and Oelfke 2004, Frese 2009, Stewart 2009)
MC Dose
Eclipse Dose
MC LET
LET profile along the beam axis
RBE – LET Relationship
Typical LET
range for
proton therapy
RBE vs. LET. The data is from a number of experiments using a number of ions, energies
and cell types. The shaded area shows the general trend of the data. (Blakely 1984)
Phenomenological models
•  Wilkens and Oelfke 2004
–  Use LQ model for biological
response
S = exp(-aD-bD2)
–  Two survival curves
•  Reference (photon) and proton
–  RBE = ratio of doses for the
same effect
ap(L) = a0 +lL, bp(L)=bx, a0 = ax
S [-]
–  Only ap depends on LET
(LSM)
0
10
Increasing
LET
-5
10
0
2
4
6
Dose [Gy]
8
10
In the limit of very small and very large doses the RBE is proportional to /
respectively.
x
and
⇥/⇥x ,
Effect of l on proton RBE
Frese, 2011
Figure 2.2: The
influence ofRice
the parameter
of the LSM
on the2014
proton RBE. A value
D. Mirkovic,
University⇤ Seminar,
Spring
obtained from in vitro experiments with V79 cells (⇤ = 0.02 µm/(keV · Gy)) is compared
with a second value (⇤1.1 = 0.008 µm/(keV · Gy)) reflecting the clinical experienced average
Clinical application
•  Use reference a and b parameters for different tissue
types from literature
–  Example: lung TRP (Seppenwoolde 2003)
a=0.0258 Gy-1 and b=0.0065 Gy-2 (a/b = 4)
•  The parameter l is not so easy to determine
–  Fit the value of l using experimental data
–  Compute the value of l such that the mean value of the RBE
inside the target is 1.1 (Frese 2009)
–  Compute the value of l such that mid SOBP RBE matches
values form literature
–  Here we use l = 0.008 mm keV-1 Gy-1 (Frese 2010)
RBE
RBE profile along the beam axis
Variable RBE dose
Constant vs. variable RBE dose
Dose difference
Collaboration areas
•  Fast and accurate solutions for radiation
transport problems
–  Fast MC
–  Numerical PDE methods
•  Efficient geometry modeling using
medical imaging data (CT or MRI)
–  Grid construction
–  Multiple length scales
•  Medical image processing
Credits and acknowledgments
•  Collaborators:
Uwe Titt, Radhe Mohan, Pablo Yepes, Philip Taddei,
Yuanshui Zheng, Annelise Giebeler, Jonas
Fontenot, Wayne Newhauser, Gabriel Sawakuchi,
Lei Dong, Luis Perles
The University of Texas M.D. Anderson Cancer
Center, 1515 Holcombe Blvd., Unit 94, Houston,
TX, 77030, USA
•  This work was supported in part by
–  NCI P01 Award MGH + MDACC
–  Northern Illinois University through a subcontract
of DOD contract W81XWH-08-1-0205
–  Varian medical systems MRA

presentation slides - DIR-Lab

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