Transcript Document

HST.187: Physics of Radiation Oncology
#9. Radiation therapy: optimization in the
presence of uncertainty
Alexei Trofimov, PhD
[email protected]
Jan Unkelbach, PhD
[email protected]
Dept of Radiation Oncology MGH
April 3, 2007
Uncertainties in RT
• Intro
– Sources of uncertainty, e.g. • Set-up, target localization (inter-fractional)
• Intra-fractional motion
– Methods to counter the uncertainties
• Volume definitions/ margins, treatment techniques
– Effect of uncertainties on the dose distribution
• Probabilistic planning techniques in the presence of
uncertainties
– Inter-fractional motion and set-up uncertainties
– Proton range variations in tissue
• Handling of intra-fractional motion (respiratory)
– Image-guided radiation therapy IGRT and “4D” planning
– Probability-based motion-compensation
– Intro to robust optimization
Target definition:
inter-observer
variation
Steenbakkers et al R&O 77:182 (2005)
Target motion (intra-fractional)
Targeting
Interplay between internal motion and
the multi-leaf collimator sequence
JH Kung
P Zygmanski
Target motion (intra-fractional)
Targeting
Radiological
depth changes
Inhale
Exhale
Liver Tx plan, PA field
Planned dose at
exhale phase
Planned by J.Adams
(TPS: CMS XiO)
As would be delivered
at inhale
50%
Set-up uncertainties: day-to-day variation
Images: © 2007 Elsevier Inc
Zhang et al IJROBP 67:620 (2007)
Variation over 8 weeks of treatment
Prostate treatment
with protons
Compensator
design
Variation
In set-up
Compensator
smear
Compensator
smear
Intrafractional
motion
Part 2:
Probabilistic approach
to account for uncertainty in
IMRT/IMPT optimization
Content
• Motivation – interfractional random setup error
• Concept of probabilistic treatment planning
• Application to interfractional motion of the
prostate
• Application to range uncertainties in IMPT
Motivation
Consider inter-fractional random setup error in a
fractionated treatment
safety margin:
irradiate entire area where tumor may be with the full dose
How can we achieve an improvement?
• Lower dose to regions where tumor is located rarely
• Have to compensate for it by higher dose to other
regions
Motivation
Example:
25 moving voxels
45 static voxels
tumor voxels are at 5
different positions equally
often
Question?
Are there static dose
fields that yield tumor
coverage and improve
healthy tissue sparing?
Motivation
Example:
integral dose: 40.8
(instead of 45.0)
Motivation
Dose in the moving tumor:
dose in moving tumor
static dose field
frequency for moving voxel i being at static voxel j
Have to solve system of linear equations to
determine static dose field which yields D = 1
Motivation
Set of solutions is affine subspace
special solution
(safety margin)
kernel of the
mapping P:
Set of static dose fields which preserve D = 1:
kernel dimension  (number of static voxels) minus
(number of tumor voxels)
Motivation
Method could in principle work if motion was
predictable and treatment was infinitely long
Intrinsic problems:
• only handles predictable motion, not uncertainty
• cannot handle systematic errors
• cannot handle irreproducable breathing pattern
 Need more general method to handle
uncertainty!
(having these ideas in mind)
Idea of probabilistic method
Main assumption:
The dose delivered to a voxel depends on
a set of random variables
fluence map to be optimized
Assign probability distribution
to random variables:
vector of random
variables which
parameterize the
uncertainty
Idea of probabilistic method
Applications:
• Inter-fractional motion
G = position of voxels
P(G) = Gaussian distribution
• respiratory motion
G = amplitude, exhale position, starting phase
(note: P(G) unrelated to `breathing PDF`)
• range uncertainty
G = range shifts for all beamlets
Idea of probabilistic method
Postulate:
optimize the expectation value of the
objective function
• incorporate all possible scenarios into the
optimization with a weighting that corresponds
to its probability of occurrence
Idea of probabilistic method
Example: quadratic objective
1st order term
difference of expected and
prescribed dose
expected dose:
2nd order term
variance of the dose
Alternative formulations
• In this talk: optimize expectation value
• alternative: optimization of the worst case
(can be solved by robust optimization techniques
in linear programming)
• most desireable might be something in between
Application to prostate
Incorporating
inter-fractional motion
of the prostate
into
IMRT optimization
application to prostate
Uncertainty G: positions of voxels
Probability distribution P(G): Gaussian
application to prostate
• expected quadratic
objective function
• 30 fractions
• large amplitude of
motion ( 8mm AP,
5mm LR/CC)
static dose field
(dose per fraction)
application to prostate
expected dose in
the moving tumor
coordinate system
• Best estimate for
the dose delivered
to a voxel
application to prostate
Problem: Uncertainty implies that we
don‘t know the dose distribution which
will be delivered
 treatment plan
evaluation difficult
standard deviation:
assess uncertainty of the
dose in each point
application to prostate
Probability for the delivered dose to be below/within/above
a 3% interval around the prescribed dose
below
(D Maleike, PMB 2006)
within
above
application to prostate
Prototype GUI to view probabilities for over/under dosage
• user may select dose intervals of interest
(D Maleike, PMB 2006)
Application to prostate
Probabilistic approach can ...
• Incorporate organ motion in IMRT planning to
overcome the need of defining safety margins
• resemble the idea of inhomogeneous dose
distributions on static targets in order to achieve
better healthy tissue sparing
• control the sacrifice of guaranteed tumor
homogeneity
Application to range uncertainties
Handling range uncertainty
in
IMPT optimization
Application to range uncertainties
Conventional IMPT treatment plans may be sensitive
to range variations
 degraded dose distribution if the actual range
differs from the assumed range
assumed range
+ 5 mm
- 5 mm
Application to range uncertainties
Why? Because ...
• pencil beams stop in front of an OAR
• dose distributions of individual beams are inhomogeneous
Application to range uncertainties
Range uncertainty assumptions for probabilistic
optimization:
• 5 mm uncertainty (SD) of the bragg peak location for
each beam spot
• Gaussian distribution for the range shifts
• is considered a systematic error (no averaging over
different range realizations in different fractions)
Application to range uncertainties
• Probabilistic optimization can significantly reduce
the sensitivity to range variations
assumed range
+ 5 mm
- 5 mm
convetional plan
Application to range uncertainties
Why? Because ...
• lateral fall-off of
the pencil beam is
used
• dose distributions
of individual
beams are more
homogeneous in
beam direction
convetional plan
Application to range uncertainties
Price of robustness:
• lateral fall-off is more shallow
 plan quality for the assumed range is slightly compromised
- higher dose to OAR or reduced target coverage
convetional plan
probabilistic plan
Application to range uncertainties
Probabilistic approach can ...
• take advantage of the characteristic features of the
proton beam and the many degrees of freedom in
IMPT to make treatment plans robust with respect to
range variations
(which cannot be achieved by other known heuristics)
Part 3: Intrafractional motion
Continuous irradiation
IMRT delivery to a moving target
Int map
no motion
motion 1 fraction
motion 4 fx
The effect of target motion on dose distribution
Coverage assured with planning margins
Gated Tx at MGH
Varian RPM-system
marker block with IR-reflecting dots
IR-source + CCD camera
External-internal correlation
Tsunashima et al IJROBP 2003
Gierga et al IJROBP 2004:
correlation differs between markers
Phase shift
H
Hoisak et al IJROBP 2003
External-internal correlation
• Generally well-correlated, but…
• Not necessarily linear
• Phase shift has been observed, not necessarily
constant on different days
• Proportionality coefficients, phase may vary
with
– marker position
– respiratory “discipline” (e.g. compliance with breathtraining/coaching)
(“Fast”) tracking delivery
Inverse optimization
• Dose calculation using (Dij) matrix:
voxel i
x
beamlet j
4D- influence
matrix (D-ij)
approach
voxel i
x
beamlet j
• Dij ’s are precalculated for all beams and all
instances of geometry (4D-CT phases)
• At instance (phase) k we have
k = 1, …, 5: breathing phase
• Determine voxel displacement vector field
between Pk and P0 (reference phase)
Eike Rietzel, GTY Chen
“Deformable registration of 4D CT data” Med Phys 33:4423 (2006)
P0 (inhale)
P4 (exhale)
• Deformations are then applied to all
pencil beams in Dij matrix
pencil beam
in P4 (exhale)
x
same pencil beam
transformed to P0
(inhale)
x
A Trofimov et al PMB 50:2779 (2005)
Continuous irradiation:
instantaneous dose distribution
From a different prospective: a moving
instant. dose in a fixed reference geometry
Approaches to temporo-spatial
optimization of IMRT
A Trofimov et al PMB 50:2779 (2005)
(1) Planning with optimal margins (Internal Target Volume)
(2) Planning with Motion kernel
(a) Uniform approach (motion PDF)
(b) Adaptive approach (sum influence matrix)
(3) Gating / Unoptimized tracking – plans optimized
separately, 1 best plan chosen out of several or all
delivered dynamically
(4) Optimized tracking – several plans optimized
simultaneously, delivered dynamically
Lung: CTV vs Internal Target Volume (ITV)
Planning with “Internal” margins - ITV
App. 1: Optimal margins (ITV): lung
DVH for ITV plan recalculated for
different geometries (CT phases): lung
Approaches to Temporo-Spatial
Optimization of IMRT
(1) Planning with expanded margins (ITV)
(2) Planning with modified dose kernel
(b) Uniform approach (motion PDF)
(a) Adaptive approach (sum influence matrix)
(3) Gating / Unoptimized tracking – plans optimized
separately, 1 best plan chosen out of several or all
delivered dynamically
(4) Optimized tracking – several plans optimized
simultaneously, delivered dynamically
Motion probability distribution function (PDF)
Motion-compensation in IMRT
treatment planning
• If the motion (PDF) is known (reproducible),
the dosimetric effect can be reduced
–
–
– .
Deconvolution of intensity map
Planning with “smeared” beams
Reduction of integral dose with motion-adaptive
planning
Motion kernel: “one-size-fits-all” vs. “custom-made”
Original beamlet

=
.
Convolved “motion” beamlet
Sum of deformed beamlets
IMRT with motion-compensated Tx Plan
Int map
no motion
motion 1 fraction
motion 4 fx
Patient data
lung
liver
App. 2a: Motion kernel plan, DVH recalculated for 5 ph’s
MK plan: DVH recalculated for diff phases
App. 2b: with averaged Dij-matrices (liver)
App. 2b: with averaged Dij-matrices (liver)
App. 2b: with averaged Dij-matrices (liver)
Inhale (recalc’d to reference)
Exhale (reference)
Inhomogeneous “per-phase” doses are designed so
that the some conforms to the prescription
Approaches to Temporo-Spatial
Optimization of IMRT
(1) Planning with expanded margins (ITV)
(2) Planning with modified dose kernel (Motion kernel)
(a) Uniform approach (motion PDF)
(b) Adaptive approach (sum influence matrix)
(3) Gating / Unoptimized tracking – plans optimized
separately, 1 best plan selected for gated delivery
or all delivered dynamically
(4) Optimized tracking – several plans optimized
simultaneously, delivered dynamically
App. 3: Gating / Unoptimized tracking (liver)
App. 3: Gating / Unoptimized tracking (lung)
Approaches to Temporo-Spatial
Optimization of IMRT
(1) Planning with optimal margins (ITV)
(2) Planning with modified dose kernel (Motion kernel)
(a) Uniform approach (motion PDF)
(b) Adaptive approach (sum influence matrix)
(3) Gating / Unoptimized tracking – plans optimized
separately, 1 best plan selected for gated delivery
or all delivered dynamically
(4) Optimized tracking – several plans optimized
simultaneously, delivered dynamically
App. 4: optimized tracking (lung)
App. 4: Optimized tracking (lung)
DVH comparison for the lung case
DVH comparison for liver case
Ideal case for tracking delivery (vs gating)
DVH and dose
for different
“gated”
(single phase)
plans for the
lung case
Delivery of gated proton treatment : Timing
Sources of delay:
RPM: 60-90 ms , 75 ms average
System response time : < 5 ms
Wait for the next modulation cycle: 0-100 ms
Delivery restricted
to complete
modulation cycles:
on/off at the stop
block position only
100 ms
Total delay: 65-195 ms, average 130 ms
Hsiao-Ming Lu
Residual motion with gating
Probability distribution
Inter-fractional variability
Liver-2
Cardiac-1
Cardiac-2
Cardiac-1
Position
Position
Time
Lung-2
Variability
between
patients
Cardiac-2
Liver-2
Robust formulation for probabilistic treatment
planning:
– Tim Chan et al: Phys Med Biol 51:2567 (2006)
– Outcome will be “acceptable” as long as the
realized motion is within the expected “limits”
Realized PDF
Planning PDF
PDF
uncertainty
bounds
Dose to moving target
Planning PDF
Realized PDF
Summary
• (Some) sources of uncertainty in RT: imaging,
target definition, dose calc, set-up, inter-,
intra-fractional motion
• Margin/ITV approach is the most robust for
target coverage, but substantially increases
dose to healthy tissue
• Image-guided RT improves dose conformity,
reduced irradiation of healthy tissues, BUT
relatively complex delivery, not error-proof
• Probabilistic motion-adaptive treatment
planning in combination with image-guided
delivery may be the optimal solution
Acknowledgements
J Adams
T Bortfeld, PhD
T Chan, PhD
S Jiang, PhD
J Kung, PhD
HM Lu, PhD
H Paganetti, PhD
E Rietzel, PhD
C Vrancic