WE – B-BRB-2: Therapy Continuing Education Course
CE-Therapy: Patient Motion: Adaptive RT
8:30 AM
Patient Motion Modeling & Adaptive
Dose Compensation – D. Yan
8:55 AM
4D IMRT optimization incorporating
organ motion– T. Bortfeld
Patient Motion Modeling
&
Adaptive Dose Compensation
Di Yan, D.Sc.
Treatment Position Variation
™ Changes
in patient anatomical position, size and shape
between the time period of the treatment simulation and
those during the treatment deliveries, which are most
likely caused by
¤ Patient positioning, motion & weight loss
¤ Organ filling & wriggling
¤ Respiratory & cardiac motion
¤ Dose induced tumor & normal organ variations, such as
tumor/organ shrinkage, lung expansion, filling reduction
Page 1
Treatment Position Variation: Statistical Description
P2 :
v
v
u1 ( t1 ), ..., u1 ( t n )
v
v
u2 ( t1 ), ..., u2 ( t n )
⋅
⋅⋅⋅
P1 :
Pm :
→
→
⋅⋅⋅
v
v
um ( t1 ), ..., um ( t n )
{M
p
{ µv1
{ µv2
→
{ µvm
→
{M
, Σ p}
Two-Parameter-Model
v
( µi )
v
, σ1}
v
, σ2}
⋅⋅⋅
v
, σm}
, Σ( µvi ) , RMS(σvi ) , Σ(σvi ) }
Four-Parameter-Model
Treatment Position Variation: Generic Target Margin
(1.5 ~ 2.5) ⋅ Σ p :
Goitein 1985 (Mp = 0)
(2.0 ~ 2.5) ⋅ Σ( µi ) + 0.7 ⋅ RMS(σ i ) :
Stroom 1999; van Herk 2000
(M(µ) = 0, Σ(σ) = 0, RMS < 5 mm)
2.5 ⋅ Σ( µ i ) + 0.7 ⋅ RMS (σ i ) ≈ 2.3 ⋅ Σ p
All generic margin recipes derived from either geometric
consideration or dosimetric consideration give us similar margin
values. However, margin recipe derived from Four-ParameterModel provides more intrinsic features…
2.5 ⋅ Σ( µi ) + 0.7 ⋅ RMS (σ i ) ,
If Σ = RMS = 4 mm
Generic Target Margin ~ 13 mm
Reduce the systematic variation alone
(Margin reduces to 5.5 mm)
Σ ( µ ) = 1 mm
Σ( µ ) = 4 mm
Reduce the additional random variation
(Margin reduces to 3 mm)
RMS(σ ) = 1mm
RMS(σ ) = 4 mm
Page 2
Impact of Patient-Specific Information
Generic Target Margin
Patient-Specific Target Margin
(small random variation)
SI
Lat
patientpatientspecific
correction
Impact of Patient-Specific Information
Generic Target Margin
PatientPatient-Specific Margin
(large random variation)
SI
Lat
patientpatientspecific
correction
Patient Specific Target Margin
“depends on the dose distribution shape”
v
v
γ i + c ⋅σi ,
v
v
γ i − residual after correction of the µi
1 .8
1 .6
IMRT
1 .4
1 .2
1
CRT
0 .8
0 .6
0 .4
0 .2
0
1
2
3
4
5
6
7
σ (mm )
Page 3
Patient Specific Target Margin
“depends on where the dose is prescribed on the target edge”
Treatment setup at the mean target position.
Breathing motion compensation for 1.5 cm excursion (σ = 5 mm)
Rx Dose at 98%: Target Margin = 4.5 mm
Rx Dose at 95%: Target Margin = 3.6 mm
Rx Dose at 90%: Target Margin = 3.1 mm
Rx Dose at 80%: Target Margin = 1.8 mm
Rx Dose at 70%: Target Margin = 1.0 mm
Rx Dose at 60%: Target Margin = 0.0 mm
Patient Specific Target Margin
“less depends on the variation distribution”
σ = 3.9 mm
m=0.9
m=0.8
m=0.9
m=1.0
Patient Specific Target Margin
“less depends on the variation distribution”
σ = 5.8 mm
m=2.0
m=2.1
m=1.6
m=2.3
Page 4
Patient Specific Target Margin
“less depends on the variation distribution”
σ = 7.7 mm
m=3.1
m=3.4
m=2.7
m=3.7
Patient Specific Target Margin
“less depends on the variation distribution”
σ = 9.6 mm
m=4.3
m=5.0
m=3.8
m=5.4
Patient Specific Target Margin
“less depends on the variation distribution”
σ = 11.6 mm
m=5.7
m=6.7
m=5.1
m=7.3
Page 5
Patient Specific Target Margin
™
Strongly depends on the dose distribution shape
™
Therefore, strongly depends on where the dose is
prescribed on the target edge
™
less depends on the patient motion distribution, i.e
patient specific target margin can be evaluated
based on the motion standard deviation alone
(assuming the systematic variation = 0)
Adapting Dose Distribution to Patient Motion
+
“4D” Dose
Distribution
Planned Dose
Distribution
Tumor Motion
Change in Beam
Planned Dose
Distribution
Dose Distribution with
Motion effect
Adaptive Dose Compensation: 4D Treatment Dose
4D treatment dose delivered to a tissue element during the n
fractions of treatment with beam on duration Ti ,
D (v) =
n
∑∫
i =1
Φ(t ) −
Ω(t ) −
v
xt (v ) −
t∈Ti
v
d& ( x t ( v ), Ω ( t ) , Φ ( t ) )
Machine output at the time t
Tissue global density distribution
represented by a CT image obtained at the time t
Tissue element position at the time t
Page 6
4D Treatment Dose
Effect of Tissue Global Density Variation
4D Treatment Dose
Effect of Tissue Global Density Variation
Can the effects of 4D attenuation & 4D scatter kernel
be approximated using those in a 3D image with the mean
density?
Dose Discrepancy of Using Mean CT vs Single CT
AP-PA beams with 40 cm separation, 4 cm target & 3 cm motion
2%
Max Dose
Discrepancy
5%
10%
15%
20%
25%
Mean CT
Target
% in 1cc
2.7%
Lung
% in 1cc
8%
Diaphragm
% in 1cc
9%
Single CT
15%
26%
25%
Page 7
Adaptive Dose Compensation: 4D Treatment Dose
4D treatment dose delivered to a tissue element during the n
fractions of treatment with beam on duration Ti ,
D (v) =
n
∑∫
t∈Ti
i =1
Φ(t ) −
Ω(t ) −
v
xt (v ) −
v
d& ( x t ( v ), Ω ( t ) , Φ ( t ) )
Machine output at the time t
Tissue global density distribution
represented by a CT image obtained at the time t
Tissue element position at the time t
Tissue Element Position: Temporal Variation
Setup
Process
Organ
Filling
Process
Dose
Response
Process
Breathing
Process
Planning
t1
t2
tk
tn
RT process
Tissue Element Position: Spatial Variation
{v0 ,
VOI
v
xt , ρ 0 }
Rigid body
motion
{vt ,
{ v0 , xv0 , ρ 0 }
mass preserved
Element : v 0
v
Position : x 0
Shrinkage
density preserved
v
xt , ρ t }
Deformation
Density : ρ 0
Density Reduction
{ vt , xvt , ρ0 }
{v0 , xvt , ρ t }
volume preserved
Page 8
Description of Patient Anatomical Variation
Patient anatomical variation during the treatment delivery
can be completely described using three random processes
of the tissue element ‘volume’, ‘position’ and ‘density’
n
⎧
⎫
v
⎨ ( v t , x t , ρ t ) t ∈ T = U Ti ⎬
i
=
0
⎩
⎭
In general, all these three parameters need to be considered.
However, only the position variation has been extensively
studied so far.
Description of Patient Anatomical Variation
1. Stationary Process for Position Variation
v
xt ~ pdf ( µv , σv )
has the ‘Time-Invariant’ mean & standard deviation
Setup
Process
Organ
Filling
Process
Description of Patient Anatomical Variation
2. Non-stationary Process for Position Variation
v
xt ~ pdf ( µv t , σv t )
has the ‘Time-Variant’ mean & standard deviation
Dose
Response
Process
Breathing
Process
Page 9
Treatment Adaptation: Goals
™ Reduce
the influence of treatment variation (by
correcting or re-planning) to maintain predefine
planning criteria
¤ Treatment QA
™ Utilize
the knowledge of treatment variation (geometry,
dose & bio-activities) to improve individual treatment
¤ Adaptive treatment optimization
Treatment Adaptation: Offline Method
Determine optimal beam delivery based on patient anatomy
and dose observed during the first k treatment for the
remaining treatments
Past Treatments
Future Treatments
Dk
pdf
Dn ( Φ ) = Dk + ( n − k ) ⋅ ∫ 3 d ( xv , Φ ) ⋅ pdf
R
v
v
( x ) ⋅ dx
Treatment Adaptation: Online Method
Determine optimal beam delivery for the present
treatment using the online patient anatomy as well as all
observations (anatomy and dose) during the previous
treatments
Past Treatments
Present Treatment
Future Treatments
(delivered dose)
(online)
(Sample Estimation)
Dn
(Φ )
=
n
⋅ ( D k + d k +1 ( Φ ))
k + 1
Page 10
Summary
™ Generic
margin recipes derived from either
treatment geometric consideration or dosimetric
consideration give us similar margins, therefore
they provide similar effect in radiotherapy
planning
™ Patient
specific margin, on the other hand, is fully
dependent on the actual dose distribution in the
individual, therefore it is appropriated for the
adaptive planning design
Summary
Control strategy of adaptive radiotherapy depends on the
intrinsic feature of patient anatomical variation, stationary or
non-stationary
™ So far, we have learned
¤ Prostate Cancer (stationary process)
‹ Offline single adaptive planning modification
‹ Online adaptive modification
¤ H&N Cancer (non-stationary process)
‹ Offline multiple adaptive planning modifications
¤ Lung Cancer (non-stationary)
‹ Offline single adaptive planning + the mean target
position control
™
Page 11