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Evidence-based NTCP modeling
MEDICAL SCHOOL
Dose-volume modeling &
clinical radiotherapy:
The art of
systematic oversimplification
E) = ε(D
D)
P(E
4D dosedistribution, D
Søren M Bentzen, Ph.D., D.Sc.
UW Comprehensive Cancer Center, Department of Human Oncology
Madison, Wisconsin, USA
bentzen@humonc.wisc.edu
Biological effect, E
Find ε(Di, zi, ti)
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The lungs
“Under normal conditions the research
scientist is not an innovator but a solver
of puzzles, and the puzzles upon which
he concentrates are just those which he
believes can be both stated and solved
within the existing scientific tradition.”
−Thomas Kuhn
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Gray’s Anatomy 1918
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1
The model
Volume
effect
in lung
Herrmann et al.
R&O 44: 35 (1997)
• left lung
half that volume
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“All models are wrong,
but some are useful”
−George E. Box (1979)
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So, are they
ALL wrong?
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2
Some mechanistic NTCP models
Critical element model
Niemierko, Goitein, Withers
Critical element w. migration
Shirato
Critical volume model
Niemierko, Goitein, Jackson
Critical volume w. migration
van Luik, van der Kogel
Relative seriality model
Kallman, Brahme, Gagliardi
Contiguous damaging of FSUs
Stavreva
Local damage model
Alber, Nüsslin
Equivalent uniform dose
Niemierko, Goitein
WMK + FSU
Judas, Bentzen
Variable critical volume
Bonta
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Mechanistic models
cell migration,
spatial
organization
cell
SF(d)
FSU
p(D)
functional &
proliferative
organization
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organ
D)
pind(D
physiological
reserve
capacity
Population
D)
P(D
heterogeneity
covariates
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Goodness of fit
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Tucker et al. IJROBP 60: 1589 (2004)
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3
Parallel/serial organisation of FSUs
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Withers et al. IJROBP 14: 751 (1988)
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Volume effect in rat spinal cord
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van der Kogel in Steel (3rd ed).
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Dose-distribution and rat spinal cord NTCP
Cervical spinal cord
irradiated with single doses
to 2,4,8, and 20 mm length +
non-uniform bath & shower +
two non-contiguous regions
of 4 mm separated by 4 or 8
mm.
14 dose-volume models
NONE OF THEM FITTED
ALL THE DATA.
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van Luik et al. IJROBP 61: 892 (2005)
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Are some of them
USEFUL then?
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4
Some phenomenologic NTCP models
Probability model
Schultheiss
Lyman model, LKB
Lyman, Kutcher, Burman
Generalized EUD, gEUD
Niemierko
Exponential tolerance
van Luik, van der Kogel
The Lyman model
Lyman’s model gives the normal-tissue complication probability
(NTCP) when a partial organ volume, V, receives a dose, D:
NTCP(t ) =
t=
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Dose-volume relationships for normal-tissues
Prescribed doses from Emami et al. IJROBP 21: 109, 1991.
Analyzed by Burman et al. IJROBP 21: 123, 1991.
RD50 (Gy)
1000
Bladder
Brain
Kidney
Lung
Rectum
Spinal cord
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D50 (1)
Vn
Lyman JT Rad Res 104: S-13 (1985)
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1
⋅
2π
s⋅( µ − µ 50 )
−∞
exp(− 12 ⋅ x 2 ) dx
These models have two parameters, quantifying steepness and
position of the dose-response or volume-response curve, plus
zero or more parameters used to derive µ from the 3D dose
distribution
0.1
For dose-response models:
1
Partial volume irradiated
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exp(− 12 ⋅ x 2 )dx
This class of models include the LKB model: they are probit doseresponse models as a function of a summary dose or volume
measure, µ , derived from the 3D dose distribution
100
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t
−∞
Generalized Lyman models
NTCP ( µ ) =
10
0.01
⋅
D − D50 (V )
m ⋅ D50 (V )
D50 (V ) =
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1
2π
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s=
γ 50 ⋅ 2π
µ50
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5
3D-CRT v IMRT in prostate cancer
MC estimates of dose escalation
“Virtual clinical trial”
3D-CRT
6MV – 3D CRT
5 consecutive patients with localized
prostate cancer
Planned with 6MV 3D-CRT
and 6 MV IMRT
Dose escalation based on NTCP
for rectum??
IMRT
Literature data:
DVH “Mean dose” NTCP model
70 Gy
Escalated dose, D [Gy]
70 Gy
120
100
80
60
40
20
128 pts w. prostate cancer
G2+ rectal bleeding within 2 years
Tucker et al IJROBP 60: 1589 (2004)
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Aoyama et al. (submitted)
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MC estimates of ∆D
Dose increment, ∆D [Gy]
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5
8000
10000
WORK IN PROGRESS
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• (e.g.) Bradley et al. IJROBP 58: 1106 (2004)
4
3
Principal component analysis
• Dawson et al. IJROBP 62: 829 (2005)
2
1
Artificial Neural Networks (ANN)
2000
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6000
Run #
Standard statistical multivariate analysis, e.g.
logistic regression (early effects) or Cox’s
Proportional Hazards Model (late effects) ±
mechanistically inspired co-variates
6
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4000
Data-driven approaches
6MV – 3D CRT
6MV – IMRT
7
2000
4000
6000
Run #
WORK IN PROGRESS
8000
• Gulliford et al. R&O 71: 3 (2004)
10000
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6
Oesophagitis after 3D-CRT
Local damage model, (f-dam)
166 patients, definitive RT for Stages I-IIIB NSCLC.
Local DP,%
NTCP,%
100
100
80
80
60
60
40
40
20
20
0
Total doses of 60-74 Gy (median, 70 Gy),1.8-2.0 Gy/F
Oesophageal contrast was used to contour the
oesophagus on CT in each case.
78 patients received cis-platin based chemotherapy (37
pre-RT and 41 concurrent)
0
VOLUME
DOSE
Oesophagitis, RTOG grades
2
vdami
i
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Andy Jackson
MEDICAL SCHOOL
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Dose-area relationship for oesophagitis
Incidence of esophagitis (%)
Significant factors
A55 (P=0.0009),
Concurrent chemotherapy (P=0.0009)
A80 (P=0.04)
Not significant
KPS
Age
Pre-RT chemotherapy
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Bradley et al. IJROBP 58: 1106 (2004)
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G2+ Oesophagitis after 3D-CRT
Ax: the area receiving dose ≥ x Gy
Logistic regression, G2+ oesophagitis
Bradley et al. IJROBP 58: 1106 (2004)
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100
90
80
70
60
50
40
30
20
10
0
• 166 patients, definitive RT for
Stages I-IIIB NSCLC.
CRT
• Total doses of 60-74 Gy
(median, 70 Gy),1.8-2.0 Gy/F
RT
• Oesophageal contrast
• 78 patients received cis-platin
based chemotherapy (37 pre-RT
and 41 concurrent)
0
30
60
90
120
150
A55 (cm2)
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Bradley et al. IJROBP 58: 1106 (2004)
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7
Sensori-neural hearing loss (SNHL)
In c id e n c e o f h e a rin g lo s s (% )
Sensori-neural hearing loss
20 patients with nasopharyngeal
carcinoma
36 ears with valid data
Pre- and post-radiotherapy audiometry
15 dB change in hearing threshold
defined as clinically relevant loss
Dose to cochlea reconstructed on CT
scans
100
80
60
40
20
0
0
20
40
60
80
Total dose (Gy)
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Honore et al. R&O 65: 9 (2002)
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Honore et al. R&O 65: 9 (2002)
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Radiological lung density change v time
10
100
Adjusting for
patient’s age
and pre-RT
hearing level
80
60
40
49 yo
20
43 dB pre-RT hearing level
0
0
20
40
60
80
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Honore et al. R&O 65: 9 (2002)
8 •
••
• •• •
•
•
6
•• • •
• •
•
4
•
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Apical lung fibrosis
Single anterior field
8 MV X-rays
36.6 Gy in 12F
•
•
2
0
Total dose (Gy)
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Change in lung density (%)
In c id e n c e o f h e a rin g lo s s (% )
Sensori-neural hearing loss
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0
2
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4
6
8
Follow-up (years)
10
Skoczylas et al. Acta Oncol 39: 181 (2000)
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8
Cumulative latent-time distributions
% of ultimate incidence
100
Late edema in the CHART trial
Incidents among 5-year survivors
Moderate and severe bladder reactions
Severe rectosigmoid reactions
80
Data from Pedersen et al. IJROBP 29: 941 (1994)
Pts with one or
more incident (%)
K-M estimate
@ 5 years
49/92
53.3%±5.2%
48.8%±2.7%
32/54
59.3%±6.2%
59.5%±3.4%
Subcutaneous fibrosis G2+
60
Data from Bentzen et al. R&O 15: 267 (1989)
40
Telangiectasia G2+
Model prediction after 70 Gy in 35 F
conventional
20
0
CHART
Data from Turesson analyzed in
Bentzen et al. R&O 18: 95 (1990)
0
1
2
3
4
Follow-up (years)
5
2P=0.49
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2P=0.02
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Where do we go from here?
Time-dose-fractionation
Patient-related risk factors
Multi-modality studies
Statistics w/ censoring for late effects
Randomized trials
Multi-institutional studies
Standardized recording and reporting
Data-banking
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9
Principal component analysis
Parotid gland
Iso-NTCP lines for 15%
incidence of SNHL
Figure 5
Liver
Pre-therapeutic hearing threshold/ dB
70
60
70 Gy
60 Gy
50
50 Gy
40
40 Gy
30 Gy
30
20 Gy
20
10 Gy
10
0
20
30
40
50
60
70
Age/ years
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Dawson et al. IJROBP 62: 829 (2005)
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Honore et al. R&O 65: 9 (2002)
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10