• Modern radiation therapy does very well at shaping
dose distributions
Parameters for and Use of
NTCP Models in the Clinic
• For tumor control, tumor localization + sufficiently high
dose (understanding tumor dose-response) are key
• For each normal tissue of interest, we know the
planned dose distribution for the entire organ volume
• IGRT will soon give information about delivered doses
Ellen D. Yorke
Memorial Sloan-Kettering Cancer Center
New York City, NY
Supported in part by NCI Grant PO1-CA-59017
Usual assumption
Probability of a particular complication has a sigmoidal
increase with dose or a dose-related metric.
NTCP=Normal Tissue Complication Probability
NTCP(%)
• Tabulated estimates of TD50/5 and TD5/5
– Doses for 50% & 5% complication probability at 5 years
– Conventional fractionation: 1.8-2 Gy/Fx
70
Most clinical data
60
50
TD50: Dose for 50%
complication probability
40
30
20
10
0
20
30
40
50
– Part of NCI funded CWG on 3D planning: IJROBP 21, 109-122, 1991
– Predates 3D-CRT era; even DVHs were new
At least one extra parameter to
describe slope
80
The 1991 Data Set
• Emami et al (9 authors – 7 MD’s, 2 PhD’s)
• Literature review up to 1991, 28 complications
100
90
• What dosimetric features should be restricted to
keep normal tissue complication risk low?
• Grading schemes: 1 is mild → 5 is lethal
• ‘Low’ is ≤ Grade 2 in any grading scheme
• What guidance is available?
• How does it apply to individual clinical practice?
60
Dose(Gy)
70
80
90
100
• For many complications, the TD’s increase if
less of the organ is irradiated
– Partial irradiation of volume fraction v of organ
– Tabulated TD50/5 and TD5/5 for v=1/3, 2/3 and 1.0
• Companion paper fit volume effects to power
law and NTCP to Lyman model
– Burman et al, IJROBP 21, 123-135
1
Volume effects according to 1991 report
Partial organ irradiation
• CT-simulation is routine
Zero dose
Uniform Dose D
Volume fraction=1-v Volume fraction=v
70
– Plus MRI, PET, 4D-CT
• 3D-CRT is the norm, IMRT explodes
TD5 vs % volume: Emami 1991
– 3D plan evaluation tools
TD5/5 (Gy)
60
50
Severe RILD
40
Radiation Pneumonitis
30
Radiation Pericarditis
esophageal stricture
20
radiation myelitis
(reference length 20
cm)
10
For many
complications, the
iso-complication dose
depends inversely on
the irradiated volume
fraction.
0
0
20
40
60
80
100
120
% Organ Irradiated
Definitions
DVH in terms of absolute dose (Gy), % volume
• Dv=highest dose that encloses v% organ volume
– D05 is thus the dose to the “hottest” 5%
• Dmax=maximum dose in structure
• VD= % volume receiving ≥ dose D
– V20=% volume receiving ≥ 20 Gy
•
1991 to Now
LUNG: AP/PA; Differential DVH
Similar definitions for ‘dose’ in % of a reference value or absolute volume
• Linear Quadratic (LQ) model:
– The smaller α/β, the greater is sensitivity to dose per fraction
• BiologicalEffectiveDose (BED)
BED= D (1+d/[α/β])
• d=dose per fraction, D=total dose
NTD=BED/(1+dstd/[α/β])
NTD is equivalent dose if delivered in fractions of dstd
• Complex dose distributions
• Huge amount of published information
– Some listed in handout bibliography
– Noisy data, various grading schemes, different calculation
methods and plans – tough to sort out
• October 2007: QUANTEC
– AAPM/ASTRO funded workshop on NTCP
– Consensus guidance for clinical use of NTCP studies
Volume effects are important!
DVH plan evaluation, dose-volume optimization
• Complications with a weak volume dependence
– Restrict Dmax or D05 to limit complication risk
– Constrain maximum dose in optimization
• Complications with strong volume dependence
– To limit complication risk, restrict mean dose or dosevolume features as guided by clinical studies
– Dose-volume or mean dose constraints in optimization
• Intermediate volume dependence
– VD for variety of doses in plan evaluation, optimization
– In the future - perhaps detailed spatial aspects of dose
distribution (high dose clusters, circumferential
irradiation) or dose-surface histograms would do better.
2
NTCP models
NTCP Models
• Statistical models
– What dosimetric features correlate with
complication?
• medical variables (chemo, co-morbidities) may be
included
– Dose distributions may be corrected for dose-perfraction (LQ model)
– Correlation alone doesn’t tell what limits to use
• Sigmoidal curves from logistic regression
• Multivariable models include several factors in a single
equation for NTCP
– Results of statistical models are used
• RTOG Nasopharynx protocol 0225, RTOG 9311 Lung
protocol, Dmax for cord ≤ 45-50 Gy
• Empirical models
–
–
–
–
Equations with parameters fit to outcomes data sets
No mechanistic foundation (except LQ if used)
Do study set characteristics apply to your practice?
Examples: Lyman model, gEUD
• Semi-mechanistic models
– Tissue architecture, as well as cellular radiosensitivity,
determine NTCP
– Parameters chosen to fit clinical data
– Do study set parameters apply to your practice?
– Examples: Serial (critical element) model, Parallel
(critical volume) model, Relative seriality model
• All models rely heavily on statistical analysis
– These papers are NOT easy reading!
Lung: Acute Radiation Pneumonitis (RP)
• Severe RP - steroids, oxygen or worse
• 20-25% incidence of RTOG Gr 3 accepted
• Usual RP onset ≤ 6 months from tx start
1991
– Total organ (v=1) is the pair of lungs
– Strong volume effect:
• TD5(1)=17.5 Gy, TD5(1/3)=45 Gy
– Low tolerance doses: TD50(1)=24.5 Gy, TD5=17.5 Gy
– Most calculations not inhomogeneity corrected
• Since 1991 Review: Seppenwoolde et al, Sem Rad Onc 11, 247-258
– Mean lung dose (MLD) is good predictive metric
– α/β~ 2-4 Gy (fractionation sensitive)
– TD50(1) ~28 Gy (inhomogeneity corrected)
50 IJROBP 54 329-39 2002
Marks and Zhou:
Oetzel (66)
40 (editorial)
Rate
Pulmonary
Toxicity (%)
Kwa (400)
30
Graham (99)
20
Hernando (201)
Yorke (49)
10
0
0
10
20
30
40
Mean Lung Dose (Gy)
•MLD<20 Gy at conventional fractionation
•Patients without special medical factors
•Low dose to large volumes surprisingly significant
•V5, V10, V1313-15 correlate with RP
• Medium doses also (V20-V40); not Dmax
• Importance of absolute volumes at low - medium doses?
• References in handout
•Evidence for regional sensitivities
•lower lung dose much more significant than upper lung dose
3
Rectal complications
• Rectal bleeding, ulceration, stricture, fistula
– Can set in early or late (up to ~ 4 years after treatment)
– 10-20% moderate rectal bleeding clinically accepted
• 1991: High TD; small volume effects
• Since 1991-motivated by prostate IMRT
• Restricting % volume ≥ 75 Gy is very important
• But the volume effect is quite complex
– Intermediate doses (V30-V72), mean dose ; High dose
clusters? Dose-surface histograms?
• α/β
β ~3-6 Gy
• Other considerations: co-morbidities, motion
Review by Jackson, Sem Rad Onc 11, p 215 (2001) and references in handout
Lyman Model Parameters
•Recent Lyman parameters for many complications:
•radiation induced liver disease (RILD), RP, xerostomia (n~1)
rectal bleeding, pericarditis, acute esophagitis
•Parameters affect model predictions for same dose
distribution
100
%TotalLungVolume
80
What is the
probability of
severe
pneumonitis for
this plan?
physical dose
NTD, alfa/beta=3
70
60
50
40
30
20
10
0
0
20
40
Dose or NTD (Gy)
60
-∞
∞
exp(-t2/2) dt
• 4 parameters
n - volume dependence; TD50(1) – dose sensitivity;
m – slope; reference volume for v=1 (often whole organ)
• TDc(v)=Dose for c% complications, partial irradiation of v
TDc(v)=TDc(1)/vn
• Histogram reduction procedures to convert a general DVH,
{Di, vi} to an equivalent partial irradiation
• Equivalent uniform dose to whole organ
Deff = ( i vi (Di)1/n)n
• Partial irradiation of effective volume to reference dose
veff= i vi (Di/Dref)1/n
Generalized Equivalent Uniform Dose (gEUD, EUD)
•gEUD=uniform dose with the same biological effect as
the true dose distribution
•Introduced by Niemierko, 1999
•Given an organ or tumor DVH {Di,vi}
i vi(Di)
a)1/a
•Normal tissue complication: a >0; gEUD=Lyman Deff, n=1/a
•Different complications of a tissue can have different a’s
•For tumor control, a<0
•One formalism handles normal tissues and tumors
80
1991 RP parameters, physical dose: NTCP=24%
1991 RP parameters, NTD:
NTCP=12%
Physical dose, 1991 TD50 & m, n=1: NTCP=11.7%
NKI study (NTD used)*:
NTCP=11.3%
*Seppenwoolde et al IJROBP 55
[D-TD50(v)]/[mTD50(v)]
NTCP=(2π
π)-1/2
gEUD=(
LUNG DVH; 72 Gy to 100% isodose, 2 Gy/fx
90
Lyman Model
•Simplicity → use in plan comparison and optimization*
•One tunable parameter for tumors and NTCP
•With two more parameters, get a sigmoidal function
•f=1/(1+(EUD50/EUD)k)
•*Wu Q et al, , IJROBP 52 and Med Phys 32
4
gEUD dependence on “a”
Normal tissues: a>0
a>>1: Weak volume dependence, high doses dominate EUD
a=1: EUD=mean dose
0<a<1: even stronger volume dependence
a<0 for tumors: a<<0, cold spot dominates EUD
0.45
0.4
0.35
Fractional Volume
0.3
0.25
0.2
0.15
0.1
0.05
0
0
10
20
30
40
50
60
70
80
a
-20
0.2
1
20
100
gEUD (Gy)
34.8
49.3
50
60.9
67.9
Dose (Gy)
Tissue architecture models
• See Withers et al, IJROBP 14, 751-759
H1:Organs are made of functional subunits (FSUs)
H2: Given a dose distribution, the probability of a
complication depends on
– FSU radiosensitivity
– FSU organization (tissue architecture)
• Assume: FSUs respond independently
– LQ model takes care of temporal/fractionation effects
• None of these models are mechanistic at the
cellular or anatomic level. Are they better than
statistical or empirical models?
– See Med Phys “Point-Counterpoint” Vol 25, p 2265 (1998)
Simple differential DVH
Serial (critical element) model
–
–
–
–
FSUs arranged “in series” (
)
)
NTCP=probability at least one FSU killed (
Weak volume dependence (like small n Lyman model)
Infrequently used: Dmax preferred
vs
• Parallel (critical volume) model
• FSUs work in parallel:
No Comp
Comp
– Complication only if ≥ critical fraction f* are damaged
– For general DVH, {Di,vi}
fdam =
i vi p (Di)
• p(D) is the probability that a dose D damages an FSU
– Strong volume dependence – fit to clinical data for
RP, RILD, xerostomia, radiation nephritis.
– Seldom used: Users prefer the other models
described here for plan evaluation and optimization.
Qualitative difference: Lyman vs parallel model
Dose=0
Volume fraction 1-v
Dose=D
Volume fraction=v
• Lyman: Deff= Dvn n=1
•As D ↑, Deff ↑, even if v small
•If Deff >>TD50(1), NTCP
100%
•Parallel: fdam= v p(D)
•As D ↑, p(D) → 1.0 and fdam → v
•NTCP can be small
•depends on f* distribution
•if v<f*, predicted NTCP is
zero, regardless of dose
•Probably neither is ‘true’
100
90
Probability of pneumonitis (%)
•
80
LymanNTCP: wholelung
MichiganParallel NTCP: whole lung
LymanNTCP: 1/3lung
70
MichiganParallel: 1/3lung
60
50
40
30
20
10
0
0
20
40
60
80
100
Dose(Gy)
5
Relative seriality model
• Assume complication has serial and parallel aspects
– Each parallel part made of serial components
– Källman et al, Int J Rad Biol 62, p 249-62
• 4-parameter model
– Published parameters for RILD, RP, late cardiac mortality ,
xerostomia, rectal bleeding, esophageal stricture
• NTCPWO(D)=whole organ response
P(D)=NTCPWO (D)=2-exp(eγγ(1-D/D50))
• γ determines slope; D50 the radiosensitivity
• LQ model for dose per fraction effects (α/β)
• For general DVH, {Di, vi}
NTCP={1-Π
Π i[(1-P(Di)s]vi}1/s
• s is the seriality parameter
– s=1 : serial structure; weak volume dependence
– s <<1: strong volume dependence
MSKCC Prostate IMRT
•Rectal wall contoured ~5 mm sup to ~ 5 mm inf of PTV
•PTV=prostate+6 mm posteriorly; prostate+1 cm otherwise
•Dose, dose-volume constraints: quadratic score function
•Strict rectal wall evaluation constraints based on analysis
of in-house data (Skwarchuk et al IJROBP 47; Jackson et al, IJROBP 49)
•V75.6≤ 30%; V47 ≤ 53%, No hot-spots in rectal wall
•Very low rate of ≥ Grade 2 rectal bleeding
• Different models or different parameter sets,
applied to the same dose distribution generally
predict different absolute and even relative
complication rates
– They can rank competing plans differently
• Model parameters may depend on nondosimetric variables
– chemotherapies, co-morbidities, age, gender, societal
backgrounds (which may influence co-morbidities)
• Nonetheless, judicious use of NTCP model
information can make treatment plans more
consistent/less planner dependent.
– We’ve probably all been using such information in daily
practice.
MSKCC Lung cancer planning
•Lyman model,1991 parameters
• NTCP ≤25% (deff ~ 20-21 Gy) and/or
•Parallel mode; parameters from Ten Haken
• fdam ≤ 0.28
• and/or at MD’s discretion; Rx lowered so at least one is met
•Intrinsic model differences give planners grief!
•Observed ≥ RTOG Grade 3 RP is ≤15%
f d a m v s d e f f f o r p a r t ia l v o lu m e ir r a d ia t io n
a t v a r i o u s p r e s c r ip t i o n d o s e s
dam
f
•<2% at 8 y; prescription=81 Gy (Zelefsky et al, J Urol 2006)
•PSA-relapse-free survival by risk group: 89%, 78%, 67%
•Maximum prescription dose 86.4 Gy (Zelefsky, ASTRO 2006)
~ (deff/D)1/0.87
0 .5
fdam
50 Gy
60 G y
81 G y
0 .4
A c c e p te d b y d e ff,
R e je c te d b y fd a m
100 G y
R e je c t e d b y b o t h
f d a m l i m it
0 .3
0 .2
fdam or partial vol
A c c e p te d b y b o th
R e je c te d b y d e ff,
A c c e p te d b y fd a m
0 .1
d e f f l i m it
0 .0
0
5
10
15
d e ff (G y )
20
25
30
A. Jackson
6
Radiobiological Indices in Optimization
• Disclaimer: Very little personal experience
• To go to “Level 2”, I anticipate a learning curve
• Literature: Evidence for gEUD advantages
– Different functions to put gEUD into score function
– Equivalent or better normal tissue protection
– Target EUD higher, distributions less homogeneous than
conventional
• Is homogeneity beneficial without detailed information about
clonogen location within target?
• Dummy normal structure to prevent overdosing target volume
• Other NTCP models could be similarly included
• “In the works” with TPS vendors
Evolution
Spares
2D
3D-CRT
IMRT
7
Statistical Models: Radiation Myelitis
Most normal organs suffer several different radiation
complications; there are several different scoring systems
• Protection against myelitis mandatory
– Delivered dose may be >planned due to setup error, scatter
• 1991: TD5(1)~47-50 Gy,TD50(1)~70 Gy
Very weak volume dependence for myelitis
• Updated information
Schultheiss et al, IJROBP 31
–
–
–
–
0 None
1 Radiographic changes (RC),
asymptomatic or symptoms not
requiring steroids
2 RC and steroids or diuretics
3 RC and symptoms requiring
oxygen
4 RC and assisted ventilation (AV)
5 Death
Weak volume dependence confirmed
α/β~2 Gy (sensitive to dose per fraction)
TD5~57-60 Gy but we routinely keep Dmax≤ 45-50 Gy
Slow damage repair component (> 8 hrs)
RTOG Grades
• Wiggle room for retreatment?
– Lit search, very small # pts (~60)
Nieder et al, IJROBP 66
– α/β=2 Gy for C, T spine, 4 Gy for L-spine
– No myelopathies reported for total BED<120 Gy2
• time between courses >6 months; individual BED’s < 98 Gy;
small risk for total BED< 135.5 Gy2
Relative seriality model
– At least 2 parameters for p(D)
• Complication if ≥ critical fraction, f*, of FSUs are damaged
– NTCP=probability that ≥ f* are damaged
f*=25%
s=0.01,
v=1/3
0.8
s=0.01,
v=2/3
0.6
s=1, v=1/3
0.5
power law
n=1, D50
v=1, 2/3, 1/3
XXXX
X X X X vs
XXXX
XXXX
No comp vs
1
0.9
0.4
power law
n=0.1, D50
v=1, 2/3, 1/3
0.3
gamma=2
0.8
gamma=4
0.7
0.6
P (D )
NTCP
0.7
0.5
0.4
0.3
0.2
0.2
0.1
0.1
0
0.5
0.7
0.9
1.1
D/D50
0
0
0.5
1
1.5
2
2.5
3
0. None
1. Asymptomatic or mild (dry
cough), slight radiographic
appearances
2. Moderate symptomatic
fibrosis or pneumonitis (severe
cough, low grade fever), patchy
radiographic appearances
3. Severe symptomatic fibrosis
or pneumonitis (severe cough);
dense radiographic changes
4. Severe respiratory
insufficiency; continuous O2;
assisted ventilation
5. Death
• FSUs work “in parallel”
• Probability of damaging a single FSU=p(D)
whole
organ,
gamma=2
1
0 None
1 Mild dry cough, dyspnea at
exertion
2 Persistent cough, dyspnea at rest
3 Severe cough- steroids and/or
intermittent oxygen
4 Severe respiratory insufficiency,
continuous oxygen or AV
5 Death
Late lung toxicity
(RTOG/EORT)
Parallel (Critical Volume) Model
Difference between relative seriality and
power law predictions
0.9
Acute Radiation Pneumonitis
NCI Grades
3.5
D/D50
Slope of whole organ response increases with γ
Volume dependence increases as s decreases
1.3
1.5
1.7
XXXX
XXXX
XXXX
XXXX
XXXX
or any other combo X X X X
4 or more damaged X X X X
XXXX
comp
• Fraction damaged= fdam = vi p(Di)
• Strong volume dependence predicted
– Applied to RP, RILD, xerostomia, nephritis
– Need at least 4 parameters for NTCP calculation
– Users prefer Lyman, relative seriality models, gEUD or VX
for plan evaluation and optimization
8