NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Outline
 Why attempt to use models?
Biological/Clinical Outcome
Models in RT Planning
 Some basic mathematical
outcomes models
 Outcomes Modeling
Randall K. Ten Haken




University of Michigan
Why consider use of models?
Pitfalls
Input data concerns
Model fitting concerns
Model use concerns
3D CRT – PTV covered!
 Are there problems that use of
100
Target dose must be
uniform to +/- 5%
Volume (%)
outcomes models could help resolve?
 Would their use make things easier or
more consistent?
 Is this relevant today?
50
0
1
- 5%
0
+ 5%
Dose (%) Desired
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
RTOG IMRT target criteria
Target volume issues
 The prescription dose is the isodose
 Are target volume hot spots beneficial?
which encompasses at least 95% of
the PTV.
 Are target volume cold spots
detrimental?
 No more than 20% of any PTV will
 How do cold spots and hot spots play
receive >110% of its prescribed dose.
off against each other?
 No more than 1% of any PTV will
 Use of TCP or EUD models could
receive <93% of its prescribed dose.
help us make rational decisions
Control of a Target DVH by a Cell-Kill
based EUD
Basic TCP Models
 Complete “birth and death” models
Only one aspect
of the target DVH is
controlled.
(M. Zaider and G. N. Minerbo, …
Volume
 Poisson (survival of clonogenic cells)
models (Webb, Nahum, ...
Add a one-sided
quadratic overdosage
penalty!
 “Tumorlet” models (Goitein, Brahme...
 EUD type approaches
Dose
Courtesy of Markus Alber
Outcome Driven Biological Optimization – Elekta/CMS MONACO
2
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Generalized Equivalent Uniform Dose (gEUD)
Equivalent Uniform Dose
DVH (fractional volume vi receives dose di )
 Uniform dose distribution that if
25
delivered over the same number of
fractions would yield the same
radiobiological or clinical effect.
 Niemierko 1996
 Brahme 1991
 Niemierko 1999 (abstract) gEUD
Volume (cc)
Volume
20
ROI with N dose points di
a
a
a
a
1 /a
=
=
=
=
1,
2,
- ∞,
+∞,
gEUD
gEUD
gEUD
gEUD
=
=
=
=
1
a

2
3
4
5
6
Dose
(Gy)
Dose (Gy)
7
8
9 10 11 12 13 14 15 16 17
1 /a
a
 N
 di
 i 1
 N




0






1 /a
a 

  v i d i 
 i

1/a
gEU D    v i d i 

a 
 N
 di 
1 /a
a 

i 1


gEUD

  v i d i 
 N 
 i





Tumors:
a is ~a negative number
Normal Tissues: a is a positive number
For
For
For
For
10
5
gEUD
i

35
90
30
85
Volume (cc)
25
80
gEUD (Gy)
gEUD
15
20
15
75
70
10
65
5
0
60
110
320
530 740
70 1580 1790
9 50 1160 13
Dose (Gy)
mean dose
rms dose
minimum dose
maximum dose
Tumors:
Min < gEUD < Mean
a is ~negative
aggressive a = -20
non
a = -5
3
-100 -80 -60
-40 -20
0
20
40
60
80
100
"a"
For a = 1, gEUD = mean dose
For a = - ∞, gEUD = min dose
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
An EUD TCP description
The TCP as a function
of uniform dose, EUD,
to the whole volume
can then be described
(for example) by the
logistic function:
Normal Tissues
D50 = 70 Gy
50 = 2
TCP ( EUD, 1) = 1 / {1 + ( D50 / EUD) 4·
50
}
NTCP, TCP, EUD Tutorial, Univ of Michigan, Dept of Radiation Oncology: RK Ten Haken , K-W Jee, 2002-08
RTOG normal tissue dose criteria
DVH Comparison - normal tissue
80
Plan 2
60
40
0
30
40
50
60
70
80
Dose (Gy)
Easy!
Plan 2 is less toxic
 minor deviation 35% to 50 Gy
40
0
20
 Rectum < 60% to receive ≥ 30 Gy
Plan 2
60
20
10
 minor deviation 30% to 40 Gy
Plan 1
80
20
0
 Small bowel < 30% to receive ≥ 40 Gy
100
Plan 1
Volume (%)
Volume (%)
100
 Bladder < 35% to receive ≥ 45 Gy
 minor deviation 35% to 50 Gy
0
10
20
30
40
50
60
70
 Femoral head ≤ 15% to receive ≥ 30 Gy
80
 minor deviation 20% to 30 Gy
Dose (Gy)
Who knows?
Depends on tissue type
4
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Normal tissue issues
Normal Tissue Complication
Probability (NTCP) Calculations
 The applicability of dose/volume
criteria alone is dependent on:
 Tissue type
 Standardization of technique
 Use of models could assimilate effects
of irregular dose distribution across
the entire normal tissue/organ under
consideration.
Basic NTCP Models
Normal Distributions
Standardized Model: in units of t = ( x – m ) / s
Fraction responding at this level
 The damage-injury/critical volume
models (Jackson & Yorke, Niemierko)
 Relative Seriality Model
 EUD type approaches
Fraction
5
m= 0,
-1
=
0
s= 1
1
1
Cumulative Fraction
 The “Lyman” model
0.8
0.6
0.4
0.2
0
-1
x
(2p)-1/2 exp (-x2/2)
0
x
Total
=
1
t
(2p)-1/2- exp (-x2/2)
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
The Lyman NTCP Description
NTCP = (2p)-1/2
The Lyman NTCP Model
t
-
 exp(-x2 / 2) dx,
where;
t = (D - TD50(v )) / (m • TD50(v )),
and;
Lyman JT: Complication probability – as assessed from dosevolume histograms. Radiat Res 104:S13-S19, 1985.
TD50(v ) = TD50(1) • v
-n
Lyman JT: Complication probability – as assessed from dosevolume histograms. Radiat Res 104:S13-S19, 1985.
The Lyman NTCP Model
DVH reduction schemes
 The Lyman NTCP model attempts to
 For non-uniform irradiation, the 3D dose
mathematically describe complications
associated with uniform partial organ
irradiation.
volume distribution (or DVH) must be
reduced to a single step DVH that could be
expected to produce an identical NTCP.
 Wolbarst & Lyman schemes reduce DVHs to
 This implies:
uniform irradiation of entire organ (V=1) to
some reduced effective dose, Deff .
 Kutcher & Burman scheme reduces a DVH to
uniform irradiation of an effective fraction of
the organ, Veff , to some reference dose, Dref.
 A fractional volume, V, of the organ
receives a single uniform dose, D.
 The rest of the organ, (1 – V ), receives
zero dose.
 i.e., a single step DVH, {D , V }
6
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Historically: Expressing the effect of a dose
distribution by its effective volume
Today: 3D dose distributions and extreme
dose heterogeneity
The effect of this dose distribution equals
an irradiation of the effective volume Veff
with the nominal dose D0
 Di 


 0
1/ n
  V  D
i
i 1
Veff
Volume
Volume
N
V eff 
Observation: irradiated volume
is frequently 100%
Switch from (Veff, D0) to
(V0, Deff)
typical 3D conf. DVH
D0
Dose
Dose
Courtesy of Markus Alber
Courtesy of Markus Alber
Outcome Driven Biological Optimization – Elekta/CMS MONACO
Outcome Driven Biological Optimization – Elekta/CMS MONACO
gEUD NTCP Description
Today: 3D dose distributions expressed in Deff
Observation: irradiated volume
is frequently 100%
Switch from (Veff, D0) to
(V0, Deff)
V0
Volume
N
D eff
1/ n


i 1
 Vi
V0
 The new standard Lyman model
1/ n
Di 
…and Deff is gEUD
Deff
Dose
Courtesy of Markus Alber
Outcome Driven Biological Optimization – Elekta/CMS MONACO
7
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
The NTCP as a function
of uniform dose, EUD , to
the whole volume can
then be described by the
integral probability:
Volume
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
100
80
t
NTCP = (2p)-1/2-  exp(-x2/2)dx
0 .0 8
0 .0 7
60
40
20
Dose (Gy)
0 .0 9
F ra c tio n o f C o m p lic a tio n s e e n
For uniform irradiation of
the whole organ, assumes
that the distribution of
complications as a function
of dose can be described
by a normal distribution
 with mean TD50
 standard deviation m •TD50
The EUD NTCP description
1.0
N T C P (% )
EUD NTCP description
0
0
where
t = (EUD - EUD50) / (m • EUD50)
0 .0 6
0 .0 5
0 .0 4
20
40
60
80
100 120 140
D o se (G y )
0 .0 3
0 .0 2
0 .0 1
0
40
60
80
D o s e (G y )

1 /a

a 
 N
 di 
1 /a
a 

i 1


gEUD

  v i d i 
 N 
 i





Tumors:
a is ~a negative number
Normal Tissues: a is a positive number
For
For
For
For
a
a
a
a
=
=
=
=
1,
2,
- ∞,
+∞,
gEUD
gEUD
gEUD
gEUD
=
=
=
=
a

1/a
gEU D    v i d i 

i
90
250
80
Volume (cc)
200
70
60
gEUD (Gy)
gEUD
150
100
50
40
30
20
50
10
0
0
1
10
3
20
5
30
7
40
950 11
60
13
70
15
80 1790
Dose (Gy)
mean dose
rms dose
minimum dose
maximum dose
Normal Tissues:
Mean < gEUD < Max
a is positive
-100 -80 -60
-40 -20
0
20
60
80
100
For a = 1, gEUD = mean dose
For a = 2, gEUD = rms dose
For a = + ∞, gEUD = max dose
Relationship to Lyman Model: a = 1/n
8
40
"a"
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Local Radiation Response Organ Functional Reserve Models
 Offer the potential for a more direct
visualization of the relationship
between the DVH and radiation
damage
 May (ultimately) offer the possibility of
linking cellular and organ subunit
radiobiology to the prediction of
radiation complications.
Courtesy of QUANTEC - Joe Deasy
Local Damage Function
Local Radiation Response Organ Functional Reserve Models
Fraction (f) of a macroscopic volume
element incapacitated by a dose D can be
described by a simple response function:
 Jackson A, Kutcher GJ, Yorke E.
Med Phys 20:613-525, 1993.
1
f = ––––––––––––––
( 1 + (D50 / D) k )
 Niemierko A, Goitein M. Int J Radiat
Oncol Biol Phys 25:135-145, 1993.
where D50 is the dose which incapacitates
half the volume and “k” describes the
steepness of the “local damage” function.
9
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Total Estimated Damage
100
100
75
75
50
50
37
25
25
25
7
1
0
Total fraction (F ) of the organ that
is incapacitated is equal to the sum
of the fractions of the individual
macroscopic volume elements
destroyed.
Fx Incapacitated
Volume ( %)
Local Damage Function
F = S fi
0
0
1
2
3
4
5
6
7
8
9
Dose (Gy)
Organ Injury Function
Organ Injury Function
C u m u la tiv e F u n c tio n a l R e s e rv e
t
NTCP = (2p)-1/2 -  exp (-x2 / 2) dx,
where
t = (F - F50) / s
(F 5 0 = 0 .4 0 ; s = 0 .0 7 7 )
100
90
N T C P (% )
80
F50 is the fraction of the total organ damaged
which would produce a 50% complication
rate,
70
60
50
40
30
20
10
s describes the steepness of the “organ”
0
response function
0
10
20
30
40
50
60
70
F ra c tio n D a m a g e d (% )
10
80
90 100
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Local response function
EUD parallel model
 Required to change non-uniformly irradiated
Fractional damage in each bin
volume to equivalent uniform dose EUD
 gEUD is one very general form of this
function
 (their can be many others):
EUDparallel,logistic
Int J Radiat Oncol Biol Phys, 55:724-735, 2003
2 parameters
3 parameters
Seppenwoolde et al, IJROBP 55:724, 2003
3 parameters
4 parameters
D50, k
n
n=1
t
2p
t
e
x
2
2
dx

EU D  EU D 5 0
m  EU D 5 0
D50 = 
EUDLogistic rdV= FD
NTCP 
EUD50, m
1
2p
x
t
e
2
k= 
VDth
2
dx

NTCP
NTCP 
1
EUDLKB
Clinical Response Data
& Modeling
VDth50, m
NTCP
EUD=MLD
VDth
EUDmodel
t 
rdV  rdV 5 0
m  rdV
50
VDth
Courtesy Y Seppenwoolde
11
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Modeling is conceptually simple
cast of thousands here...
would you believe 100’s??
...maybe tens?
 Pick a Model
 Look at some Patients
NTCP modeling:
We’ve come a long way, ...
…but,
 Have 3-D Dose Distributions
 Have 3-D Volumes
 Have Outcomes
 Use patient data to parameterize
and/or test model
OK, beware! a lot of
personal opinion
may follow
Well........
¿No Problemo?
NTCP Outcomes
model
Volumes
& dose
Iterate parameters
12
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Input Data: Dose
Outcomes Modeling: Input Data
 Dose
 Calculational algorithms are better
 Convolution-superposition
 Monte Carlo
 Volume
 Dose-Volume
 Can compute 3-D distributions
 Outcomes
 Dose distributions are complex
 Non-uniform dose to normal tissues
 Daily variations not easily included
Input Data: Volume
Input Data: Dose-Volume
 3-D yields Volumes
 Difficult to track which volume
receives what dose
 Time factors often ignored
 Physical Volume (size and shape)
 Position
 Changes not easily accommodated
 How accurate are the input data?
 Tumor shrinkage
 Inter and Intra treatment changes
 For first treatment?
 As a basis for the whole treatment?
and processes
13
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Input Data: Outcomes
Input Data: Outcomes
 Most mathematical NTCP models
 Confounding factors are often not
assume dichotomous (yes or no)
endpoints,
 in practice complications are usually
considered.
 Such as:
 the fact that patients have cancer,
 the effects of adjuvant or concomitant
graded,
 with their severity subject to
interpretation.
therapies
 other health compromising factors such
as smoking, diabetes, etc.
Outcome Modeling: Pitfalls
Model Use: A Warning
 Probably best to say that at this point
most published model fitting is still
phenomenological and the models are
“descriptive” rather than predictive.
 It can be dangerous to use the models
for treatment situations different from
the circumstances in which their
parameters were derived
14
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Model Use: A Caveat
Does use of NTCP individualize therapy?
 These prognostic models are
 Population based NTCP parameters
 Permit design of protocols that can maximize
population-based, implying they may
not be suited for prediction of outcome
in “individuals”
target dose for each patient at a equal level
of risk (e.g., 10% NTCP)
 Therefore, as the patients, their tumors
 Does the use of NTCP individualize
and geometries are all different:
 each will get their own individualized
therapy?
maximum tolerated dose treatment,
 but, as a member of the population!
 (i.e., each patient will have a 1 in 10 chance of
getting the dose limiting complication)
However, we can’t tell which 10 of
100 they will be!
10 of 100 patients will have a
complication
X
You (only) have a 1 in 10
chance of developing a
complication
X
X
X
X
X
X
X
X
X
15
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
What if we could identify which
10 of 100?
10 of 100 patients will have a
complication (which 10?)
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
X
X X
X
X
X
X
X X
X
X
X
X
X
X X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
X
What if we could identify which
10 of 100?
How could we identify which 10
of 100?
 Requires additional patient specific
 We could decrease the risk of complication
if we could determine during therapy the
10% of patients who are at greatest risk
for toxicity
information
 Biomarkers
 Functional imaging
 Other predictive assays or
 Moreover, we could potentially increase
dose for the 90% of those who would
evidence no toxicity using the current
population-based approach.
characteristics
16
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Modeling Outcome: Summary
Modeling Outcome: Summary
 Careful studies of the partial organ
 The ability to use the NTCP models
 We should be encouraged by the
 Use of the models should be
QUANTEC supplement
TCP too!
tolerance of normal tissues to
therapeutic ionizing radiation are
emerging, as are attempts to model
these data.
themselves reliably, and in a predictive
way is still an area of active
investigation as there are many
uncertainties related to patient data
progress in this area.
approached with judicious caution in a
clinical setting.
 Modeling Tumor Response to
Irradiation
 Workshop, May 28-31, 2008,
Volume 76, Suppl 1, (1 March 2010)
Edmonton, Alberta, Canada
 Articles published in
Acta Oncologica Volume 49,
Number 8 (November 2010)
17
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
Work in Progress
Report of the AAPM Task Group 166:
“All models are wrong,
but some are useful.”
THE USE AND QA OF BIOLOGICALLY RELATED
MODELS FOR TREATMENT PLANNING
X. Allen Li, Medical College of Wisconsin (Chair)
Markus Alber, Uniklinik für Radioonkologie Tübingen
Joseph O. Deasy, Washington University
Andrew Jackson, Memorial Sloan-Kettering Cancer Center
Kyung-Wook Jee, University of Michigan
Lawrence B. Marks, University of North Carolina
Mary K. Martel, UT MD Anderson Cancer Center
Alan E. Nahum, Clatterbridge Centre for Oncology
Andrzej Niemierko, Massachusetts General Hospital
Vladimir A. Semenenko, Medical College of Wisconsin
Ellen D. Yorke, Memorial Sloan-Kettering Cancer Center
G.E.P. Box, 1979*
*”Robustness in the Strategy of Scientific Model Building." IN: Robustness in
Statistics. 201-236. R. L. Launer and G. N. Wilkinson, eds. Academic Press, NY.
18