Jennifer Schultens- Heegaard genus formula for Haken manifolds
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of ...
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NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Biological/Clinical Outcome Models in RT Planning
Randall K. Ten Haken
University of Michigan
Outline
Why attempt to use models?
Some basic mathematical outcomes models
Outcomes Modeling
Pitfalls
Input data concerns
Model fitting concerns
Model use concerns
Why consider use of models?
Are there problems that use of outcomes models could help resolve?
Would their use make things easier or more consistent?
Is this relevant today?
Target dose must be
uniform to +/- 5%
Dose (%)
Volu
me (
%)
00
Desired
100
50- 5% + 5%
3D CRT – PTV covered!
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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RTOG IMRT target criteria
The prescription dose is the isodose which encompasses at least 95% of the PTV.
No more than 20% of any PTV will receive >110% of its prescribed dose.
No more than 1% of any PTV will receive <93% of its prescribed dose.
Target volume issues
Are target volume hot spots beneficial?
Are target volume cold spots detrimental?
How do cold spots and hot spots play off against each other?
Use of TCP or EUD models could help us make rational decisions
Basic TCP Models
Complete “birth and death” models
(M. Zaider and G. N. Minerbo, …
Poisson (survival of clonogenic cells) models (Webb, Nahum, ...
“Tumorlet” models (Goitein, Brahme...
EUD type approaches
Outcome Driven Biological Optimization – Elekta/CMS MONACO
Control of a Target DVH by a Cell-Killbased EUD
Dose
Volu
me
Only one aspectof the target DVH iscontrolled.
Add a one-sided quadratic overdosage penalty!
Courtesy of Markus Alber
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Equivalent Uniform Dose
Uniform dose distribution that if delivered over the same number of fractions would yield the same radiobiological or clinical effect.
Niemierko 1996
Brahme 1991
Niemierko 1999 (abstract) gEUD
Generalized Equivalent Uniform Dose (gEUD)
ROI with N dose points di
a
i
a
ii
aN
i
a
i
dvN
d
gEUD
/1
/1
1
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Dose (Gy)
Vo
lum
e (
cc
)
Dose (Gy)
Volu
me
DVH (fractional volume vi receives dose di )
gEUD
a
i
a
ii
aN
i
a
i
dvN
d
gEUD
/1
/1
1
Tumors: a is ~a negative numberNormal Tissues: a is a positive number
For a = 1, gEUD = mean doseFor a = 2, gEUD = rms doseFor a = - ∞, gEUD = minimum doseFor a = +∞, gEUD = maximum dose
60
65
70
75
80
85
90
-100 -80 -60 -40 -20 0 20 40 60 80 100
"a"
gE
UD
(G
y)
Tumors: Min < gEUD < Meana is ~negative
aggressive a = -20non a = -5
For a = 1, gEUD = mean doseFor a = - ∞, gEUD = min dose
a
a
i
i
idvgEUD
/1
0
5
10
15
20
25
30
35
1 3 5 7 9 11 13 15 17
Dose (Gy)
Vo
lum
e (
cc
)
10 20 30 40 50 60 70 80 90
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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NTCP, TCP, EUD Tutorial, Univ of Michigan, Dept of Radiation Oncology: RK Ten Haken , K-W Jee, 2002-08
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:
TCP ( EUD, 1) = 1 / {1 + ( D50 / EUD) 4·50 }
D50 = 70 Gy50 = 2
Normal Tissues
0
20
40
60
80
100
Volu
me (
%)
0 10 20 30 40 50 60 70 80
Dose (Gy)
Plan 2
Plan 1
0
20
40
60
80
100
Volu
me (
%)
0 10 20 30 40 50 60 70 80
Dose (Gy)
Plan 2
Plan 1
DVH Comparison - normal tissue
Easy! Plan 2 is less toxic
Who knows?Depends on tissue type
RTOG normal tissue dose criteria
Small bowel < 30% to receive ≥ 40 Gy minor deviation 30% to 40 Gy
Rectum < 60% to receive ≥ 30 Gy minor deviation 35% to 50 Gy
Bladder < 35% to receive ≥ 45 Gy minor deviation 35% to 50 Gy
Femoral head ≤ 15% to receive ≥ 30 Gy minor deviation 20% to 30 Gy
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Normal tissue issues
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.
Normal Tissue Complication Probability (NTCP) Calculations
Basic NTCP Models
The “Lyman” model
The damage-injury/critical volume models (Jackson & Yorke, Niemierko)
Relative Seriality Model
EUD type approaches
Normal Distributions
m= 0, s= 1
Fraction = (2p)-1/2 exp (-x2/2)
-1 0 1
x
Fra
cti
on
re
sp
on
din
g a
t th
is l
eve
l
Standardized Model: in units of t = ( x – m ) / s
0
0.2
0.4
0.6
0.8
1
-1 0 1
Cu
mu
lati
ve
Fra
cti
on
Total = (2p)-1/2-
texp (-x2/2)
x
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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The Lyman NTCP Model
Lyman JT: Complication probability – as assessed from dose-volume histograms. Radiat Res 104:S13-S19, 1985.
The Lyman NTCP Description
NTCP = (2p)-1/2-
texp(-x2 / 2) dx,
where;
t = (D - TD50(v )) / (m • TD50(v )),
and;
TD50(v ) = TD50(1) • v -n
Lyman JT: Complication probability – as assessed from dose-volume histograms. Radiat Res 104:S13-S19, 1985.
The Lyman NTCP Model
The Lyman NTCP model attempts to mathematically describe complications associated with uniform partial organ irradiation.
This implies: 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 }
DVH reduction schemes
For non-uniform irradiation, the 3D dose 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 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.
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Outcome Driven Biological Optimization – Elekta/CMS MONACO
Historically: Expressing the effect of a dose distribution by its effective volume
Dose
Vo
lum
e
Veff
D0
The effect of this dose distribution equals
an irradiation of the effective volume Veff
with the nominal dose D0
nN
i
i
ieffD
DVV
/1
1 0
typical 3D conf. DVH
Courtesy of Markus Alber
Outcome Driven Biological Optimization – Elekta/CMS MONACO
Dose
Vo
lum
e
Today: 3D dose distributions and extremedose heterogeneity
Observation: irradiated volume
is frequently 100%
Switch from (Veff, D0) to
(V0, Deff)
Courtesy of Markus Alber
Outcome Driven Biological Optimization – Elekta/CMS MONACO
Dose
Vo
lum
e
Today: 3D dose distributions expressed in Deff
Observation: irradiated volume
is frequently 100%
Switch from (Veff, D0) to
(V0, Deff)
nN
i
i
in
effD
V
VD
/1
1 0
/1
V0
Deff
…and Deff is gEUD
Courtesy of Markus Alber
gEUD NTCP Description
The new standard Lyman model
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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EUD NTCP description
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
10080604020000.0
0.2
0.4
0.6
0.8
1.0
Dose (Gy)
Volu
me
40 60 800
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
D ose (G y)
Fra
cti
on
of
Co
mp
lic
ati
on
se
en
The EUD NTCP description
The NTCP as a function of uniform dose, EUD , to the whole volume can then be described by the integral probability:
14012010080604020000
20
40
60
80
100
Dose (Gy)
NT
CP
(%
)
NTCP = (2p)-1/2-
texp(-x2/2)dx
where
t = (EUD - EUD50) / (m • EUD50)
gEUD
a
i
a
ii
aN
i
a
i
dvN
d
gEUD
/1
/1
1
Tumors: a is ~a negative numberNormal Tissues: a is a positive number
For a = 1, gEUD = mean doseFor a = 2, gEUD = rms doseFor a = - ∞, gEUD = minimum doseFor a = +∞, gEUD = maximum dose
0
50
100
150
200
250
1 3 5 7 9 11 13 15 17
Dose (Gy)
Vo
lum
e (
cc
)
10 20 30 40 50 60 70 80 90
0
10
20
30
40
50
60
70
80
90
-100 -80 -60 -40 -20 0 20 40 60 80 100
"a"
gE
UD
(G
y)
For a = 1, gEUD = mean doseFor a = 2, gEUD = rms doseFor a = + ∞, gEUD = max dose
a
a
i
i
idvgEUD
/1
Relationship to Lyman Model: a = 1/n
Normal Tissues: Mean < gEUD < Maxa is positive
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Courtesy of QUANTEC - Joe Deasy
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.
Local Radiation Response -Organ Functional Reserve Models
Jackson A, Kutcher GJ, Yorke E.Med Phys 20:613-525, 1993.
Niemierko A, Goitein M. Int J Radiat Oncol Biol Phys 25:135-145, 1993.
Fraction (f) of a macroscopic volume element incapacitated by a dose D can be described by a simple response function:
where D50 is the dose which incapacitates half the volume and “k” describes the steepness of the “local damage” function.
1f = ––––––––––––––
( 1 + (D50 / D) k )
Local Damage Function
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
10
0
25
50
75
100
0
25
50
75
100
Volu
me (
%)
0 1 2 3 4 5 6 7 8 9
Dose (Gy)
Fx
Inca
paci
tate
d
37
25
7
1
Local Damage Function
Total fraction (F ) of the organ that is incapacitated is equal to the sum of the fractions of the individual macroscopic volume elements destroyed.
F = S fi
Total Estimated Damage
F50 is the fraction of the total organ damaged which would produce a 50% complication rate,
s describes the steepness of the “organ” response function
NTCP = (2p)-1/2-
texp (-x2 / 2) dx,
where
t = (F - F50) / s
Organ Injury Function Organ Injury FunctionC u mu lative Fu n ction al R eserve
(F 50 = 0 .40 ; s = 0 .077 )
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Fraction Damaged (% )
NT
CP
(%
)
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Local response function
Required to change non-uniformly irradiated volume to equivalent uniform dose EUD
gEUD is one very general form of this function
(their can be many others):
Int J Radiat Oncol Biol Phys, 55:724-735, 2003
Fractional damage in each bin
EUD parallel model
Seppenwoolde et al, IJROBP 55:724, 2003
EUDparallel,logistic
2 parameters
EUD=MLD
3 parameters
EUDLKB
EUDmodel
NT
CP
EUD50, m
n
4 parameters
EUDLogistic
D50, k
n = 1 D50 =
dxeNTCP
t x
2
2
2
1
p
5 0
5 0
EUDm
EUDEUDt
3 parameters
VDth
VDth
VDth
NT
CP
VDth50, m
k = rdV= FD
5 0
5 0
rdVm
rdVrdVt
dxeNTCP
t x
2
2
2
1
p
Courtesy Y Seppenwoolde
Clinical Response Data& Modeling
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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NTCP modeling:We’ve come a long way, ...
…but,
cast of thousands here...would you believe 100’s??...maybe tens?
OK, beware! a lot ofpersonal opinionmay follow
Modeling is conceptually simple
Pick a Model
Look at some Patients
Have 3-D Dose Distributions
Have 3-D Volumes
Have Outcomes
Use patient data to parameterize and/or test model
¿No Problemo?
Iterate parameters
OutcomesNTCPmodel
Volumes& dose
Well........
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Outcomes Modeling: Input Data
Dose
Volume
Dose-Volume
Outcomes
Input Data: Dose
Calculational algorithms are better
Convolution-superposition
Monte Carlo
Can compute 3-D distributions
Dose distributions are complex
Non-uniform dose to normal tissues
Daily variations not easily included
Input Data: Volume
3-D yields Volumes
Physical Volume (size and shape)
Position
How accurate are the input data?
For first treatment?
As a basis for the whole treatment?
Input Data: Dose-Volume
Difficult to track which volume receives what dose
Time factors often ignored
Changes not easily accommodated
Tumor shrinkage
Inter and Intra treatment changes and processes
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Input Data: Outcomes
Most mathematical NTCP models assume dichotomous (yes or no) endpoints,
in practice complications are usually graded,
with their severity subject to interpretation.
Input Data: Outcomes
Confounding factors are often not considered.
Such as:
the fact that patients have cancer,
the effects of adjuvant or concomitant 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
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Model Use: A Caveat
These prognostic models are population-based, implying they may not be suited for prediction of outcome in “individuals”
Does the use of NTCP individualize therapy?
Does use of NTCP individualize therapy?
Population based NTCP parameters
Permit design of protocols that can maximize target dose for each patient at a equal level of risk (e.g., 10% NTCP)
Therefore, as the patients, their tumors and geometries are all different:
each will get their own individualized 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)
10 of 100 patients will have a complication
X
X X
X
X
X
X
X
X
X
However, we can’t tell which 10 of 100 they will be!
You (only) have a 1 in 10 chance of developing a
complication
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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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
XX
X
XX
X
X
What if we could identify which 10 of 100?
X
X
X
X
X
X
X
X
X
X
What if we could identify which 10 of 100?
We could decrease the risk of complication if we could determine during therapy the 10% of patients who are at greatest risk for toxicity
Moreover, we could potentially increase dose for the 90% of those who would evidence no toxicity using the current population-based approach.
How could we identify which 10 of 100?
Requires additional patient specific information
Biomarkers
Functional imaging
Other predictive assays or characteristics
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Modeling Outcome: Summary
Careful studies of the partial organ tolerance of normal tissues to therapeutic ionizing radiation are emerging, as are attempts to model these data.
We should be encouraged by the progress in this area.
Modeling Outcome: Summary
The ability to use the NTCP models themselves reliably, and in a predictive way is still an area of active investigation as there are many uncertainties related to patient data
Use of the models should be approached with judicious caution in a clinical setting.
QUANTEC supplement
Volume 76, Suppl 1, (1 March 2010)
TCP too!
Modeling Tumor Response to Irradiation
Workshop, May 28-31, 2008, Edmonton, Alberta, Canada
Articles published inActa Oncologica Volume 49, Number 8 (November 2010)
NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan
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Work in Progress
Report of the AAPM Task Group 166:
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
“All models are wrong, but some are useful.”
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.