NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of ...

NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of Michigan

1

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!


2

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


3

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


4

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


5

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


6

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.


7


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



Dose

Vo

lum

e

Today: 3D dose distributions and extremedose heterogeneity

Observation: irradiated volume

is frequently 100%

Switch from (Veff, D0) to

(V0, Deff)



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


gEUD NTCP Description

The new standard Lyman model


8

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


9

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


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

(%

)


11

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


12

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........


13

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


14

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


15

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


16

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


17

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)


18

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.

NTCP Tutorial, Randall K. Ten Haken, Ph.D., University of ...

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