Biologiske modeller i stråleterapi Dag Rune Olsen, The Norwegian Radium Hospital, University of...

Biologiske modeller i stråleterapi

R

Dag Rune Olsen,

The Norwegian Radium Hospital,

University of Oslo

Biological models

Physical dose

Biological response

or

Clinical outcome

f (var, param)

Input Model Output

Biological models

• Empirical models of clinical data

• Biophysical models of the underlying biological mechanisms

Biological models

The EUD – a semi-biological approach:

“The concept of equivalent uniform dose (EUD) assumes that any two dose distributions are equivalent if they cause the same radiobiological effect.”

• The idea based on a law by Weber-Fechner-Stevens: R Sa

A. Niemierko, Med Pys. 24:1323-4, 1997

Biological models

EUD:

EUD=vi•Dia

i

where Di is the dose of a voxel element ‘i’ and vi is the corresponding volume fraction of the element; a is a parameter.

Q. WU et al. Int. Radiat. Oncol. Biol. Phys. 52:224-35, 2002

Biological modelsEUD:The corresponding equivalent uniform dose – based on the DVH.

• a of tumours is often large, negative

• a of serial organs is large, positive

• a of parallel organs is small, positive

Q. WU et al. Int. Radiat. Oncol. Biol. Phys. 52:224-35, 2002

A typical DVH of normal tissue

Biological models

Calculation of the response probability

Normal tissue complication probability

NTCP

Tumour controle probability

TCP

Biological models

Normal tissue complication probability

t

NTCP=1/2e (-x2/2)dx -

NTCP=1/(1+[D50%/D]k)G. Kutcher et al. Int J Radiat. Oncol. Biol. Phys. 21:137-146, 1991.

A. Niemierko et al.Radiother. Oncol. 20:166-176, 1991.

H. Honore et al. Radiother Oncol. 65:9-16, 2002.

0.0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8

Damaged Organ Fraction

NT

CP

Rectal bleedinggrade 1-3 -Fenwick et al.

Hepatitis -Jackson et al.

Biological modelsNormal tissue complication

probability and the volume effect

A Jackson et al. Int J Radiat Oncol Biol Phys. 31:883-91, 1995.

JD Fenwick et al. Int J Radiat Oncol Biol Phys. 49:473-80, 2001.

t

NTCP=1/2e (-x2/2)dx -

t=D-D(v)/mD(v)

D(v)=D V-n

Biological modelsSensitivity analysis:

NTCP of Grade 1–3 rectal bleeding damage, together with the steepest and shallowest sigmoid curves (dotted lines) which adequately fit the data.

JD Fenwick et al. Int J Radiat. Oncol. Biol. Phys. 49:473-80, 2001.

Biological models

Normal tissue complication probability

Biophysical models assume that Biophysical models assume that the function of an organ is related the function of an organ is related to the inactivation probability of to the inactivation probability of the organs functional sub units - the organs functional sub units - FSU – and their functional FSU – and their functional organization.organization.

Rectum

FSU

High-dose box

Prostate

E. Dale et al. Int J Radiat Oncol Biol Phys.43:385-91, 1999

Olsen DR et al. Br J Radiol. 67:1218-25, 1994.

E. Yorke Radiother Oncol. 26:226-37, 1993.

Biological models

NTCP=1-[n](1-p)yx pn-y

y

p FSU inactivation probability

y k+n-N

N total number of FSUs

k/N fraction of FSU that needs to be intact

n irradiated FSUs

y

n

Normal tissue complication probability

Biological models

S.L.S. Kwa et al. Radiother. Oncol. 48:61-69, 1998.

Response probability calculations require:

•3D dose matrix of VOI

•Reduction to an effective dose

•Appropriate set of parameter values

•Reliable model

Biological modelsV

olum

e

Dose

DVH reduction algorithm:

Deff(v)=(Di Vi-n)

i

Lyman et al. IJROBP 1989

Kutcher et al. IJROBP 1989

Emami et al. IJROBP 1991

Burman et al. IJROBP 1991

Biological models

Dose

NT

CP

TD50%(v)

50%

100%

Mean = D50%(v)SD = m·D50%

TD

dis

trib

utio

n

t

NTCP=1/2e (-x2/2)dx -

t=D-D(v)/mD(v)

D(v)=D V-n

Lyman et al. IJROBP 1989

Kutcher et al. IJROBP 1989

Emami et al. IJROBP 1991

Burman et al. IJROBP 1991

Biological modelsProbability of radiation induced liver desease (RILD) by NTCP modelling for patients with hepatocellular carcinoma (HCC) treated with three-dimensional conformal radiotherapy (3D-CRT).

Fits from the literature and the new fits from 68 patients for the Lyman NTCP model displaying 5% and 50% iso-NTCP curves of the corresponding effective volume and dose.

J. C.-H. Cheng et al. Int J Radiat. Oncol. Biol. Phys. 54:156-62, 2002

Biological modelsTumour controle

probability

TCPTCP= exp(-no

SF)

SF=exp[-(d+d2)]

exp([d-TCD50]/k)

1+ exp([d-TCD50]/k) TCP curves that result from the set of parameters chosen for prostate cancer ( = 0.29 Gy-1; = 10 Gy; V = 107 cells/cm3.

A Nahum, S. Webb, Med.Phys. 40:1735-8, 1995

H. Suit et al. Radiother. Oncol. 25:251-60, 1992.

TCP=

Cost functions

• Cost functions are mathematical models that simulate the process of clinical assessment and judgement.

• Cost functions produce a single figure of merit for tumour control and acute and late sequela, and is as such a composit score of the treatment plan

Cost functions

Utility functionU=wi

NTCP wo(1-TCP)

where w are weight factors, NTCPi is the probability of a given toxicity (end-point) of an organ i, and TCP is the tumour control probability.wi is not always a fixed parameter but rather a function, e.g. may w= for the spinal cord, i.e. w=0 for d<50 Gy and w=1 for >50 Gt.

i

Cost functions

P+-conceptIntroduced by Wambersie in 1988 as ‘Uncomplicated Tumour Control’ and refined by Brahme:

P+=PB-PBI

where PB is the tumour control probability and PI is the normal tissue complication probability.

Cost functions

P+-concept

When no correlation between the to probabilities exist:

P+=PB-PB PI

When full correlation between the to probabilities exist:

P+=PB- PI

Cost functionsP+-concept

• Plot of P+ demonstrate what dose is optimal with respect to tumour control without late toxicity

• P+ can be used to rank plans

Fig.

Problems: how to deal with non-fatal complications and ‘softer’ end-points ?

Automatic ranking

Automated ranking and scoring of plans can be performed using artificial neural networks

Correlation between network and clinical scoring

T.R. Willoughby et al. Int J Radiat. Oncol. Biol. Phys. 34:923-930, 1996

Models in treatment plan evaluation

…is larger in practice than

in theory !” John Wilkes

“The difference between theory and practice…