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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…
