Transcript Physical and Biological Models in Treatment Plan Evaluation

Biologiske modeller i
stråleterapi
Dag Rune Olsen,
The Norwegian Radium Hospital,
I
U
M
IT
RAD
AL
N
IA
TH
E
RWE
NO
G
H OS
P
University of Oslo
Biological models
Input
Model
Output
Biological
response
Physical
dose
f (var, param)
or
Clinical
outcome
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-FechnerStevens:
R  Sa
A. Niemierko, Med Pys. 24:1323-4, 1997
Biological models
EUD:
EUD=Svi•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 models
EUD:
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/2p e (-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. 20:166176, 1991.
H. Honore et al. Radiother Oncol.
65:9-16, 2002.
Biological models
Rectal bleeding
grade 1-3 Fenwick et al.
Hepatitis Jackson et al.
0.8
NTCP
Normal tissue
complication
probability and the
volume effect
1.0
0.6
0.4
t
NTCP=1/2p e (-x2/2)dx

-
t=D-D(v)/m D(v)

D(v)=D V-n

0.2
0.0
0
0.2
0.4
0.6
0.8
Damaged Organ Fraction
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.
Biological models
Sensitivity 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 the
function of an organ is related to the
inactivation probability of the organs
functional sub units - FSU – and their
functional organization.
Biological models
Normal tissue
complication probability
Rectum
n
NTCP=1-S[ny](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
Prostate
FSU
High-dose box
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.
n
irradiated FSUs
E. Yorke Radiother Oncol. 26:226-37, 1993.
Biological models
Response probability
calculations require:
•3D dose matrix of VOI
•Reduction to an effective
dose
•Appropriate set of
parameter values
•Reliable model
S.L.S. Kwa et al. Radiother. Oncol. 48:6169, 1998.
Biological models
Volume
DVH reduction
algorithm:
Deff(v)=S(Di Vi-n)

Dose
i
Lyman et al. IJROBP 1989
Kutcher et al. IJROBP 1989
Emami et al. IJROBP 1991
Burman et al. IJROBP 1991
Mean = D50%(v)
SD = m·D50%
NTCP
TD distribution
Biological models
100%
50%
Dose
TD50%(v)
t
NTCP=1/2p e (-x2/2)dx

-
t=D-D(v)/m D(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 models
Probability of radiation
induced liver desease
(RILD) by NTCP
modelling for patients
with hepatocellular
carcinoma (HCC)
treated with threedimensional conformal
radiotherapy (3D-CRT).
J. C.-H. Cheng et al. Int J
Radiat. Oncol. Biol. Phys.
54:156-62, 2002
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.
Biological models
Tumour controle
probability
TCP
TCP= exp(-no SF)

SF=exp[-(ad+bd2)]
exp([d-TCD50]/k)
TCP=
1+ exp([d-TCD50]/k)
A Nahum, S. Webb, Med.Phys. 40:1735-8, 1995
H. Suit et al. Radiother. Oncol. 25:251-60, 1992.
TCP curves that result from the set
of parameters chosen for prostate
cancer (a = 0.29 Gy-1; a/b = 10 Gy;
rV = 107 cells/cm3.
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 function
U=Pwi NTCP wo (1-TCP)



i
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=d for the spinal cord, i.e.
w=0 for d<50 Gy and w=1 for >50 Gt.
Cost functions
P+-concept
Introduced by Wambersie in 1988 as
‘Uncomplicated Tumour Control’ and
refined by Brahme:
P+=PB-PBI
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 functions
P+-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
“The difference
between theory
and practice…
…is larger in
practice than
in theory !”
John Wilkes