Biologiske modeller i strleterapi

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Biologiske modeller i stråleterapi
Dag Rune Olsen, The Norwegian Radium Hospital,
University of Oslo
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Biological models
Input
Model
Output
Biological response or Clinical outcome
Physical dose
f (var, param)
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Biological models

• Empirical models of clinical data
• Biophysical models of the underlying biological
  mechanisms

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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. 241323-4, 1997
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Biological models

• EUD
• EUDSviDia
• 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.
52224-35, 2002
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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

A typical DVH of normal tissue
Q. WU et al. Int. Radiat. Oncol. Biol. Phys.
52224-35, 2002
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Biological models

Calculation of the response probability
Normal tissue complication probability NTCP
Tumour controle probability TCP
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Biological models

• Normal tissue complication probability

t NTCP1/?2p??e (-x2/2)dx
-? NTCP1/(1D50/Dk)
H. Honore et al. Radiother Oncol. 659-16, 2002.
G. Kutcher et al. Int J Radiat. Oncol. Biol.
Phys. 21137-146, 1991. A. Niemierko et
al.Radiother. Oncol. 20166-176, 1991.
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Biological models
Normal tissue complication probability and the
volume effect
t NTCP1/?2p??e (-x2/2)dx
-? tD-D(v)/m?D(v)
D(v)D ? V-n
A Jackson et al. Int J Radiat Oncol Biol Phys.
31883-91, 1995. JD Fenwick et al. Int J Radiat
Oncol Biol Phys. 49473-80, 2001.
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Biological models
Sensitivity analysis NTCP of Grade 13 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. 49473-80, 2001.
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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.

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Biological models
Normal tissue complication probability
n
NTCP1-Sn(1-p)yx pn-y
y
y
p FSU inactivation probability y kn-N N total
number of FSUs k/N fraction of FSU that needs
to be intact n irradiated FSUs

• E. Dale et al. Int J Radiat Oncol Biol
  Phys.43385-91, 1999
• Olsen DR et al. Br J Radiol. 671218-25, 1994.
• E. Yorke Radiother Oncol. 26226-37, 1993.

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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. 4861-69,
1998.
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Biological models
DVH reduction algorithm Deff(v)S(Di ? Vi-n)
i
Volume
Dose
Lyman et al. IJROBP 1989 Kutcher et al. IJROBP
1989 Emami et al. IJROBP 1991 Burman et al.
IJROBP 1991
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Biological models
100
NTCP
50
Dose
TD distribution
TD50(v)
Mean D50(v)
t NTCP1/?2p??e (-x2/2)dx
-? tD-D(v)/m?D(v)
SD mD50
Lyman et al. IJROBP 1989 Kutcher et al. IJROBP
1989 Emami et al. IJROBP 1991 Burman et al.
IJROBP 1991
D(v)D ? V-n
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Biological models

• Probability 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. 54156-62, 2002
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Biological models
Tumour controle probability TCP

TCP exp(-no?SF) SFexp-(adbd2) exp(d-TCD50
/k) 1 exp(d-TCD50/k)
TCP
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.
A Nahum, S. Webb, Med.Phys. 401735-8, 1995 H.
Suit et al. Radiother. Oncol. 25251-60, 1992.
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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

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Cost functions

• Utility function
• UPwi?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 wd for the spinal cord, i.e.
  w0 for dlt50 Gy and w1 for gt50 Gt.

i
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Cost functions

• P-concept
• Introduced by Wambersie in 1988 as
  Uncomplicated Tumour Control and refined by
  Brahme
• PPB-PB?I
• where PB is the tumour control probability and
  PI is the normal tissue complication probability.

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Cost functions

• P-concept
• When no correlation between the to probabilities
  exist
• PPB-PB ? PI
• When full correlation between the to
  probabilities exist
• PPB- PI

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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 ?
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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. 34923-930, 1996
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Models in treatment plan evaluation
The difference between theory and practice
is larger in practice than in theory ! John
Wilkes