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

Biological models Physical dose Biological response or Clinical outcome f (var, param) InputModelOutput

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

Biological models EUD: EUD=  v i D i a i where D i is the dose of a voxel element ‘i’ and v i 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/  2    e (-x 2 /2) dx -  NTCP=1/(1+[D 50% /D] k ) G. Kutcher et al. Int J Radiat. Oncol. Biol. Phys. 21: , A. Niemierko et al.Radiother. Oncol. 20: , H. Honore et al. Radiother Oncol. 65:9-16, 2002.

Biological models Normal tissue complication probability and the volume effect A Jackson et al. Int J Radiat Oncol Biol Phys. 31:883-91, JD Fenwick et al. Int J Radiat Oncol Biol Phys. 49:473-80, t NTCP=1/  2    e (-x 2 /2) dx -  t=D-D(v)/m  D(v) D(v)=D  V -n

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.

E. Dale et al. Int J Radiat Oncol Biol Phys.43:385-91, 1999 Olsen DR et al. Br J Radiol. 67: , E. Yorke Radiother Oncol. 26:226-37, Biological models NTCP=1-  [ n ](1-p) y x p n-y y p FSU inactivation probability yk+n-N Ntotal number of FSUs k/Nfraction of FSU that needs to be intact nirradiated FSUs y n Normal tissue complication probability

Biological models S.L.S. Kwa et al. Radiother. Oncol. 48:61- 69, Response probability calculations require: 3D dose matrix of VOI Reduction to an effective dose Appropriate set of parameter values Reliable model

Biological models Volume Dose DVH reduction algorithm: D eff (v)=  (D i  V i -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 NTCP TD 50% (v) 50% 100% Mean = D 50% (v) SD = m·D 50% TD distribution t NTCP=1/  2    e (-x 2 /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 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 models Tumour controle probability TCP TCP= exp(-n o  SF) SF=exp[-(  d+  d 2 )] 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 = 10 7 cells/cm 3. A Nahum, S. Webb, Med.Phys. 40:1735-8, 1995 H. Suit et al. Radiother. Oncol. 25:251-60, 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 function U=  w i  NTCP  w o  (1-TCP) where w are weight factors, NTCP i is the probability of a given toxicity (end-point) of an organ i, and TCP is the tumour control probability. w i 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 Gt. i

Cost functions P + -concept Introduced by Wambersie in 1988 as ‘Uncomplicated Tumour Control’ and refined by Brahme: P + =P B -P B  I where P B is the tumour control probability and P I is the normal tissue complication probability.

Cost functions P + -concept When no correlation between the to probabilities exist: P + =P B -P B  P I When full correlation between the to probabilities exist: P + =P B - P I

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: , 1996

Models in treatment plan evaluation …is larger in practice than in theory !” John Wilkes “The difference between theory and practice…