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

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

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

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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

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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 Q. WU et al. Int. Radiat. Oncol. Biol. Phys. 52:224-35, 2002 A typical DVH of normal tissue

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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 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. 21:137-146, 1991. A. Niemierko et al.Radiother. Oncol. 20:166- 176, 1991. H. Honore et al. Radiother Oncol. 65:9-16, 2002.

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Biological models Normal 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/ 2 e (-x 2 /2) dx - t=D-D(v)/m D(v) D(v)=D V -n

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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.

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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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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) 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

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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

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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

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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

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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. 54:156-62, 2002

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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, 1992. TCP=

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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 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

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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.

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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

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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. 34:923-930, 1996

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

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