Objective Functions and Plan Evaluation: Inverse Planning and/or Optimization? Benedick A. Fraass, Ph.D.

Transcription

1 Objective Functions and Plan Evaluation: Inverse Planning and/or Optimization? Benedick A. Fraass, Ph.D. Department of Radiation Oncology University of Michigan Ann Arbor, MI Supported in part by National Cancer Institute Grant P

2 Plan Optimization Parameters Treatment Planner: Modify the Plan! Calculate Dose Evaluate Plan Using Dose, DVHs Is it ok?

3 Forward Planning Parameters Treatment Planner: Modify the Plan! Calculate Dose Evaluate Plan Using Dose, DVHs Is it ok?

4 Inverse Planning Parameters Optimization Engine: Modify the Plan! Calculate Dose Evaluate Using Cost Function Cost

5 The crucial difference between normal forward planning and inverse planning is the use of a quantitative objective function for the comparison and evaluation of different prototype plans - not the different kinds of mathematical or computational optimization strategies, or the details of techniques which can be used for delivery (e.g. IMRT) or the number of degrees of freedom. So, what is the crucial difference between inverse planning and optimization?

6 Inverse Planning vs. Optimization Optimization Creation of the plan which best satisfies all the desired tradeoffs between target dose + target coverage vs. minimization of impact(s) on normal tissue; a single cost function should give optimal results for relevant patients Inverse Planning Creation of acceptable plans which satisfy the conditions or limitations set by the planner; often performed with multiple plans / patient

7 If you accept these definitions, then there is lots of inverse planning happening, but little to no optimization. This is due mainly to the way clinical protocols and objective functions are specified, and to our lack of knowledge about how to specify the necessary information.

8 90 Gy Brain Dose Escalation Protocol PTV1 = 90 Gy +/- 5% PTV2 > 70 Gy, DVH criteria PTV3 > 60 Gy, DVH criteria Chiasm < 55 Gy Normal Brain: minimize

9 Dose limits 90 Gy Brain Protocol minimize PTV3 PTV2 PTV1 Volume (%) Normal Brain 20 0 Optic Chiasm Dose (Gy) Planning Goal: Target homogeneity, spare normal tissue. Plan Evaluation Metric: Mean normal brain dose

10 Can the clinical brain protocol be satisfied by various cost function methods? Dose EUD 100 PTV3 PTV2 TCP/NTCP 80 DoseVol Volume (%) Normal Brain PTV Optic Chiasm Dose (Gy)

11 This is a MultiObjective Problem which requires a Generalized Cost Function Optimization requires full clinical knowledge, so cost function must include all clinical info 1. What doses are optimal 2. How do you trade off target dose vs. normal tissue dose 3. How do you trade off improved target dose and/or normal tissue sparing vs. complexity, time, effort, etc. 4. Issues must be optimized, not constrained

12 Costlet-based Cost Functions Cost is combination (+ or x) of costlets which represent specific clinical issues: C = c 1 * c 2 * c 3 * = w 1 f 1 * w 2 f 2 * w 3 f 3 * Costlets can be dose, dose-volume or biologically based Each costlet s shape, relative weight are independently chosen

13 Costlets have adjustable parameters that change the costlet shape Example: Dose-based Cost 1.00E E E+07 n = 10 n = 2, w = 1 n = 2, w = 10 C = w S i ( d i - d ) n 1.00E E E E E Cost Mean Dose

14 1.00E E E+07 Dose-volume C = w S i V i >d n n=10 n=2 Cost 1.00E E E E E Dose

15 1.20E+00 EUD-based cost function E E-01 n = -20 Cost 6.00E E E E+00 n = Dose C = 1/(1+(EUD 0 /EUD) n ) EUD = (1/N S i D ia ) 1/a 1. Q.Wu et al ICCR proceedings 2000

16 TCP and NTCP 1.E+00 1.E+00 8.E-01 g = 30 Cost 6.E-01 4.E-01 2.E-01 0.E+00 g = Dose C = TCP(TD 50, g) C = NTCP(n,m,TD 50 )

17 Which cost function gives the optimal plan? Who knows? Typically, the clinical protocol does not describe how important minimum target dose is versus sparing normal brain describe importance of overdose in PTV1, or more importantly in PTV2-1 or 3-2 (the rings) describe how beneficial it is to spare more chiasm what target compromise to accept when chiasm is close (actually, this protocol does) The cost function does describe those issues, but it s typically not known how to set these parameters, or how they will interact

18 Prioritizing Issues for the Cost Function Priority Structure Sp.Cord PTV66, 60,54 Parotids Oral Cavity... Clinical Goals < 45 Gy, minimize mean = 66/60/55, +/- 5% mean dose < 26Gy max < 66 Gy, minimize Costlet Power

19 Can a clinical protocol be satisfied by many cost function methods? Dose EUD 100 PTV3 PTV2 TCP/NTCP 80 DoseVol Volume (%) Yes! Now, which is better? Normal Brain PTV1 20 Optic Chiasm Dose (Gy)

20 Do we need separate plan evaluation metrics, or is the cost function enough? Can we pick the plan with the lowest cost? How do we know the optimization is working correctly? Compare to what we expect.. Plan A s score is Is that good? How much better is plan A than plan B? Plan B is simpler, but its score is Which plan should we use? The cost function pushes the solution to the right place, but plan evaluation metrics can transfer the info to the MD If you allowed a little more dose to the big toe, how much better would plan A get?

21 5 Field Beamlet IMRT: Brain Non-coplanar Axial PTV2 PTV1 Volume (%) Normal Brain PTV3 Metrics: Max Brain - No Mean Brain - Yes V 40Gy - Yes V 15Gy - No Dose (Gy) Superior-lateral P

22 Multiple Plan Evaluation Metrics Plan evaluation metrics must Be clinically relevant Be clinically understandable Differentiate between plans Be able to show the gradients - what improvements might be within reach with a little clinical compromise ==> Give the clinician some ability to make clinical decisions and assimilate the results

23 Evaluating Plan Comparisons For each plan in a comparison: Was there the same definition of planning goals Same consideration of normal structures? Was each plan optimized? Were appropriate metrics for plan eval. used? Have we controlled for other differences (e.g., degradation by setup uncert./organ motion)?

24 Target Homogeneity: Sparing Both Parotids

25 Volume (%) (%) Ipsilateral Parotid PTV60 EUD EUD Dose TCP/NTCP Dose Relaxed Dose Dose Dose Relaxed Dose Dose (Gy) Dose (Gy)

26 % Volume Change in Target Homogeneity Ipsi-lateral Parotid PTV66 +/-5% +/-10% +/-20% Dose (Gy)

27 100 Change in Target Homogeneity % Volume Ipsi-lateral Parotid +/-10% +/-20% PTV Dose (Gy)

28 Optimization is Critical for Evaluating Plan Comparison Studies If acceptable plans are compared, we can t say one technique is better than another, because maybe we didn t try hard enough. Only if we push as hard as possible on all issues to be evaluated can we judge techniques

29 Is the objective function the only important thing? No! Number (and scope) of degrees of freedom Explicit and implicit constraints (to solution space) Explicit and implicit limitations (to final plan implementation and evaluation) Staff confidence in acceptability, achievability, and optimality With a little adjustment, could I do a lot better on this patient? Or, could I at least have confidence that all the easy improvements have been made?

30 3-Fld Pancreas Plan Compare: 1) Optimized Flat Conformal Fields 2) Optimized IMRT Fields Use Identical Cost Function

31 Anterior Inferior Flat Conformal Opt-Beamlet

32 3-Fld Pancreas: Optimized Flat vs Beamlet IMRT 100 % Volume PTV Opt-Beamlet Opt-Flat 20 L Kidney R Kidney % Dose

33 Comparison Results Have difference in PTV uniformity for different plans, even though for some comparisons, identical optimization and cost functions were used. Why? A different # of degrees of freedom was allowed for response to optimization. Optimization result for normal tissues was worse than forward plan. Why? 1) Forward plan has implicit consideration of normal tissue issues. 2) Plan was evaluated using metrics not included in inverse planning

34 Many issues are critical for reasonably successful clinical plan optimization Appropriate cost function which contains terms which describe priorities for all clinically relevant issues (ie, all issues important to MD and which can be affected by the plan configuration) Number (and scope) of degrees of freedom Explicit and implicit constraints and limitations Confidence in acceptability, achievability, and optimality (or at least confidence that all the easy improvements have been made)

35 We have a long way to go... And how will we know when we get there?