Real time Optimization and Planning for Prostate Implants

Real-time Optimization and Planning for Prostate Implants Bruce Thomadsen University of Wisconsin Madison Conflict of Interest That the author knows of, he has no conflicts of interest for this presentation. Learning Objectives understand the nature of optimization for interstitial implants.  To understand the optimization process.  To understand real-time optimization  To Limitations Will only discuss low dose-rate implants, since high dose-rate brachytherapy optimization for prostate is the same as for any HDR implant. Definitions Real time — quickly enough that you don’t feel you’ve waited too long.  Optimization — a process that produces the dose distribution you desire… or close enough.  As of Now definitions change with time.  ―Real time‖ depends on our expectations.  ―Optimization‖ depends on our desires and how close we feel that we need to get to it.  Both More Careful Definition ―Real-time optimization‖ is often used to mean real-time correction of dosimetry.  Not optimization.  Reassessment of the location of seeds already implanted compared to the desired locations.  Allows replanning using whatever means were used in the first place. Real-time Reassessment available with the Nucletron FIRST/SPOT ultrasound system, and near for VariSeed.  Research using cone-beam CT.  Commercially, Real-time Reassessment: Process Plan the case and start the implant.  At intervals, re-image and correct the dose distribution for the actual location of the sources implanted.  Replan where to place remaining sources to compensate for the real locations already used.  Real-time Reassessment: Limitations of sources.  Movement of sources by implantation of other sources.  Time for replanning.  Visualization Real-time Reassessment: Limitations Also, it is not clear that the reassessments actually goes through optimization rather than simply recalculation. Old Question: Optimize or Uniformly Load 1. Uniform dose or hot center? 2. Uniform dose — how uniform? — at what price? Optimization Approaches 1. 2. 3. 4. 5. 6. Intellectual Rules Stochastic Deductive Heuristic Analytic Intellectual Optimization Trial and evaluation during treatment plan.  Not particularly fast but certainly live time.  Not what the organizer had in mind for me to address  Rules For example, Manchester spherical implant rules (1/4 source in core; 3/4 source on periphery) Again, not the topic of this talk Stochastic Optimization simulated annealing or genetic algorithm  Because they are iterative, they tend to take relatively long  No guarantee that they find the optimum, only an adequate solution (if one exists, and maybe not the best).  Examples: Objective Functions stochastic, and many other optimization methods, use objective functions to evaluate how good a trial is.  An example might be simply (dose desired-dose achieved).  The goal would be to minimize this function.  All Objective Functions (cont.) Can also include doses to normal tissue, uniformity, etc.  Example: F=(Dosedesired-Doseachieved)x (Dosenormal-Tolerance)/Homogeneity Factor  Simulated Annealing 1. 2. 3. 4. Starts with a random placement of sources in the possible solutions. Evaluate the objective function. Change some source positions. Evaluate the objective function a. If the objective function is acceptable, stop. b. If the objective function is not, go back to 3, starting from the better distribution. Simulated Annealing (cont.) At first there can be big changes in source positions, either in number of sources or in the location of the sources.  At each iteration, the size of the changes decreases.  The process improves the value for the objective function, or at least doesn’t make it worse.  Simulated Annealing (cont.) nestle into a local minimum.  To avoid that, sometimes in the middle a large change is allowed.  Can Genetic Algorithms  Start with an arbitrary distribution and make a continuous chain of the positions. Calculate the objective function. Source present No source present Pick another arbitrary distribution, and calculate the objective function.  Mate the two distributions as on the next slide.  Genetic Algorithm (cont.) Genetic Algorithm (cont.) Evaluate the objective functions,and pick the best two of the four, and mate them, or mate the best with a different random distribution.  Continue iteratively, occasionally throwing in random changes (mutations).  Stop when the objective function is adequate.  Deductive (Numerical) Methods An example is Branch and Bound  First the problem is solved with each possible source position optimized with a fractional occupancy  This is easy, mathematically, but of course is physically ridiculous.  However, calculating the objective function for this case gives the best value that function could ever have.  Branch and Bound One source position (any) is picked, and for the two possibilities, a source present (1) or source absent (0), the objective function is evaluated.  This has defined two paths, (present/absent).  The path with the better objective function is followed, and another position picked for the 0/1 options.  Again the better picked, and so on.  Branch and Bound Tree 0 yP* = 0.75 yP* = 1 2 yP* = 0 1 node yP^ = 0 3 yP^ = 1 4 branch 5 6 Warren D’Souza Branch and Bound (cont.) At each branching, the objective function gets worse because we are replacing fractional occupancy with integer.  If the objective function is worse than the value at the end of any other path, go back to the best value, and continue the process there.  Branch and Bound (cont.) The process can either continue until an adequate value for the objective function is found (relatively quick) or the best value (longer)  Does not test all possibilities.  Can give the true optimum.  Faster than stochastic methods.  Heuristic   Example: the Greedy Algorithm Process: 1. Establish a region 2. Calculate the adjoint function for the region Adjoint Function the contribution to the average dose in the region from a source placed at the test point.  The adjoint function maps this out for all space (or in the case of a prostate implant, for all possible source positions).  Determines Whole ROI Adjoint Distribution for a 2D image-slice Target Rectum Sua Yoo Normal tissue Urethra Combining All Adjoints  #23 #19  Sua Yoo  Plot each function simply sequentially for all source positions (top to bottom, left to right). Find the position with the highest ratio of dose to target to dose to the normal structures. Place a source there. Adjoint Ratio v   ( j)  ( w urethra  D , urethra  w rectum  D , rectum  w normal  D , normal ) j j j ( w t arg et  D , t arg et ) j Best location is with lowest ratio Sua Yoo Greedy Algorithm Process 3. After placing a source in the first location, see if dose criteria are met. (yes-stop; no-proceed) 4. Exclude locations within a specified isodose surface. 5. Pick the next best position in the allowed volume. 6. See if dose criteria are met. (yes-stop; noproceed) 7. Increase the exclusion isodose value and set up the new excluded volume. Greedy Algorithm   Process 8. Continue until dose criteria are met.  Advantage: Because the process is not iterative (trying distributions that don’t work), the algorithm is very fast (≈100 – 5000 times faster than branch and bound) Disadvantage: Not a true optimization, only adequacy (but not that different results). Analytic Methods methods would be solving an equation for the source positions.  There is not much going on in this arena.  Analytic Real-time Optimization  Real-time optimization would be optimization that would be fast enough that: – It could be performed intraoperatively. – It could correct the plan continually to make up for differences between the last version of the plan and the actual placement of the sources since then.  It would also require rapid, accurate, and sensitive imaging of seeds. Real-time Optimization: Where Are We? Approaching possibility.  The heuristic approach is fast enough and good enough. (In a few years, computers may be fast enough for other approaches to be feasible. Don’t forget, we are talking about potentially 20-100 optimizations).  Imaging is very rapidly improving (or at least was in 2002-2003)  Real-time Optimization: Where Will We Be? The question remains, and will for a long time – Does all this improve results (survival and quality of life)?