1. Modeling and Prediction of Abdominal Tumor Motion Haobing Wang Department of Computer Science May 9 th, 2003

2. Project Outline Topic and Goal Background and Motivation Methods Experiments Analysis Future Work

3. Topic and Goal Facilitate real-time tracking of the tumor motion during radiotherapy and allow for for precise delivery of radiation dose to mobile tumors. Find methods to model and predict abdominal tumor motion.

4. Background and Motivation Tumor position is modeled by tracking surgically implanted clips surrounding the tumor. The radiation beam has mechanical latency.

5. Template Matching Using DHMM DHMM: Deformable Hidden Markov Model Given a pattern template, recognizing the pattern in a new time series, allowing flexible deformation of time.

6. Template Matching Using DHMM Generalize the standard constant model and allow each state to generate data in the form of a regression curve. K-state segmental HMM each state of which corresponds to one segment in the piecewise linear representation of the template.

7. Template Matching Using DHMM Use a sinusoid as template The DHMM automatically find the period whose shape is similar to a sinusoid. Then the sequence is found is used as the prediction of the next breathing period.

8. Experiments of DHMM Method

9. Prediction of 100 frames

10. Analysis of DHMM Method Average error and error variance is greater than 1 millimeter. Although the computation time for each clip is around 5 minutes, it’s still cannot be done on-line.

11. Prediction by Curve Fitting A least square method to fit the data points to a third order polynomial function: f(x) = b 0 + b 1 x + b 2 x 2 + b 3 x 3. The set of coefficients [b n ] can be found by minimizing the sum:

12. Examples of Curve Fitting

13. Prediction by Curve Fitting Suppose S is the shape function which describes the trajectory of a single breathing period, and  (t) is a weighing function. I use  as a decay factor. So S(t) can be computed by: S k = f(t) + (1-  t  S k-1

14. Experiments of Curve Fitting Bob (clip 2)

15. Experiments of Curve Fitting Gary (clip 0)

16. Experiments of Curve Fitting Results of predicting approximately 550 frames on average

17. Experiments of Curve Fitting Results of predicting 100 frames

18. Comparison of Four Methods Predicting 100 frames

19. Analysis of Curve Fitting Gives better result. Average error is the best among the four methods, and error variation is the second to the best. Computation is fast. Can be done on-line.

20. Future Work Adjustment of duration of each breathing period. Improvement of the performance of the clip tracker and patients’ breathing pattern.

21. Future Work