A Network Approach for Intensity Modulated Arc Therapy (IMAT)

1. A Network Approach for Intensity Modulated Arc Therapy (IMAT) Athula D. A. Gunawardena, Michael C. Ferris and Robert R. Meyer University of Wisconsin-Whitewater, and University of Wisconsin-Madison

2. Radiotherapy: 100 years + • 1896 - Emil Herman Grubbé uses radiation to treat breast cancer - less than one month after public announcement of Roentgen’s discovery of X-rays • 1975 - Mark P. Carol, M.D. develops initial idea for IMRT • 1992 - Computer technology advances allow Carol to prototype the Peacock IMRT system. • 1996 - FDA approval won for Carol’s system

3. Radiotherapy: Impact and Challenges • > 1 million cases of cancer each year in U.S., and many times that number in other countries • Approximately 40% of U.S. patients with cancer are treated with radiation therapy • Minimizing radiation dose to nearby healthy “organs at risk” (OARs) very difficult

4. Radiation Therapy Goals • High Level Goals: Achieve prescribed radiation to tumor while minimizing dose to the surrounding organs • Some Additional Goals: • Minimize time patient spends on the treatment couch. • Minimize beam-on time (time radiation beam in “on” ) • Minimize treatment planning time

5. Intensity Modulated Radiation Therapy: A complex RT procedure • Radiation delivered from 4-9 angles selected from 360 possible angles • For eachof these 4-9 angles, Intensity Modulated Radiotherapy (IMRT) uses 50-200 small radiationbeamletseach of which is “allowed” to have a different radiation intensity • Different beamlet intensities achieved via multiple apertures at each angle

6. Leaf Sequencing in IMRT Multileaf Collimator

7. Common Machine Specific Constraints on Shapes • Single Interval Constraint - Any nonzero row of an achievable shape contains a single interval of ones • Inter-Digitization Constraint -Opposite adjacent leaves cannot cross each other

8. Intensity Modulated Arc Therapy (IMAT)A rotational IMRT system A1 , A2,…,AP : I-maps K=3; the number of sweeps along the arc Would like: • A2 • A1 • A3 • A • AP • • • AP-1 • • Introduced by C. X. Yu in 1995 as an alternative to Tomo Therapy

9. Input • A1 , A2,…,AP : nonnegative real matrices K : the number of sweeps through an arc(i.e., # of shapes per I-map) D : maximum allowable leaf movement between two adjacent angles Leaf Sequencing in IMAT • Variables • i1,…, iK : beam weights for segmentation of Ai, I=1, …, P • Si1,…, SiK : binary shape matrices for Ai • Maximum allowable leaf movement between Si,j and Si+1,j  D, MLM(Si,j and Si+1,j ) D, and other constraints on Sij.

10. Clinical Prostate Maps

11. Row-Non-Convexity Measure

12. Network Models Assignment Problems Transportation Problems Shortest Path Problems Maximum Flow Problems Critical Path in Project Plan Networks Minimum Cost Flow Problems

21. Intensity Map Segmentation Error Map • Angle 200 • Angle 260