Optimizing Radiation Treatment Planning for Tumors Using IMRT

1. Optimizing Radiation Treatment Planning for Tumors Using IMRT Laura D. Goadrich Industrial Engineering & Department of Computer Sciences at University of Wisconsin-Madison April 19, 2004

2. Overview • Radiotherapy motivation • Conformal radiotherapy • IMRT • Mechanical constraints • MIP method • Input/output • Langer, et. al. Approach • Monoshape constraints • Implementation results • References

3. Motivation • 1.2 million new cases of cancer each year in U.S. (times 10 globally) • Half undergo radiation therapy • Some are treated with implants, but most with external beams obtained using radiotherapy treatments.

4. Radiotherapy Motivation • Used to fight many types of cancer in almost every part of the body • Approximately 40% of patients with cancer needs radiation therapy sometime during the course of their disease • Over half of those patients who receive radiotherapy are treated with an aim to cure the patient • to treat malignancies • to shrink the tumor or to provide temporary relief of symptoms • In the use of radiation, organ and function preservation are important aims (minimize risk to organs at risk (OAR)).

5. Planning Radiotherapy- CAT scan • Conduct scans of the section of the body containing the tumor • Allows physicians to see the OAR and surrounding bodily structures

6. Planning Radiotherapy- tumor volume contouring • Isolating the tumor from the surrounding OAR is vital to ensure the patient receives minimal damage from the radiotherapy • Identifying the dimensions of the tumor is vital to creating the intensity maps (identifying where to focus the radiation)

7. Planning Radiotherapy- beam angles and creating intensity maps • Multiple angles are used to create a full treatment plan to treat one tumor. • Through a sequence of leaf movements, intensity maps are obtained

8. Option 1: Conformal Radiotherapy • The beam of radiation used in treatment is a 10 cm square. • Utilizes a uniform beam of radiation • ensures the target is adequately covered • however does nothing to avoid critical structures except usage of some blocks

9. Intensity Modulated Radiotherapy (IMRT) provides a shaped array of 3mm beamlets using a Multi-Leaf Collimator (MLC), which is a specialized, computer-controlled device with many tungsten fingers, or leaves, inside the linear accelerator. Allows a finer shaped distribution of the dose to avoid unsustainable damage to the surrounding structures (OARs) Implemented via a Multi-Leaf Collimator (MLC) creating a time-varying opening (leaves can be vertical or horizontal). Option 2: IMRT

10. Classical vs. IMRT

11. IMRT machine

12. IMRT: Planning- intensity map • There is an intensity map for each angle • 0 means no radiation • 100 means maximum dosage of radiation • Multiple beam angles spread a healthy dose • A collection of shape matrices are created to satisfy each intensity map.

13. Intensity map to shape matrices Original Intensity Matrix Shape Matrix 1 Shape Matrix 3 Shape Matrix 2 Shape Matrix 4

14. Program Input/Output • Input: • An mxn intensity matrix A=(ai,j) comprised of nonnegative integers • Output: • T aperture shape matrices dtijsuch that zK of the matrices are used where K < T • Non-negative integers t (t=I..T) giving corresponding beam-on times for the apertures • Apertures obey the delivery constraints of the MLC and the weight-shape pairs satisfying K is the total number of required shape matrices

15. Mechanical Constraints • After receiving the intensity maps, machine specific shape matrices must be created for treatment • There are numerous types of IMRT machines currently in clinical use, with slightly different physical constraints that determine the leaf positions (hence the shape matrices) possible for the device • Each machine has varying setup times which can dominate the radiation delivery time (beam-on time) • To limit patient discomfort and subtle movement from initial placing: limit the time the patient is on the table • Goals: • Minimize beam-on time • Minimize number of different shapes

16. Approach: Langer, et. al. • Mixed integer program (MIP) with Branch and Bound by Langer, et. al. (AMPL solver) • MIP: linear program with all linear constraints using binary variables • Langer suggests a two-phase method where • First minimized beam-on time T is the upper bound on the number of required shape matrices • Second minimize the number of segments (subject to a minimum beam-on time constraint) gt = 1 if an element switches from covered to uncovered (vice versa) = 0 otherwise

17. In Practice • While Langer, et. al. reports that solving both minimizations takes a reasonable amount of time, he does not report numbers and we have found that the time demands are impractical for real application. • To obtain a balance between the need for a small number of shape matrices and a low beam-on time we have found that numShapeMatricies*7 + beam-on time • Initializing T close to the optimal number of matrices + 1 required reduces the solution space and solution time

18. Constraint: Leaves cannot overlap from right and left • To satisfy the requirement that leaves of a row cannot override each other implies that one beam element cannot be covered by the left and right leaf at the same time ptij= 1 if beam element in row i, column j is covered by the right leaf when the tth monitor unit is delivered = 0 otherwise ltijis similar for the right leaf dtijcontains the finaltth monitor unit

19. Constraint: Full leaves and intensity matrix requirements • Every element between the leaf and the side of the collimator to which the leaf is connected is also covered (no holes in leaves).

20. Constraint: No leaf collisions • Due to mechanical requirements, leaves can move in only one direction (i.e. the right leaf to the right). On one row, the right and left leaves cannot overlap

21. Constraint: Shape matrices reqs • The total number of shape matrices expended it tallied z= 1 when at least one beam element reamins exposed when the tth monitor unit in the sequence is delivered = 0 otherwise I is the number of rows J is the number of columns • Must satisfy the intensity matrix for each monitor unit. I is the intensity assigned to beam element ij

22. Constraint: Monoshape • The IMRT delivery is required to contain only one shape matrix per monitor unit, a monoshape • First determine which rows in each monitor unit are open to deliver radiation deliveryit=1 if the ith row is being used a time t = 0 otherwise • Determine if the preceding row in the monitor unit delivers radiation dropit=1 if the preceding row (i-1) in a shape is non-zero and the current row (i) is 0 = 0 otherwise

23. Constraint: Monoshape • Determine when the monoshape ends jumpit=1 if the preceding row (i-1) in a shape is zero and the current row (i) is nonzero = 0 otherwise • There can be only one row where the monoshape begins and one row to end

24. Complexity of problem • To account for all of the constraints there is a large number of variables and constraints.

25. Comparison of results • Corvus version 4.0

26. Comparison of results • Corvus version 5.0

27. Referenced Papers • N. Boland, H. W. Hamacher, and F. Lenzen. “Minimizing beam-on time in cancer radiation treatment using multileaf collimators.” Neworks, 2002. • Mark Langer, Van Thai, and Lech Papiez, “Improved leaf sequencing reduces segments or monitor units needed to deliver IMRT using multileaf collimators,” Medical Physics, 28(12), 2001. • Ping Xia, Lynn J. Verhey, “Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments,” Med. Phys. 25 (8), 1998. • T.R. Bortfield, D.L. Kahler, T.J Waldron and A.L.Boyer, X-ray field compensation with multileaf collimators. Int. J. Radiat. Oncol. Biol. 28 (1994), pp. 723-730. • Bortfield, Thomas, et. al. “Current IMRT optimization algorithms: principles, potential and limitations” Presentation 2000. • Dink, Delal, S.Orcun, M. P. Langer, J. F. Pekny, G. V. Reklaitis, R. L. Rardin, “Importance of sensitivity analysis in intensity modulated radiation therapy (IMRT)” 2003.