Towards Unlocking the Full Potential of Multileaf Collimators

A central problem in the delivery of intensity-modulated radiation therapy (IMRT) using a multileaf collimator (MLC) relies on finding a series of leaves configurations that can be shaped with the MLC to properly deliver a given treatment. In this paper, we analyse, from an algorithmic point of view, the power of using dual-layer MLCs and Rotating Collimators for this purpose. 1 Radiation therapy planning Radiation therapy is one of the most commonly used cancer treatments and has been shown to be effective. The radiation treatment poses a tuning problem: the radiation needs to be effective enough to kill the tumor while sparing healthy tissues and organs close to the tumor – so-called organs at risk. Towards this goal, the design of radiation treatment has to be specifically customized for each patient. Once both tumor and organs at risks have been delineated, the radiation oncologist will prescribe minimal, maximal and mean irradiation quantity for each of them. The amount of radiation is measured in gray (Gy). For example, typical dose for a tumor ranges from 60 Gy to 80 Gy (a minimal dose that the treatment should achieve), whereas healthy organs should not receive more than a given threshold of radiation – for example, 20 Gy for lungs, 50 Gy for bones or 12 Gy for lens. Usually, the overall treatment dose is fractioned – e.g. 1.8 to 2 Gy per day, five days a week for an adult. Each fraction is delivered by a linear accelerator (linac) using a cone beam that rotates around the patient; achieving a concentric irradiation converging in the tumor site. In the so-called ”Step-And-Shoot” technique, the treatment design specifies some specific angles where the linac successively stops to irradiate the patient. For each of these angles, a specific intensity distribution accross the radiation beam (later on referred to as intensity matrix) is computed (for instance, with the multicriteria approach to radiation therapy planning of Hamacher and Küfer [6]) in order to achieve the desired overall dosage of the fraction. An illustration is provided in Figure 1a. The radiation generated by the accelerator is uniform. Therefore, in order to achieve the varying intensity, ? Work partially supported by ANR project BIRDS JCJC SIMI 2-2010 this radiation needs to be modulated. For this purpose, each intensity matrix is delivered through a multileaf collimator (MLC). An MLC is a device composed of parallel pairs (referred to as rows) of facing tungsten strips (referred to as leaves) that can block the radiation by moving toward each other from left and right (see Figure 1c). However, radiation can pass through the open gap between the leaves endpoint. Each intensity matrix is realized by a sequence of MLC configurations (i.e. specific leaves positions for each row of the MLC) each of which is maintained for a certain amount of time (corresponding to the intensity). In the static case, the radiation is switched off while the collimator leaves are moving. The so-called gantry denotes the whole device including the linac and the MLC. Fig. 1. a) IMRT with some intensity matrices – shown in grayscale coded grids with 5 intensities (the lighter the color the higher the radiation intensity). b) A realization of IM2 with i1 = 0, i2 = 1, i3 = 2, i4 = 3, i5 = 4. c) MLC illustration from Varian From an algorithmic point of view, the corresponding problem is a matrix decomposition problem where each intensity matrix is given as an integer matrix that has to be decomposed into a weighted sum of binary matrices (each binary matrix denotes an MLC configuration and the weight represents the associated intensity). These binary matrices are consecutive ones matrices (the 1s occur consecutively as a single block in each row) since MLC leaves are moving from left and right sides of the device on each row. For example, the intensity matrix IM2 of Figure 1b can be decomposed into three configurations. Of course, there are many ways of decomposing a given intensity matrix. It is desirable to select