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The physical basis of IMRT and inverse planning

Joint Department of Physics, Institute of Cancer Research and Royal Marsden NHS Trust, London, UK

View larger version (33K): [in a new window]   Figure 1. Illustrating the key differences between (a) conventional radiotherapy, (b) conformal radiotherapy (CFRT) without intensity-modulation and (c) CFRT with intensity modulation (IMRT). For almost a century radiotherapy could only be delivered using rectangularly-shaped fields with additional blocks and wedges (conventional radiotherapy). With the advent of the multileaf collimator (MLC) more convenient geometric field shaping could be engineered (CFRT). The most advanced form of CFRT is now IMRT whereby not only is the field geometrically shaped but the intensity is varied bixel-by-bixel within the shaped field. This is especially useful when the target volume has a concavity in its surface and/or closely juxtaposes organs-at-risk, e.g. as shown here in the head-and-neck, where tumours may be adjacent to spine, orbits, optic nerves and parotid glands.

View larger version (15K): [in a new window]   Figure 2. A diagram adapted from that in paper [25] showing how a uniform annular dose distribution surrounding a circle of zero dose could be obtained by rotating an intensity-modulated beam (see text for more detail).

View larger version (18K): [in a new window]   Figure 3. Illustrating the principles of IMRT. A single (CT) slice of a patient is shown with the contours of the prostate (PTV, planning target volume), rectum (OR, organ at risk) and bladder (OR) outlined. The prostate has a concave outline and it is desired to achieve a high dose in the PTV sparing the ORs. Three intensity-modulated beams (IMBs) are shown. For simplicity they are shown as parallel beams and at arbitrary gantry orientations. It is not intended to suggest these three orientations are the most appropriate for the treatment. Each beam has a modulated fluence.

View larger version (10K): [in a new window]   Figure 4. (a) The left graph shows a plot of a cost function for a problem with a well defined global minimum cost as well as several local minima. Cost is plotted on the vertical axis and position on the horizontal axis labels the particular stage of some iterative planning cycle. For example, the global minimum corresponds to having achieved the beams which deliver dose best matching the prescribed constraints. The very left hand position might represent the start of iteration when beams have not yet been properly formed. (b) The right graph conversely shows a cost function more typical of radiotherapy inverse planning problems. There is a wide plateau (basin) of beam arrangements all of which correspond to dose distributions that are much the same and best satisfy the planning constraints. There may be a small dip (global minimum) for the absolute best but continuing the iteration to find this might be futile when any position in the plateau would be acceptable.

View larger version (8K): [in a new window]   Figure 5. Illustrating the concept of a dose–volume constraint in inverse planning. The figure shows an integral (sometimes called cumulative) dose–volume histogram for an organ at risk (OR). The clinician specified the starred points as dose–volume constraints and the algorithm "did its best" to meet them (not entirely succeeding as not all the stars are to the right of the curve). For example, 0.85 of the OR volume receives 20 Gy or more; 0.3 of the volume receives 27 Gy or more and so on.

View larger version (19K): [in a new window]   Figure 6. An analogy for simulated annealing. The ski slope is the cost function. It has local minima (snowbumps) and a global minimum to be reached (finish flag). The skier has to occasionally ski uphill (or "tunnel through the snowbumps!") in order to avoid becoming trapped in a local minimum. The technique gets its name from the slow cooling of a solution in which the crystalline state is the global minimum and local minima are amorphous states. The grains referred to are the elemental changes in beamweight.