Intensity-modulated radiotherapy by means of static tomotherapy: A ...

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828 M. Oldham and S. Webb: Intensity-modulated radiotherapy 828 FIG. 2. The planning problem studied in this paper dimensions given in the text. The PTV is the ‘‘bean-shaped’’ invaginated region resulting from the removal of parts of two circles the OARs from an ellipse. The problem represents a prostate PTV with bladder and rectum OARs. The ‘‘I values’’ are the importance-factors used in the inverse planning. FIG. 1. A schematic illustration of the slit beam of the MIMiC and its bixels in relation to the patient. Open bixels are shown as white spaces and closed bixels as black spaces. The vanes of the MIMiC are not shown, but five of the actuating mechanisms which can open or close the vanes are shown schematically. level of intensity modulation is optimal? 3 Where does the trade-off start to become unfavorable between increasingly complex and expensive treatments and improved dose distributions? And 4 which tumor types and disease sites will the new techniques be most useful for? Two of the most central questions are how well can the intensity-modulated dose delivery be simulated with current planning algorithms, and how accurately can an intensity-modulated plan be delivered in practice given the specification constraints of linear accelerators? In this paper we present a planning and verification study, in the static-tomotherapy framework, which sheds some light on the latter two issues. Investigating the dosimetry of the MIMiC in static tomotherapy mode is easier than for rotational tomotherapy due to the lack of smearing of the dose distribution and issues of the stability of MU delivery per degree. This study is therefore a necessary first step in investigating the dosimetry of the MIMiC. II. METHOD In this paper we present a planning and verification study based on delivering radiation in ‘‘static-tomotherapy’’ mode via the NOMOS 2591 Wexford Bayne Road, Suite 315, Sewickley, PA, 15143 MIMiC 2–7 Multileaf Intensity- Modulation Collimator Fig. 1. The MIMiC device attaches to the blocking tray of the linear accelerator and positional adjustment screws and bolts enable the collimation slit to be accurately aligned with the cross wires. The center of the cross wires coincides with the center of the slit, the edges of which are made parallel with the respective cross wire. The intensity along the slit beam of the MIMiC can be modulated by small absorbing vanes illustrated in Fig. 1 that move in and out of the slit under computer control. The vanes are arranged in two parallel banks, one superiorly and one inferiorly to the slit. The MIMiC can be used in either rotational mode, where the vanes move as the gantry rotates, or static mode, where the vanes move but the gantry is fixed at some orientation. The former is conventionally termed tomotherapy and the latter we refer to as static tomotherapy. The planning problem addressed is an idealized model of the treatment of an invaginated prostate patient illustrated in Fig. 2. The patient contor was assumed elliptical with major and minor axes of lengths 29 and 25 cm, respectively. The planning-target-volume PTV was part of an ellipse, major and minor axes of 9 and 7 cm, the center of which was offset vertically below the center of the contour by 2 cm. Two circular organs-at-risk OAR were located above and below the PTV with radii 4 and 1.5 cm, respectively. The centers of the OARs were positioned 5 cm above and 4 cm below the center of the PTV, the latter being defined as the isocenter. The PTV was the invaginated region created by the subtraction of parts of the circular OARs from the ellipse. A circular radius 7.25 cm region of sensitive tissue was defined enclosing the PTV and both OARs as shown. The axial thickness of the phantom was specified as extending for 12 transaxial slices each of thickness 1 mm, with no change in the contours of any of the structures. Fitting the high-dose region to such an invaginated PTV, with directly abutting OARs constitutes a very difficult planning problem, and one that would not be achievable with conventional radiotherapy techniques. 8 A. Inverse planning and forward dose calculation by components A relative dose prescription of 1.0 in the PTV, 0.1 in the two small OARs and 0.3 in the circumscribing sensitive tissue, was specified in the planning problem of Fig. 2 see Appendix B for a discussion of these units. Then a plan consisting of nine equi-spaced co-planar fixed slit fields was designed, with gantry angles of 0°, 40°, 80°, 120°, 160°, 200°, 240°, 280°, and 320°. A set of intensity-modulated beams was computed by solving the inverse problem by least-squares iteration. 9 The planning software was written in-house to exactly simulate the geometry of the MIMiC, and Medical Physics, Vol. 24, No. 6, June 1997
829 M. Oldham and S. Webb: Intensity-modulated radiotherapy 829 the inverse algorithm assumed an elemental fluence profile for each bixel which incorporated the penumbral effects of the surrounding closed vanes. Bixel is the term used to refer to the cross-sectional area of a vane of the MIMiC through which radiation can pass if the vane is open. The planning algorithm is essentially similar to that used in the PEACOCK planning system. It was written to provide the potential to independently study effects such as bixel profile variation, inhomogeneity, and gantry sag. In this study the elemental fluence profile was found by fitting the measured dose data, delivered by a single open vane at 10 cm depth in water, to a mathematical function which obeys the superposition principle. This function is a convolution of a double exponential with a rect function equal to the bixel size. 10,11 The resulting profile, which we call the ‘‘stretched-fit’’ profile, has the property that when the fluence profiles of adjacent open bixels are combined corresponding to two bixels being open at the same time the resulting fluence profile is flat across the two bixels as it must be in reality. The terminology stretched fit signifies that the fitting procedure actually widens the elementary fluence profile since superposition of the measured profiles leads to regions of low fluence between bixels. This fitting procedure is discussed in detail in an earlier report. 11 The dose computation grid was set at 1 mm resolution, with dimensionsof300 300 12. Once the intensity-modulated profiles were determined for the nine static ports, a forward dose calculation was performed to predict the delivered dose taking into account the characteristics of the delivery method. This is a crucial point we wish to elaborate on. The key point is that during planning the elemental fluence profile used for each bixel assumes that the neighboring bixels are closed. This is necessary as a priori information of the intensity-modulated profile is not available. When it comes to the delivery of the fluence through a bixel however, the neighboring bixels may well be either open, closed, or open for part of the irradiation. In essence, the penumbral effects assumed at the planning stage do not reflect what happens during the delivery. To circumvent this discrepancy, the first step of the forward dose calculation is the decomposition of the intensitymodulated profiles into their respective components. 11 Each component is a combination of open and closed vanes through which an amount of radiation is delivered. The delivery of any intensity-modulated profile must, in practice, adopt this decomposition concept. The alternative is to deliver each bixel independently, with all other bixels closed, which would be far too time consuming and give too high a leakage dose. As with the planning software, this forward dose calculation was written in-house to allow independent study of effects such as the penumbral characteristics during delivery. The NOMOS planning system PEACOCK does not use our component delivery method to model the penumbral effects during delivery. The forward dose calculation used in this study first computed the component bixel patterns for each gantry angle Appendix A. Then the appropriate fluence profiles were assigned to each component. Between adjacent open bixels the stretched-fit profile was assigned ensuring a flat profile. FIG. 3. The variation in relative-output-factor ROF between different bixels along the MIMiC for the PHILIPS SL 75/5. ROF’s are given in percentages, defined with respect to a 10 10 cm 2 open field measured at the dose maximum. Between an open and closed bixel, the appropriate measured penumbral profile was assumed. By accurately modeling how the MIMiC delivers an intensity-modulated profile via components, this forward dose calculation takes account of the penumbral characteristics of the delivery system. Furthermore, the variation in relative-output-factor ROF for bixels at different positions in the slit was incorporated by assigning each bixel a unique ROF obtained from fitting all bixels to the measured data for the open slit field Fig. 3. It is noted that only the centrally positioned bixels numbers 6–15 have a significant amount of radiation passing through them in this study. An example of an intensity-modulated profile and its corresponding delivery components are given in Fig. 4 and Table I. Note that this is only one of many possible decomposition patterns. 12 However, as the MIMiC was operated by initially opening as many leaves as possible FIG. 4. The intensity-modulated profile found by inverse-planning for the field at gantry angle 0°. Medical Physics, Vol. 24, No. 6, June 1997
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