HANDOUT; MEDICAL PHYSICS 30 (6), 1509-1509 New e-mail: RBSWHaarlem@gmail.com A Smart Interpolation Formalism to Determine the Gy/MU-Factor (GMF) for Open and Blocked Radiation Fields from Full-Scatter Output Measurements RW de Boer, C Schneider, *AWH Minken The Netherlands Cancer Institute/Antoni van Leeuwenhoek Hospital, Amsterdam, and Maastro-clinic, Maastricht/Heerlen, The Netherlands e-mail: RdeBoer@nki.nl Gy/MU-factor (GMF) The standard approach to determine the GMF is: measure GMFs and PDDs (Percentage Depth Dose) at a fixed SSD, determine scatter correction factors Sc (collimator scatter) and Sp (phantom scatter) using a miniphantom. We present a different approach to obtain the GMF and we show that this interpolation approach: requires few measurements (all of them clinically relevant!), is conceptually simple, is better suited for small field sizes, can reliably deal with blocked fields. SSD depth source collimator Fig. 1 Required measurements For each fieldsize: GMFs at one depth (e.g. 10 cm) for two SSDs (e.g. 80 and 100 cm) one PDD (e.g. at SSD=100 cm) GMF PDD at SSD = 100 cm depth=10 cm SSD (cm) depth (cm) FS 80 100 1 1.5 2 .. 9.5 10 10.5 11 .. 29 30 3 61.10 910 982 1000 684 665 647 627 237 225 4 92.34 62.68 911 986 1000 691 671 654 637 244 232 5 94.31 64.73 914 985 1000 701 683 665 647 251 239 .. .. .. .. .. .. .. .. .. .. .. .. .. .. 24 114.95 78.31 967 1003 1000 751 736 720 705 317 303 30 117.43 79.56 968 1003 1000 757 742 726 711 324 311 40 119.55 80.61 971 1002 1000 762 746 731 716 334 319 FS = FieldSize Method The GMF is in first approximation a function of 3 parameters (fig.1): source-skin distance (SSD), fieldsize at the isocentre (FS), and depth (d). In clinical practice the GMF must be known for all relevant values of these parameters, i.e. at any position in the mathematical, three-dimensional SSD-FS-d space (fig.2). A GMF-measurement, e.g. at SSD=100 cm, d=10 cm, FS=10x10 cm2, assigns a measured GMF-value to a point in this abstract space (fig.2a). If a PDD measurement is combined with a GMF-measurement for the same FS and SSD, GMF-values are obtained along a horizontal line in the SSD-FS-d space (fig.2a). A series of measurements is needed to find the GMF for all relevant values of SSD, FS and d. This is indicated in Fig.2b, which shows: GMF-measurements (closed circles) for both SSD=100 cm and SSD=80 cm at depth=10 cm, PDD measurements for different fieldsizes and SSD=100 cm (horizontal drawn lines). The PDD at a different SSD-distance (e.g. SSD=80cm) is derived from the PDD at SSD=100cm by the Mayneord F-factor (dashed line in fig.2b). The cGy/MU factor at any position in this SSD-FS-d space is now found by interpolation or prudent extrapolation in this 3D space. Conclusions: The principle of the interpolation approach is: “What You Measure Is What You Need.” Advantages of the new method over the standard Sc / Sp-approach are: The method is conceptually very simple because all results are directly derived from full-scatter – hence clinically relevant – measurements in a straight­ forward manner. The method requires no further assumptions, and is intrinsically insensitive to issues as electron contamination or reference distances. In all cases, the MUs or doses calculated using this method are directly derived from measured data. For each fieldsize, only one PDD-meas-urement and two GMF-measurements (at different SSDs) are needed; this is also feasible for small fieldsizes where the measurement of Sc and Sp is imprac-tical. Hence, this method is especially profitable when applied to small fields as used in IMRT-treatments. If additional measurement data are available, they will increase the precision of interpolation. E.g. measured GMF-data at SSD=90 cm or SD=120 cm can easily be added to the formalism. To apply this method to blocked fields, only a small number (12) of additional GMF-measurements are needed. All corrections for blocked fields are directly derived from measured values, and so the influence of block-trays is taken into account automatically. Fig. 2 Determine the GMF at each point in the mathematical 3D parameter-space 80 100 cm 10 cm depth SSD FS computed PDDs at SSD=80 GMF measurements at SSD = 80 and depth = 10 all required measurements PDD measurements at SSD=100 GMF measurements at SSD = 100 and depth = 10 PDD measurement at SSD = 100, FS = 10 GMF measurement at SSD = 100 FS = 10, depth = 10 results of an PDD- and GMF measurement 2a 2b Required measurements The interpolation approach requires  for each fieldsize  full-scatter measure-ments of the GMF at two different SSDs, and the measure-ment of one Percentage Depth Dose (PDD) (see Table). Blocked fields In clinical practice the effect of blocking is small, because blocking of more than 50% of the total field is seldom used, and even for 50% blocking the change in the GMF is less then 10 %. Therefore a quadratic function can adequately describe the effect of blocking, with f the blocked fraction (<0.5): GMFblocked = GMFunblocked · [1 + α·f + β·f2 + γ·f·(SSD-100) + δ·f·(FS-10) + ε·f·(d-10)] A number of additional blocked-field GMF-measurements is performed to estimate the parameters α, β, γ, δ and ε. An example set of measurements is: f is taken as 0%, 20% or 50%; SSD=80, 90, 100 cm; FS=5, 10, 25 cm; and d=5, 10, 20 cm. Approximately 12 additional GMF-measurements are then needed. Next, the parameter values are obtained by linear regression. Results Results from a spreadsheet implementation of the interpolation-approach correspond within less than 0.3 % with the standard way of calculation for open fields. Using the quadratic function for the block-correction, also the GMF for blocked fields corresponds better than 0.3% with the standard approach.