Photon-beams monitor-unit calculations

Transcription

1 Photon-beams monitor-unit calculations Narayan Sahoo March 24, 2011 The materials included in this lecture notes are from previous lecture notes for this course by Karl Prado, Ph.D.

2 Introduction Standard calibration geometry Treatment units are calibrated such that the absolute dose is known at a single point in a predetermined (standard) geometry For linear accelerators at MD Anderson, and commonly elsewhere, this point is located at d max in a water phantom, 100 cm SSD, along the central axis of an open 10x10 field. At this point, the unit is calibrated such that 1 monitor unit (MU) is equal to 1.0 cgy muscle Introduction Corrections to standard geometry At depths other than dmax, and SSDs other than 100 cm, and for field sizes other 10x10, and points off of the central axis, corrections become necessary These corrections are given in tabulated beam data where relationships to the standard geometry have been established Corrections are also necessary to account for transmission through beam attenuators such as wedges 2

3 Corrections to standard geometry Depth corrections Field-size corrections stance corrections Off-axis corrections Attenuation corrections PDD, TAR, TMR Output (scatter factors) S T, S P, S C Inv. Sq. SAD Factor OAFs WFs, TFs, etc. Formalism In general, the dose (D) at any point in a water phantom can be calculated using the following formalism: D MU O OF ISq DDF OAF TF Where: MU monitor-unit setting O calibrated output (cgy/mu) OF output (scatter) factor(s): S C, S P, S T ISq inverse-square correction (as needed) DDF depth-dose factors (PDD, TMR, TAR) OAF off-axis factors TF transmission factors 3

4 Formalism: SSD Beams When the treatment unit is calibrated in a SSD geometry, then for SSD beams, the formalism becomes: D MU SC SP PDD OAF TF where it is assumed that output (scatter) factors are given by S C and S P, and where it is also assumed that the calibrated output 1.0 cgy/mu. Note that no inverse-square term is needed since the distance to the point of dose normalization (SSD + d max ) is equal to the distance to the point of dose calibration. Formalism: SAD Beams When the treatment unit is calibrated in a SSD geometry, then for SAD (isocentric) beams, the formalism becomes: D MU SC SP ISq TMR OAF TF where the inverse-square factor accounts for the change in output produced by the differences in the distances between the source and the point of calibration (SCD) and between the source and the point of normalization (SPD): ISq ( SCD ) 2 SPD 4

5 Formalism: Important Notes The inverse-square term of the SAD equation accounts for the increased output that exists at the isocenter distance relative to the output that exists at isocenter + d max (where the machine output is 1 cgy/mu). This inverse square factors is sometimes called the SAD Factor For 6 MV, the SAD Factor is: ISq F SAD 2 2 ( SCD ) ( ) SPD 100 Formalism Notes Field sizes, unless otherwise stated, represent collimator settings For most accelerators, field sizes are defined at 100 cm (the distance from the source to isocenter) For SSD beams, field sizes are defined at the surface (normally 100 cm SSD) For SAD beams, field sizes are defined at the depth of dose calculation (normally 100 cm SAD) For field sizes at distances other than 100 cm, field sizes must be computed using triangulation: FS FS ( SSD ) SSD, d d 100 5

6 Formalism Notes Depth Dose and Scatter Factors S C is a function of the collimator setting S P is a function of the size of the field: at the phantom surface for SSD beams at the depth of calculation for SAD beams Depth-dose factors are a function of: field size at the phantom surface for SSD beams field size at depth for SAD beams Formalism Notes: Prescribed Dose In general, one wishes to compute the MU setting necessary to deliver a certain dose. This dose is prescribed. It value must be known at the point of calculation. When fields are combined to produce a prescribed dose at a point, the doses from each field are computed from the relative weights of each field. Thus, if a dose D Rx is prescribed through multiple fields i each having a relative weight wt i, then the dose D i from each field is: D Rx wt i i wt 6

7 Formalism: Summary For SSD beams: MU i S C S For SAD beams: P PDD OAF TF MU i S C S P ISq TMR OAF TF Examples Example 1 (Fundamental Quantities) The PDD for a 15x15 field at depth 20 is 41.0%. (a) What is the TMR depth 20? TMR 2 x15 max / SSD + d d PDDd SSD + d 2 ( ) x15 TMR d / 120 7

8 Examples Example 1 (Continued) (b) What is the field size to which the previous TMR applies? FS d FSd 0 ( SSD + d ) SSD ( 120 ) 18 FS d Examples Example 1 (Continued) (c) What is the tabulated TMR for this (correct) field size, and why is there disagreement? 18 TMR d The inverse-square correction overestimates the contribution of scatter at the closer distance. 8

9 Examples Example 1 (Continued) TMR (d) How can this overestimate be accounted for? Apply a correction using the ratio of phantomscatter factors: Sp ( ) 0. (0.5696) 18 x15 15 d 20 TMRd Sp Examples Example 2 (MU Calculations) A 30 x 30 x 30 cm 3 water phantom is centered at isocenter in a pair of Varian 6 MV x-ray beams, a right lateral and a left lateral. Each field has a collimator setting of 12x18 and is further collimated to a 10x14 using the MLC. (a) What are the MU settings of each field if a total dose of 200 cgy is to be delivered using a relative weighting of 2:1 with the right lateral having the higher weight? Make a picture! 9

10 Examples Example 2 First compute the relative doses of the rightand left-lateral fields: Rt Lat (wt 2): Lt Lat (wt 1): D Rx D wti Rx wti i i ( 2 ) wt 3 ( 1 ) wt 3 Examples Example 2 Then compute the equivalent squares of the open and blocked fields: 12x18: EqSq ( 2 LW ) ( ) L + W x14: EqSq ( 2 LW ) ( ) L + W

11 Examples Example 2 Determine equation (for SAD beams): MU i S C S P ISq TMR OAF TF S C (for 14.4) S P (for 11.7) ISq TMR (depth 15, for 11.7) OAF and TF 1.0 Examples Example 2 Rt Lat: 133 MUi Lt Lat: 67 MUi