Photon Beam Monitor-Unit Calculations Introduction to Medical Physics III: Therapy Steve Kirsner, MS

Overview Introduction Linear Accelerator MU Calculations General Formalism for MU Calculations Linear Accelerator MU Calculations SSD Formalism- Equations SAD Formalism - Equations Important Facts Summary: Equations SSD and SAD Examples

Introduction Standard calibration geometry Linear Accelerators are calibrated under standard conditions. These standard conditions enable us to know the absolute dose under these conditions At MD Anderson, and commonly elsewhere, this point is located at dmax in a water phantom, 100 cm SSD, along the central axis of an open 10x10 field. Other option is defined at 100 cm SAD. At this point, the unit is calibrated such that 1 monitor unit (MU) is equal to 1.0 cGy muscle

Introduction Corrections Needed if not at Standard Geometry Depths other than dmax, and SSDs other than 100 cm, and for field sizes other 10x10, and points off the central axis, corrections become necessary These corrections are found in an institutions clinical data tables. Where these relationships to the standard geometry have been established Corrections are also necessary to account for anything that is placed in the beam that will attenuate the radiation. Wedges, compensators, blocks.

Corrections to standard geometry Depth corrections Field-size corrections Distance corrections Off-axis corrections Attenuation corrections PDD, TAR, TMR,TPR Output (scatter factors) ST, SP, SC Inv. Sq. “SAD Factor” OAFs-wedge and open WFs, TFs, compensator factors

Formalism In general, the dose (D) at any point in a water phantom can be calculated using the following formalism: Where: MU = monitor-unit setting for given conditions O = calibrated output (cGy/MU) for standard conditions OF = output (scatter) factor(s): SC, SP, ST ISq = inverse-square correction (as needed) depending on calibration conditions and treatment conditions. DDF = depth-dose factors (PDD, TMR, TPR, TAR) OAF = off-axis factors, open and wedge TF = transmission factors-attenuation

SSD Treatments and Calibration When the treatment unit is calibrated in a “SSD” geometry, then for “SSD” beams, the formalism becomes: where it is assumed that output (scatter) factors are given by SC and SP, and where it is also assumed that the calibrated output = 1.0 cGy/MU for a 10 x 10 field at dmax Note that no inverse-square term is needed since the distance to the point of dose normalization (SSD + dmax) is equal to the distance to the point of dose calibration. This is true unless treating at extended ssd. Then inverse square is given by: (scd/(ssd +dmax))2

SAD Setup-SSD Calibration When the treatment unit is calibrated in a “SSD” geometry, then for “SAD” (isocentric) beams, the formalism becomes: 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):

Important Facts to Remember 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 + dmax” (where the machine output is 1 cGy/MU) due to calibration conditions chosen. This inverse square factors is sometimes called the “SAD Factor”, not to be confused with other inverse square factor. This is solely adjust for calibration conditions. For 6 MV, the SAD Factor is:

More Important Facts 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:

Points to Remember Depth Dose and Scatter Factors SC is a function of the collimator setting SP 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

Prescription Dose Calculate Monitor units per field for a given Prescription dose. This dose is “prescribed” by the Physician. Value must be known at the point of calculation. With multiple fields, the dose per field is calculated using the beam weights. If a dose DRx is prescribed through multiple fields i each having a relative weight wti, then the dose Di from each field is:

Prescription Dose If the physician then prescribes the dose to a specific isodose line. The dose per field then becomes: Di/IDL where IDL is the isodose line that is prescribed to.

Calculation Equations For SSD beams: Inverse square if extended SSD not shown. If extended SSD add inverse square. (scd/(ssd +dmax))2 For SAD beams:

Examples A patient is planned to deliver a four field box. The weightings of the beams are as follows: AP=25%, PA = 20%, Rt lat=25%, Lt. Lat= 30% What is the dose per field if the Physician prescribes 180 cGy to the 95 % isodose line.

Examples AP and Rt Lateral – ((180 x .25)/(0.95))=47.4 cGy PA = ((180 x .30)/(.95)) = 56.8 cGy Lt. Lateral = ((180 x .20)/(0.95)) = 37.9 cGy

Examples A patient is to be treated with parallel opposed fields that are weighted 3:2 Anterior to Posterior. The prescription dose is 200 cGy to isocenter. What is the dose per field?

Examples Total weight is 5. Dose from anterior is 200 x 3/5 = 120 cGy Dose from posterior is 200 x 2/5 = 80 cGy

Examples What monitor-unit setting is necessary to deliver 200 cGy to a point at 5 cm depth in a water phantom. The field size is 12 x 20. Energy used is 6 MV. 100 cm SSD is set to the surface of the phantom.

Examples First calculate the equivalent square it is 15.0 . Next determine which formula to use based on SSD or SAD set-up. This is an ssd set-up so pdd will be used and the ssd equation.

Examples Sc for 15 = 1.021 Sp for 15 = 1.013 PDD for 15 at 5cm = 0.87 Dose = 200 cGy MU = (200)/(1.021 x 1.013 x 0.87)) = 222

Examples What monitor-unit setting is necessary to deliver 200 cGy to a point at mid-seperation in a phantom 10 cm thick. The phantom is irradiated with parallel opposed fields with a collimator setting of 12 x 20 cm. Fields are blocked to a 10 x 16 cm field using MLC. A 6 MV beam is used. Fields are weighted 3 to 1 and the dose is prescribed to the 98% idl.

Examples First calculate the equivalent squares: 12 x 20 = 15 ; 10 x 16 = 12.3 Next determine from type of set-up which equation will apply. Next determine which field size is used to look up each factor. Calculate dose per field.

Examples First Field: Dose = ((200 x ¾)/(0.98) = 153.1 Second Field : Dose = ((200 x ¼)/(0.98) = 51.0 Sc for 15 = 1.021 Sp for 12.3 = 1.007 DD at 5cm for 12.3 = .8664

Examples MU field 1 = ((153.1)/ (1.021 x 1.007 x.8664)) = 172

Examples Recalculate the monitor units necessary from the previous problem. If now the blocking is done with cerrobend. The prescription point at mid seperation is now 5 cm off-axis. Only difference is need to look up off axis factor for 5 cm off axis at 5 cm depth and include tray factor for blocks.

Examples MU field 1 = ((153.1)/ (1.021 x 1.007 x.8664 x 1.019 x .97)) = 174 MU field 2 = ((51) / (1.021 x 1.007 x .8664 x 1.019 x .97)) = 58

Examples A patient is to be treated with an isocentric wedged pair on a Varian Linac with 6 MV. Field 1 is 8 x 14 tht is blocked to a 6.5 x 14. The SSD for this field is 94 cm. Field 2 is 12 x 14 that is blocked to a 7 x 14, its SSD is 88cm. Both fields use 30 degree dynamic wedges. The prescribed dose is to isocenter and is 180 cGy, beams are weighted 2 to 1.

Examples Calculate Dose per field: Field 1: Dose = ((180 x 2/3)/(0.95)) = 126.3 Field 2 : Dose = ((180 x 1/3)/(0.95) = 63.2 Determine depths of treatment per field. Field 1: SSD= 94 therefore depth = 6 cm Field 2: SSD= 88 therefore depth = 12 cm

Examples Calculate Equivalent Squares for each field. Field 1: 8 x 14 = 10.1; 6.5 x 14 = 8.9 Field 2: 12 x 14 = 12.9 ; 7 x 14 = 9.3 Determine which depth factor to use: isocentric set-up indicates TMR.

Examples Field 1: TMR at 6 cm for 8.9 field = ..8912 Wedge factor for 8.9 field = 0.872 Sc for 10.1 field is 1.0 Sp for 8.9 field is 0.996 Inverse square = (101.5/100)2 = 1.030 Tray factor for 8.9 field = 0.97

Examples Monitor Units from field Number 1 (126.3)/ (1.0 x .996 x 1.03 x .8912 x (0.97 x .872)) = 163

Examples Field 2 TMR at 12 cm for 9.3 field = 0.7161 Wedge factor for 9.3 field = 0.865 Sc for 12.9 field = 1.025 Sp for 9.3 field = 0.998 Inverse square = 1.03 Tray factor for 9.3 field= 0.97

Examples Monitor Units for field number 2 (63.2)/ (1.025 x 0.998 x 1.03 x 0.7161 x (0.97 x 0.865))= 100

Examples A 30 x 30 x 30 cm3 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!

Examples First compute the relative doses of the right- and left-lateral fields: Rt Lat (wt = 2): Lt Lat (wt = 1):

Examples Then compute the equivalent squares of the open and blocked fields: 12x18: 10x14:

Examples Determine equation (for “SAD” beams): SC (for 14.4) = 1.019 SP (for 11.7) = 1.005 ISq = 1.030 TMR (depth 15, for 11.7) = 0.651 OAF and TF = 1.0

Examples Rt Lat: Lt Lat:

Examples Calculate the Monitor Units Necessary to deliver a dose of 200 cGy to a depth of 8 cm from parallel opposed fields equally weighted. The field size is 15 x 15 blocked to an 8 x 8 field. The patient has to be treated with an extended distance of 120 cm SSD. Assume that the field size given is defined at 120 cm. The energy that is used is 6 MV.

Examples Field size at 100 cm is 15 x (100/120)= 12.5 Sc for 12.5 = 1.023 Sp for 8 cm field = 0.993 PDD for 8 x 8 field = .732 at 100 cm which equals .732 x 1.02 = .747 at 120 cm. Inverse square factor for extended SSD is (101.5/121.5)2 = 0.698 Dose per field is 200/2 = 100 cGy

Examples Monitor Units per field (100/(1.023 x 0.993 x .747 x 0.698)) = 189