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Photon-beams monitor-unit calculations: Schema and
Examples Narayan Sahoo
Main sources of the materials included in this lecture notes are:(1) Radiation Oncology Physics: A Handbook for Teachers and Students Edited by E. B. Podgorsak(2) The physics of Radiation Therapy by F. M. Khan(3) Previous lecture notes for this course by Karl Prado (4) Stern et al.: AAPM TG114 report, Medical Physics 38, 504-530 (2011)
Prescribed dose to a depth (d cm), D(d) with known PDD, what would be dose at dmax D(dmax )?Answer: PDD = D(d)/D(dmax )
If BSF is known, what would be the dose in free space (fs)?Answer: Dose(fs) = D(d)/BSF
If dose rate is given in free space, what would be the timer setting?Answer: T = Dose(fs)/Dose rate in fs
Treatment time Calculation, Orthovolatge X-rays, Co- 60 and other low MVX beams with Fixed SSD
Treatment time = Prescribed dose at depth d * 100 / (PDD* dose rate in free space* BSF)
Dose rate in free space = exposure rate * rad / R factor * K (rmed )
Timer or shutter correction time (τ): This has to be added or subtracted from the calculated time
Measure dose (D) for a long exposure time T, Dose rate (d) = D / (T+τ)Divide T into n intervals with tn, T = n tnMeasure accumulated Dn with n exposures each for time tnd = Dn / (T+ nτ)τ = (Dn – D) . T / (nD-Dn )
Actual time used = Claculated time - τ
Example 1, From Khan’s book
Beam: Orthovoltage x-rays, HVL 3mm CuCalibration: Exposure rate in air, 100 R/min at 50 cm from source, field
size = 8 cm x 8 cmTreatment: SSD = 50 cm, prescription 200 cGy to 5 cm depthBeam data: BSF or PSF = 1.20, rad/R=0.95, K(rmed) =1, PDD (d=5cm,
r = 8 cm, SSD= 50 cm) = 64.8Calculate the treatment timeDose rate in free space = exposure rate x rad/R factor X K(rmed) = 100
x 0.95 x 1 = 95 cGy/minTreatment time = Prescribed dose at depth d x 100 / (PDD x dose rate
in free space X BSF)= 200 x 100 / (64.8 x 95 x 1.20) = 2.71 min
Example 2, From Khan’s book
Beam: Co-60Calibration: Dose rate in free space, 150 cGy /min at 80.5
cm from source, field size = 10 cm x 10 cmTreatment: SSD = 80 cm, prescription 200 cGy to 8 cm
depthBeam data: BSF or PSF = 1.036, PDD (d=8 cm, r= 10 cm,
f= 80 cm) = 64.1 Calculate the treatment timeTreatment time = Prescribed dose at depth d x 100 / (PDD
x dose rate in free space X BSF)= 200 x 100 / (64.1 x 150 x 1.036) = 2.01 min
Co-60 and other low MVX beams at Fixed SADGiven prescribed dose at depth d in tissue, D(d),
TAR and dose rate in free space (K cGy/min) same SAD and field size, determine treatment time, T.
TAR(d) = D(d) / Dose in free space, (same SAD and field size)
Dose in free space = D(d) / TAR(d)T = Dose in free space / K (cGy/min)
= D(d) / (TAR(d) x K)Treatment time = Prescribed dose at depth d / (dose
rate in free space for the treatment field x TAR )Rotation TherapyTreatment time = Prescribed dose at depth d /
(dose rate in free space for the treatment field x Average TAR)
Example 3, From Khan’s book
Beam: Co-60Calibration: Dose rate in free space, 120 cGy /min at 80 cm from
source, field size= 6 cm x 12 cmTreatment: SAD = 80 cm, prescription 200 cGy to 10 cm depthBeam data: TAR (d=10 cm, r= 8 cm) = 0.681 Calculate the treatment timeSize of the equivalent square field = 4 x 6 x 12 /(2 x (6+12)) = 8 cmTreatment time = Prescribed dose at depth d / (dose rate in free space
for the treatment field X TAR)= 200 / (120 x 0.681) = 2.45 minIf the dose rate in free space is given for a field size other than the
treatment field size, it has to be converted to the dose rate in free space for the treatment field by multiplying with the appropriate area factor or collimator scatter factor.
Example: Treatment time (T) for Arc Therapy- Co-60, From Khan’s bookDetermine T to deliver 200 cGy at the center of rotation for a 6 cm x 6cm Open field, givenDose rate in free space: 86.5 cGy/min at the SAD
TAR = Dose in tissue / Dose in free space at same SADDose to be given in free space = 200 / Av TAR= 200 / 0.538 =371.7 cGyT= 371. 7/ 86.5 = 4. 3 min
Irregular field of Co-60 and other low MVX beams
Fixed SADTreatment time = Prescribed dose at depth d
/ ( dose rate in free space for the treatment field x Average TAR)
Average TAR = TAR (0) + Average SAR
BSF can be calculated from average TAR at dmax
Fixed SSD
Net SAR for QC = SAR for QC – SAR for QB + SAR for QA
Determine net SAR for each segmentTake average to determine Average SAR Same for SMR
Given: Doe rate in free space for this field at 80.5 cm as 120 cGy/minPatient treated at 80 cm SSDPrescribed dose = 200 cGy to 10 cm depthCalculate the treatment time and dose under the block considering 5% transmission of primary beam through itAssume a very flat beam, and Tray Factor = 0.97
Open field size at 10 cm depth, 90 cm SAD = 15 x (90/80) = 17 cm eq square , 9.6 cm radius eq. circleEffective open field size around P at 10 cm depth, 90 cm SAD = (5.5 cm x 15 cm) x (90/80) = 9 cm eq square , 5.1 cm radius eq. circleEffective blocked field size around Q at 10 cm depth, 90 cm SAD = (4.5 cm x 15 cm) x (90/80) = 7 cm eq square , 4 cm radius eq. circle
TAR at P = TAR (10, 0) + SAR (10, 5.1) = 0.534 + 0.163 = 0.697Dose rate in fs for 90 cm SAD = 120 x (80.5/90)2 = 96 cGy/minTime = 200 / (96 x 0.697 x 0.97) = 3.08 minsSAR for Q = SAR(10, 9.6) – ((1-0.05) x SAR (10, 4)) = 0.237 – 0.95*0.136 = 0.108TAR at Q = 0.534 x 0.05 + 0.108 = 0.135Dose at Q = 3.08 x 96 x 0.135 x 0.97 = 38.7 cGy
How the dose rate under treatment condition differs from that under reference calibration condition
For isocentric treatment
For fixed SSD treatment
MU = Dose / (Dose/MU)
Dose/MU = K x (PDD (d, r, f)/100 x Sc (rc ) x Sp (r) x SSD factor x TF x WF X CF X OAF
Dose/MU = K x (TPR (d, rd, f) x Sc (rc) x Sp (rd) x SAD factor x TF x WF X CF X OAF
Given beam calibration factor Dose/MU, K, under reference condition
MVX beams, Fixed SSDMU = Prescribed dose at depth d of the treatment field X 100
K x (PDD (d, r, f) x Sc (rc ) x Sp (r) x SSD factor x TF x WF X CF X OAF
Where K = dose per MU under the reference calibration condition, usually 1 cGy/MU, rc is the collimator field size, given by rc = r x SAD for beam isocenter / treatment SSD,SSD factor = (Source to Calibration Distance (SCD) / (treatment SSD+depth of calibration))2.All field sizes refer to the side of the equivalent square field.r is the field size at the surface.The Sc should be tabulated as a function of r, the field size at source to isocenter distance.
TF is the tray attenuation factor, WF is the wedge factor, CF is other correction factor, OAF is the off-axis factor.
Example 4
Beam: 6 MVX, (use the beam data table given to you)Calibration: K = 1 cGy / MU, 100 cm SSD at d = 1.5 cm for a 10 cm x 10 cm fieldTreatment: SSD = 120 cm, FS = 12 cm x 15 cm at 120 cm SSD, prescription 200 cGy
to 10 cm depth on the central axisBeam data: PDD (d=10 cm, r=13.3 cm, f=100cm) = 68.3, Sc (11.1 cm) = 1.003, Sp
(13.3 cm) = 1.009, No tray or wedgeCalculate MU
Size of the equivalent square field = 4 x 12 x 15 /(2 x (12+15)) = 13.3 cmrc = 13.3 x 100 / 120 = 11.1 cm
SSD factor for K = (101.5 / 121.5)2 = 0. 698PDD (d=10 cm, r=13.3 cm, f = 120 cm) = 68.3 x 1.026 (Mayneord F factor) = 70.1
MU = Prescribed dose at depth d for 13.3 cm field x 100 / (K x (PDD (d, r, f) x Sc (rc ) x Sp (r) x SSD factor)
= 200 x 100 / (1 x 70.1 x 1.003 x 1. 009 x 0.698) = 403.9
MVX beams, Fixed SADMU = Prescribed dose at depth d of the treatment field
K x (TPR (d, rd , f) x Sc (rc ) x Sp (rd ) x SAD factor x TF x WF X CF X OAF
Where K = dose per MU under the reference calibration condition, usually 1 cGy/MU, rc is the collimator field size, given by rc = rd x SAD for beam isocenter / treatment SAD,SAD factor = (SCD / (treatment SAD))2.TMR can substitute TPRAll field sizes refer to the side of the equivalent square fieldrd is the field size at the treatment depth and SAD.The Sc should be tabulated as a function of r, the field size at source to isocenter distance.TF is the tray attenuation factor, WF is the wedge factor, CF is other correction factor, OAF is the off-axis factor.
Example 5
Beam: 6 MVX, (use the beam data table given to you)Calibration: K = 1 cGy / MU, 100 cm SSD at d = 1.5 cm for a 10 cm x 10 cm fieldTreatment: SSD = 120 cm, FS = 12 cm x 15 cm at 120 cm SSD, prescription 200 cGy
to 10 cm depth on the central axisBeam data: TMR(d=10 cm, rd=14.4 cm) = 0.801, Sc (11.1 cm) = 1.003, Sp (14.4 cm)
= 1.011, No tray or wedgeCalculate MUTreatment SAD = 120 + 10 = 130 cmSize of the equivalent square field = 4 x 12 x 15 /(2 x (12+15)) = 13.3 cm at 120 cm
SSD or13.3 x 130 /120 =14.4 cm at 130 cm SADrc = 14.4 x 100 / 130 = 11.1 cm
SAD factor for K = (101.5 / 130)2 = 0. 610
MU = Prescribed dose at depth d / (K x ( TMR (d, rd) x Sc (rc ) x Sp (r) x SAD factor)= 200 / (1 x 0.801 x 1.003 x 1. 011 x 0.610) = 403.7
MVX beams, Arc Therapy
TMR can replace the TPR
Divide the patient contour exposed to the arc to equal segments, and calculate the TPR or TMR for radius of each segment and then take the average to Determine the average TPR or TMR and follow the fixed SAD MU calculationprocedure
K.
Irregular field• Clarkson segmental integration to determine average
SAR / SMR for irregular field• Determine the TAR (0) or TMR (0)• Determine Average TAR or Average TMR from TAR (0)
or TMR(0) and average SAR or average SMR, Sp and Sp (0)
• Equivalent square for the irregular field can be determined by finding the square field in the tabulated data that has the same SAR or SMR
• Complex and time consuming• Equivalent effective rectangular field can be determined
by simple approximations• Determine the area of the effective open field and divide
it with the length of the treatment field to determine the width of effective rectangular field
OPF can be written as Sc xSp and proper correction can be made for change in Sp for irregular blocked field
or
