Ch 10. A System of Dosimetric Calculations The physics of Radiation Therapy, pp. 200 - 224 Ch 10. A System of Dosimetric Calculations

Introduction Dose Calculation Parameters Collimator Scatter Factor Phantom Scatter Factor Tissue-Phantom and Tissue-Maximum Ratios Practical Application Accelerator Calculations Irregular Fields Asymmetric Fields Other Practical Methods of Calculating Depth Dose Distribution Point Off-Axis Point Outside the Field

Introduction Limitation of using TARs, SAR & Percent depth dose for calculating absorbed dose in a patient Percent depth dose is suitable for SSD treatment technique. Tissue-air-ratios (TAR) suitable for SAD treatment technique, but limited to energies no higher than Co-60. Increase the size of chamber build-up cap Material of build-up cap is different from phantoms Overcome the limitation of the TAR Tissue-Phantom Ratio (TPR) Tissue-Maximum Ratio (TMR)

Dose Calculation Parameters Introduction Dose Calculation Parameters Collimator Scatter Factor Phantom Scatter Factor Tissue-Phantom and Tissue-Maximum Ratios Practical Application Accelerator Calculations Irregular Fields Asymmetric Fields Other Practical Methods of Calculating Depth Dose Distribution Point Off-Axis Point Outside the Field

Collimator Scatter Factor (Sc) The beam output measured in air depends on the field size Field size ↑; output ↑; collimator scatter ↑ “Output factor” Definition The ratio of the output in air for a given field to that for a reference field (10 x 10 cm) Direct measurement SAD AIR Reference field Build-up cap Reference field 1.0 ↓ Sc → Field Size

Phantom Scatter Factor (Sp) The change in scatter radiation originating in the phantom reference depth as the field side is change Definition The ratio of the dose rate for a given field at a reference depth (e.g. depth of Dmax) to the dose rate at the same depth of the reference field size (10 x 10 cm), with the same collimator opening Related to the change in the volume of the phantom irradiated

Phantom Scatter Factor (Sp) Indirect measuring Sp #1 through backscatter factor (BSF) BSF can be accurately measured for the photon beam (e.g. 60Co and 4 MV)

Phantom Scatter Factor (Sp) Indirect measuring Sp #2 Through total scatter factor (Sp) Contains both the collimator and phantom scatter SAD PHANTOM Reference field Reference depth Reference field 1.0 ↓ Sc,p → Field Size

Tissue-Phantom and Tissue-Maximum Ratios Definition of TPR The ratio of the dose at a given point in phantom to the dose at the same point at a fixed reference depth, usually 5 cm d t0 S × rd Dd Dt0

Tissue-Phantom and Tissue-Maximum Ratios Definition of TMR The ratio of the dose at a given point in phantom to the close at the same point at the reference depth of maximum dose Special case of TPR Adopted the point of central axis Dmax as a fixed reference depth

TMR data for 10 MV x-ray beams Properties of TMR Like TAR, TMR is independent of SSD, increases with energy and field size. TMR 3030 1010 00 Is caused entirely by the primary beam Depth in water TMR data for 10 MV x-ray beams

Tissue-Phantom and Tissue-Maximum Ratios Relationship between TMR and effective linear attenuation coefficient (μ) Obtain the effective linear attenuation coefficient (μ) Plotting μ(determined from TMR data) as a function field size Extrapolating it back to 0 × 0 field size

Tissue-Phantom and Tissue-Maximum Ratios Relationship between TMR and percent depth dose (P) Relationship between TMR and TAR

Tissue-Phantom and Tissue-Maximum Ratios

Scatter-Maximum Ratio (SMR) Definition The ratio of the scattered dose at a given point in phantom to the effective primary dose at the same point at the reference depth of maximum dose For Co-60 γ-rays SMRs are approximately at the same as SARs For higher energies SMRs should be calculated from TMR

Practical Application Introduction Dose Calculation Parameters Collimator Scatter Factor Phantom Scatter Factor Tissue-Phantom and Tissue-Maximum Ratios Practical Application Accelerator Calculations Irregular Fields Asymmetric Fields Other Practical Methods of Calculating Depth Dose Distribution Point Off-Axis Point Outside the Field

Practical Applications (accelerator calculations) Machine are usually calibrate to deliver 1 rad per MU At reference depth (t0) For a reference field size (10 × 10 cm) Source to calibration point distance of SCD

Practical Applications (accelerator calculations) SSD technique: Dose / MU = K dose rate under calibration conditions  Sc (rc)  Sp(r) field size changed  (SSD factor) distance (SSD) changed  PDD(d,r)/100 depth changed MU = TD / (Dose / MU)

Practical Applications (accelerator calculations ) example 1 SSD technique: Machine: 4 MV photons Calibration conditions: SSD = 100 cm, dmax = 1 cm, field size = 10  10 cm2. Calibration dose rate = 1 cGy / MU Treatment conditions: SSD = 100 cm, d = 10 cm, field size = 15  15 cm2, Sc(1515)=1.020, Sp(1515)=1.010, %DD=65.1, TD = 200 cGy. Dose/MU = 1  1.02  1.01  65.1 × 1 = 67.07 MU = 200  100 / 67.07 = 298

Practical Applications (accelerator calculations) example 2 SSD technique: Machine: 4 MV photons Calibration conditions: SSD = 100 cm, dmax = 1 cm, field size = 10  10 cm2. Calibration dose rate = 1 cGy / MU Treatment conditions: SSD = 120 cm, d = 10 cm, field size = 15  15 cm2, Sc(12.512.5)=1.010, Sp(1515)=1.010, %DD=66.7, TD = 200 cGy. Dose/MU = 1  1.01  1.01  [(100+1)/(120+1)]2  66.7 = 47.4 MU = 200  100 / 47.4 = 422

Practical Applications (accelerator calculations) SAD technique: Dose / MU = K dose rate under calibration conditions  Sc (rc)  Sp(rd) field size changed  (SAD factor) distance (SSD) changed  TMR(d,rd) depth changed MU = ID / (Dose / MU)

Practical Applications (accelerator calculation) example 3 SAD technique: Machine: 4 MV photons Calibration conditions: SCD = 100 cm, dmax = 1 cm, field size = 10  10 cm2. Calibration dose rate = 1 cGy / MU Treatment conditions: SAD = 100 cm, d = 8 cm, field size = 6  6 cm2, Sc(66)=0.970, Sp(66)=0.990, TMR(8, 66)=0.787, TD = 200 cGy. Dose/MU = 1  0.970  0.990  0.787 × 1 = 0.756 MU = 200 / 0.756 = 265

Irregular fields Calculation of percent depth dose for an irregular field Obtain average SMR by using Clarkson type integration SMR(d,rd) is then converted to TMR(d,rd) TMR(d,rd) may be converted into percent depth dose Final expression

Computer Program Data permanently stored in this computer program A table of SMRs as functions of radii of circular fields The off-axis ratios (Kp) The following data are provided for a particular patient Contour point outline of the irregular field The coordinate (x,y) of the point of calculation Reference point Patient measurements Patient thickness at various points of interest SSDs Source to film distance

As soon as a given area reaches its prescribed dose, it is shielded during subsequent treatments

can be assumed equal to symmetrical field Asymmetric Fields Independent jaw Field center positioned away from the true central axis of the beam Parameters changes after a field is collimated asymmetrically Collimator scatter Phantom scatter Off-axis beam quality Beam-flattening filters – greater beam hardening close to the central axis can be assumed equal to symmetrical field

Practical Applications (asymmetric fields) SSD technique: Dose / MU = K  Sc (rc)  Sp(r)  (SSD factor)  PDD(d,r)/100  OARd(x) SAD technique:  Sc (rc)  Sp(rd)  (SAD factor)  TMR(d,rd) MU = TD / (Dose / MU) MU = ID / (Dose / MU)

Asymmetric Fields OARd(x) off-axis ratio at depth d data are derived from cross-beam profiles measured at a number of depths in a phantom for the largest field available (e.g. 40 ×40 cm)

Other Practical Methods of Calculating Depth Dose Distribution Introduction Dose Calculation Parameters Collimator Scatter Factor Phantom Scatter Factor Tissue-Phantom and Tissue-Maximum Ratios Practical Application Accelerator Calculations Irregular Fields Asymmetric Fields Other Practical Methods of Calculating Depth Dose Distribution Point Off-Axis Point Outside the Field Point under a block

Irregular Fields Clarkson’s technique is not practical for routine manual or computerized calculation Time consuming Considerable amount of input data

Irregular Fields Approximate method Reasonably accurate calculations for most blocked field Effective field blocked field Sc Collimator field unblocked field, defined by the collimator Percent depth dose, TMR, Sp ×2 ×1

Point Off-Axis Clarkson’s technique is also not practical for manual calculation Day’s method PPD can be calculated at any point within the medium using the central axis data ＋ a b c d P Q

Point Off-Axis The dose at depth d along the axis through Q 2a 2b 2c ＋ a b c d P Q The dose at depth d along the axis through Q

Point Outside the Field ● a b c a c b

Points under a block a b c ● ‘t’ is the block transmission factor.

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