1. Ch 10. A System of Dosimetric Calculations
The physics of Radiation Therapy, pp
Ch 10. A System of Dosimetric Calculations

2. 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

3. 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)

4. 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

5. 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

6. 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

7. 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)

8. 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

9. 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

10. 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

11. 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

12. 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

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

14. Tissue-Phantom and Tissue-Maximum Ratios

15. 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

16. 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

17. 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

18. 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)

19. 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 / = 298

20. 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

21. 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)

22. 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    × 1 = 0.756
MU = 200 / = 265

23. 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

24. 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

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

27. 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

28. 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)

29. 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)

30. 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

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

32. 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

33. 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

34. 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

35. Point Outside the Field● a b c a c b

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

37. Thanks for your attention!