1. Therapy Shielding Calculations
Melissa C. Martin, M.S., FACR, FACMP
American College of Medical Physics
21st Annual Meeting & Workshops
Scottsdale, AZ
June 13, 2004

2. Therapy Shielding Design Traditionally Relies on NCRP Reports
Primary and secondary barrier calculation methodology
Applicable up to 60Cobalt and linacs up to 10 MV
NCRP Report 51
Extended NCRP 49 methodology up to 100 MV
Empirical shielding requirements for maze doors
NCRP Report 79
Improved neutron shielding methodology
NCRP Report 144
Update of NCRP 51 primarily aimed at non-medical facilities
Reports reflect progress in linac design and shielding research

3. Goal: Improved accuracy
Revised NCRP Report in Drafting Stage by AAPM Task Group 57, NCRP SC 46-13
Design of Facilities for Medical Radiation Therapy
4 MV - 50 MV (including 60Co)
Calculation scheme generally follows NCRP 49
All shielding data (TVLs) reviewed and updated
Updated for intensity modulated radiation therapy (IMRT)
Improved accuracy of entrance requirements
Both with and without the use of maze
Laminated barriers for high energy x-rays
Photoneutron generation due to metal in primary barrier
Goal: Improved accuracy

4. Linear Accelerator Energy and Workload
BJR #11 megavoltage (MV) definition used here
British Journal of Radiology (BJR) Supplement No. 11
Comparison of BJR #11 and BJR #17 MV definitions
Workload assumptions typically used for shielding design
Workload identified by symbol “W” in calculations
For MV  10 MV: W = 1000 Gy/wk at 1 meter from the target
Based on NCRP 49 Appendix C Table 2
For MV > 10: W = 500 Gy/wk
Based on NCRP 51 Appendix B Table 5
BJR #11 MV 4 6 10 15 18 20 24
BJR #17 MV 16 23 25 30

5. Radiation Protection Limits for People
Structural shielding is designed to limit exposure to people
Exposure must not exceed a specific dose equivalent limit
Limiting exposure to unoccupied locations is not the goal
NCRP 116 design dose limit (P)
0.10 mSv/week for occupational exposure
0.02 mSv/week for the general public
Typical international design dose limits
0.12 mSv/week for controlled areas
0.004 mSv/week for uncontrolled areas 
NCRP 116 dose limit is a factor of 5 lower than NCRP 49 value

6. Radiation Protection Limits for Locations
Permissible dose outside vault depends on occupancy
Occupancy factor (T):
Fraction of time a particular location may be occupied
Maximum shielded dose (Smax) at protected location
Assuming occupancy factor T for protected location T P S =
max
Maximum shielded dose is traditionally referred to simply as P/T

7. Occupancy Values from NCRP 49
Full occupancy for controlled areas by convention (T=1)
Full occupancy uncontrolled areas (T=1)
Offices, laboratories, shops, wards, nurses stations, living quarters, children’s play areas, and occupied space in nearby buildings
Partial occupancy for uncontrolled areas (T=1/4)
Corridors, rest rooms, elevators with operators, unattended parking lots
Occasional for uncontrolled areas (T=1/16)
Waiting rooms, toilets, stairways, unattended elevators, janitor’s closets, outside areas used only for pedestrian or vehicular traffic

8. Hourly Limit for Uncontrolled Areas
0.02 mSv hourly limit for uncontrolled areas
20 Gy/hr common assumption for calculation
Implies a lower limit for occupancy factor
T  20 / ( U W )
T  0.16 for higher energy accelerators (500 Gy / wk workload)
T  0.08 for lower energy accelerators (1000 Gy wk workload)
Not applied to low occupancy locations with no public access
e.g., unoccupied roof, machinery room
T = 1/10 rather than 1/16 typically used for exterior walls

9. NCRP 134 Impact on Linac Shielding
NCRP 134 distinguishes general employees from public
NCRP 134 maintains NCRP 116 limit of 0.02 mSv/wk for both
Limit 25% of 0.02 mSv/wk from individual facility for general public
Occupancy assumptions proposed for general public
T=1/40 for occasional occupancy
Equivalent to T=1/10 occasional for general employees
Similar to P/T required by hourly limit for primary barriers
Slightly increase from T = 1/16 used for secondary barriers
T=1/16 still appropriate for locations with no public occupancy
e.g., machine rooms, unoccupied roofs, etc.
Impact increases if higher occupancy than T=1/40 adopted

10. Basic Primary Barrier Calculation Unchanged from NCRP 49
Unshielded dose calculation
Attenuation in tenth-value layers
Barrier thickness (tc) calculation 2
pri d U W S = ú û ù ê ë é = T P S n
pri /
log 10 e C
TVL n t ) 1 ( - + =
Margin in primary barrier thickness is recommended to compensate for potential concrete density variation

11. Anticipate upcoming NCRP report to review and update TVL data
Primary Barrier Photon Tenth-Value Layers (mm) Come from a Variety of Sources
Lead
Concrete
Steel
Earth
Borated Poly MV
TVL1
TVLe
TVL1
TVLe
TVL1
TVLe
TVL1
TVLe
TVL1
TVLe
0.2
1.7 84
2.9 94
4.8
104
8.3
109
11.9
117 26
147 42
210 53
292 56 15 19 22 29 33 54 51 76 69 91
100
104
108
109
110
135 84
151 94
167
104
175
109
188
117
236
147
336
210
468
292
343
740
379
752
390
773
401
0.25
0.3
0.4
0.5 1 2 4 6
367
323
410
377
445
416
462
432
470
442
483
457
572
648
720
379 10 15 18 20 24
NCRP 49
NCRP 51
Nelson & LaRiviere
McGinley
Estimated from Concrete
Anticipate upcoming NCRP report to review and update TVL data

12. Primary Barrier Width
0.3 meter margin on each side of beam rotated 45 degrees
Barrier width required assuming 40 cm x 40 cm field size
Field typically not perfectly square (corners are clipped)
35 cm x 35 cm field size typically used to account for this ft d w C . 1 2 4 ' + =

13. Slant Factor and Obliquity Factor
Path from target to protected location diagonally through barrier
Incident angle q of line with respect to perpendicular
Required barrier thickness reduced by cos(q)
Same total distance through barrier to protected location
Scatter causes slant factor to underestimate exit dose
Multiplying thickness by obliquity factor compensates for this
Lead
Concrete
Steel
Angle
4 MV
10 MV
18 MV
1.00 30
1.03
1.02
1.04 45
1.07
1.10
1.08 60
1.21
1.22
1.20
1.14
1.17 70
1.44
1.47
1.52
1.28
1.48
1.42
1.45

14. Photoneutron Generation Due to Metal in Primary Barrier (Linacs  10 MV)
Dose-equivalent 0.3 m beyond barrier (McGinley)
N is neutron production constant (Sv neutron per Gy workload)
1.9 x 10-3 for lead, 1.7 x 10-4 for steel at 18 MV (from McGinley)
Recent safety survey indicated somewhat higher 3.8 x 10-4 value for steel at 18 MV is appropriate
N adjusted versus MV based on neutron leakage fraction vs MV
F is field size (conventionally 0.16 m2), t2 is metal thickness (m)
X-Ray attenuation prior to metal layer: 10^(-t1 / TVLp)
Neutron attenuation after metal layer: 10^(-t3 / TVLN) N P
TVL t F U W S / 3 2 1 10
305 . - + =

15. Avoid metal as inside layer of primary barrier if MV > 10
Patient Photonuclear Dose Due to Metal in Primary Barrier for MV > 10
Metal in primary barrier can increase patient total body dose if MV > 10
Lead inside layer approximately doubles patient total body dose
Increases risk of secondary cancer
Concrete or borated polyethylene inside metal in primary barrier is recommended if MV >10
Each inch of borated poly decreases patient dose from metal barrier photoneutron by approximately factor of 2
Impact of IMRT on patient photonuclear dose is addressed later
Avoid metal as inside layer of primary barrier if MV > 10

16. Secondary Barrier ) 400 / ( d F W a S = 10 d W S =
Patient scatter unshielded dose
F is field size in cm2
typically 1600
a = scatter fraction for 20 x 20 cm beam
Leakage unshielded dose
Assumes 0.1% leakage fraction 2
sec )
400 / ( d F W a S
sca p = 2
sec 3 10 d W S L - =

17. Leakage Photon Tenth-Value Layers (mm) Also Come from a Variety of Sources
Lead
Concrete
Steel
Earth
Borated Poly MV
TVL1
TVLe
TVL1
TVLe
TVL1
TVLe
TVL1
TVLe
TVL1
TVLe 4 53 53
292
292 91 91
468
468
292
292 6 56 56
341
284 96 96
546
455
341
284 10 56 56
351
320 96 96
562
512
351
320 15 56 56
361
338 96 96
578
541
361
338 18 56 56
363
343 96 96
581
549
363
343 20 56 56
366
345 96 96
586
552
366
345 24 56 56
371
351 96 96
594
562
371
351
Kleck & Varian
Average
Estimated
from Concrete
NCRP 49
Nelson & LaRiviere

18. Neutron Leakage Same form as photon leakage calculation
Based on dose-equivalent neutron leakage fraction vs MV
0.002%, 0.04%, 0.10%, 0.15% and 0.20% for 10, 15, 18, 20 and 24 MV
Based on Varian and Siemens neutron leakage data
Assumes quality factor of 10 for absorbed dose
Shielded dose equivalent based on leakage neutron TVLs
211 mm for concrete
96 mm for borated polyethylene

19. Intensity Modulated Radiation Therapy (IMRT)
IMRT requires increased monitor units per cGy at isocenter
Typical IMRT ratio is 5 MU per cGy, as high as 10 for some systems
Percent workload with IMRT impacts shielding
50% typically assumed; 100% if vault is dedicated to IMRT
Account for IMRT by multiplying x-ray leakage by IMRT factor
IMRT Factor = % IMRT x IMRT ratio + (1 - % IMRT)
3 is typical IMRT factor (50% workload with IMRT ratio of 5)
IMRT factor lower for neutrons if machine is dual energy
e.g., 1.5 if dual energy linac with 50% of treatments below 10 MV
Pessimistic since most IMRT is performed at 6 MV (next chart)

20. IMRT above 10 MV Significantly Increases Patient Photonuclear Dose
Neutrons dominate patient total body dose for high energy linacs
Neutron dose equivalent as high as ten times photon dose
Potentially 1% of workload vs 0.1% photon leakage
0.05% required absorbed neutron dose x 20 quality factor
Typical neutron dose equivalent is lower than requirement
0.1 to 0.2% of workload
IMRT factor of 5 increases patient incidental dose 5X
Results in typical neutron total body exposure of 0.5 to 1.0% of WL
Significantly increases risk of secondary cancer
Most IMRT is performed at 6 MV to mitigate increased secondary cancer risk from photoneutrons

21. Patient Scatter Significant Adjacent to Primary Barrier
Scatter traditionally neglected for lateral barriers
Generally a good assumption
90 degree scatter has low energy
Scatter is significant adjacent to primary barrier
Calculations indicate comparable to leakage
Slant thickness through barrier compensates for the increase in unshielded dose due to scatter
Barrier thickness comparable to lateral is adequate for same P/T

22. Patient Scatter Fraction for 400 cm2 Field
Based on recent simulation work by Taylor et.al.
Scatter fraction increases as angle decreases
Scatter fraction vs MV may increase or decrease
Tends to increase with MV at small scatter angles
Decreases with increasing MV at large scatter angles
Angle (degrees) MV 10 20 30 45 60 90
135
150 4
1.04E-02
6.73E-03
2.77E-03
2.09E-03
1.24E-03
6.39E-04
4.50E-04
4.31E-04 6
1.39E-03
8.24E-04
4.26E-04
3.00E-04
2.87E-04
1.66E-02
5.79E-03
3.18E-03
1.35E-03
7.46E-04
3.81E-04
3.02E-04
2.74E-04 15
1.51E-02
5.54E-03
1.05E-03
5.45E-04
2.61E-04
1.91E-04
1.78E-04 18
1.42E-02
5.39E-03
2.53E-03
8.64E-04
4.24E-04
1.89E-04
1.24E-04
1.20E-04
1.52E-02
5.66E-03
2.59E-03
8.54E-04
4.13E-04
1.85E-04
1.23E-04
1.18E-04 24
1.73E-02
6.19E-03
2.71E-03
8.35E-04
3.91E-04
1.76E-04
1.21E-04
1.14E-04

23. Patient Scatter Energy
Mean Scatter Energy
No standardized scatter Tenth-Value Layer
Primary MV rating based on peak MV in spectrum, not mean energy
Primary TVL at slightly higher MV (e.g, 50%) appears reasonable
% increase little more than wild guess; more research is needed
Scatter Angle (degrees) MV 20 45 90 6
1.7
1.2
0.6
0.25 10
2.8
1.4 18
5.0
2.2
0.7
0.3 24
5.7
2.7
0.9
Ambiguity remains as to TVL to use for scatter

24. Maze Calculation Likely Revised in Upcoming NCRP Report
New method identifies and evaluates specific mechanisms
Patient Scatter, Wall Scatter, Leakage scatter
Direct leakage
Neutrons, capture gammas
Mechanisms calculated at most stressing orientation
Scatter calculations multiplied by 2/3 to compensate for this
Scatter energy relatively low at maze door
Primary 0.3 MV TVLs used for patient and wall scatter (2 bounces)
Primary 0.5 MV TVLs used for leakage scatter (1 bounce)
Scatter is significant typically only for low energy linacs
Goal: More-precise calculation avoiding over or under-shielding

25. Maze: Patient Scatter ) 400 / ( d A F W a S = Unshielded dose where
a0.5 is 0.5 MV scatter fraction
Second bounce fraction
0.02 per m2 typically used
Other constants as before, e.g.,
a = patient scatter fraction
F = field size in cm^2
h = room height 2 3 1 5 . )
400 / ( P C p d A F W a S =

26. Maze: Wall Scatter d A W f a = Unshielded dose where
f = patient transmission
a1 = first reflection coefficient
0.005 per m2 for 6 MV
0.004 per m2 for  10 MV
A1 = beam area (m2) at wall
AM = Maze cross section (m2)
dM x room height 2 3 1 5 . S M d A W f a =

27. Maze: Leakage Scatter 10 d A W S a = Unshielded dose where
Constants as previously defined 2 1 3 10 L C LS d A W S a - =

28. Maze: Direct Leakage 10 d W S = Unshielded dose
Same as standard secondary photon leakage calculation
Standard neutron leakage not typically used
Use only if it exceeds the maze neutron calculation
e.g., if maze wall not sufficiently thick 2 / 3 ' 10 L
TVL t d W S D - =

29. Maze Neutron Calculation Based on Modified Kersey Method
Unshielded dose equivalent
where
Ln is neutron leakage fraction
Same as used for secondary neutron leakage calculation
Modification to Kersey is assuming first tenth-value distance is 3 m instead of 5 m ] 5 / ) 3 ( 1 [ 2 10 - + = N d n NT L W H
Upcoming NCRP report may recommend a more-complex approach than this

30. Maze Neutron Shielding
Modeled as 50% thermal neutrons and 50% fast neutrons
1 inch borated poly effectively eliminates all thermal neutrons
Fast neutron TVL is 2.4 inches for the first 4 inches
Fast neutron TVL is 3.6 inches beyond 4 inches thickness

31. Maze Capture Gammas from Concrete
Gamma rays generated by neutron capture in the maze
Very significant for high energy linacs
Unshielded dose is a factor of 0.2 to 0.5 of the neutron dose equivalent at the treatment room door
Use the conservative factor (0.5)
Capture gammas have moderate energy (3.6 MeV)
TVL of 61 mm for lead
Limited attenuation also provided by polyethylene (278 mm TVL)
Dominates X-Ray dose at maze entrance for high energy linacs

32. Direct-Shielded Door Neutron Door is simply a secondary barrier
Typically more layers and different materials than a wall
Lead to attenuate leakage photons
Borated polyethylene to attenuate leakage neutrons
Typically sandwiched between layers of lead
Steel covers
Specialized shielding procedure adjacent to door
Compensates for relatively small slant thickness in this location
Vault entry toward isocenter similar to maze
Vault entry away from isocenter is secondary barrier
But with specialized geometry

33. Direct-Shielded Door: Far Side of Entrance
Extra material added to corner
Lead to entrance wall
Borated polyethylene or concrete beyond wall
Uses standard secondary barrier calculation
Goal: provide same protection as wall or door for path through corner

34. Direct-Shielded Door: Near Side of Entrance
Geometry similar to short maze
Maze calculation can be used but is likely pessimistic
Requires less material than far side of entrance
Lower unshielded dose
Lower energy

35. Shielding for Heating, Ventilation, and Air Conditioning (HVAC) Ducts
HVAC penetration is located at ceiling level in the vault
For vaults with maze, typically located immediately above door
For direct-shielded doors, located in a lateral wall as far away from isocenter as possible
Ducts shielded with material similar to the door at entrance
Material thickness 1/2 to 1/3 that required of the door
Path through material is at a very oblique angle due to penetration location with slant factor between 2 and 3
Factor of at least 5 reduction in dose at head level (the protected location) vs. at the HVAC duct opening
NCRP 49 recommends that shielding extend at least a factor of three times the width of the HVAC penetration

36. Photon Skyshine
Unshielded dose
where
W (steradians) =
for 40 x 40 cm beam
Multiplying by additional factor of two is recommended
Primary TVLs used to calculate attenuation 2 1 3 .
0249 Y
sky d U W S =
New construction seldom shields solely for skyshine due to vigilance required to prevent unauthorized roof access

37. Neutron Skyshine p 2 10 4 . 5 W ´ = H Unshielded dose where
W = (steradians) typical (target above isocenter)
Hpri is neutron dose-eq in beam ( , 0.002, , , and times W for 10, 15, 18, 20, and 24 MV, respectively)
Use factor is not applied since neutrons in all orientations
Multiplying by additional factor of two is recommended p 2 10 4 . 5 W = -
pri
sky H

38. Primary Goal of Upcoming NCRP Report is Improved Shielding Calculation Accuracy
Very little impact for low energy accelerators
Primary and secondary barrier calculation method unchanged
Very little impact to calculated shielding for given protection limit
Improved accuracy for high-energy accelerators
Avoids extra cost of over design due to pessimistic calculations
Avoid extra cost of retrofitting if inaccurate calculations underestimate required shielding

39. References
Biggs, Peter J. “Obliquity factors for 60Co and 4, 10, 18 MV X rays for concrete, steel, and lead and angles of incidence between 0º and 70º,” Health Physics. Vol. 70, No 4, ,
British Journal of Radiology (BJR) Supplement No Central axis depth dose data for use in radiotherapy, 1972.
Chibani, Omar and C.C. Ma. “Photonuclear dose calculations for high-energy beams from Siemens and Varian linacs,” Medical Physics, Vol 30, No. 8: , August 2003.
Kleck, J. “Radiation therapy facility shielding design.” AAPM Annual Meeting

40. References (Continued)
McGinley, P.H. Shielding Techniques for Radiation Oncology Facilities, 2nd ed. Madison, WI: Medical Physics Publishing, 2002.
National Council on Radiation Protection and Measurements. Structural shielding design and evaluation for medical use of x-ray and gamma rays of energies up to 10 MeV. Washington, DC: NCRP, NCRP Report 49, 1976.
National Council on Radiation Protection and Measurements. Radiation protection design guidelines for MeV particle accelerator facilities. Washington, DC: NCRP, NCRP Report 51, 1977.

41. References (Continued)
National Council on Radiation Protection and Measurements. Neutron Contamination from Medical Accelerators. Bethesda, MD: NCRP, NCRP Report 79, 1984.
Nelson, W.R., and P.D. LaRiviere. “Primary and leakage radiation calculations at 6, 10, and 25 MeV,” Health Physics. Vol. 47, No. 6: , 1984.
Rodgers, James E. “IMRT Shielding Symposium” AAPM Annual Meeting, 2001.
Shobe, J., J.E. Rodgers, and P.L. Taylor. “Scattered fractions of dose from 6, 10, 18, and 25 MV linear accelerator X rays in radiotherapy facilities,” Health Physics, Vol. 76, No. 1, 27-35, 1999.

42. References (Continued)
Taylor, P.L., J.E. Rodgers, and J. Shobe. “Scatter fractions from linear accelerators with x-ray energies from 6 to 24 MV," Medical Physics, Vol. 26, No. 8, , 1999.