chapter 16 shielding calculation helvecio-bw

1

Shielding CalculationTechniques

Objective

Ø Design of shield with adequate attenuation to achieve the required (or acceptable) dose equivalent (rate) limitation (or ALARA)

Shielding Issues

Ø Calculation MethodsØ Linac Rooms

vBarrier MaterialsvPrimary, scatter and leakage Barriers

vMaze DesignvNeutron Shielding

Ø Simulator (x-ray and CT)Ø HDR

Ø Brachytherapy RoomsØ Special Topics

Ø Reports

Factors do be considering in shielding design

Ø ALARAØ Available space

Ø Constructions techniquesØ Regulatory limits (or constraints)

Ø Shielding materialsØ Source term

Ø Trends in regulatory limits with times

Calculation MethodØ We calculate the dose rate at a certain distance from the

source due to primary, scattered and leakage radiation and from it derive how many TVL’s we need to bring the radiation levels to the dose constraints (occupational or public). [if the attenuation curves are not exponential, use attenuation curves]

Ø bibliographyv NCRP Report§ No. 49, for accelerators operating at 10 MV or less§ No. 51 (144), for higher energy machines

v Patton H. McGinley: Shielding Techniques for Radiation Oncology Facilities. Medical Physics Publishing, Madison, Wisconsin.

Conventional Primary Barrier

P

WU

dpri

2

Patient Scatter

P1

W dsec

dsec

P2

Leakage

P

W

dl

IMRT Maze and Door

P

W

dmL

2@pri

unshieldedpri dWUT

HdRateDose ==

Primary Barrier: Source term

Ø What is the Dose Rate at a certain distance from the source?vW – Workload = average dose per week at one meter

from the target (source)vU – Use Factor (orientation) = average fraction of time

per week that the primary beam falls on the barriervT – Occupancy Factor = fraction of the time that a

person will be in the area outside of that barrier (the most exposed individual)vdpri – distance from source to the point (zone to

protect) where person will be standing

ØØ Calculate the Calculate the transmission of the Barriertransmission of the Barrier ((BBxx or or TTxx) ) to bring the Dose Rate to constraint Levelsto bring the Dose Rate to constraint Levels

vvHHshieldedshielded = dose per week required outside of = dose per week required outside of the protection barrierthe protection barrier

ØØ Do the calculation for each primary barrierDo the calculation for each primary barrier

WUT

dH

HH

B prim

unshielded

shieldedx

2

==

Primary Barrier

Regulatory constraint

Secondary Barrier

Ø Transmission for Secondary BarriersvConsider

§ Scatter from Patient, Bp, U=1§ Scatter from Barrier, Bs

§ Leakage thru Barrier, Bl, U=1vDo the calculation for each barrier

3

FaWTddH

B imp

40022sec=

Scatter from Patient

vvddsecsec = distance from the scattering surface to the point to = distance from the scattering surface to the point to be protectedbe protectedvvddii = distance from the x= distance from the x--ray source to the patient ray source to the patient vva = ratio of scattered radiation at one meter from the a = ratio of scattered radiation at one meter from the

scattering object to the primary radiation at 1 m from the scattering object to the primary radiation at 1 m from the xx--ray target (derived with field size 20x20)ray target (derived with field size 20x20)vvF = field size at patient (cmF = field size at patient (cm22))

AWTUddH

B ims α

22sec=

Scatter from Barriers

vvddsecsec = distance from the scattering surface to the point = distance from the scattering surface to the point to be protectedto be protectedvvddii = distance from the x= distance from the x--ray source to the barrier ray source to the barrier

vvαα = reflection coefficient for the barrier material, = reflection coefficient for the barrier material, scattering angle, and xscattering angle, and x--ray beam energy (per mray beam energy (per m22))

vvA = area of beam at the scattering surface in mA = area of beam at the scattering surface in m22

WTdH

B ml

2sec1000

=

Leakage thru Linac Head

vv1/1000 = Leakage factor thru the head of linac1/1000 = Leakage factor thru the head of linacvvddsecsec = distance from the isocenter (or target) to the = distance from the isocenter (or target) to the

point to be protectedpoint to be protected

vvEnergy (@90Energy (@90oo) is about the produced by 2E) is about the produced by 2E00/3 but /3 but conservatively assumed equal to the primaryconservatively assumed equal to the primary

Workload Considerations

vvChoose the maximum weekly expected average Choose the maximum weekly expected average value of the dose at a meter from the target.value of the dose at a meter from the target.vvSurvey (Survey (KlechKlech et al, 1994)et al, 1994)

§§ For single xFor single x--ray beams W=350 ray beams W=350 GyGy/week/week§§ For dual xFor dual x--ray beams W = 250 ray beams W = 250 GyGy /week for the /week for the

highest energy xhighest energy x--ray beamray beamvvDisregard electron beam workloadDisregard electron beam workload

vv IMRT IMRT –– affect all barriersaffect all barriersvvTBI TBI –– affect only one barrieraffect only one barrier

GycGyWweekdays

MUcGy

fieldMU

patientfields

daypatients

W

50050000

5150540

==

=

Workload Example

vvAverage No. of patients/day = 40 Average No. of patients/day = 40

vvAverage No. of fields/patient = 5Average No. of fields/patient = 5vvAverage No. of MU/field = 50Average No. of MU/field = 50

vv1 MU = 1 1 MU = 1 cGycGyvvNo. of days/week = 5No. of days/week = 5

Dose Constraint

ØØ ControlledControlledvvHmHm = 50 = 50 mSvmSv/year (actually 20 /year (actually 20 mSvmSv/year)/year)

(= 20/50 = 0.4 (= 20/50 = 0.4 mSvmSv/week)/week)vvDue to ALARADue to ALARA

HmHm = 0.10 to 0.20 = 0.10 to 0.20 mSvmSv/week (NCRP116)/week (NCRP116)

ØØ Uncontrolled = General PublicUncontrolled = General PublicvvHmHm = 1.0 = 1.0 mSvmSv/year or 0.02 /year or 0.02 mSvmSv/week/weekvvDue to ALARADue to ALARA

HmHm = 0.010 to 0.02 = 0.010 to 0.02 mSvmSv/week/week

4

Scatter-primary ratio

ScatterScatter--primary ratio (a) at 1 m from a humanprimary ratio (a) at 1 m from a human--size phantom size phantom for a size 400 cmfor a size 400 cm22 at the phantom, target to phantom at the phantom, target to phantom distance of 1 mdistance of 1 m

Scattering angleScattering angle 6 MV6 MV 10 MV10 MV3030oo 0.0070.007 0.00300.00304545 oo 0.00180.0018 0.00100.00106060oo 0.00110.0011 0.00050.0005

9090oo 0.00060.0006 0.00030.0003135135oo 0.00040.0004 0.00020.0002

Since scatter radiation has low penetration compared with Since scatter radiation has low penetration compared with leakage radiation it can be ignored above 10 MVleakage radiation it can be ignored above 10 MV

Scattering from barriers

Occupancy Factor

Full occupancyFull occupancy: work areas, such as offices, shops, : work areas, such as offices, shops, laboratories, childrenlaboratories, children’’s play areas, occupied nearby s play areas, occupied nearby buildings, living quarters, wards, nurse's stationsbuildings, living quarters, wards, nurse's stations

Partial occupancyPartial occupancy: corridors, rest rooms, elevators : corridors, rest rooms, elevators using operatorsusing operators

Occasional occupancyOccasional occupancy: waiting rooms, toilets, : waiting rooms, toilets, stairways, unattended elevators, janitorstairways, unattended elevators, janitor ’’s closet, outside s closet, outside areas used only for pedestrians or vehicular traffic areas used only for pedestrians or vehicular traffic parking lotsparking lots

1

½ to 1/5

1/8 to 1/40

Type of areaType of areaTT

Barrier Materials

Physical Properties of Common Shielding MaterialsPhysical Properties of Common Shielding Materials

ShieldingShielding DensityDensity AtomicAtomic RelativeRelativeMaterialMaterial (gcm(gcm--33)) NumberNumber Cost/massCost/mass

Ordinary concreteOrdinary concrete 2.32.3 1111 1.01.0Heavy concreteHeavy concrete 3.73.7--4.84.8 2626 5.85.8LowLow--carbon steelcarbon steel 7.877.87 2626 2.22.2LeadLead 11.3511.35 8282 22.222.2Earth, dryEarth, dry --packedpacked 1.51.5 -- lowlow

Barrier Thickness

•• Transmission Transmission curves can be curves can be used to calculate used to calculate barrier thicknessbarrier thickness

6 MV

scattered radiation

Barrier Thickness

Or we can use the tenth value layer (TVL).Or we can use the tenth value layer (TVL).The number (n) of TVL can be obtained byThe number (n) of TVL can be obtained by

The thickness S can be obtained byThe thickness S can be obtained by

e

x

TnTS

Bn

)1(

)/1(log

1

10

−+=

=

5

Barrier ThicknessTenth value layers (TVL) in concrete, steel, and leadTenth value layers (TVL) in concrete, steel, and leadData based on NCRP 51Data based on NCRP 51

ShieldShield TVLTVL11 TVLTVLee

Energy/MVEnergy/MV MaterialMaterial (m)(m) (m)(m)66 concreteconcrete 0.350.35 0.350.35

steelsteel 0.0990.099 0.0990.099leadlead 0.0550.055 0.0570.057

1010 concreteconcrete 0.410.41 0.390.39steelsteel 0.1040.104 0.1040.104leadlead 0.0570.057 0.0560.056

Barrier Thickness

Tenth value layers (TVL) in concrete, steel, and leadTenth value layers (TVL) in concrete, steel, and leadData based on NCRP 51Data based on NCRP 51

ShieldShield TVLTVL11 TVLTVLee

Energy/MeVEnergy/MeV MaterialMaterial (m)(m) (m)(m)1515 concreteconcrete 0.460.46 0.430.43

steelsteel 0.1080.108 0.1080.1081818 concreteconcrete 0.470.47 0.430.43



steelsteel 0.1090.109 0.1090.109

Primary Barrier Photon Tenth-Value Layers (mm) Come from a Variety of Sources

Lead Concrete Steel Earth Borated PolyMV TVL1 TVLe TVL1 TVLe TVL1 TVLe TVL1 TVLe TVL1 TVLe0.2

0.250.30.40.5124

1.7 1.7 84 842.9 2.9 94 944.8 4.8 104 1048.3 8.3 109 10911.9 11.9 117 11726 26 147 14742 42 210 21053 53 292 292

61015

572 572648 648720 720

379 379379 379

182024

367 323410 377445 416462 432470 442483 457

56 5656 5656 5656 5656 5656 56

15 1519 1922 2229 2933 3354 5176 6991 91100 100104 104108 108109 109110 110110 110

135 135 84 84151 151 94 94167 167 104 104175 175 109 109188 188 117 117236 236 147 147336 336 210 210468 468 292 292

343 343

740 740 379 379752 752 390 390773 773 401 401

NCRP 49 NCRP 51 Nelson & LaRiviere Estimated from ConcreteMcGinley

Barrier Thickness

Tenth value layers (TVL) for primary and secondary Tenth value layers (TVL) for primary and secondary leakage radiation at 90leakage radiation at 90oo. Data from Varian. . Data from Varian. Megavoltage from BJR 17Megavoltage from BJR 17

XX--rayray ShieldingShielding TVL primTVL prim TVL 90lkggTVL 90lkggMVMV MaterialMaterial (m)(m) (m)(m)66 concreteconcrete 0.3430.343 0.2790.279

earthearth 0.5720.572 --steelsteel 0.0980.098 0.0800.080leadlead 0.0550.055 0.0450.045

1010 concreteconcrete 0.3890.389 0.3050.305earthearth 0.6480.648 --steelsteel 0.1050.105 0.0850.085leadlead 0.0560.056 0.0460.046

Barrier Thickness

Tenth value layers (TVL) for primary and secondary Tenth value layers (TVL) for primary and secondary leakage radiation at 90leakage radiation at 90oo. Data from Varian. Megavoltage . Data from Varian. Megavoltage from BJR 17from BJR 17


earthearth 0.7200.720 --steelsteel 0.1080.108 0.0870.087leadlead 0.0570.057 0.0470.047

1818 concreteconcrete 0.4440.444 0.3300.330earthearth 0.7400.740 --steelsteel 0.1110.111 0.0870.087leadlead 0.0560.056 0.0470.047

Barrier Thickness

Tenth value layers (TVL) for primary and secondary Tenth value layers (TVL) for primary and secondary leakage radiation at 90leakage radiation at 90oo. Data from Varian. . Data from Varian. Megavoltage from BJR 17Megavoltage from BJR 17


steelsteel 0.1120.112 0.0880.088leadlead 0.0550.055 0.0490.049

2424 concreteconcrete 0.4700.470 0.3560.356steelsteel 0.1070.107 0.0890.089leadlead 0.0520.052 0.0510.051

6

First and third TVL for head leakage radiation*First and third TVL for head leakage radiation*AngleAngle TVLTVL11/TVL/TVL33

66MVMV 10MV10MV 25MV25MV3535--5555 0.353/0.2930.353/0.293 0.366/0.3280.366/0.328 0.377/0.3670.377/0.3678080--100100 0.341/0.2840.341/0.284 0.349/0.3110.349/0.311 0.359/0.347 0.359/0.347 125125--145145 0.333/0.2690.333/0.269 0.347/0.3290.347/0.329 0.355/0.3250.355/0.325

* * Adapted from Nelson and Adapted from Nelson and LaRiviereLaRiviere (1984) for ordinary concrete(1984) for ordinary concrete

SS

aa

θθ

tt

1.1. If the barrier is composed of concrete, If the barrier is composed of concrete, an attenuation of 1000 is required, an attenuation of 1000 is required, andand θ θ is 50is 50oo, increase the barrier 2 , increase the barrier 2 HVL for low energy and 1 HVL for HVL for low energy and 1 HVL for high energy radiation. The additional high energy radiation. The additional shielding is required to account for shielding is required to account for scattering shown by ray (a) in the fig.scattering shown by ray (a) in the fig.

2.2. For angles of 60For angles of 60oo and 70and 70oo each of the each of the thickness need to be increase by 1 thickness need to be increase by 1 and 2 HVL respectivelyand 2 HVL respectively

3.3. For lead shielding with a required For lead shielding with a required attenuation of 1000, the barrier is attenuation of 1000, the barrier is increased by 1 HVL at 60increased by 1 HVL at 60oo

Rule of thumb for oblique radiation based on NCRP Rule of thumb for oblique radiation based on NCRP 49 rules for 49 rules for 6060Co and Co and 137137Cs:Cs:

Rules for Rules for 6060Co, 4, 10 and 18 MV xCo, 4, 10 and 18 MV x--rays. Biggs (1996)rays. Biggs (1996)

1.1. For For 6060Co and Co and θθ <45<45oo, deviations from obliquity , deviations from obliquity are noticeable for barrier transmission factors are noticeable for barrier transmission factors less than 4x10less than 4x10--33; for; for θθ =60=60oo; they are noticeable ; they are noticeable below 1x10below 1x10--22. .

2.2. The concrete shielding thickness for xThe concrete shielding thickness for x--rays of rays of 10 MV or greater can be based on the slant 10 MV or greater can be based on the slant thickness (t) providing thickness (t) providing θθ is less than 70is less than 70oo..

3.3. For steel the slant thickness should not be used For steel the slant thickness should not be used for an 18 MV beam if the value of q is greater for an 18 MV beam if the value of q is greater than 60than 60oo and t is greater than 35 cm.and t is greater than 35 cm.

4.4. For lead the slant thickness should not be used For lead the slant thickness should not be used for 18 MV beams if the value of q is greater than for 18 MV beams if the value of q is greater than 6060oo and t is greater than 17 cm.and t is greater than 17 cm.

Width and Length of Primary Barrier

The width of a primary barrier is equal to the maximum The width of a primary barrier is equal to the maximum beam size at the barrier plus 1 foot (0.305 m) on beam size at the barrier plus 1 foot (0.305 m) on either side to prevent radiation from leaking through either side to prevent radiation from leaking through the secondary barrier. the secondary barrier.

The maximum field size is normally 40x40 cm and the The maximum field size is normally 40x40 cm and the maximum width is the diagonal of the field which maximum width is the diagonal of the field which will be equivalent to a width of 56.6 cm.will be equivalent to a width of 56.6 cm.

The required width W isThe required width W isW = 0.566 X + 0.61 (m)W = 0.566 X + 0.61 (m)

X is the distance of the barrier in meters from source.X is the distance of the barrier in meters from source.

Ø 0.3 meter margin on each side of beam rotated 45 degreesvBarrier width required assuming 40 cm x 40 cm field size

Ø Field typically not perfectly square (corners are clipped)v35 cm x 35 cm field size typically used to account for this

Primary Barrier Width

C'

* Target

IsocenterTarget toNarrow Point

Distance(d

C ')

wC

0.3 m 0.3 m

C C'

* Target

IsocenterTarget toNarrow Point

Distance(d

C ')

wC

0.3 m 0.3 m

C

* Target

Isocenter

wC

0.3 m 0.3 m

Metal

Target toNarrow Point

Distance(d

C ')

mdw CC 6.024.0 '+=

Figure 2.3

7

Maze Calculations for up to 10 MV beams

PW

dm

L

1.1. Primary beam Primary beam scattered from room scattered from room surfacesurface

2.2. Head leakage photons Head leakage photons scattered by room scattered by room surfacesurface

3.3. Primary scatter from Primary scatter from the patient (Sp)the patient (Sp)

If space is at premium If space is at premium use a door with use a door with secondary barrier secondary barrier thicknessthickness

Scattered radiation to the door from the Scattered radiation to the door from the primary beam (Ss)primary beam (Ss)

==

==

==

===

=

2

1

1

2

2

1

1

2211

2211

)(

r

r

o

s

rr

os

d

d

d

A

A

D

S

dddAAD

S

α

α

αα

wherewhere Dose at doorDose at door

Workload of acceleratorWorkload of accelerator

Reflection coefficient at first reflection basedReflection coefficient at first reflection basedon a beam energy of on a beam energy of ½½ the MV of linacthe MV of linac

Beam area at first reflection (mBeam area at first reflection (m22))

Reflection coefficient at second reflection Reflection coefficient at second reflection Based on a beam energy of 0.5 MV Based on a beam energy of 0.5 MV

Cross section of maze (mCross section of maze (m22))

Distance from target to first reflection (m)Distance from target to first reflection (m)

Centerline distance along first leg of maze (m)Centerline distance along first leg of maze (m)

Centerline distance along second leg of maze (m)Centerline distance along second leg of maze (m)

Figure 3.2Figure 3.2

The following restrictions apply to Ss. The height The following restrictions apply to Ss. The height to width ratio of the maze must be between one to width ratio of the maze must be between one and two, and the value of dand two, and the value of dr2r2/(A/(A22)) 1/21/2 must be must be between two and six.between two and six.

Values of the reflection coefficient may be Values of the reflection coefficient may be obtained from Figure 3.3. For photon energies obtained from Figure 3.3. For photon energies higher than 10 MV, the 10 MV reflection higher than 10 MV, the 10 MV reflection coefficient is used. This is considered to be a coefficient is used. This is considered to be a conservative estimation of the dose at the conservative estimation of the dose at the door.door.


8


Scattered radiation at the door from head Scattered radiation at the door from head leakageleakage

===

==

=

=

=

s

i

o

o

is

oo

ddA

D

L

Ldd

ADLL

1

1

211

)(

α

α

wherewhere Dose at door due to head leakageDose at door due to head leakage


Ratio of dose due to head leakage at 1m fromRatio of dose due to head leakage at 1m fromtarget to the dose at the isocentertarget to the dose at the isocenter

Reflection coefficient for wall reflection Reflection coefficient for wall reflection

Area of wall C that can be seen from maze (mArea of wall C that can be seen from maze (m22))

Distance from target to maze centerline (m)Distance from target to maze centerline (m)

Centerline distance along the maze (m)Centerline distance along the maze (m)

McGinley and James (1997) observed a factor of 2 McGinley and James (1997) observed a factor of 2 between the calculated and measured head between the calculated and measured head leakage scatter. The head leakage used was leakage scatter. The head leakage used was the measured not the standard 0.1%. The the measured not the standard 0.1%. The energy assigned to the head leakage was 1.4 energy assigned to the head leakage was 1.4 and 1.5 MV for the 6 and 10 MV linac as and 1.5 MV for the 6 and 10 MV linac as suggested by Nelson and suggested by Nelson and LaRiviereLaRiviere..

Scattered dose at the door from the Scattered dose at the door from the patient scatterpatient scatter

===

=

===

=

=

=

1

sec

1

1

21sec

11

)()400/(

r

sca

o

p

rsca

op

ddd

A

FaD

S

dddAFaD

S

α

α

wherewhere Dose at door due to the patient scatterDose at door due to the patient scatter


Reflection coefficient for patientReflection coefficient for patient

Field area at patient (cmField area at patient (cm22))

Reflection coefficient for wall reflection E=0.5MVReflection coefficient for wall reflection E=0.5MV

Area of maze back wall that can be seen fromArea of maze back wall that can be seen fromouter maze entrance (mouter maze entrance (m22))

Distance from patient to maze centerline (m)Distance from patient to maze centerline (m)

Centerline distance along maze (m)Centerline distance along maze (m)

Distance from target to patient (m)Distance from target to patient (m)

Transmitted dose at the door thru leg of Transmitted dose at the door thru leg of mazemaze

9

=

=

=

''

2'' )(

d

Bd

BDLT oo

wherewhere Barrier transmission factor for wall DBarrier transmission factor for wall D’’

Distance from target to the door (m)Distance from target to the door (m)

Total Dose (Dc) when beam is pointing at Total Dose (Dc) when beam is pointing at wall Cwall C

=

=+++=

f

TLfSSD cpc

Fraction of beam transmitted through patientFraction of beam transmitted through patient

Values of f for 6 MV (0.23) and 10 MV (0.27) have been Values of f for 6 MV (0.23) and 10 MV (0.27) have been reported by reported by McGingleyMcGingley and James (1997)and James (1997)

Total Dose (Total Dose (DDtt) from all sources of ) from all sources of radiation at the doorradiation at the door

ct DD 64.2=For typical case in which the factors U are For typical case in which the factors U are ¼¼ each. This each. This equation can be used for rooms with a similar layout asequation can be used for rooms with a similar layout asFigure 3.1.Figure 3.1.The transmission factor required for the door shieldingThe transmission factor required for the door shieldingis calculated by dividing the permissible dose at door by is calculated by dividing the permissible dose at door by DD tt..The thickness of lead for a 6 MV can be calculated from The thickness of lead for a 6 MV can be calculated from Figure 3.6. For a 10 MV beam the thickness can be based Figure 3.6. For a 10 MV beam the thickness can be based on broad beam data for 0.21 MV photons.on broad beam data for 0.21 MV photons.When the energy of the linac is above 10 MV. This When the energy of the linac is above 10 MV. This technitechni--QueQue still applies. We need to consider the neutrons.still applies. We need to consider the neutrons.

Photoneutrons

Relative yield of Relative yield of photoneutronsphotoneutrons in semiin semi--infinite thick infinite thick target as a function of incident electron energytarget as a function of incident electron energy

TargetTarget Electron Energy (MeV)Electron Energy (MeV)ElementElement 1010 1515 2020 2525AlAl 0.00.0 0.00.0 0.00.0 0.030.03CuCu 0.00.0 0.00.0 0.110.11 0.250.25FeFe 0.00.0 0.00.0 0.070.07 0.170.17PbPb 0.00.0 0.250.25 0.700.70 0.930.93WW 0.00.0 0.250.25 0.700.70 1.001.00

Figure of linac headFigure of linac head Figure 4.3Figure 4.3

10

thscdir Φ+Φ+Φ=ΦTotal flux is due to direct neutron production between a Total flux is due to direct neutron production between a

photon and a neutron in the nucleus of the target atom, the photon and a neutron in the nucleus of the target atom, the scattered neutrons from the concrete surfaces of the room, scattered neutrons from the concrete surfaces of the room, and a thermal neutron energy group.and a thermal neutron energy group.

McCall et al (1979) have found that the direct neutron fluence, McCall et al (1979) have found that the direct neutron fluence, which accounts for 15% of the which accounts for 15% of the photoneutronphotoneutron. is given by. is given by

where a is the transmission factor for neutrons that penetrate where a is the transmission factor for neutrons that penetrate the head shielding, d is the distance (cm) from target to the the head shielding, d is the distance (cm) from target to the point where fluence is evaluated and Q is the neutron point where fluence is evaluated and Q is the neutron source strength in neutrons emitted by unit photon dose. source strength in neutrons emitted by unit photon dose. The factor a is 1.0 for lead and 0.85 for tungsten shieldingThe factor a is 1.0 for lead and 0.85 for tungsten shielding

cc

24/ daQdir π=Φ

The room scatter and thermal neutron fluence are The room scatter and thermal neutron fluence are constant in the room given byconstant in the room given by

S is the surface area of the treatment room in cmS is the surface area of the treatment room in cm22..The total fluence is given byThe total fluence is given by

SQ

SaQ

daQ

SaQ

SQ

sc

th

26.14.54

/4.5

/26.1

2++=Φ

=Φ

=Φ

π

Neutron source strength for medical acceleratorsNeutron source strength for medical acceleratorsManufacturerManufacturer ModelModel Stated MVStated MV QQ

neutrons/neutrons/GyGySiemensSiemens KDKD 2020 0.92x 100.92x 101212

VarianVarian 18001800 1818 1.221.22VarianVarian 18001800 1515 0.760.76VarianVarian 18001800 1010 0.060.06PhilipsPhilips SLSL--2525 2222 2.372.37PhilipsPhilips SLSL--2020 1717 0.690.69GEGE SaturneSaturne 4343 2525 2.402.40GEGE SaturneSaturne 4343 1818 1.501.50GEGE SaturneSaturne 4141 1515 0.470.47GEGE SaturneSaturne 4141 1212 0.240.24

Varian 2100C/D and 2300 C/D are similar to the 1800 seriesVarian 2100C/D and 2300 C/D are similar to the 1800 series

State Rules and Regulations for Head LeakageState Rules and Regulations for Head Leakage

1.1. For operations producing the maximum leakage For operations producing the maximum leakage radiation, the absorbed dose due to neutrons and radiation, the absorbed dose due to neutrons and photons, at any point in a circular plane (patient photons, at any point in a circular plane (patient plane or area) of 2 m radius centered on and plane or area) of 2 m radius centered on and perpendicular to the CAX of the beam at the perpendicular to the CAX of the beam at the isocenter and outside of the maximum beam size, isocenter and outside of the maximum beam size, shall not exceed 0.1% of the absorbed dose due to shall not exceed 0.1% of the absorbed dose due to the xthe x--rays at the isocenter. rays at the isocenter.

2.2. Points outside the patient area and at 1 m from the Points outside the patient area and at 1 m from the path of the electron beam through the accelerator path of the electron beam through the accelerator shall receive an absorbed dose due to photons that shall receive an absorbed dose due to photons that is <= 0.1% of the xis <= 0.1% of the x--ray dose at the isocenter and < = ray dose at the isocenter and < = 0.005% due to neutrons.0.005% due to neutrons.

Activation of MaterialsActivation of Materials

RadionuclidesRadionuclides produced in medical acceleratorsproduced in medical accelerators

ReactionReaction Mode of decayMode of decay HalfHalf--lifelife Photon energyPhoton energy2727Al(n,Al(n,γγ ))2828AlAl ββ -- 2.3 min2.3 min 1.780 MeV1.780 MeV6363Cu(Cu(γ,γ, n)n)6262CuCu ββ ++ 9.7 min9.7 min 0.511 MeV0.511 MeV5656Mn(n,Mn(n,γγ ))5656MnMn ββ -- 2.6 hour2.6 hour 0.847 MeV0.847 MeV6363Cu(n,Cu(n,γγ ))6464CuCu ββ + + //ββ−− 12.7 hour12.7 hour 1.346 MeV1.346 MeV6565Cu(Cu(γ,γ, n)n)6464CuCu ββ + + //ββ−− 12.7 hour12.7 hour 1.346 MeV1.346 MeV186186W(n,W(n,γγ ))178178WW ββ -- 23.9 hour23.9 hour 0.479/0.6860.479/0.6865858Ni(Ni(γ,γ,n)n)5757NiNi ββ ++ 36.0 hour36.0 hour 1.378/1.9201.378/1.920

Activation of MaterialsActivation of Materials

Near the accelerator the dose rate immediately after treatment Near the accelerator the dose rate immediately after treatment is dominated by 28Al and 62Cu, and after one hour the is dominated by 28Al and 62Cu, and after one hour the longerlonger--lived isotopes 187W and 57Ni produce the majority lived isotopes 187W and 57Ni produce the majority of the dose rate. It was found by of the dose rate. It was found by AlmenAlmen et al (1991) that et al (1991) that the annual dose received by the technician from induced the annual dose received by the technician from induced activity was in the range of 1.0 to 2.8 activity was in the range of 1.0 to 2.8 mGymGy for the trunk for the trunk region of the body and 0.7 to 3,3 region of the body and 0.7 to 3,3 mGymGy for the hands. A for the hands. A workload of 240 days per year and 3500 highworkload of 240 days per year and 3500 high--energy ports energy ports treated per year was used to estimate the annual dose.treated per year was used to estimate the annual dose.

McGinley measured the dose rate at the distal end of the McGinley measured the dose rate at the distal end of the collimator for several Varian collimator for several Varian linacslinacs operating at 18 MV and operating at 18 MV and found the average level of 0.80 found the average level of 0.80 mGy/hmGy/h, two minutes after , two minutes after the machine had been running for 30 minutes. The the machine had been running for 30 minutes. The engineer should wait for 40 minutes before repair near the engineer should wait for 40 minutes before repair near the target, after a long run.target, after a long run.

11

Materials for Neutron ShieldingMaterials for Neutron Shielding

Properties of shielding materialsProperties of shielding materialsHydrogenHydrogen TVLTVL TVLTVL TVLTVLcontentcontent fastfast slowslow capture Neutroncapture Neutron

MaterialsMaterials (atoms/cm3)(atoms/cm3) neutronsneutrons gammas activationgammas activationConcreteConcrete 0.80.8--2.4x102.4x1022 22 21.021.0 34.034.0 45.045.0 lowlowPolyethylenePolyethylene 8.0x108.0x102222 4.54.5 77.077.0 -- very lowvery low5% Boron5% Boron -- -- 1.271.27 -- very lowvery lowSteelSteel -- -- 10.710.7 13.513.5 mediummediumLeadLead -- -- 410.0410.0 6.16.1 lowlow

TVL in cmTVL in cm

Mazes and Doors for HighMazes and Doors for High--Energy RoomsEnergy Rooms

Most medical accelerators operating above 10 MV use Most medical accelerators operating above 10 MV use a maze with a door shielded for neutrons and a maze with a door shielded for neutrons and photons at the outer maze entrance. photons at the outer maze entrance.

A typical door consists of a steel case 0.635 cm thick A typical door consists of a steel case 0.635 cm thick containing 10.2 cm of borated polyethylene (5% B containing 10.2 cm of borated polyethylene (5% B by weight) and a 1.27 cm lead slab. by weight) and a 1.27 cm lead slab.

The polyethylene is used to moderate the fast and The polyethylene is used to moderate the fast and intermediate energy neutrons, which react with the intermediate energy neutrons, which react with the boron ant produce a 0.473 MV photon. boron ant produce a 0.473 MV photon.

The lead is placed after the polyethylene, where it will The lead is placed after the polyethylene, where it will attenuate the photons produced in the boron and attenuate the photons produced in the boron and any capture gamma rays generated in the maze by any capture gamma rays generated in the maze by neutron capture in the concrete walls, ceiling and neutron capture in the concrete walls, ceiling and floor.floor.Method was developed by Kersey (1979).Method was developed by Kersey (1979).

ININ

SteelSteel0.635 cm0.635 cm

Polyethylene 10.2 cmPolyethylene 10.2 cmLead 1.27 cmLead 1.27 cm

Kersey TechniqueKersey Technique

H is the neutron dose equivalent at the entrance of the mH is the neutron dose equivalent at the entrance of the maze per aze per unit dose of xunit dose of x--ray at the isocenter.ray at the isocenter.Ho is the neutron dose equivalent at a distance do from the Ho is the neutron dose equivalent at a distance do from the target.target.T/To is the ratio of the outer maze area to the inner maze entraT/To is the ratio of the outer maze area to the inner maze entrance nce area.area.d1 is the distance from the isocenter to the point on the maze d1 is the distance from the isocenter to the point on the maze center line from which the isocenter is just visible.center line from which the isocenter is just visible.For a maze with one bend, d2 is the distance from A to B of For a maze with one bend, d2 is the distance from A to B of Figure 5.1. Figure 5.1. TVD is the tenth value distance = 5 m for neutrons.TVD is the tenth value distance = 5 m for neutrons.

5/

2

1

210 do

oo d

dTT

HH −

=

Neutron dose equivalent Ho at 1.41 m from the target per Neutron dose equivalent Ho at 1.41 m from the target per unit dose unit dose of xof x--ray at the isocenter (ray at the isocenter (mSv/GymSv/Gy X)X)

Accelerator Accelerator ModelModel StatedStated BeamBeam Ho*Ho* ReferenceReferencemanufacturermanufacturer (MV)(MV) MVMVVarianVarian 18001800 1818 16.816.8 1.021.02--1.60 Unpublished1.60 Unpublished

18001800 1515 UU 0.790.79--1.30 Unpublished1.30 Unpublished18001800 1010 UU 0.04 0.04 UnpublishedUnpublished

SiemensSiemens KDKD 2020 16.516.5 1.101.10--1.24 McGinley 19881.24 McGinley 1988MDMD 1515 UU 0.170.17 UnpublishedUnpublished

PhilipsPhilips SLSL--2525 2525 22.022.0 2.00 2.00 McGinley et alMcGinley et alSLSL--2020 2020 17.017.0 0.440.44 19931993

GE GE SaturneSaturne 4343 2525 18.518.5 1.38 1.38 FennFenn andand4343 1818 14.014.0 0.550.55 McGinley 1995McGinley 19954141 1515 12.512.5 0.320.324141 1212 11.211.2 0.090.09

*Ho in *Ho in mSv/GymSv/GyxxU = unknownU = unknown

Distance dDistance d33 is equivalent to distance between points Bis equivalent to distance between points B’’ and and C of Figure 5.1.C of Figure 5.1.

The neutron dose equivalent a the door will depend on the The neutron dose equivalent a the door will depend on the collimator opening and gantry angle.collimator opening and gantry angle.

31

1010 5/5/

2

1

32 ddo

oo d

dTT

HH −−

=

12

Relative neutron and photon dose equivalent at the outer Relative neutron and photon dose equivalent at the outer maze maze entrance as a function of beam direction*. Beam direction based entrance as a function of beam direction*. Beam direction based on on Figure 5.1.Figure 5.1.

StatedStatedEnergy Energy Relative neutronRelative neutron Relative photonRelative photon(MeV)(MeV) dose equivalentdose equivalent dose equivalentdose equivalent

1 to 3 3 to 1 up down1 to 3 3 to 1 up down 1 to 3 3 to 1 up down1 to 3 3 to 1 up down1818 0.68 1.17 0.74 1.000.68 1.17 0.74 1.00 0.75 1.13 0.89 1.000.75 1.13 0.89 1.001515 0.83 1.20 1.09 1.000.83 1.20 1.09 1.00 0.88 1.25 0.90 1.000.88 1.25 0.90 1.00

The average neutron energy at the maze entrance has been reporteThe average neutron energy at the maze entrance has been reported d to be around 100 keV, and the corresponding TVL in polyethylene to be around 100 keV, and the corresponding TVL in polyethylene is is 4.5 cm (NCRP 1984).4.5 cm (NCRP 1984).

ØØ Most linac room have a leaded door designed to attenuate the Most linac room have a leaded door designed to attenuate the scattered xscattered x--rays from the treatment room into the maze.rays from the treatment room into the maze.

ØØ For highFor high--energy xenergy x--rays beams, there is a need to shield for rays beams, there is a need to shield for capture gammacapture gamma--rays produced in the maze. The average of the rays produced in the maze. The average of the capture gammacapture gamma--rays in concrete is 3.6 MeV.rays in concrete is 3.6 MeV.

ØØ A method was devised by McGinley et al (1995b) to determine A method was devised by McGinley et al (1995b) to determine the dose due to the capture gammathe dose due to the capture gamma--ray per unit dose of xray per unit dose of x--ray at ray at the isocenter.the isocenter.

where K is the ratio of the capture gamma dose to the total where K is the ratio of the capture gamma dose to the total neutron fluence at point A in Figure 5.1 Based on experimental neutron fluence at point A in Figure 5.1 Based on experimental data, an average value of 0.77x10data, an average value of 0.77x10--12 cm2 12 cm2 GyGywas found for K. was found for K. The TVD2 is approximately 6.2 m for 16.2 to 22 MV xThe TVD2 is approximately 6.2 m for 16.2 to 22 MV x--ray ray beams.beams.

2/210 TVDdtotalKD −Φ=

Capture Gamma Ray ShieldingCapture Gamma Ray Shielding

Radiation dose equivalent rate due to capture gamma rays Radiation dose equivalent rate due to capture gamma rays and and neutrons at the outer maze entranceneutrons at the outer maze entrance

Type ofType of Capture gammaCapture gamma Neutron doseNeutron dose TotalTotalmaze and maze and dose equivalentdose equivalent equivalentequivalent N+gN+gdoordoor rate (rate (nSv/snSv/s)) rate (rate (nSv/snSv/s)) rate (rate (nSv/snSv/s))ConventionalConventional 38.838.8 116.3116.3 166.1166.1a. Reduced innera. Reduced inner

openingopening 17.517.5 38.838.8 56.356.3b. Inner B doorb. Inner B door 12.712.7 31.931.9 44.644.6c. Inner poly doorc. Inner poly door 6.96.9 10.210.2 17.117.1

The maze length is 6.5 m and the dose rate at the isocenter is 6The maze length is 6.5 m and the dose rate at the isocenter is 6.67 .67 cGy/scGy/s..The reduce inner opening (a) was done with a 45.7 cm thick wall The reduce inner opening (a) was done with a 45.7 cm thick wall around the inner opening which was 1.22x2.13 m.around the inner opening which was 1.22x2.13 m.A panel 7 mm thick containing 8.9% boron by weight was used in tA panel 7 mm thick containing 8.9% boron by weight was used in the he technique b.technique b.A 5 cm thick polyethylene (5% boron) door was used for techniqueA 5 cm thick polyethylene (5% boron) door was used for techniquec.c.

Total radiation dose equivalent at the outer maze entranceTotal radiation dose equivalent at the outer maze entrance for a for a workload of 500 workload of 500 cGycGy per week and a maze length of 6.5 m.per week and a maze length of 6.5 m.

Type ofType of Photon dosePhoton dose Neutron doseNeutron dose Total doseTotal dosemaze and maze and equivalent/wequivalent/w equivalent/wequivalent/w equivalent/wequivalent/wdoordoor ((cSvcSv)) ((cSvcSv)) ((cSvcSv))ConventionalConventional 0.02500.0250 0.07100.0710 0.09600.0960a. No doora. No door 0.01050.0105 0.02460.0246 0.03510.0351b. Inner B doorb. Inner B door 0.00770.0077 0.01870.0187 0.02640.0264c. Inner poly doorc. Inner poly door 0.00410.0041 0.00580.0058 0.00990.0099

Direct Shielded DoorsDirect Shielded Doors

Figure 5.3 and 5.4Figure 5.3 and 5.4

Maximum dose equivalent rates at the sliding door, console, and Maximum dose equivalent rates at the sliding door, console, and gonad levels below the HVAC penetration.gonad levels below the HVAC penetration.

Dose equivalent rateDose equivalent rateNeutron PhotonNeutron Photon TotalTotal

Beam directionBeam direction LocationLocation ((nSv/snSv/s)) ((nSv/snSv/s)) ((nSv/snSv/s))DownDown door facedoor face 0.940.94 0.890.89 1.831.83

door framedoor frame 1.641.64 3.313.31 4.954.95below HVAC below HVAC <0.20 1.09<0.20 1.09 <1.29<1.29consoleconsole <0.20<0.20 0.330.33 <0.53<0.53

UpUp door facedoor face 1.061.06 0.640.64 1.701.70door framedoor frame 1.391.39 3.063.06 4.454.45below HVAC below HVAC <0.20 1.09<0.20 1.09 <1.29<1.29consoleconsole <0.20<0.20 0.330.33 <0.53<0.53

DownDown door facedoor face 2.862.86 0.670.67 3.533.53door framedoor frame 2.062.06 3.313.31 5.375.37below HVAC below HVAC <0.20 1.09<0.20 1.09 <1.29<1.29consoleconsole <0.20<0.20 0.330.33 <0.53<0.53

13

Maximum dose equivalent expected in any one hour of Maximum dose equivalent expected in any one hour of operation, in seven consecutive days, and in one year.operation, in seven consecutive days, and in one year.

LocationLocation Total dose equivalentTotal dose equivalentOne hourOne hour Seven DaysSeven Days AnnualAnnual((mSvmSv)) ((mSvmSv)) ((mSvmSv))

Door faceDoor face 1.061.06 17.417.4 870870Door frameDoor frame 1.771.77 38.738.7 19301930Below HVACBelow HVAC 0.970.97 9.59.5 475475ConsoleConsole <0.17<0.17 <4.0<4.0 <200<200

Primary ceiling shield for 18 MV accelerator facilityPrimary ceiling shield for 18 MV accelerator facilityAcceleratorAccelerator Layer No.Layer No. Shielding Shielding ThicknessThickness

materialmaterial (m)(m)Varian 2100CVarian 2100C 11 concreteconcrete 0.3050.305

22 leadlead 0.2030.20333 polyethylenepolyethylene 0.1780.17844 concreteconcrete 0.3050.30555 leadlead 0.0510.05166 concreteconcrete 0.1140.114

Laminate Primary Shield

Patient Neutron Dose

One linac room with a 14 cm steel slab in one wallOne linac room with a 14 cm steel slab in one wallAnother linac room with a 20 cm lead slab in one wallAnother linac room with a 20 cm lead slab in one wallBoth 18 MVBoth 18 MVLead increased the total body dose by 42%Lead increased the total body dose by 42%Steel increased the total body dose by 10%Steel increased the total body dose by 10%For TBI lead increased the total body dose by a factor of For TBI lead increased the total body dose by a factor of

2.3 and 1.2 for steel.2.3 and 1.2 for steel.

Skyshine

Roof shielding transmission ratioRoof shielding transmission ratio

Photon dose equivalent rate at ground level (Photon dose equivalent rate at ground level (nSv/snSv/s))

Distance (m) from isocenter to point where dose Distance (m) from isocenter to point where dose equivalent rate is Dequivalent rate is D

Distance (m) from xDistance (m) from x--ray target to a point 2 m above ray target to a point 2 m above the roofthe roof

X ray dose rate at 1 m from target (X ray dose rate at 1 m from target (cGy/scGy/s))

Solid angle of radiation beam (Solid angle of radiation beam (steradianssteradians=Ω=

=

==

=Ω

= −

O

s

XS

O

sXS

Dd

dDB

DddD

xB

1

1

3.11

216 )(

1002.4 Skyshine

14

RoofRoof shieldingshielding transmissiontransmission ratioratio

NeutronNeutron dose dose equivalentequivalent rate at rate at groundground levellevel ((nSv/snSv/s))

DistanceDistance (m) (m) fromfrom xx--rayray targettarget to a to a pointpoint 2 m 2 m aboveabovethethe roofroof

NeutronNeutron fluencefluence rate at 1 m rate at 1 m fromfrom targettarget (cm(cm--22ss--11))

SolidSolid angleangle of of radiationradiation beambeam ((steradianssteradians=Ω

=Φ=

==

ΩΦ= −

0

1

0

2161019.1

d

HB

HdxB

NS

NS

Measured and calculated xMeasured and calculated x--ray ray skyshineskyshinefor an 18 MeV accelerator for an 18 MeV accelerator with no ceiling shieldwith no ceiling shield

Distance fromDistance fromisocenter isocenter dsds Measured photonMeasured photon Calculated photon Calculated photon RatioRatio(meters)(meters) rate (rate (nSv/snSv/s)) rate (rate (nSv/snSv/s)) m/cm/c7.5 (at wall)7.5 (at wall) 13.913.9 56.256.2 0.250.259.49.4 31.231.2 35.435.4 0.880.8810.610.6 41.741.7 26.926.9 1.51.513.613.6 43.743.7 17.417.4 2.52.519.219.2 27.827.8 8.38.3 3.33.325.425.4 20.820.8 4.94.9 4.24.233.033.0 15.315.3 2.92.9 5.35.348.348.3 6.96.9 1.31.3 5.35.3

Measured neutron Measured neutron skyshineskyshine for an 18 MeV accelerator for an 18 MeV accelerator with no ceiling shieldwith no ceiling shield

Distance fromDistance fromisocenter isocenter dsds Measured neutron dose equivalent rateMeasured neutron dose equivalent rate(meters)(meters) ((nSv/snSv/s) )

5.14 5.14 19198.508.50 585811.211.2 525214.314.3 424217.317.3 363618.918.9 292920.820.8 2323

Considerations for Intensity Modulated Radiation Therapy (IMRT)

Ø IMRT requires increased monitor units per cGy at isocenter

vTypical IMRT ratio is 5 MU per cGy, as high as 10 for some systems

Ø Percent workload with IMRT impacts shielding

v50% typically assumed; 100% if vault is dedicated to IMRTØ Account for IMRT by multiplying x-ray leakage by IMRT factor

v IMRT Factor = % IMRT x IMRT ratio + (1 - % IMRT)v3 is typical IMRT factor (50% workload with IMRT ratio of 5)

Ø IMRT factor lower for neutrons if machine is dual energyve.g., 1.5 if dual energy linac with 50% of treatments below

10 MV

Simulator

Fdd

aWTP

KUX

raysxkVforleadmmHVLHVLNSBN

WTIdP

B

WUTPd

K

sca

L

UX

40012528.0),(

)/1(log32.3

2600)(

2sec

2

10

sec

2

=

−===

=

=

PatientPatient scatteringscattering coefficientcoefficient (a) for 125 kV (a) for 125 kV xx--rayrayfromfrom NCRP No. 49NCRP No. 49

AngleAngle((degdeg)) 3030 4545 6060 9090 120120 135135aa 0.00180.0018 0.00150.0015 0.00150.0015 0.00150.0015 0.00230.0023 0.00250.0025

W is in W is in milliamperesmilliamperes x minutesx minutesRadiographyRadiography 160160FluoroscopyFluoroscopy 300300CTCT 32003200

15

CT Isodose (horizontal)

µGy/slice

120 kV, 130 mA, 1.5 s

CT Isodose (vertical)

120 kV, 130 mA, 1.5 s

µGy/slice

Transmission in Steel for CT

mm

Bu

x

Bu

x

mm

Transmission in Concrete for CT

mm

Bu

x

Transmission in Lead for CT

mm

Transmission in plaster for CT

Bu

x

16

HDR

timetCiactivityA

RcGyfmhCiR

fAtWWT

PdB

=====

=

)(/96.0

///48.0

2

γγ

)(/96.0

80.0

2

mCiactivityARcGyffactorgamma

AfPd

B

==

−=

=

γγ

Brachytherapy RoomsLDR Brachytherapy

Shielding LAB (homework)

vShielding calculation for a Linac room for regular work and considering IMRT

vShielding calculation for a CT room (simulator)

end

chapter 16 shielding calculation helvecio-bw

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