Class Pdd Tpr Bsf

Chapter XIII

PDDTARTMR

Dose Free Space

Ver 2.11

Joseph F. Buono RTTAllied Health ScienceNassau Community College1 Education DriveGarden City, NY 11530-6793

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Menu

Menu

- Objectives - next by default

- Dose in free space

- BackScatter Factor ( BSF )

- Percentage Depth Dose ( PDD )

- Tissue Air Ratio ( TAR )

- Tissue Maximum Ratio ( TMR )

- Relationship between BSF, PDD, TAR, TMR

- Conversion between PDD & TAR (also TMR)

- Dose to second point ( i.e. - Cord Dose ) for SSD setup

- Dose to second point ( i.e. - Cord Dose ) for SAD setup

obj 1

Objectives

MENU

1 - Define Dose in Free Space.

2 - Define BackScatter Factor ( BSF ).

3 - State the factors that effect BackScatter Factor ( BSF ).

4 - Define Percantage Depth Dose ( PDD ).

5 - State the factors that effect Percentage Depth Dose ( PDD ).

6 - Define Tissue Air Ratio ( TAR ).

7 - State the factors that effect Tissue Air Ratio ( TAR ).

8 - Define Tissue Maximum Ratio ( TMR ).

9 - State the factors that effect Tissue Maximum Ratio ( TMR ).

10 - State the relationship between TAR, TMR and BSF.

11 - State the relationship between TAR table and BSF.

Dose in Free Space

DFS 0

Dose in Free Space

MENU

DFS 1

MENU

Dose in Free Spacesource

point in space

ionization chamber

build-up cap

radiation beam

The exposure measured in Air at the center of the

chamber is:

Xexposure =

Correction factors due toTemperature

PressureStem error

Exposure measured in

Roentgen

Calibration factor

CT,P,S ×Meterreading × Nx

Xexposure

DFS 2

MENU

Dose in Free Spacesource

Xexposure = CT,P,S ×Meterreading × Nx

The reading from the ionization chamber

gives the Xexposure at the center of the beam without the perturbing

influence of the chamber.

Next, need to place a small mass of tissueat the center of the

beam, who's radius is equal to depth dmax. The dose at the center

of the mass of tissueis referred to as the dose in "free space"

which is equal to:

Dfs = Xexposure × ftissue × Aeq

where:

ftissue

is the Roentgen to rad conversion factor for tissue

ENDDose in Free Space

nextBackScatter Factor

BackScatterFactor

BSF 0

BackScatter Factor

MENU

BSF 1

MENU

BackScatter Factor

fixeddistance

(usually machine operating distance)

generally100 cm Linac80 cm Co60

central axis

beam

Find dosein "free space“

on the central axis.Df.s.

Df.s.Find maximum

dose in a phantom on the central axis at a fixed distance.

Ddmax

Ddmax

BSF 2

MENU

BackScatter Factor

Df.s.Ddmax

Definition:

BSF = ———Df.s.

Ddmax

As the photon energy increases the BSF will become closer to 1.

NOTE:Since the dose at Dmax (Ddmax ) will always be equal to OR greater then the dose in“free space” (Df.s.), BackScatter Factors (BSF) will always be equal to OR greater then 1.

BSF is dependent on:

1) Energy

2) Field Sizeincrease in F.S. increases BSF

3) SSDindependent of SSD

increase in energy decrease in BSF(max BSF ≈ .6 to .8 mm Cu HVL)

depending on field size can be as large as 1.5

PercentageDepth Dose

PDD 0

Percentage Depth Dose

MENU

PDD 1

MENU


Ddmaxphantom

FixedSSD


Beam

central axis

Find maximum dose on central axis.

Ddmax Find dose at some other depth on central

axis.Dd

Dd

PDD 2

MENU


Ddmax

Dd

Percentage Depth Dose @ depthhas been defined as:

PDDd = ——————— × 100%Dose @ depthDose @ Dmax

PDDd = ——— × 100%Ddmax

Dd

PDD 3

MENU


Ddmax

Dd

Percentage Depth Dose @ depthhas been defined as:

PDDd = ——————— × 100%Dose @ depthDose @ Dmax

PDDd = ——— × 100%Ddmax

Dd

PDD is dependent on:

1) Energyan increase in energy increases PDD

2) Field Sizean increase in F.S. increases PDD(because of an increase in scatter)

3) Depth of Tissuean increase in depth decreases PDD

4) SSDan increase in SSD increases PDD

( due to the inverse square lawand the fact that PDD is definedat two different points )

two different distances from

the sourceSSD + dmaxSSD + depth

SSD

Tissue Air Ratio

TAR 0

Tissue Air Ratio

MENU

TAR 1

MENU

Tissue Air Ratio

Beam

central axis

Distancefrom source




Df.s.

TAR 2

MENU

Tissue Air Ratio

Beam

central axis

Dd

Distancefrom source




Df.s.

Find dose in phantom at depth on the central

axis at the same distance from source.

Dd

d

TAR 3

MENU

Tissue Air Ratio

Beam

central axis

Dd

Distancefrom source


Df.s.

d

Definition:

TARd = ———Df.s.

DdTAR is dependent on:

1) Energyan increase in energy increases TAR

2) Field Sizean increase in F.S. increases TAR(because of an increase in scatter)

3) Depth of Tissuean increase in depth decreases TAR

4) SAD (distance)independent of distance

both reading at same distance from the source

DdDf.s.

Ddmax

TAR 3

MENU

Tissue Air Ratio

Beam

central axis

Dd

Distancefrom source


Df.s.

d

Definition:

TARd = ———Df.s.

DdTAR is dependent on:

1) Energy

2) Field Size

3) Depth of Tissuean increase in depth decreases TAR

DdDf.s.

Note:If depth is changed to dmax then:

TARdmax = ———Df.s.

Ddmax BSF = ———Df.s.

Ddmax=

an increase in F.S. increases TAR(because of an increase in scatter) both reading at same

distance from the source


an increase in energy increases TAR

Tissue Maximum Ratio

TMR 0


MENU

TMR 1

MENU


BeamDistance

from source

100 cm Linac80 cm Co60

IonizationChamber

Place phantom such that the ionization chamber is at depth

of maximum dose.depth = dmax

dmax

central axis

Turn beam on and record dose reading.

Ddmax

Ddmax

generally

central axis

TMR 2

MENU



dmax

central axis

Ddmax

Find dose at depth in the phantom at the same

distance from the source.Dd d

Dd

central axis

TMR 3

MENU



dmax

central axis

Ddmax

d

Dd

Definition:

TMRd = ———Ddmax

Dd

an increase in F.S. increases TMR(because of an increase in scatter)

3) Depth of Tissuean increase in depth decreases TMR


both reading at same distance from the source

DdDdmax.

TMR is dependent on:

an increase in energy increases TMR

2) Field Size

1) Energy

Relationshipbetween

BSF, PDD, TAR, TMR

REL 0

Relationship between BSF, PDD, TAR, TMR

MENU

REL 1

MENU


SOURCE

f(SAD)

IONIZATION CHAMBER

BUILDUP CAP Ddmax1

BSF = ———Df.s.1

Ddmax1

Df.s.1

Dd1

REL 2

MENU


SOURCE

f(SAD)

Ddmax1


Ddmax1

Df.s.1

d1

TARd1 = ———Df.s.1

Dd1

Dd1

REL 3

MENU


SOURCE

f(SAD)

Ddmax1


Ddmax1

Df.s.1

d1


Dd1 TMRd1 = ———Ddmax1

Dd1

Dd1

REL 4

MENU


SOURCE

f(SAD)

Ddmax1


Ddmax1

Df.s.1

d1



Dd1

dmax2

f(ODI,SSD)

Dd2

d2

PDDd2 = ———Ddmax2

Dd2

Ddmax2

Note: d1 = d2

REL 6

MENU


Ddmax1 TARd1 = ———Df.s.1


Dd1 PDDd2 = ———Ddmax2

Dd2

Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

f(SAD)

f(ODI,SSD)


REL 7

MENU





Dd2

Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

f(SAD)

f(ODI,SSD)


solve BSF equation for

Df.s.1

BSFDf.s.1

Ddmax1=

solve TARd1 equation for

Df.s.1

TARd1Df.s.1

Dd1=

Both equations are equal to "Dose in free space", therefore

they are equal to each other.

=

REL 8

MENU





Dd2

Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

f(SAD)

f(ODI,SSD)


Df.s.1 =

BSFDdmax1

TARd1

Dd1= rearranging terms:

REL 9

MENU





Dd2

Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

f(SAD)

f(ODI,SSD)


BSFDdmax1

TARd1

Dd1= rearranging terms:

BSF Ddmax1

TARd1 Dd1= BUT:TMRd1=therefore:

BSFTARd1=TMRd1

rearranging terms:

BSFTARd1 = TMRd1 ×

REL 10

MENU





Dd2

Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

f(SAD)

f(ODI,SSD)


BSFTARd1 = TMRd1 ×

One other important relationship is between TAR's and BSF.


Dd1

If depth d1 is equal to dmax1 then:


Ddmax1 BUT:Therefore:At depth Dmax TARs are equal to BSFs

Conversionbetween

PDD & TAR(also TMR)

TMR 0

Conversion between PDD & TAR (& TMR)

MENU

TMR 1

MENU


Dd1

SOURCE

f(SAD)

Ddmax1Df.s.1

d1

dmax2

f(ODI,SSD)

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

TMR 2

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

=

TMR 3

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1

note: This is for field sizeat distance f

Ddmax1Df.s.1

=

TMR 4

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

note: This is for depth d2.This is for the field size at a distance equal to f + d2.Which can be said to be an SAD equal to f + d2.

=

TMR 5

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

Substitute this intoPDD2 equation for Dd2.

Ddmax2

TAR2 Df.s.2×

Solving this equation for Dd2

=

TMR 6

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

= TAR2Dd2 Df.s.2× =PDD2

At this point need to realize thatDmax1 and Dmax2

are related by the"Inverse Square Law"

Thus:

I1

I2

d22

d12=

Ddmax2

TAR2 Df.s.2×

=

TMR 7

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

=PDD2

I1

I2

d22

d12=

Ddmax1

f2=

Ddmax2

TAR2 Df.s.2×

=

TMR 8

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

=PDD2

I1

I2

d22

d12=

Ddmax1 =Ddmax2

f dmf2

+( )2

Ddmax2

TAR2 Df.s.2×

=

TMR 9

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

=PDD2

I1

I2

d22

d12=

Ddmax1 =Ddmax2

f dm

f2

+( )2solving this equation for:

Ddmax2

Ddmax2 = f dm+( )2

f2

× Ddmax1Substitute this into

PDD2 equation.

TAR2 Df.s.2×=PDD2

Ddmax2

TAR2 Df.s.2×

=

TMR 10

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

=PDD2

I1

I2

d22

d12=

Ddmax1 =Ddmax2

f dm

f2

+( )2

Ddmax2 = f dm+( )2

f2

×Ddmax1

TAR2 Df.s.2×=PDD2

Ddmax1

f2f dm+( )2

×

Ddmax1 Df.s.1

=

TMR 11

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

Ddmax1

TAR2 Df.s.2×=PDD2 f2f dm+( )2

× BUT:=BSF1

Ddmax1Df.s.1

Solving for:Dmax1

= BSF1 ×

Ddmax1 Df.s.1

=

TMR 12

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

Ddmax1


× BUT:=BSF1

Ddmax1Df.s.1

Solving for:Dmax1

= BSF1 ×

Substituting for:Dmax1


×Df.s.1BSF1 ×

Df.s.1

Df.s.2

=

TMR 13

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

Ddmax1


×

TAR2 ×=PDD2 f2f dm+( )2

×BSF1 ×

BUTthe relationship between

Df.s.1 and Df.s.2is by the

"Inverse Square Law". THUS:

I1

I2

d22

d12=

invertI2

I1

d12

d22=

substituting into the equation

=d2

f2

f ++( )2substituting

into the equation

Df.s.2Df.s.1

Df.s.1

Df.s.2

=

TMR 14

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

Ddmax1


×

TAR2=PDD2 BSF1×

=d2

f2

f ++( )2

d2

f2

f ++( )2 f2f dm+( )2

×

=

TMR 15

MENU


Dd1Ddmax1Df.s.1

d1

dmax2

Dd2

d2Ddmax2

Note: d1 = d2

d2

Df.s.2

f(SAD)

f(ODI,SSD)

BSF1Ddmax1Df.s.1

=TAR2Dd2Df.s.2

=PDD2Dd2

Ddmax2

Ddmax1


×

TAR2=PDD2 BSF1× f2

d2f ++( )2 f2f dm+( )2

×TAR2=PDD2 BSF1 d2f ++( )2

f dm+( )2

×TAR2=PDD2 BSF1 d2f ++( )2

f dm+( )2END

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