Estimation of TLD dose measurement uncertainties and thresholds at the Radiation Protection Service Du Toit Volschenk SABS

Estimation of TLD dose measurement uncertainties and thresholds at the Radiation

Protection Service

Du Toit Volschenk

SABS

Purpose

To give an overview of some of the factors that cause uncertainties in TLD dose measurement

To quickly describe how lower limits of detection and measurement uncertainties can be determined conventionally and to give the results of such measurements at the RPS, in order to give an impression of the status of the RPS TLD system in this regard

To describe a method of computer simulation to estimate uncertainties in reported dose due to the dose algorithm used at the RPS

Topics of Discussion

General considerations for uncertainty estimation of a TLD system

Lower limits of detection Uncertainty budget Computer simulation to estimate uncertainties due to the

dose algorithm used

General considerations for uncertainty estimation of a TLD system

Calibrations of dosimetry systems and tests to determine uncertainties are done under laboratory conditions

Dosimeters are used under field conditions, the specifics of which is not often known (e.g. angle of incidence, geometry of irradiation, movement of wearer, position of dosimeter on body)

The method(s) used to determine uncertainties in reported dose must take as many of the unknown factors into consideration as possible

Uncertainties in reported dose differ from radiation type to radiation type as well as for magnitude of given dose

Lower limits of detection: Definitions

Detection threshold LC (also known as: decision limit, critical level)

– That dose level above which measured doses can be regarded (in this case 95% confidence) as being not of the background population (i.e. definitely a dose)

– Lc = tnsb

tn is the student t factor (one-sided) for n measurements and the required confidence level

sb is the standard deviation of the background population

Lower limits of detection: Definitions (Continued)

Lower limit of detection LD (also known as detection limit)

– The lowest dose that can be detected with a specified level of confidence (in this case 95% confidence)

– Does not specify the precision of the minimum dose, only the probability that it will be reported greater as zero

– LD = 2(tnsb + tm22sm

2Db) / (1 - tm2sm

2)

tn is the student t factor (one sided) for n measurements of the background

sn is the standard deviation of the background population

tm is the student t factor (one-sided) for m measurements at a dose level significantly higher than the required lower limit of detection

sm is the relative standard deviation at the above dose level

Db is the average of the background readings

Lower limits of detection: Definitions (Continued)

Determination limit LQ

– The lowest dose that can be measured with a given precision

k is the inverse of the desired maximum relative standard deviation (and therefore related to the precision of the measurement)

sm is the relative standard deviation of the measured doses at a level significantly higher than the required lower limit of detection

Db is the average of the background readings

sb is the standard deviation of the background population

Confidence level = 1,96 / k

LQ

k s D k s D k s k s

k s

m b m b b m

m

2 2 4 4 2 2 2 2 2

2 2

1

1

12[ ( )]

Lower limits of detection and determination levels(Determination levels for +/- 30% uncertainty at 95% confidence)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

LI 0.029

MF

G 0.051

Am

0.06

MF

I 0.07

Cs 0.662

Co 1.25

Tl 0.24

Sr 0.57

Radiation type and energy (MeV)

LD

an

d L

Q (

mS

v)

Ld (Deep)

Ld (Skin)

LQ (Deep)

LQ (Skin)

Ld (Deep) corresponds to a precision of on average +/- 56% at the 95% confidence level

Ld (Skin) corresponds to a precision of on average +/- 78% at the 95% confidence level

Lc (Deep)

Lc (Skin)

Uncertainty budget: General

The basic question here is “If a dose is reported, what is the 95% confidence interval for that dose?”

The confidence interval for reported dose should be calculated for each type (energy) of radiation, as well as for dose magnitude ranges

An upper (maximum) acceptable limit should be established based on internationally acceptable criteria

Uncertainty budget: Criteria

Interpretation of ICRP35 and ICRP60 requirements (based on limits of 20 mSv/a and 500 mSv/a for body and skin dose respectively)

Dose range(mSv)

Deep Skin

Uncertaintylevel (95%confidence)

Lowerbound

Upperbound

Bound on S

> 4 > 100 1,5 - 33% + 50% |S| < 0,212

4 100 2 - 50% + 100% |S| < 0,383

Uncertainty budget: calculation and results

Examples of random uncertainties:

inhomogeneity of detectors, reader sensitivity, reader background, etc. Examples of systematic uncertainties:

energy dependence, directional dependence, non-linearity, fading, light-exposure, calibration errors, etc.

“Rough” results (to be used as an indication only of the system as a whole):

– SDeep = 0,21

– SSkin = 0,27

S r s

s

2 2 ,where

is the standard deviation of random uncertainties, and

is the standard deviation of systematic uncertaintiesr

Computer simulation: uncertainties due to dose algorithm - Background

Question:

– Why look at uncertainties due to the dose algorithm separately and not do an uncertainty budget study only?

Some of the answers:

– The dose algorithm uses the ratios of the four elements of a dosimeter to determine the energy of incident irradiation and then do a conversion to dose.

– Small differences in the element values of different dosimeters may lead to different incident irradiation types being identified even though the dosimeters were exposed to the same type and magnitude of dose.

– Some parts of the dose algorithm may be prone to causing larger uncertainties than others and they must be identified

– In short: to design an accurate algorithm and to verify that existing algorithms are accurate and do minimize errors due to misidentification

Computer simulation: uncertainties due to dose algorithm - Background (continued)

Question: Why a computer simulation? Answers:

– To process many dosimeter readings manually through the dose algorithm will be very time consuming and error prone

– Many dosimeters will have to be irradiated to test the various branches of the algorithm with an acceptable degree of accuracy, which will be time consuming and costly

– To analytically determine the uncertainties inherent to the algorithm will be difficult because of the many branches in the algorithm and their interdependencies

– New and changed algorithms can be tested relatively painlessly by means of a computer simulation and problem areas so identified

Photons

C > 1.5

C < 21

D > 0.98

E >= 0.40and

C > 7.0

C > 10and

A > 13

C > 5and

A > 10

D > 1.55

GammaItype = 11Hs = E4Hd = E4

LGItype = 13Hs = 2.01*E2Hd = 0.87*E2

LG = GammaItype = 16XG = -0.3873+0.08195*C+0.002234*C^2FG = 1/(1+XG)FX = 1 - FGHs = 1.85*FX*E2 + FG*E2Hd = 0.80*FX*E2 + FG*E2

A > 13.5

LI + GammaItype = 15XG = -2.487 + 0.7897*C - 0.02831*C^2FG = 1/(1 + XG)FX = 1 - FGHs = 1.52*FX*E2 + FG*E2Hd = 1.10*FX*E2 + FG*E2

LIItype = 14Hs = 1.62*E2Hd = 1.13*E2

MFGItype = 18Hs = 1.43*E2Hd = 1.32*E2

LKItype = 17Hs = 1.37*E2Hd = 1.14*E2

MFIItype = 19Hs = 1.39*E2Hd = 1.34*E2

MIDItype = 22Hs = 1.18*E2Hd = 1.11*E2

LG 20 keVLI 29 keVLK 39 keVMFC 36 keVMFG 51 keVMFI 70 keVMID ~120 keV

FUNEL

FUNEL

FUNEL

FUNEL

A = E3/E2B = E1/E2C = E3/E4D = E4/E2E = E1/E4F = (E2-E4)/(E1-E4)

PanasonicAlgorithm1994-08-19Page 3 of 4

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

E1 or E2 Ei = (Ei/ECFi - BgLi - Resbg1)/BCF*LiFF - BAYes

Ei = (Ei/ECFi - BgCa - Resbg2)/BCF*CaFF - BA

No

For i=1 to 4Ei=Ei+BA/4Tag = 1

Any Ei<-6Any Ei<-6For i=1 to 4Ei=Ei+BA/4Tag = 2

Any E<-6 Any Ei>=50Itype = 30Tag = 4

Tag = 3i = 1

i<=4 Ei<=0

i = i + 1

Ei = 1

All Ei <= ETR Itype = 30

E1 < 30Do checks and ifpositive, flagdosimeter with ** onEdit List (Possiblydamaged)

E2 > 10^5 orE3 > 10^7 orE4 > 10^7

Hd = E2Hs = E2Itype = 26Flag dosimeter with <= onEdit List. Requires manualintervention

Yes Yes

Yes

Yes

Yes

Yes

Yes

No

Yes

No

No

No

No

Yes

No

No No

No

Next Page

Stop

Stop

Stop

Stop


FUNEL

Tot = E1 + E2 + E3 + E4Emax = Max( E1,E2,E3,E4 )

E2 > Max(E1,E3,E4)

E4 > Max(E1,E2,E3)

E1 < Min(E2,E3,E4)

E3 < Min(E1,E2,E4)

E1/Tot < 0.03

E2/Tot < 0.015

Itype = 9Hs = EmaxHd = Emax

T1 = E2 / Max(E1,E3,E4)

T1 = E4 / Max(E1,E2,E3)

T1 = E1 / Min(E2,E3,E4)

T1 = E3 / Min(E1,E2,E4)

T1 > 1.3 + 5/E2

T1 > 1.2 + 5/E4

T1 < 0.6 - 5/E1

T1 < 0.8 - 5/E3

Stop

Stop

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

PanasonicAlgorithm1994-08-19Page 4 of 4(Hs>=20) or (Hd>=20) Stop

Yes

Flag dosimeter with<= on Edit List.Requires manualintervention


B>8 or ( A<15 and E>=1.5 )

Photons

Yes

Gamma = E4

F>NPand

( E2 - E4 ) > 25

Gamma + Betaor

Gamma + Neutron

No

Beta + Gamma

Neutron + GammaBFs = 2.92 - 2.96*FBFs = Min(Max(0.95 ,BFs),2.92)

BFe = 0.0

F > 0.25

BFe = 0.12

BETAs = BFs*( E1 - E4 )BETAe = BFe*( E1 - E4 )Itype = 12Hs = BETAs + GammaHd = Gamma

NF = 4.86Neutron = NF*( E2 - E4 )Itype = 28Hs = E4Hd = E4

FUNELFUNEL

Yes

YesNo

No


Do checks and if positive,flag dosimeter with <= onEdit List. Requires manualintervention

Computer simulation: uncertainties due to dose algorithm - Background (continued)

An example of part of an algorithmPhotons

C > 1.5

C < 21

D > 0.98

E >= 0.40and

C > 7.0

C > 10and

A > 13

C > 5and

A > 10

D > 1.55

GammaItype = 11Hs = E4Hd = E4

LGItype = 13Hs = 2.01*E2Hd = 0.87*E2

LG = GammaItype = 16XG = -0.3873+0.08195*C+0.002234*C^2FG = 1/(1+XG)FX = 1 - FGHs = 1.85*FX*E2 + FG*E2Hd = 0.80*FX*E2 + FG*E2

A > 13.5

LI + GammaItype = 15XG = -2.487 + 0.7897*C - 0.02831*C^2FG = 1/(1 + XG)FX = 1 - FGHs = 1.52*FX*E2 + FG*E2Hd = 1.10*FX*E2 + FG*E2

LIItype = 14Hs = 1.62*E2Hd = 1.13*E2

MFGItype = 18Hs = 1.43*E2Hd = 1.32*E2

LKItype = 17Hs = 1.37*E2Hd = 1.14*E2

MFIItype = 19Hs = 1.39*E2Hd = 1.34*E2

MIDItype = 22Hs = 1.18*E2Hd = 1.11*E2

LG 20 keVLI 29 keVLK 39 keVMFC 36 keVMFG 51 keVMFI 70 keVMID ~120 keV

FUNEL

FUNEL

FUNEL

FUNEL



Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Computer simulation: uncertainties due to dose algorithm - Specifics

Purpose:– To estimate the uncertainties in reported dose of the RPS TLD system for

doses above the determination limits and for various types of radiation Method:

– Irradiate a small group of dosimeters (16 or less) to a certain dose and type of radiation

– Use the element responses of the group and a student t data generator to generate a very large set of test data for input into the dose algorithm (E i = f(t)s + xMean)

– Generate a frequency distribution of the dose values output of the algorithm– Generate frequency distributions of the radiation types identified by the

algorithm– Calculate confidence intervals (indicating the uncertainties) for the deep and

skin dose

Computer simulation: uncertainties due to dose algorithm - Results (continued)

Deep DoseSimulated data (outer limits)

Measured data from small groups (inner limits)

-50

-40

-30

-20

-10

0

10

20

30

40

50

LG

80

0.0

2

LI1

50

0.0

29

LI1

00

0 0

.02

9

MF

G2

40

0.0

51

Am

30

0 0

.06

Am

10

00

0.0

6

MF

I28

0 0

.07

MF

I10

00

0.0

7

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs3

00

0.6

62

Cs4

00

0.6

62

Cs5

00

0.6

62

Cs1

00

0 0

.66

2

Cs4

00

0 0

.66

2

Co

20

0 1

.25

Tl1

00

0.2

4

Tl2

00

0.2

4

Tl1

00

0 0

.24

Sr1

00

0.5

7

Sr1

00

0.5

7

Sr2

00

0.5

7

Sr1

00

0 0

.57

Radiation Type and Energy (MeV)

95

% C

on

fid

en

ce

in

terv

al (%

)

Computer simulation: uncertainties due to dose algorithm - Results (Continued)

Confidence intervals for deep dose

0.0

5.0

10.0

15.0

20.0

25.0

LG

80

0.0

2

LI1

50

0.0

29

LI1

00

0 0

.02

9

MF

G2

40

0.0

51

Am

30

0 0

.06

Am

10

00

0.0

6

MF

I28

0 0

.07

MF

I10

00

0.0

7

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs3

00

0.6

62

Cs4

00

0.6

62

Cs5

00

0.6

62

Cs1

00

0 0

.66

2

Cs4

00

0 0

.66

2

Co

20

0 1

.25

Tl1

00

0.2

4

Tl2

00

0.2

4

Tl1

00

0 0

.24

Sr1

00

0.5

7

Sr1

00

0.5

7

Sr2

00

0.5

7

Sr1

00

0 0

.57


Siz

e o

f c

on

fid

en

ce

in

terv

al (%

)

Small groups

Simulation


Skin DoseSimulated data (outer limits)

Measured data from small groups (inner limits)

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

LG

80

0.0

2

LI1

50

0.0

29

LI1

00

0 0

.02

9

MF

G2

40

0.0

51

Am

30

0 0

.06

Am

10

00

0.0

6

MF

I28

0 0

.07

MF

I10

00

0.0

7

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs3

00

0.6

62

Cs4

00

0.6

62

Cs5

00

0.6

62

Cs1

00

0 0

.66

2

Cs4

00

0 0

.66

2

Co

20

0 1

.25

Tl1

00

0.2

4

Tl2

00

0.2

4

Tl1

00

0 0

.24

Sr1

00

0.5

7

Sr1

00

0.5

7

Sr2

00

0.5

7

Sr1

00

0 0

.57

Radiation Type and Energy (MeV)

95

% C

on

fid

en

ce

in

terv

al (%

)


Confidence intervals for skin dose

0

10

20

30

40

50

60

70

80

90

LG

80

0.0

2

LI1

50

0.0

29

LI1

00

0 0

.02

9

MF

G2

40

0.0

51

Am

30

0 0

.06

Am

10

00

0.0

6

MF

I28

0 0

.07

MF

I10

00

0.0

7

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs2

00

0.6

62

Cs3

00

0.6

62

Cs4

00

0.6

62

Cs5

00

0.6

62

Cs1

00

0 0

.66

2

Cs4

00

0 0

.66

2

Co

20

0 1

.25

Tl1

00

0.2

4

Tl2

00

0.2

4

Tl1

00

0 0

.24

Sr1

00

0.5

7

Sr1

00

0.5

7

Sr2

00

0.5

7

Sr1

00

0 0

.57


Siz

e o

f c

on

fid

en

ce

in

terv

al (%

)

Small groups

Simulation

Computer simulation: uncertainties due to dose algorithm - Results (Final)

The sizes of the 95% confidence intervals calculated from the measured data of the small groups are in some cases unrealistically small

For deep dose the 95% confidence intervals calculated from the simulated data are all smaller than 25%

For skin dose the 95% confidence intervals for photon radiation are all less than 30%, but there is definitely a problem for beta radiation (In part due to mis-identification of the radiation type but primarily because of the high spread in response values of the small groups.)

Computer simulation: uncertainties due to dose algorithm - Conclusions

The computer simulation yields results comparable with the “rough” results of the uncertainty budget, although it must be kept in mind that no input data for different angles of incidence were used

The simulation method can be used effectively to test existing dose algorithms, and to design new algorithms and changes to existing algorithms

The simulation method can be used to identify problem areas in a dose algorithm

The uncertainty in reported dose of a TLD system can be estimated relatively painlessly and quickly from small suitable input data sets by effectively treating the TLD system as a “black box” into which data are fed and which delivers calculated doses and their associated confidence intervals

The simulation method can be used without extensive knowledge of and experience with statistical data analysis

Documents

Estimation of TLD dose measurement uncertainties and thresholds at the Radiation Protection Service Du Toit Volschenk SABS