Larry A. DeWerd, PhD, FAAPM UW ADCL & Dept. Medical Physics University of Wisconsin

Transcription

1 Larry A. DeWerd, PhD, FAAPM UW ADCL & Dept. Medical Physics University of Wisconsin NCCAAPM meeting April 17, 2015

2 Larry DeWerd has partial interest in Standard Imaging Inc.

3 Determination of your uncertainty with TG 51 addendum Presented the TG 51 addendum last October. Short review of TG 51 addendum Uncertainty determination

4 What are reference class ionization chambers %dd(10) is used for k Q No lead foil to be used anymore caused errors. Use eq. 15 in TG 51 Use of small volume chambers in relative dosimetry

5 Majority are 0.6 cm 3 Farmer-type chambers A-150 chambers explicitly excluded 5 scanning chambers, NO microchambers (Exception A26 from some preliminary measurements. Long term to come) No parallel plate chambers are included

6 A. k Q factors for new chambers B. Comparison of measured and calculated k Q factors: Measured k Q data is available for some types of chambers C. Non-water phantoms only water for dosimetry D. Uncertainty analysis for implementation of TG-51

7 1. TG-51 made the deliberate decision not to include uncertainties. 2. Other protocols have included uncertainty budgets and/or detailed reviews of uncertainty components. 3. TG 51 addendum gives some guidance on: i. How to develop an uncertainty budget ii. Typical values for individual components. 4. The ISO GUM is the starting point or NIST publication

8 Uncertainty tables and determinations are important for the goodness of your measurements. Uncertainty gives an indication of where you would expect your measurements to fall each time you measure it. Uncertainty is larger than precision of measurement

9 Systematic errors: Results from a bias on part of observer or a faulty calibration of equipment. Random errors: Fluctuations in observations. Generally a standard deviation can account for these. Reduce all sources of error. Now use Type A (random) and Type B Errors are truly errors something done wrong

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11 Accuracy and Precision Accurate but not precise Precise but not accurate Precise and accurate

12 1 0.9 primary standard measurement frequency of result clinical measurement conventional true value a.u.

13 Today possible variation in readings are given by uncertainties. The difference between the measured value - measurand - and the conventional true value is generally never zero. There are uncertainties involved in the measurement that can be expressed. Uncertainty is a methodology to express the goodness of the value as to its accuracy.

14 The uncertainty associated with a measurement characterizes the dispersion of values that can be reasonably associated with the measurand. What is the difference between uncertainty, precision and accuracy or the error in measurement?

15 Type A and Type B uncertainties are used Type A uncertainty is estimated by the standard deviation of the mean value. These are measured results. Any valid statistical method for treating data can be used for Type A uncertainties

16 Type B is based on scientific judgment using all relevant information available such as: previous measurement data experience or general knowledge of behavoir of instruments used manufacturers specifications data of calibration or other reports uncertainties assigned to reference data taken from handbooks.

17 A limit(confidence interval) is generally used for Type B, designated by k. For Guassian distributions, If we are certain that the value lies between + L then 99% lie here and the confidence limit is designated by k. For 99% k=3. Express L in %, call it L % The uncertainty is then u=l % /k and expressed in a %. For 95%, k=2 and for 66% k=1

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19 Also can assume some type of probability distribution, e.g. rectangular or triangular Rectangular - all values fall within these maximum limits, +M (express in %) then u=m/ 3. For example, this is used when a manufacturer gives maximum limits for a parameter, such as the range of the calibration extends from 4.7 to 5.3. (3.5%)

20 Triangular is when all values fall with limits of + M, but the values are more weighted toward the central value. All values do not have equal probability. Then the uncertainty is estimated by u=m/ 6 This isn t used as much. Manufacturer may say: the general value is centered at 5, with a range from 4.7 to 5.3 Triangular would be value is 5.0, with some outliers at 4.7 to 5.3 Then 2.4%

21 Procedure is outlined in NIST Technical Note 1297 (1994) Each uncertainty component is propagated sequentially throughout the measurement pathway by quadrature summation: Square root of sum of squares for k=1

22 Generally the symbol u is used Say you measure a quantity a number of times and the standard deviation of the measurement is + 0.5% Therefore your type A uncertainty for this measurement is u A =+ 0.5% (precision of measurement)

23 Uncertainties in % are combined as u c =(u A2 + u B2 ) 1/2 Therefore in a simple example, we have u c =( ) 1/2 = (8.66) 1/2 ~ 2.92% Note that the greatest uncertainty governs the overall uncertainty So at k=2, total uncertainty is 5.84%

24 Standard Uncertainty: Expected range of values that are attributed to a measured quantity (source strength) Expanded Uncertainty: Defined here as the Standard Uncertainty multiplied by a coverage factor of 2. This corresponds to a coverage probability or confidence level of approximately 95%

25 The uncertainty in the laboratory from all aspects of your measurement are determined. - all possible contributions Make your best estimate. You can list your best (lowest) uncertainty and your worst (highest) uncertainty.

26 The calibration of the chamber progresses from NIST through the ADCL to the clinic. The traceability to NIST is given by the ADCL as 0.7% at k=1 u total u 2 clinic u 2 ADCL ADCL uncertainty tables available if necessary

27 Further treatment of Uncertainty AAPM Summer School 2009

28 NIST has produced an explanatory document (a guide to the Guide) - NIST Technical Note 1297 Uncertainty budget broken down into: Measurement Calibration data Influence quantities Typical values discussed but emphasis on individual users constructing site-specific uncertainty budgets for their calibration situations

29 Want to take into account your measurement process Values and quantities are representative. You need to determine your clinic values Start with dose measurement.

30 TG 51 gives a measure of the absorbed dose to water using an ADCL calibrated ion chamber. D N 60 Co k M w,q D,w Q ion k Q is the factor that converts from the calibration beam ( 60 Co) to the user linac beam, defined by beam quality Q

31 Quantity Type A Type B Comment Calibration N Dw ADCL 0.7% ADCL Traceability to NIST uncertainty k Q 0.4% Picking Maximum P elec 0.1% Correction for charge reading for M corr

32 M corr,w M raw P TP P ion P pol P elec Each of these parameters have an uncertainty associated with them. There is also an uncertainty involved in the setup, which we will deal with as yet.

33 Many times the manufacturer of the barometer (thermometer) will give a response range, e.g. +0.5%. Assume a rectangular distribution % Keep in mind the equation for TP correction. Generally most clinics have a 0.1% k=1 for P TP

34 Uncertainty components examples Temperature Pressure correction P TP T w P air For T in C, P in kpa Need water temperature at ion chamber: Water should be in equilibrium with room Ion chamber should be in equilibrium with water P TP does not take account of thermal expansion of thimble Need air pressure in air volume: Only realistic to measure room air pressure Need to confirm air communication of ion chamber (ADCL)

35 Thermal equilibration Chamber at 22 C placed in water at 10 C Equilibration is pretty quick, but not instantaneous Reference: Das and Zhu (Med. Phys., 2004)

36 Quantity Type A Type B Comment Influence Quantities P TP 0.10 Clinic Measurement of P TP P Pol 0.05 Measurement P ion 0.10 Measurement P leak 0.05 If present Pre irrad leak 0.10 If present

37 M raw M(x,y,z,SSD,FS) Wherever the chamber actually is positioned and whatever the actual geometry, M will be assigned to: x = y = 0 cm (on axis) z = 10 cm (d ref ) SSD = 100 cm (assuming SSD setup) Field size = 10 cm x 10 cm By writing the equation out this way we identify the influence quantities, and therefore uncertainty components Uncertainty analysis is also a procedural review

38 Quantity Type A Setup Parameters SSD Setting 0.10 Depth Setting Linac Stability Type B Comment If not measured, then type B estimated 0.25 If not measured, then type B estimated 0.10 If not measured, then type B estimated

39 Quantity Type A Type B Calibration 0.81 Influence 0.19 Quantities Setup 0.29 Parameters Combined uncertainty Comment 0.88% combined uor Relative Expanded u= 1.76%

40 The majority of the uncertainty comes from the calibration. What does this say to you You can measure with better precision than this. Your overall accuracy to the conventional true value is confident to 1.76% - or 1.8%

41 Thanks are due to Students and staff of the UW ADCL All those who send us calibration instruments that support the research program of the UW Medical Radiation Research Center.