Concepts of Uncertainty and their Application in Gamma Knife SRS. David J. Schlesinger, Ph.D. University of Virginia

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1 Concepts of Uncertainty and their Application in Gamma Knife SRS David J. Schlesinger, Ph.D. University of Virginia

2 Disclosures Research support: Elekta, AB

3 Learning Objectives Review definitions and concepts of uncertainty as they apply to total treatment uncertainty for SRS Understand the primary sources of uncertainty that must be considered for Gamma Knife SRS procedures Learn some techniques for evaluating total uncertainty and working in-spite of procedural uncertainty.

4 Basic concepts of uncertainty Gamma Knife beam delivery uncertainty Other radiosurgery uncertainty How to work in an uncertain environment

5 Y Measurement error Measurand (true value of quantity being measured) Error: Result of the measurement minus the true value of the measurand X

6 Accuracy: The closeness of the agreement between the result of a measurement and the true value of the measurand. Precision: The closeness of agreement between independent test results obtained under stipulated conditions.

7 Accurate, but not precise Precise, but not accurate Accuracy and precision are NOT interchangeable! Images:

8 Repeatability: Closeness of measurements when measured under identical conditions Reproducibility: Closeness of measurements when measured under changing conditions Both are part of the concept of precision.

9 Precision Resolution Resolution: The range in stimulus that will produce the same indicated output.

10 Uncertainty: Parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand.

11 Add (independent) uncertainties in quadrature An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2 nd Edition J. R. Taylor, University Science Books, 1997

12 A very basic uncertainty budget Source of Uncertainty resolution alignment temperature repeatability ruler calibration Combined standard uncertainty Expanded uncertainty (k=2, 95% confidence) Standard Uncertainty (1 standard deviation) mm mm mm mm mm mm mm Adapted from:

13 Basic concepts of uncertainty Gamma Knife beam delivery uncertainty Other radiosurgery uncertainty How to work in an uncertain environment

14 Why is understanding treatment uncertainty important? Collimator 16mm 8mm 4mm Distance from 50% to 25% isodose line (axial) 4.6mm 2.0 mm 1.3 mm Gamma Knife 4mm isocenter Source: Leksell GammaPlan version 10.1

15 Change in obliteration probability (AVMs) Change in control probability (mets) Impact of target point deviations on control and complication probabilities in stereotactic radiosurgery of AVMs and metastases. Treuer H, Kocher M, Hoevels M, et al. Radiother Oncol Oct;81(1): Epub 2006 Sep 26.

16 Radiosurgery chain of uncertainty Dosimetric calibration Dose calculation Mechanics 3D Imaging Target definition Biological model Patient positioning Target localization A. Mack, H. Czempiel, H-J Kreiner, et. al., Med Phys 29(4), 2002

17 Gamma Knife Perfexion Patient Positioning System Shielding doors 60 Co sources Shielding Collimator Body Sector Drives

18 Heidenhain linear encoders Resolution: 0.01 µm Accuracy over entire length of scale: ± 5 µm THK rotational encoders 2000 pulses per rotation Pitch on sector screws is 1mm Resolution: 0.5 µm

19 Sector Position Calibration d Linear and rotational encoders both monitor sector position Outer 4mm beam channels mechanically aligned with source bushing location in sector Procedure is performed at the factory for every beam channel and for every sector

20 Patient Positioning System (PPS) Mechanical calibration of orthogonality of movements of bed Creation of compensation curves for orthogonality of movements once mated Calibration Laser interferometer verifies calibration of absolute positioning (<0.01mm absolute accuracy) Mechanical interface

21 How is this validated? Normalized Diode signal Center of Profile Leksell X [mm] Master diode calibrated at reference unit at Timone Hospital, Marseille Center diode < 0.08 mm repeatability at installation Site-diode tool (Focus Precision Tool) calibrated offset to master Manufacturer tolerance for monthly test < 0.5 mm radial

22 Mechanical Specifications Specification Tolerance Source RFP vs PPS (master diode, center target, 4mm isocenter) RFP vs PPS (master diode, center target, 8/16 mm isocenter) RFP vs PPS (master diode, off-center target, 4mm isocenter) <0.15mm (0.08 mm at installation) <0.2mm <0.4mm Preventive maintenance procedures Preventive maintenance procedures Preventive maintenance procedures RFP vs PPS (site diode) <0.5mm Perfexion user s manual Film RFP vs PPS Sector positions <0.3mm per axis, <0.4mm radial, at 50% line <0.1mm, all sectors/sector positions Acceptance procedures Preventive maintenance procedures

23 What do we achieve in practice? Control limit (3σ) determined from first 5 measurements

24 SU GG T 279: Current Practice in Small Radiosurgery Field Dosimetry Preliminary Results from 21 Centers Participating in the International Leksell Gamma Knife Calibration Survey J Novotny, Jr., M Desrosiers, J Bhatnagar, et. al. Med Phys 37(6), 2010 Output Calibration Uncertainty NO calibration standard! Various centers use TG-21, TG-51, IAEA TRS-277, IAEA TRS 398 Elekta-provide polystyrene(?) phantom, solid water phantom, custom phantom Various ion chambers

25 Source reload Change in Phantom NRC 10CFR 35 output ±3% Protocol: TG-51* Chamber: PR-05P Phantom: Elekta spherical (polystyrene) IROC OSLD Ratio: 2012: : 1.01 *with modified assumptions

26 Frame and Docking Uncertainty Frame mechanical uncertainty: mm (mostly in pin fixation) Frame adapter x play: <0.15 mm Frame adapter angle play: <60 µm Frame adapter deflection: mm Leksell Gamma Knife Perfexion Planned Maintenance Manual L. Lunsford, D. Kondziolka, D. Leksell, in Textbook of Stereotactic and Functional Neurosurgery, 2009.

27 Fiducial Registration Uncertainty Worst-case image registration error mean (max): 0.1mm (1.4mm) Resulting localization error mean (max): 0.0 mm (0.2 mm) J-H Park, J. H. Han, C-Y Kim, et al., Med Biol Eng Comput, 2011

28 Co-registration uncertainty MR/CT results Comparison and Evaluation of Retrospective Intermodality Brain Image Registration Techniques, West, et al., J. of Computer Assisted Tomography, 21(4), 1997

29 Small-Field Uncertainty 4mm/18mm output factor, by detector type and study Determination of the 4 mm Gamma Knife helmet relative output factor using a variety of detectors B. Heck, A. Jess-Hempen, H. Kreiner, H. Schöpgens, A. Mack Med Phys 37(6), 2010

30 TMR dose algorithm uncertainty Electronic disequilibrium at air interface Dose away from cavity is underattenuated, so overdose regions further from cavity In most cases, this isn t an issue Moskvin, et al., Monte Carlo simulation of the Leksell Gamma Knife: II. Effects of heterogeneous versus homogeneous media for stereotactic radiosurgery, Phys Med Bio 49(21), But.now there is a convolution option!

31 Skull Contour Uncertainty Peripherally-located targets most effected Effect of skull shape approximations in Gamma Knife dose calculations A. Berndt, J. Beck J. Appl Clin Med Phys 8(3) Shot time differences of up to 4% (most less than 1%)

32 Basic concepts of uncertainty Gamma Knife beam delivery uncertainty Other radiosurgery uncertainty How to work in an uncertain environment

33 Localization uncertainty Modality Radial Deviation (mean ± STD) (mm) CT 0.4±0.2 *MR (T1- weighted) *MR (T2- weighted) 1.4± ±0.5 PET 1.1±0.5 SPECT 1.6±0.5 *Siemens Magnetom Symphony Siemens CTI ECAT EXACT HR Siemens MULTISPECT 3 Stereotactic imaging for radiotherapy: accuracy of CT, MRI, PET, and SPECT C.P. Karger, P. Hipp, M. Henze, G. Echner, et al. Phys Med Biol 48, 2003.

34 Contouring uncertainty Modality Ratio Largest:Smallest volume (for each of 5 patients) CT 2.8, 1.8, 1.8, 1.9, 1.7 MR + CT 2.4, 1.7, 1.9, 2.7, patients, 9 observers Interobserver variations in gross tumor volume delineation of brain tumors on computed tomography and impact of magnetic resonance imaging C Weltens, J Menten, M Feron Radiotherapy and Oncology 60, 2001

35 Timing of contrast injection can have significant effects on GTV definition Br J Radiol. 77, 2004 Delineation of brain metastases on CT images for planning radiosurgery: concerns regarding accuracy K. Sidhu, P Cooper, R. Ramani, et. al. Mean delay: 65 min 92% would select larger collimator sizes

36 Radiobiological Uncertainty Overall, LQ model underpredicts SRS biological effect But, in-vitro cell survival data leads to predicted doses below those used clinically. Microvascular damage has been shown to occur at doses > 10Gy. SRS biological effect may involve DNA damage + vascular damage The Linear-Quadratic Model is Inappropriate to Model High Dose per Fraction Effects in Radiosurgery J. Kirkpatric, J. Meyer, L.B. Marks

37 Patient-specific outcome uncertainty Radiation necrosis Pre-SRS 4 months post R. Shah, et al, RadioGraphics 32(5), months post

38 Basic concepts of uncertainty Gamma Knife beam delivery uncertainty Other radiosurgery uncertainty How to work in an uncertain environment

39 End to End Tests Quality assurance in stereotactic space: A system test for verifying the accuracy of aim in radiosurgery A. Mack, H. Czempiel, H-J Kreiner, et. al. Med Phys 29(4), 2002

40 Gross Tumor Volume (GTV) Known (imagingevident) tumor Clinical Target Volume (CTV) uncertainty in tumor extent Internal Target Volume (ITV) uncertainty in size/ shape/position (due to motion) Planning Target Volume (PTV) uncertainty in setup and delivery Margins GTV PTV ITV CTV OAR ICRU Report 62 SRS violates margin formula assumptions! PRV Organ at Risk (OAR) Known organ at risk Planning Organ at Risk Volume (PRV) accounts for positional uncertainties

41 Summary Conclusion Scope and terminology are critical considerations when describing treatment uncertainty There are MANY potential sources of uncertainty in an SRS procedure One consequence of summing in quadrature is smaller sources of uncertainty drop out: Understand your largest sources of uncertainty!

42 Selected References Metrology and Uncertainties Gum, I. S. O. "Guide to the expression of uncertainty in measurement." BIPM, IEC, IFCC, ISO, IUPAP, IUPAC, OIML (1995). Gamma Knife Beam Delivery Uncertainties Leksell Gamma Knife Perfexion Planned Maintenance Manual, Elekta, AB J. Park, et. al, Application of the gamma evaluation method in Gamma Knife film dosimetry, Med Phys 38(10), Mack, Quality assurance in in stereotactic space. A system test for verifying the accuracy of aim in radiosurgery, Med Phys 29(4), Moskvin, et al., Monte Carlo simulation of the Leksell Gamma Knife: II. Effects of heterogeneous versus homogeneous media for stereotactic radiosurgery, Phys Med Bio 49(21), 2004.

43 Acknowledgements Elekta Stockholm: Håkan Nordstöm, Jonas Johansson, Peter Fröberg, Per Carlsson UC Davis: Sonja Dieterich

44 Uncertainty is a parameter which describes. 50% 1. a distribution of measurements around a measurand 29% 9% 6% 6% 2. the difference between measurement and measurand 3. the closeness of successive measurements 4. the resolution of a measurement instrument 5. the effect of changing experimental conditions

45 Answer Uncertainty is a parameter which describes. 1. A distribution of measurements around a measurand. Source: JCGM 100:2008. Evaluation of measurement data Guide to the expression of uncertainty in measurement, Joint Committee for Guides in Metrology.

46 The focus precision (diode) test for the Gamma Knife Perfexion should be reproducible to less than. 7% mm 10% mm 57% mm 24% mm 2% mm

47 The focus precision (diode) test for the Gamma Knife Perfexion should be reproducible to less than mm Answer Source: Leksell Gamma Knife Perfexion, Instructions for Use, Elekta, AB

48 A study by Mack, et. al. of 170 hidden target tests found a mean targeting accuracy of. 1% mm 13% mm 61% mm 12% mm 13% mm

49 Answer A study by Mack, et. al. of 170 hidden target tests found a mean targeting accuracy of mm Source: A. Mack, H. Czempiel, H-J Kreiner, et. al., Quality assurance in stereotactic space: A system test for verifying the accuracy of aim in radiosurgery, Med Phys 29(4), 2002

50 Concepts of Uncertainty and their Application in Gamma Knife SRS David J. Schlesinger, Ph.D. University of Virginia

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