Appendix A Numbers, Formulas, and Normal Range of Values Numbers 1. Radiation Safety The table below describes common radiation exposure limits. Occupational exposure limits Whole body 5 rem (50 mSv)/year Skin or any extremity 50 rem (500 mSv)/year Any organ or tissue 50 rem (500 mSv)/year Lens of eye 15 rem (150 mSv)/year Fetus of radiation worker 0.5 rem (5 mSv)/year General public exposure limits Whole body 0.1 rem (1 mSv)/year Steves and Wells (2004) 2. Department of Transportation (DOT) Labels Department of Transportation regulates the shipment of the radioactive materials; therefore, appropriate labels must be affixed to radioactive shipment packages. Exposure rate at the package Exposure rate at 1 m from the Class surface cannot exceed (mR/h) package cannot exceed (mR/h) Radioactive I (white) 0.5 No detectable radiation Radioactive II (yellow) 50 1 Radioactive III (yellow) 200 10 Steves and Wells (2004) A. Moniuszko and D. Patel, Nuclear Medicine Technology Study Guide: A Technologist’s 241 Review for Passing Board Exams, DOI 10.1007/978-1-4419-9362-5, © Springer Science+Business Media, LLC 2011 242 Appendix A 3. Radiation Signs • Caution: Radioactive Materials – Posted in area where radioactive materials are stored and exceed the limit of 2 mR/h (millirem per hour) or 0.02 mSv/h (millisievert per hour) • Caution: Radiation Area – Posted where one can receive more than 5 mR/h (0.05 mSv) at 30 centime- ters (cm) • Caution: High Radiation Area – Posted where one can receive more than 100 mR/h (1 mSv) at 30 cm • Grave Danger: Very High Radiation Area – Posted in the front of area where one can receive more than 500 rads (5 grays) in 1 h at 1 m from the radiation source Steves and Wells (2004) 4. Radiopharmacy • Reactor produced isotopes: – Mo-99/Tc-99m, I-131, I-125, Xe-133, Cr-51, Sr-89, Sm-153, and P-32 • Accelerator produced radionuclides: – I-123, Ga-67, Tl-201, In-111, and all positron emitters • Molybdenum limits per millicurie of technetium: – Amount of Mo-99 (molybdenum) per mCi (millicurie) of Tc-99m (Technetium) allowed is ≤0.15 mCi (microcurie) • MAA particles: – Size of the MAA particles should be 10–90 μm and recommended parti- cles for adult dose is 200,000–700,000 • Sulfur colloid particles: – Sulfur colloid particles for the liver–spleen scan should be at size 0.01–1 μm Steves and Wells (2004) Appendix A 243 5. Half-Life and Energy of Radioisotopes Half-life and energy of the commonly used radioisotopes are critical and should be memorized for the exam. Isotope Half-life Energy (keV, kiloelectron volt) Tc-99m 6 h 140 Tl-201 73 h 68, 81 In-111 2.83 days 173, 247 Xe-133 5.3 days 81 F-18 110 min 511 Co-57 270 days 122 I-123 13.2 h 159 I-125 60 days 35 I-131 8 days 365 Ga-67 78 h 92, 184, 300 Steves and Wells (2004) Positron emitters Isotope Half-life Rb-82 75 s O-15 2.1 min N-13 9 min C11 20 min F-18 110 min Christian et al. (2004) 6. Decay Scheme The table below describes the decay scheme with arrow and the change in atomic number (Z) during the decay process. Schemes of decay Arrow description Atomic number change(Z) Alpha (a) Arrow going downward left Decreased by two (−2) Beta (ß−) Arrow going downward right Atomic number increased by one (+1) Beta (ß+) (positron) Arrow going downward left Decreased by one (−1) Electron capture (EC) Arrow going downward left Decreased by one (−1) Gamma emission (g) Arrow going downward straight No change in atomic number Christian et al. (2004) 244 Appendix A 7. Quality Control of Dose Calibrator The quality control of dose calibrator, type of the test, frequency, and description of tests are given in the following table. Type of testa Rate of recurrence Reason of the test Constancy Daily before use To check the reproducibility of dose calibrator by the source of the known activity from day to day Linearity Quarterly To check the ability of dose calibrator to measure the wide range of activity from millicurie (mCi) to microcurie (mCi) amounts Accuracy Annually To check the ability of dose calibrator to measure the different levels of gamma energy (100–500 keV) Geometry At installation Test for the measurement of activity as the volume of radioactive source changes Steves and Wells (2004) a All tests should be performed after installation of the new equipment, after adjustment, and after repair 8. Quality Control of Scintillation Camera Quality control of scintillation camera varies upon camera manufactures’ recom- mendation. The following table describes the tests, frequency of occurrence, and reason for the test. Type of testa Frequency of the test Description Field uniformity Daily Ability of the detector to produce uniform image when source provides uniform photon distribution Spatial resolution Weekly Ability of the detector to distinguish small objects in space Spatial linearity Weekly Ability of the detector to depict true straight line, corresponding straight line in phantom (actual depiction of true organ) SPECT center of Weekly or monthly Used to correct slight variation in the detector rotation (COR) position as it rotates Steves and Wells (2004) a These tests should be performed after repair or preventative maintenance Testing frequencies are recommended by the camera manufacturer Appendix A 245 9. Unit Conversions A. Conversion from Ci (curie) to mCi (millicurie) to mCi (microcurie), and GBq (gigabecquerel) to MBq (megabecquerel) to kBq (kilobecquerel) • 1 Ci = 1,000 mCi = 1,000,000 mCi • 1 GBq = 1,000 MBq = 1,000,000 kBq B. Conversion between Ci and GBq • 1 Ci = 37 GBq = 37,000 MBq = 37,000,000 kBq • 1 GBq = 0.027 Ci or 27 mCi or 27,000 mCi • 1 Bq = 2.7 × 10−11 Ci C. Conversion between rad (radiation absorbed dose) and gray (Gy) • 1 Gy = 100 rad = 10,000 mrad • 1 rad = 0.01 Gy = 0.0001 mGy D. Conversion of Sievert and rem (roentgen equivalent in man) • 1 Sv = 100 rem • 1 rem = 0.01 Sv E. Conversion between pound and kilogram • 1 lb = 0.45 kg • 1 kg = 2.2 lb F. Conversion of length • 1 ft = 12 in. = 30.5 cm Wells and Martha (1999) Formulas 10. Calculation of Percent Error or Percent Difference A. Percentage error or percentage difference Expected− Actual Percent error or percent difference 100% • =×Expected B. Correction factor Expected activity • Correction factor = Actual activity Wells and Martha (1999) 11. Net Counts Net counts = Gross counts − Background counts Wells and Martha (1999) 246 Appendix A 12. Standard Deviation of Series of Values ()nn− 2 • SD = ∑ N −1 – ∑ = symbol of sum, meaning value following this needs to be summed Sum of all values – Mean = Total number of values – n = mean of value – n = individual value – N = total number of values 13. Standard Deviation for a Single Value • CI = confidence interval • n = the single value • 68% confidence interval (±1 standard deviation): CI68% =±nn or CI68% =±n 1 SD • 95% confidence interval (±2 standard deviation): CI95% =±nn 2 or CI95% =±n 2 SD • 99% confidence interval (±3 standard deviation): CI99% =±nn 3 or CI99% =±n 3 SD Wells and Martha (1999) 14. Percentage Error of Single Value or (%SD) Standard deviation or confidence interval 100% %68 SD = • N (2) (100%) • %95 SD = N (3) (100%) • %99 SD = N Wells and Martha (1999) a Use these above formulas to calculate minimum counts required to determine % error at a given confidence level. Where (N) = number of counts. The level most commonly used in nuclear medi- cine is 95% Wells and Martha (1999) Appendix A 247 15. How to Convert Counts Per Minute (cpm) to Disintegration Per Minute (dpm) Using Well Counter Efficiency Gross cpm− Background cpm • dpm = Efficiency expressed as decimal – Simply convert given efficiency in % to decimal, dividing by 100 Wells and Martha (1999) 16. Inverse Square Law 22 • (ID11)( ) = ( ID 2)( 2) – I1 = intensity at original distance D1 – I2 = intensity at newer distance D2 Wells and Martha (1999) 17. How to Calculate Change in Exposure Rate due to Shielding −(0.693)(x /HVL) • II= Oe – I = exposure rate being calculated – Io = original exposure rate – e = 2.718 constant know as Euler’s number – x = thickness of the shielding material – HVL = half-value layer for a given shielding material Wells and Martha (1999) 18. Effective Half-Life TTPb× • Te = TTPb+ – Te = effective half-life – Tp = physical half-life – Tb = biological half-life Wells and Martha (1999) 248 Appendix A 19. Energy Resolution (Full-Width at Half-Maximum) FWHM in keV • % Energy resolution =×100% Energy of radionuclide in keV Maximum counts – Half maximum = 2 – FWHM = Upper limits − Lower limits in keV Wells and Martha (1999) 20. Chi-Square Value ()nn− 2 • c 2 = ∑ n 2 – c = chi-square – n = individual values – n = mean value – N = number of value used – SD = standard deviation – Degree of freedom = N − 1 where N = number of values used Wells and Martha (1999) 21. Well Counter Efficiency Counts per unit of time (cpm or cps) • % Efficiency =×100% (Disintegration per unit time)(Mean number per disintegration) Wells and Martha (1999) 22. How to Calculate Energy Window for Pulse Height Analyzer and Percentage Dose Range A. Energy window • Energies within windows = Energy in keV ± Energy in keV× Percentage window as decimal 2 B. Acceptable dose range • Acceptable dose range = dose amount ± dose amount × percentage as decimal Wells and Martha (1999) Appendix A 249 23. Gamma-Camera Sensitivity Source cpm− Background cpm • Sensitivity as cpm /m Ci = Source activity in mCi Wells and Martha (1999) 24.