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Cyclotron-based production of radioisotopes for medical imaging studies Hou, Xinchi 2014

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    CYCLOTRON-BASED PRODUCTION OF RADIOISOTOPES FOR MEDICAL IMAGING STUDIES  by Xinchi Hou  M.Sc., The Liaoning University, 2009 B.Sc., The Liaoning University, 2006      A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in  THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES  (Physics)    THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  October 2014  © Xinchi Hou, 2014  ii Abstract The cyclotron-based 100Mo(p,2n)99mTc reaction has been proposed as an alternative method for solving the recent shortage of 99mTc, which is the most commonly used radioisotope in nuclear medicine. With this production method, however, even if highly enriched molybdenum is used, various radioactive and stable isotopes can be produced simultaneously with 99mTc and they may affect the diagnostic outcome and radiation dosimetry in human studies. The objective of this thesis was to investigate the feasibility of the cyclotron-based production of 99mTc. Towards this aim, theoretical predictions and experimental measurements were performed to investigate the quantity and purity of cyclotron-produced technetium. In this thesis, the production cross sections and yields of cyclotron-produced 99mTc and various other radioactive and stable isotopes were calculated. Radiation doses from three radiopharmaceuticals labeled with cyclotron-produced technetium were estimated. Different conditions were considered for both yield and dosimetry calculations in order to investigate the optimal reaction parameters for producing maximum 99mTc and minimizing other contaminants. To facilitate the complex and time-consuming calculations, a graphical user interface was developed allowing users to perform the theoretical predictions in only a few seconds.  Besides theoretical estimations, quantitative experimental measurements of 99mTc samples were performed. Gamma spectra from different cyclotron runs were analyzed. In order to investigate the image qualities for using cyclotron-produced   iii technetium, phantom scans for both cyclotron- and reactor-produced 99mTc at different times after end of beam were performed using SPECT. Large quantities of produced 99mTc proved the capability of cyclotron production of 99mTc. Both theoretical predictions and experimental analysis showed over 9 Ci of 99mTc can be produced in a 6 hours cyclotron run when using enriched 100Mo target. Besides 99mTc, the main contributors, which influenced the production activities, patient doses and quality of images, were 94g-96gTc. These results indicated the molybdenum target used in cyclotron production should have relatively small content of 95-97Mo, which are the “reaction parents” for 94g-96gTc. Furthermore, we demonstrated that incident proton beam energies in the range of 16-19 MeV, target thicknesses degrading beam energy to 10 MeV and relatively short irradiation times (3-6 hours) corresponded to the most advantageous region for 99mTc production.   iv Preface A version of Chapter 2 was published in the journal of Physics in Medicine and Biology in 2011: Celler A, Hou X, Bénard F and Ruth T. (2011) Theoretical modeling of yields for proton-induced reactions on natural and enriched molybdenum targets. Phys. Med. Biol. 56: 5469-5484. In this study, I was responsible for all the calculations and data analysis and I was involved in writing the manuscript. The work presented in Chapter 3 was published as a paper: Hou X, Celler A, Grimes J, Bénard F and Ruth T (2012) Theoretical dosimetry estimations for radioisotopes produced by proton-induced reactions on natural and enriched molybdenum targets. Phys. Med. Biol. 57: 1499-1515. I performed the data analysis and wrote most of the manuscript with contributions from Dr. Anna Celler and other co-authors. A version of Chapter 4 has been published as: Hou X, Celler A, Vuckovic M, Buckley K, Bénard F, Schaffer P and Ruth T (2014) Graphical user interface for yield and dose estimations for cyclotron-produced technetium. Phys. Med. Biol. 59: 3337-3352. I developed the software described in this work and wrote the manuscript. The cyclotron experiments for the work described in Chapter 5 were performed by the collaborators in BC Cancer Agency, Canada. The details of cyclotron experiments and the results was published as: Bénard F, Buckley K, Ruth T, Zeisler S, Klug J, Hanemaayer V, Vuckovic M, Hou X, Celler A, Appiah J, Valliant J,   v Kovacs M and Schaffer P. (2014) Implementation of multi-curie production of 99mTc by conventional medical cyclotrons. J. Nucl. Med 55:1017-1022. I performed the data analysis based on the gamma spectrum measurements from BC Cancer Agency. Furthermore, the work described throughout this thesis has been presented at several conferences including: the 2010 IEEE Medical Imaging Conference in Knoxville, USA; the 2011 joint meeting of the American Association of Medical Physicists and the Canadian Organization of Medical Physicists in Vancouver, BC ; the 2013 European Association of Nuclear Medicine Congress in Lyon, France; the 2013 IEEE Medical Imaging Conference in Seoul, South Korea and the 2014 Canadian Chemistry Conference and Exhibition in Vancouver, Canada.    vi Table of Contents Abstract ........................................................................................................................................ ii Preface ......................................................................................................................................... iv Table of Contents ..................................................................................................................... vi List of Tables ............................................................................................................................. ix List of Figures .......................................................................................................................... xiv List of Abbreviations ............................................................................................................ xxi Acknowledgements ............................................................................................................. xxii Dedication ............................................................................................................................. xxiii Chapter 1 Introduction ........................................................................................................... 1 1.1 Aim ..................................................................................................................................... 1 1.2 Outline of dissertation ................................................................................................. 2 1.3 Background review ...................................................................................................... 4 1.3.1 Nucleus ................................................................................................................................... 4 1.3.2 Radioactive decay ............................................................................................................... 6 1.3.2.1 Radioactive decay mode .......................................................................................... 6 1.3.2.2 Radioactive decay formulae ................................................................................... 8 1.3.3 Radioisotopes used in nuclear medicine ................................................................... 9 1.3.4 Production of radioisotopes ........................................................................................ 11 1.3.5 Radioisotope of 99mTc .................................................................................................... 13 1.3.5.1 Traditional method for 99mTc production ...................................................... 15 1.3.5.2 Shortage of 99mTc and its alternative production methods .................... 16 Chapter 2 Theoretical Yields Estimations ..................................................................... 21 2.1 Cyclotron-produced 99mTc ....................................................................................... 21 2.2 Aim of this chapter ..................................................................................................... 23 2.3 Physics concepts of cyclotron reactions............................................................. 24 2.3.1 Cross sections and yields of cyclotron products ................................................. 24   vii 2.3.2 Stopping power ................................................................................................................ 27 2.4 Methods ......................................................................................................................... 29 2.4.1 Theoretical cross section calculations..................................................................... 29 2.4.2 Reaction yield formulae ................................................................................................ 30 2.4.3 Calculation parameters ................................................................................................. 34 2.5 Results ............................................................................................................................ 35 2.5.1 Results of the cross section calculations ................................................................ 35 2.5.2 Reaction yields results ................................................................................................... 41 2.6 Discussion ..................................................................................................................... 48 2.7 Summary ....................................................................................................................... 50 Chapter 3 Theoretical Dosimetry Estimations ............................................................ 51 3.1 Introduction ................................................................................................................. 51 3.2 General concepts of NM dosimetry ...................................................................... 53 3.2.1 Definition of dose ............................................................................................................ 53 3.2.2 Dosimetry estimations in NM ..................................................................................... 54 3.2.3 Cumulated activity and effective half-life .............................................................. 55 3.3 Dosimetry estimation method ............................................................................... 57 3.3.1 Productions of technetium isotopes used in dosimetry estimations .......... 57 3.3.2 Dosimetry estimations .................................................................................................. 58 3.4 Results ............................................................................................................................ 59 3.5 Discussion ..................................................................................................................... 70 3.6 Summary ....................................................................................................................... 75 Chapter 4 Graphical User Interface-CYD ....................................................................... 76 4.1 Introduction ................................................................................................................. 76 4.2 Description of the GUI functions ........................................................................... 77 4.2.1 CYD - yield calculation layer ........................................................................................ 78 4.2.2 CYD - gamma spectrum analysis layer .................................................................... 84 4.2.3 CYD - dosimetry estimation layer ............................................................................. 86 4.3. Results ........................................................................................................................... 90 4.3.1 Example of results from yield calculation layer .................................................. 90   viii 4.3.2 Example results from spectrum analysis layer .................................................... 91 4.3.3 Example results from dosimetry estimation layer ............................................. 93 4.4 Discussion ..................................................................................................................... 93 4.5 Summary ....................................................................................................................... 96 Chapter 5 Quantitative Activity Measurements .......................................................... 97 5.1 Gamma-ray spectrometry ....................................................................................... 97 5.1.1 Mechanisms of gamma interaction ........................................................................... 98 5.1.2 Gamma spectrum ........................................................................................................... 100 5.1.3 Detection of gamma spectrum ................................................................................. 102 5.1.4 Activity determination ................................................................................................ 105 5.2 Method ......................................................................................................................... 107 5.3 Results .......................................................................................................................... 110 5.4 Discussion ................................................................................................................... 113 5.4 Summary ..................................................................................................................... 116 Chapter 6 SPECT Imaging Studies of Cyclotron-produced 99mTc ........................ 117 6.1 Single photon imaging system ............................................................................. 117 6.1.1 Structure of gamma camera ...................................................................................... 118 6.1.2 SPECT ................................................................................................................................. 121 6.2 Phantom imaging experiments ........................................................................... 123 6.3 Results .......................................................................................................................... 126 6.4 Discussion ................................................................................................................... 129 6.4 Summary ..................................................................................................................... 131 Chapter 7 Conclusion and Future Work ...................................................................... 132 7.1 Conclusions ................................................................................................................ 132 7.2 Future work................................................................................................................ 134 Bibliography .......................................................................................................................... 136    ix List of Tables Table 1–1. Radioactive decay modes............................................................................................... 7 Table 1–2 Production methods of radioisotopes used in nuclear medicine. ................ 13 Table 1–3 Strategies for 99Mo and 99mTc production. ............................................................ 18 Table 2–1 Isotope composition (%) of the natural and enriched molybdenum (Target I-III) used for calculations in this study. Target I is from Trace company; Target II and III are from Isoflex 2011[53, 54]. ............................ 22 Table 2–2 The theoretically calculated cross sections for the production of radioactive and stable technetium isotopes by proton induced reactions on molybdenum targetsa. The respective half-lives and decay products are also listed.  Stable isotopes (i.e. T1/2>103 y) are marked by an asterisk. .............................................................................................................................................. 39 Table 2–3 The theoretically calculated cross sections for the production of radioactive isotopes (other than technetium) by proton induced reactions on molybdenum targetsa. The respective half-lives and decay products are also listed. Stable isotopes (i.e. T1/2>103 y) are marked by an asterisk. ............................................................................................................................. 40 Table 2–4 The calculated number of nuclei of 99mTc and other reaction products obtained at EOB for 3 h, 6 h, 9 h, and 12 h irradiation of Target II (99.54% enriched thick molybdenum) with 16-10 MeV, 19-10 MeV and 24-10 MeV protons with 200 A current. Additionally, the percent ratios of 99mTc to   x all technetium, to stable technetium, to all radioactive technetium and to the sum of all radioactive isotopes are listed. .................................................... 43 Table 2–5 Calculated thick target saturated yields (MBq/μA) for the dominant radioactive products. Enriched and natural molybdenum targets were irradiated with proton energies 16-10 MeV, 19-10 MeV and 24-10 MeV. .............................................................................................................................................. 45 Table 3–1 The summary of time-integrated-activity-coefficients as̃ (hour) for all radioactive technetium isotopes that would be contributing to patient absorbed dose after a standard radiotracer injection of sestaMIBI™, phosphonates and pertechnetate when labeled with cyclotron-produced 99mTc. .................................................................................................................................. 61 Table 3–2 The summary of relative contributions (%) to the total effective dose from all radioactive technetium isotopes (ground and isomeric states are considered separately) for sestaMIBI™ injection. Cyclotron 6 h irradiation of the three enriched targets and a natural molybdenum target by a proton beam with 19-10 MeV energy and the injection times at 0 h, 2 h, 8 h, 12 h and 24 h after EOB were considered. ............................ 62 Table 3–3 The percent differences in total effective doses between cyclotron- and reactor-produced Tc-labeled sestaMIBI™, phosphonates and pertechnetate for injection times at 0 h, 2 h, 8 h, 12 h and 24 h after EOB. Cyclotron productions correspond to 3 h, 6 h and 12 h irradiation of enriched targets (Target I and III) with proton beams with energies of 16-10 MeV, 19-10 MeV and 24-10 MeV. ............................................................... 63   xi Table 3–4 The percent (%) difference between absorbed doses following injections of radiopharmaceuticals labeled with a cyclotron–produced 99mTc and pure 99mTc obtained from a reactor. Cyclotron productions correspond to 6 h irradiation of the enriched Target I (97.39% enrichment) by a proton beam with energy 19-10 MeV. Doses corresponding to injection periods of 0 h, 2 h, 8 h, 12 h and 24 h after the EOB are compared. .......................... 67 Table 3–5 The percent (%) difference between absorbed doses following injections of radiopharmaceuticals labeled with a cyclotron-produced 99mTc and pure 99mTc obtained from a reactor. Cyclotron productions correspond to 6h irradiation of the enriched Target III (99.01% enrichment) by a proton beam with energy 19-10 MeV. Doses corresponding to injection periods of 0 h, 2 h, 8 h, 12 h and 24 h after the EOB are compared. .......... 68 Table 4–1 Reaction channels leading to different technetium products that are being considered by CYD. ....................................................................................................... 81 Table 4–2 Activities (GBq) at EOB calculated by the CYD Yield Calculation layer for all radioactive reaction products. These results correspond to 3 h irradiation using different proton beam energies and 100 μA current. Products with half-lives shorter than 5 min were considered as decaying directly to their daughters. ........................................................................................ 91 Table 4–3 Absolute intensities of the strongest gamma emissions (photons/sec) of radioactive products estimated by CYD for three different targets. Results correspond to 3 h irradiation using 18-10 MeV proton beam energy and 100 μA current. The gamma observation time was set as 3 h after EOB.   xii Only one gamma emission per isotope is listed and gammas’ intensities smaller than one photon per second are omitted. ............................................ 92 Table 4–4 Results of absorbed dose calculations (mSv) for different organs from sestaMIBITM labled cyclotron-produced technetium radioisotopes. The doses were calculated assuming beam current of 100 μA for 18-10 MeV proton beam energy and 3 h irradiations of Target I. The injection time was 3 h after EOB. The differences between pure 99mTc and mixture of technetium produced by the cyclotron are listed in the last column. ....... 95 Table 5–1 Inelastic gamma interactions with material......................................................... 99 Table 5–2 Irradiation and observation information for samples used for gamma spectrum analysis. ....................................................................................................... 108 Table 5–3 Summary of main gamma peaks, corresponding isotope contributors and the times, when peaks were observed from gamma spectra of cyclotron samples. ........................................................................................................................... 111 Table 5–4 99mTc activities determined from four cyclotron runs and corresponding CYD estimations. The ratio of experimental to theoretical estimations are shown in the last column. ......................................................................................... 111 Table 5–5 Other radioisotopes activity results (MBq) from the four cyclotron runs and CYD estimations under different reaction conditions. The comparison of experimental results with theoretical estimations is shown in the last column of each cyclotron runs. The “- -“ in the cells indicate either that the corresponding gamma peaks were not observed   xiii or the detected activities were so small that the measurement cannot be trusted. ............................................................................................................................. 112 Table 6–1 The summary of details of two rounds of scans. For each scan date, 5 min background scans were performed before sample scans............................ 125 Table 6–2 Photon counts measured in three energy windows for the technetium samples from cyclotron and reactor and background. ................................. 129    xiv List of Figures Figure 1–1 (Left): Nuclear “Line of stability” on the nuclides distribution chart. The black square is the distribution of stable isotopes in the chart of nuclides distribution [6]. (Right): Nuclide groups and decay transitions shown on the chart of nuclides distribution. .............................................................................. 6 Figure 1–2 The usage of 99mTc in different diagnostic fields. The data is from IMV 2007 nuclear medicine market summary report, October 2007, SECOR Analysis. ............................................................................................................................ 14 Figure 1–3 The reactors with its supply proportions to the world usage of 99Mo. Data is from Natural Resources Canada webpage. ..................................................... 16 Figure 2–1 Potential routes for 99mTc isotope production using a cyclotron. The main route is 100Mo(p,2n) reaction ( in red color). Two other ways are the decay of 99Mo from 100Mo(p,pn) reaction and 98Mo (p,) reaction. .......... 23 Figure 2–2 The curve of saturation factor as a function of the ratio of radiation time/half-life of the produced radioisotope[55]............................................... 27 Figure 2–3 The two types of stopping powers and the range of protons when passing through a solid pure 100Mo. ....................................................................... 29 Figure 2–4 Excitation functions corresponding to the 100Mo+p reaction products with the highest cross sections in the investigated energy range. Stable isotopes are marked by an asterisk. ....................................................................... 37 Figure 2–5 Comparison of the 100Mo(p,2n)99mTc excitation function to the other technetium isotopes (isomeric and ground states) produced through the   xv (p,n) reaction. The excitation function for 99mTc is marked with red circles and stable isotopes are marked by an asterisk. .................................. 38 Figure 2–6 Comparison of the 100Mo(p,2n)99mTc excitation function to the other technetium isotopes (isomeric and ground states) produced through the (p,2n) reaction. The excitation function for 99mTc is marked with red circles and stable isotopes are marked by an asterisk. .................................. 38 Figure 2–7 The EOB ratios of the number of 99mTc nuclei to the total number of nuclei of all other radioactive technetium (i.e.≠99mTc) isotopes (solid line) and to the total number of nuclei of other radioactive elements (dashed line) produced with 99.54% enriched molybdenum target irradiated for 3 h, 6 h, 9 h and 12 h with proton beam with 16-10 MeV, 19-10 MeV and 24-10 MeV. ....................................................................................... 44 Figure 2–8 The EOB ratios of 99mTc nuclei to all stable and radioactive technetium isotopes (including 99mTc) produced with 99.54% enriched molybdenum target irradiated for 3 h, 6 h, 9 h and 12 h with proton beam with 16-10 MeV, 19-10 MeV and 24-10 MeV. ............................................................................ 44 Figure 2–9 Comparison of the theoretical saturated thick target yields for the 99mTc production with four other radioactive products with highest yields. In this example, a 99.54% enriched molybdenum target was irradiated with proton energies of 16 MeV, 19 MeV and 24 MeV. ............................................. 46 Figure 2–10 Comparison of the theoretical saturated thick target yields for the 99mTc production with several other radioactive products with highest yields.   xvi In this example, a natural molybdenum target was irradiated with proton energies of 16 MeV, 19 MeV and 24 MeV. ............................................................ 46 Figure 2–11 Calculated change of the number of nuclei of 99mTc and cumulative number of nuclei of other radioactive and stable technetium. In this example, a 99.54% enriched molybdenum target was irradiated for 6 h with 200 μA proton beam at 19 MeV and then allowed to decay for additional 24 hours. ...................................................................................................... 47 Figure 3–1 The percent difference (%) between the total effective doses following the injections of sestaMIBI™ labeled with technetium produced in a cyclotron and obtained from reactor. Cyclotron production corresponded to irradiation of a Target I (left) and Target III (right) with proton beams with energies equal to 16-10 MeV, 19-10 MeV, and 24-10 MeV for 3 h (red column), 6 h (blue column) and 12 h (yellow column) irradiation times. Dose differences resulting from injections performed at 0 h, 2 h, 8 h, 12 h and 24 h after EOB are compared (please note the difference in scale). ................................................................................................................................. 64 Figure 3–2 The percent difference (%) between the total effective doses following the injections of sestaMIBI™ labeled with technetium produced in a cyclotron and obtained from reactor. Cyclotron production corresponded to 6 h irradiation of a Target I (left) and Target III (right) with proton beams. Doses resulting from target thicknesses leading to beam energy degradation from 16-, 19-, 24-10 MeV and from 16-, 19-, 24-6 MeV are compared for injection periods varying from 0 h-24 h after EOB. Dark   xvii color column bars represent the dose differences for beam energy decreasing to 6MeV, while the light color bars are for the energy decreasing to 10 MeV. .................................................................................................. 65 Figure 3–3 The percent dose difference between injections of sestaMIBI™ (left), phosphonates (middle) and pertechnetate (right) labeled with cyclotron-produced technetium and reactor-produced pure 99mTc. Cyclotron production corresponds to 6 h irradiation by a proton beam with energy 19-10 MeV of Targets I and III. The dashed lines in the figures represent the percent dose differences using enriched Target I (97.39% enrichment), while the solid lines represent the percent dose differences using Target III (99.01% enrichment). ................................................................. 69 Figure 4–1 Block diagram showing the main structure of CYD calculations. ............... 78 Figure 4–2 Screenshot of Yield Calculation layer of CYD. .................................................... 82 Figure 4–3 Screenshot of sub-GUI for Target Selection. ....................................................... 82 Figure 4–4 Screenshot of sub-GUI for single reaction yields calculations. .................... 84 Figure 4–5 Screenshot of Gamma spectrum analysis of CYD. ............................................ 86 Figure 4–6 The workflow of dosimetry estimations. ............................................................. 87 Figure 4–7 Screenshot of Dosimetry Estimation layer of CYD. .......................................... 89 Figure 4–8 Screenshot of sub-GUI for S-factor. ........................................................................ 89 Figure 4–9 Screenshot of sub-GUI for residence time. .......................................................... 90 Figure 5–1 A simplified decay scheme of 99Mo and 99mTc including the main gamma emissions from their decays. The decay information was obtained from [6]. ....................................................................................................................................... 98   xviii Figure 5–2 Total mass attenuation coefficient and the attenuation coefficient corresponding to different types of gamma interaction of germanium (Ge).................................................................................................................................... 100 Figure 5–3 Schematic graphs of ideal (left) and real-world (right) gamma spectra of 137Cs. ................................................................................................................................. 102 Figure 5–4 A scheme of gamma spectrum formation from the detected electrical pulses using MCA. The horizontal blue lines represent the channels defined by MCA. The same color of vertical histograms represents the pulses fall into the same channel, which corresponds to the gamma energies in the spectrum. The number of photon counts detected at different energies in the spectrum is proportional to the number of pulses in the corresponding channels. ................................................................ 103 Figure 5–5 The FWHM and efficiency curves used into the activity analysis. (Upper): FWHM curve. The green points are the photopeaks used for the calibration. (Lower): Efficiency curve. Different color points represent different isotopes. The red curves are the best-fit curves for the FWHM and efficiency calibrations. The curves besides best fittings represent the FWHM and efficiency uncertainties. .................................................................... 109 Figure 5–6 Activity comparison ratio of experimental results over theoretical estimations for each cyclotron run. The average of ratio for each product is shown in black lines. The uncertainty of activity results includes uncertainties of determination of the net peak area, detection efficiency and calibration source. .............................................................................................. 113   xix Figure 6–1 A simplified schematic of a gamma camera. Photons indicated in red are emitted from the patient and one of them interacts with scintillation detector by emitting scintillated light (yellow arrows) after traveling through the collimator. The light is converted to electric signals via photoelectric effect and is amplified by the photomultiplier tubes (shown in orange color). After analyzing the position and energy, a projection image can be stored and shown on the computer screen. .......................... 118 Figure 6–2 An example of a dual headed SPECT/CT system: GE Infinia Hawkeye. The two detector heads, CT component and other main part of the system are indicated with red arrows. ....................................................................................... 122 Figure 6–3 Experiment setup for round 1. (Left): A water filled Jaszczak phantom with four identical bottles (33 ml) was used. Two bottles were filled with cyclotron-produced and reactor-produced 99mTc, two other bottles were filled with air. (Right): Configuration used in SPECT/CT acquisition. .... 124 Figure 6–4. (Left): Phantom configuration for experimental round 2. (Right): The co-registered SPECT/CT phantom image. ................................................................ 125 Figure 6–5 Sample projections corresponding to the tomographic scans of Day 1 and Day 2 (scan #1-1 and #1-2 in table 6-1). The profiles are drawn as indicated by the lines shown in the projections. The number on each profile corresponds the line numbers shown on the projection. Two technetium samples are shown in the projection, the upper one corresponds to the reactor-produced 99mTc; where the lower one corresponds to the technetium sample from the cyclotron........................ 127   xx Figure 6–6 Sample projections corresponding to the planar scans of Day 2 and Day 5 with and without phantom (scan #1-3, #1-4 and #1-5 in table 6-1). The profiles are drawn as indicated by the lines shown in the projections. The number on each profile corresponds to the line numbers shown on the projection. Two technetium samples are shown in the projection, the upper one corresponds to the reactor-based 99mTc; where the lower one corresponds to the technetium sample from cyclotron. .............................. 127 Figure 6–7 Projections from the photopeak, upper and lower windows and their horizontal and vertical profiles. The data were acquired during the second round of scans on Day 1 (#2-2). In the profiles, the red line corresponds to the cyclotron technetium sample, the black line to the reactor 99mTc sample. ................................................................................................. 128 Figure 6–8 The sample projections from photopeak, upper and lower windows and their horizontal and vertical profiles from second round scans of Day 5 (#2-4). In the profiles, the red line corresponds to the cyclotron technetium sample, the black line to the reactor 99mTc sample. ............... 129   xxi List of Abbreviations  ADS Accelerator-Driven Subcritical B.R. Branching Ratio BNL Brookhaven National Laboratory  CT Computed Tomography  CYD Cyclotron production Yields and Dosimetry  EC Electron Capture  EOB End of Beam F.P. Fission Product  FWHM Full-Width-at- Half-Maximum  GUI Graphical User Interface  HEU Highly Enriched Uranium HFR High Flux Reactor  HPGe High-Purity Germanium  ICRP International Commission on Radiological Protection  IT Isomeric Transition  LEU Lower Enriched Uranium  MCA Multichannel Analyzer  MIRD Medical Internal Radiation Dose  NM Nuclear Medicine NNDC National Nuclear Data Center NRU National Research Universal PMTs Photomultiplier Tubes  SF Saturation Factor SPECT Single Photo Emission Computed Tomography   xxii Acknowledgements First and foremost, I would like to extend my heartfelt gratitude to my supervisor, Dr. Anna Celler, for her constant encouragement and continuous support. Thank you Anna for your patience, motivation, and immense knowledge. I could not have imagined having a better supervisor for my Ph.D study. I will never forget the encouragement and help you gave to me. I also would like to express my deep gratitude to my committee members, Dr. François Bénard, Dr. Alex Mackay and Dr. Stefan Reinsberg, who offered me valuable guidance and support. I also want to thank the instructors in the Physics Department, especially in the Medical Physics program for their devoted teaching and enlightening lectures I have benefited a lot.  Additional thank goes to all the members of MIRG for the unselfish help and support you provided, for the days we were working together, and for all the fun we had.  Finally, I would like to give my special thank to my beloved family. Thank you Mom and Dad for giving me endless love. Although the distance between us is over 8000 kilometer, you have always been there to help me out of difficulties. Thank you to my husband, Chengcheng Zhang, for his unconditional love and support without a word of complaint. Without him, I could not have done this.     xxiii DedicationTo My Dear Parents & My Husband 1. Introduction  1 Chapter 1 Introduction In today’s medicine, nuclear medicine (NM) imaging plays an essential role in disease diagnosis. Its sensitive measurements can identify symptoms of a wide range of disorders, from neurological diseases, coronary artery diseases to thyroid and parathyroid disorder, and orthopedic injuries. There are approximately 50 million nuclear medicine imaging procedures performed globally every year, and this number is still growing [1]. Nuclear medicine employs radiopharmaceuticals (radiotracers), which are molecules labeled with radioactive isotopes, to target specific tissues/organs or physiologic functions inside patients. When performing a NM imaging scan, a radiotracer is administered to a patient allowing the uptake by body tissues/organs. The distribution of radiotracer will be measured by detecting its electromagnetic emissions using gamma detectors of single photon imaging or positron imaging systems [2, 3]. Subsequently, the physiological functions of the patient can be investigated by measuring the internal distribution of the radiotracer. Therefore, radioactive isotopes are crucially important for nuclear medicine applications.  1.1 Aim This thesis focuses on one of the radioactive isotopes most commonly used for nuclear medical imaging, namely technetium-99m (99mTc). Since 2009, 99mTc is experiencing supply shortages all around the world due to the shut down of nuclear 1. Introduction  2 reactors. The use of cyclotrons for producing 99mTc, has emerged as a possible approach for resolving this problem. The goal of this thesis is to investigate the feasibility of the cyclotron-based production of 99mTc. Towards this goal, several questions have to be answered:   How much of 99mTc can be produced using a cyclotron? Will it be sufficient for medical usage?  Will any contaminants (other isotopes) be produced as well? If so, what are they and how much of them will be produced?  What will be the optimum production conditions for producing 99mTc, including irradiation time, beam energy, target enrichment and thickness?  How will patient doses change when cyclotron-produced 99mTc is used in diagnostic procedures?  Will the contaminants affect image quality? 1.2 Outline of dissertation The objective of this thesis is to answer the above questions by quantitative studies of production yields, dosimetry and nuclear medicine imaging scans. The structure of this thesis is as follow:  In Chapter 1, the goal and the outline of the thesis are provided. The topics related to radioactivity and radioisotopes, including 99mTc with its shortage problem 1. Introduction  3 are discussed.  Chapters 2 and 3 focus on the theoretical estimations of cyclotron production of 99mTc and other isotope products. Chapter 2 describes the theoretical calculations of reaction cross sections and production yields, including number of atoms and/or activity of cyclotron products. By comparing different irradiation conditions and targets, the optimal parameters for producing maximum 99mTc and minimizing other contaminant are discussed. In Chapter 3, doses for the cyclotron-produced 99mTc are estimated and compared with doses from pure 99mTc. The optimal injection times, which could give smallest additional dose, are also discussed. Chapter 4 describes new software that was developed to automate the theoretical estimations of yields and dosimetry. Chapters 5 and 6 turn the view from theoretical estimations to experiments. In Chapter 5, quantitative gamma spectroscopy measurements of samples from cyclotron experiments are presented. Chapter 6 describes imaging studies of cyclotron-produced technetium using single photon imaging techniques. The characteristics of cyclotron-produced 99mTc images are reported. Finally, conclusions and a discussion of potential future work are included in Chapter 7. 1. Introduction  4 1.3 Background review This chapter gives a review of physics related to radioactivity and radioactive isotopes (especially 99mTc), and provides the necessary background information about the methods and applications described in the thesis. 1.3.1 Nucleus As shown by Rutherford in 1910, atom consists of a positively charged core, i.e. nucleus, and surrounding negatively charged electrons. The atomic nucleus is composed of protons and neutrons, collectively known as nucleons. A specific nuclide of a chemical element X is usually described as 𝑋𝑍𝐴𝑁, where A, Z and N represent the mass number (number of nucleons), atomic number (number of protons) and number of neutrons in the nuclide, respectively [2]. Traditionally, a shorter but still complete form AX is accepted. Based on the number of A, Z and N, nuclides can be grouped into different nuclear families, i.e. isotopes, isotones, isobars and isomers. Isotopes are the nuclides which have the same atomic numbers Z but different mass numbers A, e.g. 131I, 127I. Since chemical behavior depends on the number of protons instead of neutrons, isotopes are the group of nuclides with same chemical characteristics but different physical properties. Isotones are different elements with the same number of neutrons, where isobars are nuclides with same number of nucleons, and isomers represent atoms of the same nuclide with when one of them being in the excited state (with higher energy than ground state) with measureable half-life. 1. Introduction  5 So far, more than 3000 isotopes are known in the world; however, only one tenth of them are stable [4]. These stable nuclides are found at their special neutron (N)/proton (Z) ratio where they have about the same number of neutrons and protons for light elements. However, for heavy elements, the number of neutrons may exceed by 50% of the number of protons. An imaginary line called “line of stability” can be drawn in the nuclide chart (atomic number versus neutron number) to represent the trend of stable nuclides, as shown in Figure 1–1(Left). Any nucleus far from the “line of stability” is unstable. Those unstable nuclei emit particles to form nuclei with higher stability. This process is called radioactive decay, and the unstable nuclides are radionuclides or radioisotopes. A definition of activity of a radioactive sample is used to describe the radionuclide decay rate in units of Becquerel (Bq), named after Henri Becquerel who discovered radioactivity in 1896 [5]. One Bq stands for one radioactive decay per second. The speed of a radioactive decay of a radioisotope can be described by its decay constant. Alternatively, the parameter of half-life (T1/2) can be introduced which is defined as the time required for a radionuclide to decay to 50% of its initial activity level.  1. Introduction  6  Figure 1–1 (Left): Nuclear “Line of stability” on the nuclides distribution chart. The black square is the distribution of stable isotopes in the chart of nuclides distribution [6]. (Right): Nuclide groups and decay transitions shown on the chart of nuclides distribution. 1.3.2 Radioactive decay  1.3.2.1 Radioactive decay mode Radioactive decay is a process in which an unstable nucleus transforms to a more stable nucleus by emitting photons and/or particles and releasing energy. Radioactive decay usually occurs when the energy of a parent nucleus is larger than the sum of energies of a daughter nucleus and the emitted radiation. There are several types of radioactive decays, the most common are summarized in Table 1–1 and their isotope transformations are shown in Figure 1–1 (right).    1. Introduction  7 Table 1–1. Radioactive decay modes. Decay Type Process Isotope Transformation Beta- (𝛽−) Decay 𝑛 → 𝑝 + 𝛽− + ?̅? 𝑋𝑍𝐴𝑁 → 𝑌𝑍+1𝐴𝑁−1 + 𝛽− + ?̅? Beta+ (𝛽+)/Position Decay 𝑝 → 𝑛 + 𝛽+ + 𝜈 𝑋𝑍𝐴𝑁 → 𝑌𝑍−1𝐴𝑁+1 + 𝛽+ + 𝜈 Electron Capture (EC) 𝑝 + 𝛽− → 𝑛 +  𝜈 𝑋𝑍𝐴𝑁 + 𝛽− → 𝑌𝑍−1𝐴𝑁+1 + 𝜈 Alpha () decay 2𝑝 + 2𝑛 → 𝛼 𝑋𝑍𝐴𝑁 → 𝑌𝑍−2𝐴−4𝑁−2 + 𝛼 Isomeric Transition (IT) Isomeric states decay with emission of gammas and/or conversion electrons. 𝑋∗𝑍𝐴𝑁→ 𝑋𝑍𝐴𝑁 + 𝛾 or 𝛽− Nuclear Fission One heavy nuclide decays to two lighter nuclides with neutrons and/or photons emission 𝑋𝑍𝐴𝑁 → 𝑌𝑍′𝐴′𝑁′ + 𝑊𝑍′′𝐴′′𝑁′′ + 𝑥𝑛 + 𝑜𝑟 𝑥′𝛾  Each radioisotope has its preferable decay mode; the nucleus internal structure and its position relative to the “line of stability” defines its decay mode, as radioisotopes decay toward the stability line. Neutron-rich nuclides (below the stability line), mostly undergo 𝛽−  decays, which convert them into daughter nuclides with atomic numbers increased by one by emission of electrons (𝛽− particle) and antineutrinos (?̅?). On the contrary, the nuclides above the stability line, which usually have more protons than neutrons, decay by 𝛽+ or EC which converts one of their protons into neutron with emission of neutrinos (𝜈). Some unstable heavy nuclides follow  decays, which transfer them to lighter nuclides by emitting 𝐻𝑒24  ( particles). Finally, the heaviest nuclei undergo nuclear fissions, which break them into two lighter nuclei with emission of several neutrons and/or photons.  Usually, a radioactive decay results in an excited state of its daughter nucleus instead of a ground state. If the daughter nucleus resulting from a nuclear decay is left in an excited state with a relatively long lifetime, such excited state is called metastable or isomeric state. An isotope in metastable state can be described as AmX, where m stands for metastable state, such as 99mTc. Corresponding to metastable 1. Introduction  8 state, AgX represents the ground state of the same isotope, such as 99gTc. When a nucleus in its metastable state decays to its ground state, gamma rays and conversion electrons are emitted. This transition is called isomeric transition (IT). Conversion electron decay occurs when the excited nucleus decays by transferring its energy directly to an orbital electron as an alternative to a gamma-ray emission. Once a conversion electron is emitted, a vacancy on the corresponding electron orbit is left behind. In this situation, an outer orbit electron can drop to this vacant position with emissions of X-ray or another electron. The emitted X-ray is called characteristic radiation, while the secondary emitted electron is named as Auger electron. The probability that the vacancy will be filled by emitting X-rays rather than an Auger electron is fluorescent yields. 1.3.2.2 Radioactive decay formulae Decay of a radioactive nuclide is a spontaneous statistical process, which makes it impossible to predict the precise moment of its radioactive transformation. The description of radioactive decay is on the basis of probabilities and average decay rates. The average decay rate of a sample containing N atoms can be given by:   𝑑𝑁𝑑𝑡= −𝜆𝑁 (1-1) where 𝜆 represents the decay constant, which is the fraction of the nuclei of that radioisotope decays per unit of time. Some radioisotopes can undergo more than one type of decay (e.g. 96mTc: 2% EC decay to 96Mo and 98% IT decay to its ground state 96gTc). Such fraction of radioisotope decay is called the branching ratio (B.R.).  1. Introduction  9 Then, the activity of a sample (A) can be defined as the quantity of its average decay rate:  𝐴 = |𝑑𝑁𝑑𝑡| = 𝜆𝑁 (1-2) Solving the equation (1-1) and (1-2), the number of atoms (𝑁(𝑡)) and the activity (𝐴(𝑡)) of a radioactive sample at time t can be written as:  𝑁(𝑡) = 𝑁0𝑒−𝜆𝑡 (1-3)  𝐴(𝑡) = 𝜆𝑁(𝑡) = 𝜆𝑁0𝑒−𝜆𝑡 = 𝐴0𝑒−𝜆𝑡  (1-4) where 𝑁0 and 𝐴0 are the initial number of atoms and the initial activity of the radioisotope when time 𝑡 = 0, respectively. Then the half-life has the relationship with the decay constant as:  𝑇12⁄=𝑙𝑛2𝜆≈ 0.693/𝜆 (1-5) 1.3.3 Radioisotopes used in nuclear medicine  Since 1900s, after the discovery of radioactive polonium and radium by Marie and Pierre Curie in 1898 [7], radioactive isotopes have been employed in medicine. The first patient injection of radioactive isotope was reported in 1913 when Frederick Proescher injected radium for treatment of leukemia [8]. In 1920s, Hermanm Blumgant used 214Bi for studying human blood flow rate, which opened the usage of radioactive isotopes in diagnostic nuclear medicine [9]. 1. Introduction  10  However, not all the radioactive isotopes can be used in nuclear medicine since each radioactive nuclide has a set of characteristic properties, including its decay mode, transition energy, average lifetime and production methods. These properties should be taken into consideration when selecting radioisotopes for particular imaging or therapy application [10]. An ideal radioisotope for nuclear medicine imaging provides sufficient information for patient diagnosis while delivering minimum radiation dose and is detectable by nuclear medicine techniques. In summary, several properties need to be considered:  a. Type and energy of emissions from a radioisotope should be detectable by existing cameras. For example, photons or gamma rays in the 70-400 keV energy range are suitable for single photon cameras. b. The physical half-life of a radioisotope in NM should be long enough for radiopharmaceutical preparation and imaging, meanwhile, it should also be short enough to minimize the dose to the patients. Usually, it is within the range of a few hours to days.  c. The purity of a radioisotope, defined as the fraction of the total radioactivity in a sample that is in the form of the desired radioisotope, will influence the radiation dose to the patient. Radioactive contaminants other than the desired radioisotope may increase the dose undesirably. d. Another important factor is the chemical properties of a radioisotope. Radioisotopes, which are easily incorporated into biomolecules without changing their properties, are required. 1. Introduction  11 e. The cost and complexity of radioisotope production also need to be considered. All these factors need to be taken into account when considering a radioisotope for medical usage. 1.3.4 Production of radioisotopes So far, of all isotopes in existence, only around 10% are found in nature, and most of the naturally occurring radioisotopes are not suitable for NM due to their long half-lives and/or unsuitable emissions. The radioisotopes used in today’s NM are all produced artificially.  Mostly, radioisotope production methods are based on fission or on nuclear reactions where a nucleus of a stable atom is “hit” by sub-nuclear particles: neutrons, protons, alpha particles, etc.  I. Nuclear reactor-produced radioisotopes The nuclear reactor contains a large amount of fissionable material, e.g. natural uranium. The material undergoes nuclear fission, splitting into two lighter nuclear fragments with emitting fission neutrons. The fission products can be used in NM. Alternatively, the target material can be placed in a flux of neutrons to undergo neutron activations, such as 23Na(n,γ)24Na [11]. Radioisotopes produced using nuclear reactors are always neutron-rich; therefore they tend to decay by β- emissions. The fission products are usually carrier-free with high specific activities, 1. Introduction  12 while products from (n,γ) reactions have the same chemical characteristics as reaction targets which are hard to separate. II. Accelerator (Cyclotron)-produced radioisotopes Another method for radioisotope production is using accelerators. When a cyclotron is employed, accelerated charged particles, such as protons, are injected into a target material to produce radioisotopes. Cyclotron products used for nuclear medicine imaging studies are, for example, short-lived positron emitters 11C (T1/2=20.3 min) and 18F (T1/2=109.8 min) [12, 13]. Radioisotopes can be directly prepared on site with a dedicated biomedical cyclotron which can be installed in a hospital. When a proton beam is added to the target material, products mostly tend to undergo β+ or EC decay.  Additionally, a portable generator can also be used for radioisotope productions. A radioisotope generator consists of a parent (long lived)-daughter (short-lived) pair contained in an apparatus that permits separation and extraction of the daughter from its parent. The parent is usually produced in a nuclear reactor. Table 1–2 gives examples of production methods of some radioisotopes used in nuclear medicine. This thesis focuses on the radioisotope of 99mTc and its production method.   1. Introduction  13 Table 1–2 Production methods of radioisotopes used in nuclear medicine. Product Half-life Decay Mode Production Method Production Reaction 99mTc 6 hour IT Generator 99Mo decay 68Ga 68min β+, EC Generator 68Ge decay 113mIn 100min IT Generator 113Sn decay 32P 14.26 d β- Reactor 31P(n, ) or 32S(n,p) 131I 8.02 d (β-,) Reactor 130Tc(n, )131Te131I 24Na 15.0h (β-,) Reactor 23Na(n,) 90Y 64.1 h β- Reactor 14N(n,p)14C 11C 20min β+ Cyclotron 10B(d,n) or 11B(p,n) 18F 109.77min β+, EC Cyclotron 20Ne(d, ) or 18O(p,n)18F 67Ga 3.26 d (EC, ) Cyclotron 68Zn(p,2n) 111In 2.80 d (EC, ) Cyclotron 111Cd(p,n) or 109Ag(,2n)  1.3.5 Radioisotope of 99mTc Technetium-99m is one of the most widely used radioisotopes in diagnostic nuclear medicine studies. It is employed in 30 million diagnostic procedures worldwide annually and the demand is increasing [14, 15]. The main applications of 99mTc are in myocardial perfusion imaging for diagnosis of ischemic heart disease [16-18] and in bone scans for evaluating various bone-related pathology, like bone pain, stress fracture, infections and the spread of cancers to the bone [19]. Also, it can be used to diagnose diseases related to brain, thyroid, lung, blood and other disorders [20-23]. Figure 1–2 shows the usage spread in different fields [24]. 1. Introduction  14  Figure 1–2 The usage of 99mTc in different diagnostic fields. The data is from IMV 2007 nuclear medicine market summary report, October 2007, SECOR Analysis. 99mTc was discovered in 1938 by G.T. Seaborg and E. Segrè who analyzed molybdenum targets bombarded by deuterons and neutrons [25]. In the following 10 years after its discovery, 99mTc was just a scientific curiosity. However, the 99Mo/99mTc generator developed by Brookhaven National Laboratory (BNL) in 1950s opened the gate for medical usage of 99mTc [26]. In the early 1960’s, Dr. Claire Shellabarger of the Brookhaven Medical Department employed 99mTc in medical research. She observed the localization of 99mTc in thyroid tissue when studying thyroid physiology with different radioisotopes [27]. Since then, the usage of 99mTc for nuclear medicine studies rapidly increased. Its popularity is related to its very favorable characteristics: (a) the 6 hours half-life, which is long enough for image acquisition and short enough for minimum patient dose; (b) gamma emission of 140 1. Introduction  15 keV from isomeric transition which could be used by single photon camera; (c) and its easy availability from a 99Mo/99mTc generator which allows for distribution of a longer half-life parent (99Mo, T1/2=66 hours) to several sites [28, 29].  1.3.5.1 Traditional method for 99mTc production Nowadays, most of 99mTc is obtained from 99Mo decay using 99Mo/99mTc generator. The production process for 99mTc supply is as follows: 99Mo is produced by neutron fission of highly enriched uranium (HEU, >20% of 235U) using nuclear reactors [30], and sent to a central processing facility, where 99Mo is extracted and purified. This 99Mo is shipped to generator manufacturers where it is embedded on alumina columns and packaged into lead shielded generators. The generators are then shipped to individual nuclear medicine sites. After elution, 99mTc is used to label different medical agents for patient scans.  For minimizing potential proliferation issues and misusage of HEU, lower enriched uranium (LEU, less than 20% 235U) was proposed as an alternative target [31]. The major producers of 99Mo are shown in Figure 1–3. Currently seven nuclear reactor sites, i.e. Canada, Netherlands, Belgium, France, South Africa, Poland and Australia, are providing more than 95% of world’s supply of 99Mo using neutron fission reactions of 235U. The two largest producers in the world are the National Research Universal (NRU) reactor at Chalk River Laboratory in Canada and High Flux Reactor (HFR) in Netherland providing over 60% of 99Mo production for the whole world. Among these reactor sites, only OPAL reactor in Australia uses LEU, while all others use HEU as targets [32]. 1. Introduction  16  Figure 1–3 The reactors with its supply proportions to the world usage of 99Mo. Data is from Natural Resources Canada webpage. 1.3.5.2 Shortage of 99mTc and its alternative production methods Given the widespread availability of affordable 99mTc from fission with high yield, there was not much interest in exploring alternative production methods. However, in the spring of 2009 the NRU reactor in Chalk River was unexpected shut down for more than a year for repairs related to a heavy water leak which coincided with a scheduled service shut down of the HFR [33]. This caused an unprecedented shortage of 99mTc. Although the NRU reactor resumed its operation in summer 2010, considering the age of all nuclear reactors involved in 99mTc production and the proliferation of reactors, the nuclear medicine community realized that the supply of neutron fission radioisotopes remains fragile [34]. Since similar shortages may occur again in the future, explorations of alternative production methods remain vitally important.  1. Introduction  17 Various strategies of 99Mo or 99mTc production have been proposed and studied for solving this problem. Most of these strategies can be divided into two groups: one is still based on the use of nuclear reactors and the other is based on accelerator reactions. The nuclear reactor technologies have two subsets: fission reactions of uranium [30, 31, 35-39] and neutron activation reactions of molybdenum-98 (98Mo) [40-42]. On the other hand, as a major technology alternative to the use of reactors, accelerator-based approaches that could be used to produce 99Mo or 99mTc were proposed [43-50]. Table 1–3 summarizes these potential alternative approaches (traditional neutron fission is included as a reference). The production reaction details, advantages and disadvantages of each approach are listed. 1. Introduction  18 Table 1–3 Strategies for 99Mo and 99mTc production. Reactor-based Strategies Methods Nuclear Reactions Advantages Disadvantages Related Studies Neutron fission in nuclear reactor 235U+n 99Mo+fission product (F.P.)+2.5n   High yield   20% yield from HEU when using LEU  Pure final product  Mature technique and widely usage     High power reactor needed  Complex chemical processes  Significant amount of radioactive waste  Proliferation concerns for HEU and waste  [30, 31, 35-37] Neutron fission in solution reactor 235U+n99Mo+F.P.+2.5n    Only LEU used in the reactions  Low cost for installation and operation  Simple structure  No dissolution step    High risks of leaks of highly radioactive solution  Technologic challenges for uranium fuel clean up  Complex chemical processes  [38, 39] Neutron activation in reactor 98Mo+n99Mo+    Negligible radioactive waste  Low cost using natural Mo  Negligible security and non-proliferation concerns  Widely distribution of production capability  Pure final product   Low yield of 99Mo production  High cost of enriched 98Mo  Difficult in recovering and recycling target [40-42]     1. Introduction  19 Table 1–3 (Continued).  Strategies for 99Mo and 99mTc production. Accelerator-based Strategies Methods Nuclear Reactions Advantages Disadvantages Related Studies Direct production of 99mTc using cyclotron 100Mo+p99mTc+2n  It can be produced locally  Low nuclear waste  No proliferation concerns  No hazardous, explosive or fissile materials  Relative high cross sections comparing with other non-reactor methods   High cost of enriched 100Mo  Long-term availability  Large number of cyclotron needed  Contaminants of other radioactive Tc cannot be purified. Low reaction cross section comparing with reactor-based methods  [46-49, 51] Photon fission using electron accelerator 238U+99M++F.P.+2n  Natural uranium can be used  Low cost of target  Could use existing generator technologies   Extremely low reaction cross section  High cost and challenges for high power machines  High waste volume  [34, 45] Photon-induced transmutation 100Mo+99Mo+n  Negligible radioactive waste  No proliferation concerns   Low reaction cross section  High cost of 100Mo  High cost and challenges for high power machines  [43, 50]  Accelerator-Driven Subcritical (ADS) Step1: Pb/Ta/W/.etc +pn Step2: n+98Mo99Mo+ or n+235U99Mo+F.P.  Relative high yield of (n, ) reaction  Processes safer than reactors   Difficult chemical and physical form of target  High cost of machines design.  It is in the basic theoretical concept stage  [44] 1. Introduction  20 As shown in Table 1–3, one of the proposed approaches is to directly produce 99mTc in a cyclotron using a beam of energetic protons via the 100Mo(p,2n)99mTc reaction (bolded in Table 1.3). This method was initially demonstrated in the early seventies[52]. The main advantage of this method is that it avoids the usage of nuclear reactors and could produce relatively high amounts of 99mTc comparing with other non-reactor approaches. However, the subsidized low cost and convenience of reactor based 99Mo/99mTc strategy limited the interest in further investigations of proton-induced reactions. Due to the recent low supply of 99mTc, a number of studies of cross sections, yields, as well as other aspects of accelerator-based isotope production sprang up [46-49, 51]. In this thesis, the feasibility of this method is investigated using both theoretical predictions and experimental analysis. 2. Theoretical Yields Estimations  21 Chapter 2 Theoretical Yields Estimations Although ultimately a careful experimental verification of 99mTc production using a cyclotron must be performed, theoretical modeling can provide an initial guidance for the experiments as it allows for extensive investigation of experimental parameters at little cost to the user. In this chapter, the properties of cyclotron-produced 99mTc are discussed. Quantitative studies of theoretically calculated reaction cross sections and yields for the production of 99mTc and other radioactive and stable isotopes created during proton irradiations are reported. Different reaction conditions and molybdenum (Mo) targets enrichments are investigated in order to optimize production yields. 2.1 Cyclotron-produced 99mTc As mentioned in Chapter 1, when a cyclotron is used for 99mTc production, proton beams irradiate Mo target materials. However, at any given proton energy, a large number of different reactions can occur simultaneously (each reaction channel can be denoted as (p,x), where p stands for the incident protons and x stands for any combination of the exiting particles). Each reaction channel opens only when the proton energy is higher than the threshold for this reaction, which is usually called Q-value. Molybdenum has seven stable isotopes, thus even for an enriched 100Mo target, there are always some components of other stable molybdenum isotopes in 2. Theoretical Yields Estimations  22 the target leading to additional reactions during cyclotron irradiations. Sample compositions of commercially available enriched 100Mo are given in Table 2–1. Table 2–1 Isotope composition (%) of the natural and enriched molybdenum (Target I-III) used for calculations in this study. Target I is from Trace company; Target II and III are from Isoflex 2011[53, 54]. Isotopes Natural Enriched Target Target I Target II Target III 92Mo 14.85 0.005 0.0060 0.09 94Mo 9.25 0.005 0.0051 0.06 95Mo 15.92 0.005 0.0076 0.10 96Mo 16.68 0.005 0.0012 0.11 97Mo 9.55 0.01 0.0016 0.08 98Mo 24.13 2.58 0.41 0.55 100Mo 9.63 97.39 99.54 99.01  Therefore, besides 99mTc, many different radioisotopes will be produced either through various 100Mo(p,x) channels or from reactions on contaminating Mo isotopes present in the target. At the same time, isotopes will also be produced in decays of the reaction products. Thus, when estimating the yields of each of the products from cyclotron runs, all the reaction and decay channels leading to the same isotope product must be considered. Figure 2–1 is diagrammatic sketch showing reaction/decay channels leading to 99mTc production. 99mTc can be mainly created in three different ways, which are 100Mo(p,2n) reaction, the decay of 99Mo from 100Mo(p,pn) reaction and 98Mo (p,) reaction. 2. Theoretical Yields Estimations  23  Figure 2–1 Potential routes for 99mTc isotope production using a cyclotron. The main route is 100Mo(p,2n) reaction ( in red color). Two other ways are the decay of 99Mo from 100Mo(p,pn) reaction and 98Mo (p,) reaction. 2.2 Aim of this chapter  The aim of this chapter is to provide the information which is necessary to answer basic questions related to the practicality of the proposed approach. This includes an estimate of the number of cyclotron runs that would be required to fulfill the daily needs of an average nuclear medicine department. In parallel, the production yields for various other radioactive technetium isotopes that could be created in the process are investigated as these may affect radiation dosimetry in patient studies. Further, the yields of radioactive impurities with medium and long half-lives, such as molybdenum, niobium and zirconium isotopes, are estimated as they would constitute radioactive waste and be potential sources of contamination 2. Theoretical Yields Estimations  24 in the labs. Additionally, until it can be demonstrated that these contaminants can be chemically isolated from technetium, these isotopes may potentially also impose dosimetric considerations in patient studies. Finally, the very long-lived technetium isotopes 97gTc, 98Tc and 99gTc (considered stable in this study as they have T1/2>103 y) would decrease the specific activity of the final product, which may adversely impact some of the labeling procedures. Taking these factors into account, the optimal conditions need to be determined (beam and target characteristics and irradiation time) that would maximize the amount of 99mTc and minimize impurities.  In summary, the questions which are investigated in this work are as follows: (a) what is the maximum amount of 99mTc which can be produced by the (p,2n) reaction and what are the corresponding irradiation parameters; (b) what are the amounts of different (technetium and other elements) radioactive isotopes that could be produced; (c) how much of the “stable” (i.e. very long-lived) technetium isotopes can be produced; and finally, taking all these parameters into account, (d) what are the optimal irradiation condition for 99mTc production using a cyclotron?  2.3 Physics concepts of cyclotron reactions 2.3.1 Cross sections and yields of cyclotron products When a cyclotron is used to produce radioisotopes, accelerated charged particles are injected onto a target. The quantity of activity produced by any given reaction during the irradiation depends on the intensity of the particle beam and the number of target nuclei in the material and this reaction cross section (which 2. Theoretical Yields Estimations  25 describes the probability of this interaction). The cross section (σ) can be described as a “characteristic area” where a larger area means a larger probability of interaction. Thus, the unit for cross section is the same as area, and most commonly used unit is the barn (1b=10-28 m2) or millibarn (1mb=10-31 m2). The quantity of cross section depends on the type of interaction, the involved particles and their energies.  The reaction cross sections are usually used in the determination of the isotope production rates. Suppose there is a beam of protons perpendicularly bombarding a target material with a flux of 𝜙 (particles/sec.cm2). Let’s assume that the target is sufficiently thin that protons do not lose their energies when traveling through the target. The reaction rate 𝑅 can be written as:  𝑅 = 𝑁𝑡𝜎𝜙 (2-1) where 𝜎 is the activation cross section in mb and 𝑁𝑡 is the number of target nuclei. When a nuclide that is being produced in a cyclotron is radioactive, it will further decay to its daughter.  Thus, combining equations (1-1) and (2-1), the decay rate can be written as:  𝑑𝑁𝑑𝑡= 𝑅 − 𝜆𝑁 (2-2) Solving the equation (2-2), the number of atoms and activity of produced isotope are:  𝑁(𝑡) =𝑅𝜆(1 − 𝑒−𝜆𝑡) =𝑁𝑡𝜎𝜙𝜆(1 − 𝑒−𝜆𝑡) (2-3) 2. Theoretical Yields Estimations  26  𝐴(𝑡) = 𝜆𝑁 = 𝑅(1 − 𝑒−𝜆𝑡) = 𝑁𝑡𝜎𝜙 (1 − 𝑒−𝜆𝑡) (2-4) Clearly, the yields (activities or number of atoms) of products would depend on the time of irradiation (t). However, when considering the case of t → ∞, the production yield will reach its saturation value. The part (1 − e−λt) is called saturation factor (SF). Figure 2–2 shows the curve of SF as a function of the ratio of cyclotron irradiation time and half-life of the produced radioisotope. It shows that production of radioisotope will reach 50% of its saturation yield when irradiation time is equivalent to its half-life.  For practical reasons, irradiation time should be no longer than three or four half-lives after which produced activity reaches close to 90% of its saturation yield [55]. 2. Theoretical Yields Estimations  27  Figure 2–2 The curve of saturation factor as a function of the ratio of radiation time/half-life of the produced radioisotope[55]. 2.3.2 Stopping power In reality, as a charged particle passes through a medium, it undergoes more than one interaction with the target material. During these processes, a charged particle will deposit its energy and slow down until it completely stops. The slowing (loss of energy) of a charged particle per unit distance is called the stopping power of the target material 𝑆(𝐸) =  𝑑𝐸𝑑𝑥. The quantity of the stopping power depends on the type and energy of the bombarding particles and the type and density of the target material. The range (𝑥) that the charged particle can travels through the target is:  𝑥 = ∫1𝑆(𝐸)𝑑𝐸𝐸00 (2-5) where 𝐸0 is the initial incident energy of the bombarding particles.  0 0.2 0.4 0.6 0.8 1 1.2 0 1 2 3 4 5 6 7 8 9 10 Saturation Factor (SF) Ratio of Radiation Time/Half-life of Produced Radionuclide  2. Theoretical Yields Estimations  28 Usually, stopping power has two types: one is electronic stopping power, which means the slowing down of a charged particle due to inelastic collisions between bound electrons in the target and the particle; the other is nuclear stopping power, which is due to the elastic collisions between a charged particle and nuclei of the target. Nuclear stopping power can be larger than electronic stopping power at low energies. However, for very light ions travelling in heavy materials, the nuclear stopping power is weaker than the electronic at all energies. Figure 2–3 shows the two types of stopping powers and the range of protons when passing through a solid pure 100Mo material. The data was obtained from SRIM, which is a software program for calculating stopping powers [56]. 2. Theoretical Yields Estimations  29  Figure 2–3 The two types of stopping powers and the range of protons when passing through a solid pure 100Mo. 2.4 Methods 2.4.1 Theoretical cross section calculations In this study, excitation function, which is the function describing the dependence of the cross section on the projectile energy, was firstly calculated. The calculations were performed for each of the seven stable molybdenum isotopes [6]. The cross sections leading to the production of nuclei in isomeric and ground states were estimated separately.  There are a number of codes that can be used to perform theoretical calculations of the reaction excitation functions. The ALICE code, developed in the seventies by M. Blann (1973) [57], uses geometry-dependent hybrid or Hybrid Monte Carlo simulation pre-equilibrium models. However, it does not allow the user 0.00E+00 2.00E+02 4.00E+02 6.00E+02 8.00E+02 1.00E+03 1.20E+03 1.40E+03 1.60E+03 1.80E+03 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 0 5 10 15 20 25 30 Stopping Power (MeV / (mg/cm2)  Incident Proton Energy (MeV) Electric stopping power Nuclear stopping power Range Range of Incident Protons ( (µm) 2. Theoretical Yields Estimations  30 to independently calculate the isomeric and ground states cross sections. For this study, the next generation code EMPIRE-3 was used [58]. EMPIRE is a very versatile modular code, which includes several different nuclear reaction models and is able to handle a broad range of energies and incident particles. 2.4.2 Reaction yield formulae When molybdenum targets are irradiated, some of the reaction channels lead to the production of radioactive isotopes resulting in chains of radioactive decays. As a consequence, the same isotope may be created through a number of production-decay channels and all of them must be considered when estimating the final cumulative yield.  In general, the situation may be represented by the following production-decay chain [59]:   𝑁𝑡𝜎→𝑁1𝑓1,   𝜆1→   𝑁2𝑓2,   𝜆2→   …𝑓𝑛−1,   𝜆𝑛−1→       𝑁𝑛𝑓𝑛 ,   𝜆𝑛→    𝑁𝑠 (2-6) where 𝑁𝑡  , 𝑁𝑖  (𝑖 = 1,2, … 𝑛) and 𝑁𝑠  correspond to the number of target nuclei, radioactive daughter nuclei and stable daughter nuclei (all per unit volume), respectively; 𝜎  is the reaction cross section, 𝜆𝑖  are the corresponding decay constants. Additionally, in order to account for multiple decay modes of some radioisotopes, the formulae must include the branching ratios 𝑓𝑖  leading to each particular decay product. Since the (p,x) cross sections are relatively low (of the order of mb), in these calculations only reactions on target nuclei were considered, while the possibility of 2. Theoretical Yields Estimations  31 any secondary reaction which might occur on one of the newly produced isotopes was ignored. Similarly, the change of the number of target nuclei during the irradiation process was considered negligible. The variation in number of nuclei of different radioactive chain members is governed by the following set of differential equations:  𝑑𝑁1𝑑𝑡= 𝑁𝑡𝜎𝜙 − 𝜆1𝑁1 (2-7)  𝑑𝑁2𝑑𝑡= 𝑓1𝜆1𝑁1 − 𝜆2𝑁2  …  𝑑𝑁𝑛𝑑𝑡= 𝑓𝑛𝜆𝑛𝑁𝑛 where 𝜙 is the number of protons in the beam per second per cm2. If the proton beam is switched off (end-of-beam, EOB) after the bombardment time 𝑡𝐵, the reaction will cease, but decays will continue for the additional period 𝑡𝐷 , where 𝑡𝐷 starts being measured at the EOB moment.  In order to calculate the thick target reaction yield one needs to consider the decrease of protons’ energy as they pass through the target, and integrate the cross-sections over the entire energy range. The saturated thick target reaction yield 𝑌 per unit beam current (Bq/μA) can be calculated using the following formula [60]:   𝑌 = 6.24 × 1012 ×𝑁𝐴𝑀∫𝜎(𝐸)𝑆(𝐸)𝐸𝑖𝑛𝐸𝑜𝑢𝑡𝑑𝐸 (2-8) 2. Theoretical Yields Estimations  32 where: 6.24 × 1012 is the number of protons per second per A, 𝑁𝐴 is the Avogadro number, M is the target atomic mass in gram,  𝜎(𝐸)  is the reaction cross section (excitation function) as a function of energy expressed in cm2, and 𝑆(𝐸) is the target stopping power expressed in units  MeV ∙ cm2/g.  When solving the equation group of (2-7) using the saturated thick target reaction yield, there are several particular cases which need to be considered separately: Case A: When the reaction product is a stable nuclide the following scheme applies:  𝑁𝑡𝜎→𝑁s (𝑠𝑡𝑎𝑏𝑙𝑒) (2-9) Solving equation (2-7) the number of produced nuclei is:  𝑁s = 𝑌𝑡𝐵𝐼0 (2-10) where 𝐼0 is the incident proton beam current in the unit of A. Case B: When the reaction product decays to a stable daughter the following scheme applies:  𝑁𝑡𝜎→𝑁1𝑓1,𝜆1→  𝑁𝑠 (𝑠𝑡𝑎𝑏𝑙𝑒)  (2-11) In this case, the solution to equation (2-7) provides the numbers of radioactive nuclei 𝑁1 that will be created in the target material at the time of EOB and time 𝑡𝐷 after EOB:   2. Theoretical Yields Estimations  33  𝑁1(𝐸𝑂𝐵) =1𝜆1𝑌𝐼0(1 − 𝑒−𝜆1𝑡𝐵) (2-12)  𝑁1(𝑡𝐷) = 𝑁1(𝐸𝑂𝐵)𝑒−𝜆1𝑡𝐷 =1𝜆1𝑌𝐼0(1 − 𝑒−𝜆1𝑡𝐵)𝑒−𝜆1𝑡𝐷 (2-13) while the number of nuclei of the stable daughter product at EOB and 𝑡𝐷 will be:  𝑁𝑠(EOB) = 𝑓1[𝑌𝑡𝐵𝐼0 −𝑁1(𝐸𝑂𝐵)] = 𝑓1𝑌𝐼0 [𝑡𝐵 −(1 − 𝑒−𝜆1𝑡𝐵)𝜆1] (2-14)  𝑁𝑠(𝑡𝐷) = 𝑁𝑠(𝐸𝑂𝐵) + 𝑓1[𝑁1(𝐸𝑂𝐵) − 𝑁1(𝑡𝐷)]              = 𝑓1𝑌𝐼0 [𝑡𝐵 +1𝜆1(𝑒−𝜆1𝑡𝐵 − 1)𝑒−𝜆1𝑡𝐷] (2-15) Case C: When the produced isotope 𝑁1 undergoes further radioactive decay to 𝑁2 which in turn decays to a stable product 𝑁𝑠:  𝑁𝑡𝜎→𝑁1𝑓1,𝜆1→  𝑁2𝑓2,𝜆2→  𝑁𝑠 (𝑠𝑡𝑎𝑏𝑙𝑒) (2-16) Then, the corresponding formulae allow us to calculate the number of produced nuclei, respectively:  𝑁1(𝐸𝑂𝐵) =1𝜆1𝑌𝐼0(1 − 𝑒−𝜆1𝑡𝐵) (2-17)  𝑁2(𝐸𝑂𝐵) = 𝑓1𝑌𝐼0 [1𝜆2( 1 − 𝑒−𝜆2𝑡𝐵) +1𝜆2 − 𝜆1(𝑒−𝜆2𝑡𝐵 − 𝑒−𝜆1𝑡𝐵)] (2-18)  𝑁s(𝐸𝑂𝐵) = 𝑓2[𝑓1(𝑌𝐼0𝑡𝐵 − 𝑁1(𝐸𝑂𝐵)) − 𝑁2(𝐸𝑂𝐵)] = 𝑓2𝑓1𝑌𝐼0 [𝑡𝐵 −1𝜆1(1 − 𝑒−𝜆1𝑡𝐵) −1𝜆2(1 − 𝑒−𝜆2𝑡𝐵) −1𝜆2 − 𝜆1(𝑒−𝜆2𝑡𝐵 − 𝑒−𝜆1𝑡𝐵)]   (2-19)  𝑁1(𝑡𝐷) = 𝑁1(𝐸𝑂𝐵)𝑒−𝜆1𝑡𝐷 =1𝜆1𝑌𝐼0(1 − 𝑒−𝜆1𝑡𝐵)𝑒−𝜆1𝑡𝐷 (2-20) 2. Theoretical Yields Estimations  34  𝑁2(𝑡𝐷) =𝑓1𝑌𝐼0𝜆2{[ 1 − 𝑒−𝜆2𝑡𝐵 +𝜆2(𝑒−𝜆2𝑡𝐵 − 𝑒−𝜆1𝑡𝐵)𝜆2 − 𝜆1] 𝑒−𝜆2𝑡𝐷                        +𝜆2 (1 − 𝑒−𝜆1𝑡𝐵)𝜆2 − 𝜆1(𝑒−𝜆1𝑡𝐷 − 𝑒−𝜆2𝑡𝐷)} (2-21)  𝑁𝑠(𝑡𝐷) = 𝑓1𝑓2𝑌𝐼0 [𝑡𝐵 −(1−𝑒−𝜆1𝑡𝐵)𝑒−𝜆1𝑡𝐷𝜆1−1𝜆2(1 +𝜆1𝑒−𝜆2𝑡𝐵−𝜆2𝑒−𝜆1𝑡𝐵𝜆2−𝜆1) 𝑒−𝜆2𝑡𝐷   +(1 − 𝑒−𝜆1𝑡𝐵)𝜆2 − 𝜆1 (𝑒−𝜆1𝑡𝐷 − 𝑒−𝜆2𝑡𝐷)] (2-22) In situations where longer radioactive chains are produced the calculations follow the same pattern, correspondingly leading to more complicated formulae.  2.4.3 Calculation parameters In the reaction yield calculations, natural and enriched molybdenum Target I and Target II listed in the Table 2–1 were used. Yields for each molybdenum target were calculated as a linear combination of the individual yields from its seven stable isotopes.  The cross section calculations resulted in a large body of data, however, only some of the produced isotopes were included in the subsequent analysis leading to the reaction yield estimates. The following limiting criteria were employed (the information about each isotope decay modes, branching ratios and half-life based on the data compiled in Nation Nuclear Data Center (NNDC) [6]): a. For cross section calculations proton energy range was set at 1-30 MeV. The cross section for 100Mo(p,2n)99mTc reaction starts only at about 8 MeV, peaks at 15-16 MeV and drops by a factor of 4 at 24 MeV, while at higher energies 2. Theoretical Yields Estimations  35 the cross sections for production of main contaminants significantly increase. For this reason, yield calculations were performed only up to 24 MeV protons as, in our opinion, considering reactions at higher proton energies for 99mTc production was not justified.  b. The reaction channel was not included in the analysis if its cross section in the whole considered energy range was never higher than 1 mb. c. Produced isotopes or isomeric states with half-lives T1/2 shorter than 5 min were considered as leading directly to the production of their daughters.  d. Isotopes with half-lives T1/2 longer than 103  years were considered stable for the calculation purposes.  2.5 Results 2.5.1 Results of the cross section calculations When taking into account all creation/decay possibilities following the selection criteria listed in Section 2.4.3, 99mTc can be mainly produced by two dominant reaction channels, namely: 100Mo(p,2n)99mTc and 100Mo(p,pn)99Mo99mTc. However, as mentioned, other reactions on 100Mo and other molybdenum isotopes will lead to the creation of a number of different (i.e. ≠ 99mTc) technetium isotopes.  Table 2–2 summarizes the cross sections for the proton-induced production of all technetium isotopes. For each isotope its half-life and decay products are listed, together with the corresponding branching ratios. The asterisk next to the isotope 2. Theoretical Yields Estimations  36 symbol signifies a stable product (i.e. T1/2 >103 y). Table 2–3 presents the same data for the production of radioactive isotopes other than technetium. The data presented in both tables follow the criteria listed in Section 2.4.3. Figure 2–4 shows the excitation functions for the four reaction channels which have the highest cross sections for the 100Mo + p reaction. Fortunately 99Mo, which yield increases at higher energies, decays to 99xmTc (with branching ratio of 87.6%), therefore contribution from this (p,pn) reaction will only increase the 99mTc production yield. Additionally, Figure 2–5 and Figure 2–6 compares the excitation functions for the 100Mo(p,2n)99mTc production to the six radioactive most abundant (isomeric and ground states) technetium isotopes produced through the (p,n) reaction and (p,2n) reaction channels. 2. Theoretical Yields Estimations  37  Figure 2–4 Excitation functions corresponding to the 100Mo+p reaction products with the highest cross sections in the investigated energy range. Stable isotopes are marked by an asterisk.  2. Theoretical Yields Estimations  38  Figure 2–5 Comparison of the 100Mo(p,2n)99mTc excitation function to the other technetium isotopes (isomeric and ground states) produced through the (p,n) reaction. The excitation function for 99mTc is marked with red circles and stable isotopes are marked by an asterisk.  Figure 2–6 Comparison of the 100Mo(p,2n)99mTc excitation function to the other technetium isotopes (isomeric and ground states) produced through the (p,2n) reaction. The excitation function for 99mTc is marked with red circles and stable isotopes are marked by an asterisk. 2. Theoretical Yields Estimations  39 Table 2–2 The theoretically calculated cross sections for the production of radioactive and stable technetium isotopes by proton induced reactions on molybdenum targetsa. The respective half-lives and decay products are also listed.  Stable isotopes (i.e. T1/2>103 y) are marked by an asterisk. Isotope T1/2 Decay Products (with their T1/2) Reaction Cross Section (mb) 10 MeV 16 MeV 19 MeV 20 MeV 24 MeV 30 MeV 93gTc 2.75 h → 93Mo (4.0x103 y) → 93Nb* 92Mo (p,γ) 5.56 1.08 0.68 0.54 0.13 0.014 94Mo (p,2n) 0 322 576 615 610 285.5 95Mo (p,3n) 0 0 0 0 66.1 340.8 93mTc 43.5 min 77% →93gTc (2.75 h) → 93Mo (4.0x103 y) → 93Nb*  23% → 93Mo (4.0x103 y) → 93Nb* 92Mo (p, γ) 2.00 0.19 0.09 0.06 0.01 0.003 94Mo (p,2n) 0 48.5 100 101 73.6 29.1 95Mo (p,3n) 0 0 0 0 4.79 31.2 94gTc 293 m → 94Mo* 94Mo (p,n) 452 338 129 96.2 33.9 16.7 95Mo (p,2n) 0 442 645 680 597 204 96Mo (p,3n) 0 0 0 0 40.7 378.6 94mTc 52 m → 94Mo* 94Mo (p,n) 187 67.2 24.2 19.0 11.1 7.48 95Mo (p,2n) 0 84.3 100.0 98.4 71.0 27.7 96Mo (p,3n) 0 0 0 0 5.55 46.7 95gTc 20 h → 95Mo* 94Mo (p, γ) 1.54 0.7 0.49 0.39 0.08 0.02 95Mo (p,n) 528 285 108 78.2 30.2 15.9 96Mo (p,2n) 0 573 747 773 730 259 97Mo (p,3n) 0 0 0.41 15.8 300 552 95mTc 61 d 4% →95gTc (20 h) → 95Mo* 96% → 95Mo* 94Mo (p, γ) 0.86 0.24 0.14 0.10 0.02 0.007 95Mo (p,n) 165 54.7 23.3 18.6 11.4 7.6 96Mo (p,2n) 0 186 197 193 142 53.6 97Mo (p,3n) 0 0 0.03 1.69 57.3 82.1 96gTc 4.28 d → 96Mo* 96Mo (p,n) 594 222 88.1 68.0 33.4 19.4 97Mo (p,2n) 0 720 841 837 532 163.3 98Mo (p,3n) 0 0 0 0.95 276 601 96mTc 51.5 m 98% →96gTc (4.28 d) → 96Mo* 2% → 96Mo* 96Mo (p,n) 122 42.6 14.9 11.1 5.5 3.2 97Mo (p,2n) 0 140 150 145 80.0 24.0 98Mo (p,3n) 0 0 0 0.20 50.1 96.5 97gTc*  4.2x106 y → 97Mo* 97Mo (p,n) 608 154 61.7 48.5 26.2 16.6 98Mo (p,2n) 0 825 933 948 648 182.2 97mTc 91.4 d 96% →97gTc* (4.2x106 y) →97Mo* 4% → 97Mo* 97Mo (p,n) 111 24.6 13.1 11.4 8.23 5.74 98Mo (p,2n) 0 156 143 135 82.9 30.7 98Tc* 4.2x106 y → 98Ru* 98Mo (p,n) 728 110.0 51.9 43.7 28.5 18.9 100Mo (p,3n) 0 0 101 210 691 723 99gTc* 2.1x105 y → 99Ru* 100Mo (p,2n) 318.4 864 858.9 777.8 356.3 110.3 99mTc 6.01 h → 99gTc* (2.1x105 y) → 99Ru* 100Mo (p,2n) 157 213.5 179.8 155.8 74.9 31.9 a Only reactions defined by the criteria outlined in Section 2.4.3 are listed.2. Theoretical Yields Estimations  40 Table 2–3 The theoretically calculated cross sections for the production of radioactive isotopes (other than technetium) by proton induced reactions on molybdenum targetsa. The respective half-lives and decay products are also listed. Stable isotopes (i.e. T1/2>103 y) are marked by an asterisk. Isotope T1/2 Decay Products (with their T1/2) Reaction Cross Section (mb) 10 MeV 16 MeV 19 MeV 20 MeV 24 MeV 30 MeV 91Mo 15.5 m → 91Nb (6.8x102 y) → 91Zr* 92Mo (p,pn) 0 28.5 332 429 665 668 93mMo 6.9 h →93Mo* 94Mo (p,pn) 0 0.26 0.97 1.67 8.39 17.64 99Mo 65.9 h 17.8% → 99gTc* (2.1x105 y) → 99Ru* 82.2% →99mTc (6.01 h)→ 99gTc (2.1x105 y) → 99Ru* 100Mo (p,pn) 0 8.07 37.0 51.2 89.6 95.8 89gNb 2.0 h → 89Zr (78.4 h) → 89Y* 92Mo (p,α) 0.07 7.72 39.6 51.8 54.3 13.4 89mNb 66 m → 89Zr (78.4 h) → 89Y* 92Mo (p,α) 0.04 1.25 3.77 3.98 2.25 1.2 90Nb 14.6 h →90Zr* 94Mo (p,αn) 0 0 0.55 2.20 28.8 65.3 91mNb 60.9 d 97% → 91Nb (6.8x102 y) → 91Zr* 3% → 91Zr* 92Mo (p,2p) 0 8.36 40.6 47.5 52.2 47.1 94Mo (p,α) 4.41 12.3 10.8 9.62 6.03 6.83 95Mo (p,αn) 0 2.55 9.29 11.6 18.5 19.0 92mNb 10.2 d → 92Zr* 95Mo (p,α) 3.09 18.1 12.9 12.0 8.02 6.05 96Mo (p,αn) 0 1.00 10.2 13.8 25.2 23.9 93mNb 16 y → 93Nb* 96Mo (p,α) 0.64 5.04 4.21 3.83 2.95 2.14 97Mo (p,αn) 0.004 1.62 4.42 5.50 8.75 9.03 94mNb 6.3 m →94Nb*(2.0x104 y) →94Mo* 97Mo (p,α) 1.60 14.5 12.3 11.1 7.39 5.49 98Mo (p,αn) 0 1.37 9.77 13.0 25.2 25.1 95gNb 35 d 95Mo* 98Mo (p,α) 0.49 13.9 13.8 12.0 8.61 6.41 95mNb 3.6 d 94% →95gNb (35 d)→ 95Mo* ;  6% →95Mo* 98Mo (p,α) 0.06 0.97 1.13 1.06 0.98 0.89 96Nb 23.4 h → 96Mo* 100Mo (p,α) 0 3.08 12.1 15.6 26.9 24.5 97Nb 72.1 m → 97Mo* 100Mo (p,α) 0.26 8.62 9.31 9.33 7.52 6.22 88Zr 83.4 d →88Y(106.6 d) →88Sr* 92Mo (p,αp) 0 0.01 1.30 3.50 33.0 62.2 a Only reactions defined by the criteria outlined in Section 2.4.3 are listed.2. Theoretical Yields Estimations  41 2.5.2 Reaction yields results In order to identify the optimal conditions for the cyclotron production of 99mTc the enriched molybdenum thick target yields were calculated for irradiation times of 3 h (hours), 6 h, 9 h, and 12 h. The current of proton beam of 200 μA were used and the beam energies were set as 16-10 MeV, 19-10 MeV and 24-10 MeV. This energy range was selected based on the analysis of the results of cross section calculations. The excitation functions presented in Figure 2–5 and Figure 2–6 indicate that in the 6-10 MeV energy range the contributions from the (p,n) reactions dominate, while for the 100Mo(p,2n)99mTc reaction, significant production begins only at about 9 MeV. Therefore, in order to optimize the ratio of 99mTc to (p,n) reaction products it would be beneficial to use targets thickness that would allow protons with energies lower than about 10 MeV to escape. Table 2–4 compares the number of 99mTc nuclei that would be created at EOB with the corresponding cumulative production of all stable technetium isotopes (i.e. T1/2>103 y), all other radioactive technetium isotopes and all other (non-technetium) radioactive products. Additionally, the percent ratios of 99mTc to all technetium (stable and radioactive), all radioactive technetium and all radioactive isotopes are listed.  The data from Table 2–4 were used to calculate ratios of the number of 99mTc nuclei to the total number of nuclei of other radioactive technetium and of other radioactive elements. These data are presented in Figure 2–7. Figure 2–8 shows 2. Theoretical Yields Estimations  42 similar ratios of the number of 99mTc nuclei to the total number of all technetium nuclei.  The results of the calculations of the saturated thick target yields (MBq/μA) for the cumulative creation of the dominant radioactive reaction product are summarized in Table 2–5. Yields correspond to enriched and natural molybdenum targets irradiated with 16-10 MeV, 19-10 MeV and 24-10 MeV proton beam. Figure 2–9 compares the 99mTc production yield with the four other radioactive products with highest yields for the 99.54% enriched target. Figure 2–10 shows a similar comparison for the irradiation of a natural molybdenum target.           2. Theoretical Yields Estimations  43 Table 2–4 The calculated number of nuclei of 99mTc and other reaction products obtained at EOB for 3 h, 6 h, 9 h, and 12 h irradiation of Target II (99.54% enriched thick molybdenum) with 16-10 MeV, 19-10 MeV and 24-10 MeV protons with 200 A current. Additionally, the percent ratios of 99mTc to all technetium, to stable technetium, to all radioactive technetium and to the sum of all radioactive isotopes are listed.  3 h 6 h 9 h 12 h  Proton Energy = 16-10 MeV 99mTc 5.13E15 8.75E15 1.13E16 1.31E16 Total stable Tc 2.06E16 4.27E16 6.59E16 8.99E16 Total other radioactive Tc 1.72E13 3.38E13 5.00E13 6.60E13 Total radioactive other 1.26E14 2.12E14 2.87E14 3.59E14      99mTc/all technetium 19.9% 17.0% 14.6% 12.7% 99mTc/all stable technetium 24.9% 20.5% 17.2% 14.6% 99mTc /all radioactive technetium 99.7% 99.6% 99.6% 99.5% 99mTc /all radioactive isotopes 97.3% 97.3% 97.1% 96.9%  Proton Energy = 19-10 MeV 99mTc 7.74E15 1.32E16 1.71E16 1.99E16 Total stable Tc 3.58E16 7.38E16 1.13E17 1.54E17 Total other radioactive Tc 2.85E13 5.59E13 8.26E13 1.09E14 Total radioactive other 7.24E14 1.32E15 1.71E15 1.99E15      99mTc/all technetium 17.8% 15.2% 13.1% 11.4% 99mTc/all stable technetium 21.6% 17.9% 15.1% 12.9% 99mTc /all radioactive technetium 99.6% 99.6% 99.5% 99.5% 99mTc /all radioactive isotopes 91.1% 90.4% 89.5% 88.5%  Proton Energy = 24-10 MeV 99mTc 1.06E16 1.81E16 2.35E16 2.73E16 Total stable Tc 6.70E16 1.37E17 2.09E17 2.83E17 Total other radioactive Tc 6.29E13 1.23E14 1.82E14 2.40E14 Total radioactive other 3.57E15 6.83E15 9.93E15 1.29E16      99mTc/all technetium 13.6% 11.6% 10.1% 8.8% 99mTc/all stable technetium 15.8% 13.2% 11.2% 9.6% 99mTc /all radioactive technetium 99.5% 99.4% 99.3% 99.1% 99mTc /all radioactive isotopes 74.4% 72.2% 69.9% 67.5%   2. Theoretical Yields Estimations  44  Figure 2–7 The EOB ratios of the number of 99mTc nuclei to the total number of nuclei of all other radioactive technetium (i.e.≠99mTc) isotopes (solid line) and to the total number of nuclei of other radioactive elements (dashed line) produced with 99.54% enriched molybdenum target irradiated for 3 h, 6 h, 9 h and 12 h with proton beam with 16-10 MeV, 19-10 MeV and 24-10 MeV.  Figure 2–8 The EOB ratios of 99mTc nuclei to all stable and radioactive technetium isotopes (including 99mTc) produced with 99.54% enriched molybdenum target irradiated for 3 h, 6 h, 9 h and 12 h with proton beam with 16-10 MeV, 19-10 MeV and 24-10 MeV.  0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 3.50E+02 0 2 4 6 8 10 12 14 99mTc/Radioactive Products Irradiation Time (h) 16MeV 19MeV 24MeV 16MeV 19MeV 24MeV Radioactive technetium isotopes Other  radioactive elements 2. Theoretical Yields Estimations  45 Table 2–5 Calculated thick target saturated yields (MBq/μA) for the dominant radioactive products. Enriched and natural molybdenum targets were irradiated with proton energies 16-10 MeV, 19-10 MeV and 24-10 MeV.     Target I  (97.39% Enriched Mo) Target II  (99.54% Enriched Mo)  Natural Mo Product T1/2 16 MeV 19 MeV 24 MeV 16 MeV 19 MeV 24 MeV 16 MeV 19 MeV 24 MeV Radioactive technetium isotopes 99mTc 6.01 h 2748 4144 5640 2809 4235 5765 272 410 558 97mTc 91.4 d 41.2 69.7 108 6.35 9.51 15.8 468 734 1125 96mTc 51.1 m 0.178 0.295 8.62 0.034 0.054 1.38 339 470 710 96gTc 4.28 d 0.862 1.50 46.4 0.164 0.270 7.40 1914 2332 3782 95mTc 61 d 0.143 0.226 0.392 0.140 0.175 0.224 463 738 1198 95gTc 20 h 0.507 0.819 1.59 0.561 0.707 0.920 1640 2693 4765 94mTc 52 m 0.122 0.172 0.242 0.134 0.204 0.304 252 394 604 94gTc 293 m 0.450 0.735 1.24 0.512 0.912 1.65 975 1793 3357 93mTc 43.5 m 0.009 0.043 0.105 0.009 0.044 0.108 16.8 79.9 196 93gTc 2.75 h 0.054 0.240 0.688 0.055 0.245 0.709 102 446 1293 Radioactive other elements 99Mo 65.9 h 27.3 215 1196 27.9 220 1222 2.70 21.3 118 93mMo 6.9 h 0.0000 0.0002 0.004 0.0000 0.0002 0.004 0.006 0.372 6.51 91Mo 15.5 m 0.0034 0.009 0.476 0.004 0.103 0.57 9.85 256 1413 97Nb 72.1 m 42.5 92.3 175 43.4 94.3 179 4.20 9.13 17.3 96Nb 23.4 h 10.1 74.3 369 10.3 76.0 377 1.00 7.31 36.5 95mNb 3.6 d 0.173 0.382 0.751 0.027 0.061 0.119 1.62 3.57 7.03 95Nb 35 d 2.25 5.02 8.68 0.358 0.800 1.38 21.0 47.0 81.1 94mNb 6.3 m 0.120 1.38 8.36 0.019 0.219 1.33 12.9 33.7 111 92mNb 10.2 d 0.009 0.016 0.037 0.013 0.021 0.035 27.0 53.2 120 91mNb 60.9 d 0.008 0.026 0.077 0.009 0.030 0.094 18.34 66.5 215.2 89mNb 66 m 0.0003 0.001 0.004 0.0004 0.002 0.004 1.00 4.24 10.7 89Nb 2.0 h 0.002 0.012 0.052 0.002 0.014 0.062 5.07 35.0 154 90Nb 14.6 h 0.0000 0.0001 0.014 0.0000 0.0001 0.014 0.0005 0.233 25.2 93mNb 16 y 0.003 0.007 0.019 0.0006 0.0014 0.0034 7.15 15.4 32.6 88Zr 83.4 d 0.0000 0.0002 0.012 0.0000 0.0003 0.014 0.0043 0.649 34.9  2. Theoretical Yields Estimations  46  Figure 2–9 Comparison of the theoretical saturated thick target yields for the 99mTc production with four other radioactive products with highest yields. In this example, a 99.54% enriched molybdenum target was irradiated with proton energies of 16 MeV, 19 MeV and 24 MeV.   Figure 2–10 Comparison of the theoretical saturated thick target yields for the 99mTc production with several other radioactive products with highest yields. In this example, a natural molybdenum target was irradiated with proton energies of 16 MeV, 19 MeV and 24 MeV.  2. Theoretical Yields Estimations  47 It needs to be noted that due to the presence of a variety of radioactive products (each decaying at a different rate), the composition of the irradiated target will continue to change over time following irradiation. For this reason, we have also investigated the change of the ratio of number of 99mTc nuclei to the cumulative number of nuclei of other radioactive and stable technetium isotopes over a time tD post irradiation. The results are presented in Figure 2–11 for the incident proton energy of 19 MeV. In this example, the 99.54% enriched thick molybdenum target was irradiated for 6 hours and then allowed to decay for additional 24 hours. Please note that the total number of stable technetium isotopes continues to increase after EOB fed by contributions from the decay of other radioactive isotopes (e.g. 99mTc99gTc).   Figure 2–11 Calculated change of the number of nuclei of 99mTc and cumulative number of nuclei of other radioactive and stable technetium. In this example, a 99.54% enriched molybdenum target was irradiated for 6 h with 200 μA proton beam at 19 MeV and then allowed to decay for additional 24 hours.   1.00E+12 1.00E+13 1.00E+14 1.00E+15 1.00E+16 1.00E+17 0 5 10 15 20 25 30 Number of Atoms Time (h) 99mTc Tc radioactive Tc stable 99m2. Theoretical Yields Estimations  48 2.6 Discussion In this chapter, a comprehensive investigation of several aspects of the cyclotron-based production of 99mTc was presented. A summary of theoretically calculated cross sections for the productions of radioactive and stable (i.e. T1/2>103y) technetium and radioactive other non-technetium isotopes were reported. The analysis of calculated cross sections clearly indicates that in the investigated energy range the (p,n) and (p,2n) reactions are responsible for creation of the majority of contaminants as they have the highest cross section values (the only exception is 100Mo(p,3n)98Tc reaction which begins at about 18 MeV). Figure 2–5 and Figure 2–6 compare the 100Mo(p,2n)99mTc cross section with (p,n) and (p,2n) reaction cross sections. For both reaction channels the cross section for creation of an isotope in isomeric state is typically about three to five times smaller than that corresponding to the ground state of the same isotope.  The results of this study clearly demonstrate that if natural molybdenum is used as the reaction target (i.e. substantial amounts of isotopes other than 100Mo are present in the target) several of the reaction channels have sufficiently large cross sections in the investigated energy range to compete with (and overwhelm) the 99mTc production. The situation is substantially improved if an enriched target is used, because then the competition from reactions occurring on molybdenum isotopes other than 100Mo becomes less important. Nevertheless, even in the case of reaction on pure (i.e. 100%) 100Mo the cross sections for production of 99gTc and, for higher energies, 98Tc are substantial (see Figure 2–4). 2. Theoretical Yields Estimations  49 Table 2–4 and Table 2–5 summarize the results of the model-based calculations of the reaction yields. Careful analysis of these data confirms that in order to determine the optimum conditions for 99mTc production one should consider the ratios of different production yields rather than the absolute production values.  Although the data in Table 2–4 clearly show that the production of 99mTc steadily increases from 16 MeV to 24 MeV, it is important to realize that the production of other stable and radioactive isotopes increases even faster. Based solely on the analysis of the theoretical calculations (see also Figure 2–7 and Figure 2–8), one may suggest that the most favorable proton energy for 99mTc production would be somewhere in the region between 16 MeV-19 MeV. The results of these theoretical calculations must however be confirmed by experimental yield measurements. The yields presented in Table 2–5, Figure 2–9 and Figure 2–10 confirm the earlier finding that the amount of contaminants produced in the proton induced reaction on natural molybdenum target will preclude its use in nuclear medicine. On the other hand, using enriched targets significantly decreases the yields for other isotopes confirming feasibility of cyclotron 99mTc production. Although proton beam currents up to 1.2 mA are possible, medical cyclotrons are typically designed to produce only about 200 A beam currents (with possible upgrades to 500 μA). The results indicate that a single 19 MeV cyclotron with a 200 A proton beam could, in theory, produce about 430-440 GBq of 99mTc in a 6 hour cyclotron run.  2. Theoretical Yields Estimations  50 2.7 Summary Cross sections for the proton induced reactions on molybdenum targets have been theoretically calculated. Based on that, reaction yields for the production and decay of radioactive and stable isotopes were estimated. The proposed approach allows us to theoretically estimate the amount of 99mTc and its ratio to 99gTc and other stable and radioactive isotopes in order to minimize patient dose which may arise from other radioactive technetium isotopes, minimize radioactive waste and optimize labeling procedures.  Although absolute production yields are higher at proton energies of 19 MeV or even at 24 MeV, the analysis of ratios of 99mTc to other reaction products indicate that proton energies closer to 16-19 MeV may correspond to the most advantageous energy region, where 99mTc production is high while the amount of contaminants is minimized. Moreover, these yield results will be used to estimate potential patient doses that may occur in a number of clinical diagnostic procedures and to compare dosimetry for the cyclotron- and reactor-produced 99mTc, which will be presented in the next chapter. Furthermore, the calculations in this study are based purely on theoretical estimations. Although such predictions may be very useful as guidance in experiments involving 99mTc cyclotron production, all theoretical calculation results have to be verified by direct experimental measurements, which will be discussed in Chapter 5. 3. Theoretical Dosimetry Estimations  51 Chapter 3 Theoretical Dosimetry Estimations The aim of this chapter is to estimate dosimetry for the cyclotron-produced technetium and to investigate the changes of patient doses that may occur when using cyclotron-produced 99mTc as compared with the reactor/generator-produced pure 99mTc.  3.1 Introduction In chapter 2, the estimations of cyclotron production of technetium radioisotopes have been performed including theoretically calculated cross sections and production yields for all stable and radioactive isotopes. These calculations confirmed a well-known fact that, unlike the reactor-produced pure 99mTc, in cyclotron production a large number of various radioactive and stable isotopes of technetium, molybdenum (Mo), niobium (Nb) and zirconium (Zr) would be created through different reaction channels. Considering different beam energies, irradiation times and target enrichments, we searched for the optimal reaction conditions which would maximize the production of 99mTc while minimizing the amount of these contaminants. All other-than-technetium radioactive isotopes that would be produced during the proton irradiation on molybdenum targets (which includes Mo, Nb and Zr) constitute radioactive waste and are potential sources of contamination in the labs. But, providing that chemical separation is performed correctly and efficiently, these radioisotopes do not need to be considered in patient dosimetry calculations as they will not be present in the injected radiotracer [61]. 3. Theoretical Dosimetry Estimations  52 Chemical purification, however, will not be able to separate different technetium isotopes, which will be present in each produced batch. Thus, patient radiotracer injection will contain, besides 99mTc, other radioactive technetium isotopes as they will remain in the sample, be incorporated into the labeled radiotracer and contribute to patient radiation doses. The list of these isotopes is presented in Table 2–5. As before, the three long-lived (T1/2>103 year) technetium isotopes (97gTc, 98Tc, and 99gTc) are considered as stable. Although they can decrease the specific activity of the produced technetium, their very slow decay will not contribute to patient radiation dose in any meaningful way. Therefore, only the remaining relative short-lived technetium isotopes are potential contributors to patient doses. In this chapter, absorbed doses are estimated for the three most commonly used Tc-labeled imaging radiotracers, namely a) sestaMIBI™, which is used for myocardial perfusion scans [62], b) phosphonates, which are bone imaging agents [63], and c) pertechnetate, which is used for imaging of the thyroid [64]. The information about the relative amounts of 99mTc and its contaminants for different production conditions is obtained from the theoretical calculations following the yield equations shown in section 2.4.2. These conditions include the energy of the proton beam, irradiation and cooling times (time after EOB) and isotope enrichment of the target. The relative increase in patient absorbed doses due to admixture of other technetium isotopes are compared to doses from pure 99mTc that would be obtained when using the traditional reactor-produced 99Mo/99mTc. Furthermore, the question as to which technetium isotopes are the most significant contributors to the effective doses is investigated. Finally, the optimal conditions for cyclotron-3. Theoretical Dosimetry Estimations  53 production of 99mTc and the ‘ideal’ injection period of the Tc-labeled agents that would result in minimal dose increase to the patient are explored. 3.2 General concepts of NM dosimetry  3.2.1 Definition of dose As shown in Chapter 1, two types of radiation, photons and charged particles, can be emitted during radioactive decays. When these emissions pass through matter the energy is deposited. Absorbed radiation dose (𝐷) is defined as the total energy deposited by radiation per unit mass of organ or tissue, shown in equation (3-1). The basic unit of radiation dose is the Gray (Gy), which equals to 1 joule of energy deposited per kilogram of material.  𝐷 =𝑑𝐸𝑑𝑚 (3-1) Since different types of radiation can cause different levels of biological damage, equivalent dose (H) in unit of Sievert (Sv) is introduced to represent the dose quantity that takes into account the relative biological effects caused by radiation interacting with organ or tissue. It is related to the absorbed dose 𝐷 by:  𝐻 = 𝐷 × 𝑄 (3-2) where Q is the weighting factor of a given radiation type. For photons and electrons the Q=1; while for  particles, Q=20.  Not only radiation types affect the radiation effect, but also each organ or tissue may have different radiation sensitivity. In general, this sensitivity is 3. Theoretical Dosimetry Estimations  54 proportional to the rate of proliferation of cells and inversely proportional to the degree of cell differentiation. Considering different probabilities of the occurrence of stochastic radiation effect in various organs and tissues, International Commission on Radiological Protection (ICRP) provides the definition of effective dose in [65]:  𝐸 =∑𝐻𝑇𝑤𝑇𝑇 (3-3) where the subscript 𝑇 represents the type of an organ or tissue, while 𝑤𝑇 represents tissue weighting factors. Such effective dose provides an estimate of the total probability of the occurrence of radiation effects.  3.2.2 Dosimetry estimations in NM A generic equation for the absorbed dose in a target region from a source region can be given as [66, 67]:  𝐷𝑟𝑇←𝑟𝑆 = 𝐴?̃?∑ 𝑛𝑖𝑖 𝐸𝑖𝜙𝑖(𝑟𝑇 ← 𝑟𝑆)𝑚𝑇 (3-4) where: 𝐷𝑟𝑇←𝑟𝑆  is the mean absorbed dose in the target region T from activity in the source region S,  𝑟𝑇 represents the target region and 𝑟𝑆 represents the source region. 𝑛𝑖  is the number of radioactive emissions with energy 𝐸𝑖 (MeV) per nuclear decay, 𝜙𝑖  is the absorbed fraction (the fraction of energy emitted from the source rS that is deposited in the target rT) and 𝑚𝑇 is the mass of the target region. The summation i is performed over the number of radioactive emissions from the given radioisotope that contribute to the dose. 𝐴?̃? (MBq-s or uCi-h) is the cumulated activity in the 3. Theoretical Dosimetry Estimations  55 source organ, which represents the total number of nuclear decays, integrated over a time period for which dose is calculated.  The dose to a target region from multiple source regions requires summation over all these regions. The calculations can be substantially simplified using Medical Internal Radiation Dose (MIRD) system:   𝐷 𝑟𝑇 =∑𝐴?̃?𝑆(𝑟𝑇 ← 𝑟𝑆)𝑠 (3-5) with all terms other than the cumulated activity lumped in the factor S:  𝑆(𝑟𝑇←𝑟𝑆) =∑ 𝑛𝑖𝑖 𝐸𝑖𝜙𝑖(𝑟𝑇 ← 𝑟𝑆)𝑚𝑇 (3-6) Thus, the S factor represents the pre-calculated dose per unit of cumulated activity of a given radioisotope. 3.2.3 Cumulated activity and effective half-life To estimate the cumulated activity 𝐴?̃? in a source organ 𝑆, injected activity needs to be integrated over total time spent by the radioisotope of interest in this organ considering that the radioisotope decays following the equations (1-1) and (1-2). However, the decay factor in the formulae should be replaced by the effective disappearance constant 𝜆𝑒𝑓𝑓, which combines the physical decay factor with a factor indicating the biological washout (disappearance):  𝜆𝑒𝑓𝑓 = 𝜆𝑝ℎ𝑦 + 𝜆𝑏𝑖𝑜 (3-7) 3. Theoretical Dosimetry Estimations  56 where 𝜆𝑝ℎ𝑦 represents the physical decay factor of radioisotopes; 𝜆𝑏𝑖𝑜 represents the biological washout constant. In turn, the effective half-life (𝑇12𝑒𝑓𝑓) of the injected radioisotope for a source organ can be written as:   1𝑇12𝑒𝑓𝑓=1𝑇12𝑝ℎ𝑦+1𝑇12𝑏𝑖𝑜 (3-8) where 𝑇12𝑝ℎ𝑦 is the half-life of radioisotope while 𝑇12𝑏𝑖𝑜 is the biological half-life in which half of the remaining material is removed by biological processes and has the relationship with 𝜆𝑏𝑖𝑜 :  𝜆𝑏𝑖𝑜 =ln(2)𝑇12𝑏𝑖𝑜 (3-9) Thus the cumulated activity in the source organ 𝑆 is:  𝐴?̃? = ∫ 𝐴𝑠∞0(𝑡)𝑑𝑡 = ∫ 𝐴𝑠0∞0𝑒−𝜆𝑒𝑓𝑓𝑡 =𝐴𝑠0𝜆𝑒𝑓𝑓 (3-10) where 𝐴𝑠0 is the administrated activity.  The ratio of cumulated activity to the administrated activity is presently referred to as the time-integrated-activity-coefficient aS̃  (traditional name was residence time) and accordingly the absorbed dose coefficient 𝑑𝑟𝑇←𝑟𝑆 can be defined as:   𝑑𝑟𝑇←𝑟𝑆 = 𝑎?̃?∑ 𝑛𝑖𝑖 𝐸𝑖𝜙𝑖(𝑟𝑇 ← 𝑟𝑆)𝑚𝑇 (3-11) 3. Theoretical Dosimetry Estimations  57 3.3 Dosimetry estimation method  3.3.1 Productions of technetium isotopes used in dosimetry estimations When using the cyclotron production method, the relative amount of each radioisotope depends not only on the energy of the proton beam and the enrichment of the target (thus its isotopic composition), but also on the irradiation time and the time after the end of beam (EOB) which refers as the cooling time. It should be noted here that although the beam current determines the total quantity of the produced isotopes, it would not affect isotopic composition of the product. Thus, it will not have any influence on the dosimetry outcomes.  In order to not restrict the dosimetry study to only the optimal conditions which were concluded from Chapter 2, the dose calculations were performed for the whole range of irradiation parameters previously investigated. Namely, the production yields obtained with beam energies 16-10 MeV, 19-10 MeV and 24-10 MeV using beam current of 200 A and irradiation times of 3 h (hours), 6 h and 12 h were employed. The results of yield studies suggested that the target thickness should be such as to not degrade beam energy below 10 MeV because for lower proton energies the (p,n) reactions dominate resulting in higher contaminants level. In order to confirm this finding, the effect of using targets with different thicknesses (thus - different energy ranges) on the absorbed doses were also investigated. In this dosimetry study, in addition to a natural and two previously used target enrichments (Target I and Target II in Table 2–1), which differed mostly in 3. Theoretical Dosimetry Estimations  58 their relative amounts of 98Mo, a third enrichment option was investigated (Target III). Although in this option, 99.01% of the target corresponds to 100Mo, other isotopes are present in relatively equal quantities (contrary to Target I and II) significantly altering the amount of produced contaminants. Finally, since each produced batch has to undergo chemical processing, necessary to extract technetium from the target, we estimated absorbed doses that the patient would be receiving if the radiotracer injection would occur at 0 h, 2 h, 8 h, 12 h and 24 h after EOB.  3.3.2 Dosimetry estimations The dosimetry estimation in this study was performed following the equation (3-5). In the situation when radiotracer injection includes more than one radioisotope, the total absorbed dose in the target organ from the source organ originating from a mixture of radioisotopes becomes:   𝐷𝑟𝑇←𝑟𝑆 =∑𝑓𝑖 𝑖𝐷𝑟𝑇←𝑟𝑆 ,𝑖 (3-12) where 𝑓𝑖  is the fraction of the total activity corresponding to each radioisotope and 𝐷𝑟𝑇←𝑟𝑆 ,𝑖 is the dose to target organ for each pure isotope product.  In dosimetry calculations, the three most widely used imaging radiotracers were modeled, namely sestaMIBI™, phosphonates, and pertechnetate. Biokinetic information from ICRP Publication 53 [68] was used to extract for each agent its organ-specific biological half-life. These were combined with physical half-life for each radioactive technetium isotope to generate their respective (theoretically 3. Theoretical Dosimetry Estimations  59 estimated) time-integrated-activity-coefficients, 𝑎?̃? (summarized in Table 3–1). Dose calculations were performed using the OLINDA/EXM 1.1 software [69] and the theoretically estimated 𝑎?̃? in organs with significant uptake were input into the program. In order to determine the resulting dose distribution at the organ level, OLINDA employs tables of dose factors pre-calculated using Monte Carlo simulations of a series of reference phantoms. For this study, the adult male reference phantom was used. The doses calculated for the mixture of technetium isotopes (cyclotron-produced 99mTc) were compared to the doses resulting from the same agents labeled with pure 99mTc, corresponding to the pure 99mTc produced by reactor.  3.4 Results The first step in the dosimetry calculations was to compare the relative dose contributions to the total effective radiation dose from each of the ten radioactive technetium products (ground and isomeric states were considered separately). Table 3–2 presents an example of these results calculated for sestaMIBI™. The activities used in these calculations correspond to those obtained after 6 h irradiation of a target by a 200 A proton beam with energy 19-10 MeV. The radiation doses were estimated for injection periods of 0 h, 2 h, 8 h, 12 h and 24 h.  In the next step, the contributions from all ten products were summed and radiation-absorbed doses were calculated for the three considered imaging agents labeled with the mixture-Tc (corresponding to a cyclotron production) and 3. Theoretical Dosimetry Estimations  60 compared with those labeled with reactor-produced pure 99mTc. Table 3–3 summarizes the percent differences in effective radiation dose after the injection of technetium labeled sestaMIBI™, phosphonates and pertechnetate performed at 0 h, 2 h, 8 h, 12 h and 24 h after the end of beam (EOB). In this case molybdenum target I and III were irradiated for 3 h, 6 h and 12 h with a 200 A proton beam with energies equal to 16-10 MeV, 19-10 MeV and 24-10 MeV. Target II has nearly the same abundance of the 92-97Mo isotopes as Target I and thus was not included in this table. Natural thick molybdenum target was also not included since it is clear that the doses resulting from the use of natural Mo would be prohibitive. Figure 3–1 presents these data in graphical form for sestaMIBI™ injections labeled with technetium produced using I and III enriched targets. 3. Theoretical Dosimetry Estimations  61 Table 3–1 The summary of time-integrated-activity-coefficients 𝒂?̃? (hour) for all radioactive technetium isotopes that would be contributing to patient absorbed dose after a standard radiotracer injection of sestaMIBI™, phosphonates and pertechnetate when labeled with cyclotron-produced 99mTc.  93mTc 93gTc 94mTc 94gTc 95mTc 95gTc 96mTc 96gTc 97mTc 99mTc 𝑇1/2𝑝ℎ𝑦𝑠 43.5 min 2.75 h 52 min 293 min 61 d 29 h 51.5 min 4.28 d 91.4 d 6.01 h  sestaMIBI™ Heart 0.014 0.041 0.016 0.061 0.23 0.13 0.016 0.19 0.23 0.069 Liver 0.13 0.29 0.15 0.38 1.21 0.69 0.15 1.04 1.21 0.42 Kidneys 0.13 0.40 0.16 0.58 1.41 1.05 0.15 1.32 1.41 0.65 Muscles 0.20 0.71 0.24 1.17 6.81 3.15 0.24 5.61 6.85 1.39 Salivary glands 0.015 0.053 0.018 0.088 0.51 0.24 0.018 0.42 0.51 0.10 Thyroid 0.0023 0.0050 0.0026 0.0061 0.0086 0.0079 0.0026 0.0085 0.0086 0.0065 Small intestine 0.15 0.36 0.17 0.46 0.72 0.63 0.17 0.70 0.72 0.49 Upper large intestine 0.036 0.27 0.049 0.52 2.32 1.42 0.048 2.09 2.33 0.64 Lower large intestine 0.0028 0.071 0.0045 0.22 4.24 1.43 0.0044 3.33 4.26 0.31 Bladder contents 0.016 0.089 0.022 0.15 0.55 0.34 0.021 0.50 0.56 0.17 Remainder tissues 0.46 1.60 0.54 2.63 15.3 7.08 0.54 12.6 15.4 3.12  Phosphonates Cortical bone 0.17 0.71 0.21 1.22 27.9 4.06 0.21 10.8 28.3 1.48 Trabecular bone 0.17 0.71 0.21 1.22 6.98 4.06 0.21 10.8 7.09 1.48 Kidneys 0.024 0.069 0.028 0.12 1.26 0.31 0.0278 0.79 1.28 0.13 Bladder contents 0.25 0.83 0.32 1.07 2.14 1.49 0.31 1.86 2.15 1.15 Remainder tissues 0.41 0.72 0.44 0.90 4.52 1.60 0.44 3.08 4.58 0.97  Pertechnetate Thyroid 0.013 0.027 0.015 0.035 0.068 0.052 0.015 0.063 0.068 0.037 Stomach wall 0.12 0.21 0.13 0.24 0.29 0.27 0.13 0.29 0.29 0.25 Small intestine 0.17 0.55 0.19 0.51 0.80 0.70 0.19 0.78 0.80 0.55 Upper large intestine 0.040 0.71 0.054 0.58 2.58 1.57 0.054 2.33 2.59 0.71 Lower large intestine 0.0031 0.35 0.0050 0.24 4.71 1.59 0.0048 3.70 4.74 0.35 Bladder contents 0.046 0.32 0.059 0.28 1.68 0.57 0.058 1.02 1.72 0.32 Remainder tissues 0.72 2.32 0.85 3.68 28.3 9.91 0.84 20.7 28.5 4.31 3. Theoretical Dosimetry Estimations  62 Table 3–2 The summary of relative contributions (%) to the total effective dose from all radioactive technetium isotopes (ground and isomeric states are considered separately) for sestaMIBI™ injection. Cyclotron 6 h irradiation of the three enriched targets and a natural molybdenum target by a proton beam with 19-10 MeV energy and the injection times at 0 h, 2 h, 8 h, 12 h and 24 h after EOB were considered.  93mTc 93gTc 94mTc 94gTc 95mTc 95gTc 96mTc 96gTc 97mTc 99mTc Injection time after EOB 43.5 min 2.75 h 52 min 293 min 61 d 20 h 51.5 min 4.28 d 90.4 d 6.01 h 97.39% target enrichment (Target I) 0 h 0.00 0.04 0.03 0.23 0.00 0.07 0.00 0.17 0.09 99.34 2 h 0.00 0.03 0.01 0.22 0.00 0.08 0.00 0.22 0.12 99.32 8 h 0.00 0.01 0.00 0.18 0.00 0.13 0.00 0.43 0.23 99.00 12 h 0.00 0.01 0.00 0.16 0.00 0.18 0.00 0.65 0.37 98.62 24 h 0.00 0.00 0.00 0.11 0.01 0.45 0.00 2.23 1.36 95.84  99.54% target enrichment (Target II) 0 h 0.00 0.04 0.03 0.28 0.00 0.06 0.00 0.03 0.01 99.52 2 h 0.00 0.03 0.01 0.27 0.00 0.07 0.00 0.04 0.02 99.57 8 h 0.00 0.01 0.00 0.22 0.00 0.11 0.00 0.08 0.04 99.53 12 h 0.00 0.01 0.00 0.20 0.00 0.16 0.00 0.12 0.06 99.46 24 h 0.00 0.00 0.00 0.14 0.01 0.39 0.00 0.40 0.22 98.84  99.01% target enrichment (Target III) 0 h 0.02 0.43 0.38 3.27 0.01 1.37 0.02 1.84 0.02 92.41 2 h 0.00 0.34 0.10 3.10 0.02 1.61 0.00 2.35 0.02 92.45 8 h 0.00 0.15 0.00 2.57 0.03 2.54 0.00 4.42 0.05 90.25 12 h 0.00 0.08 0.00 2.23 0.05 3.38 0.00 6.58 0.07 87.60 24 h 0.00 0.01 0.00 1.27 0.14 7.01 0.00 19.08 0.23 72.26  Natural molybdenum target 0 h 0.21 5.78 5.11 44.54 0.16 18.42 0.20 21.56 0.08 0.78 2 h 0.04 4.65 1.32 42.88 0.21 21.98 0.05 27.97 0.10 0.79 8 h 0.00 1.60 0.02 28.17 0.32 27.49 0.00 41.64 0.16 0.61 12 h 0.00 0.71 0.00 19.50 0.39 29.22 0.00 49.51 0.19 0.48 24 h 0.00 0.05 0.00 5.13 0.56 27.85 0.00 65.95 0.28 0.18  3. Theoretical Dosimetry Estimations  63 Table 3–3 The percent differences in total effective doses between cyclotron- and reactor-produced Tc-labeled sestaMIBI™, phosphonates and pertechnetate for injection times at 0 h, 2 h, 8 h, 12 h and 24 h after EOB. Cyclotron productions correspond to 3 h, 6 h and 12 h irradiation of enriched targets (Target I and III) with proton beams with energies of 16-10 MeV, 19-10 MeV and 24-10 MeV. SestaMIBI™ Beam Energy Irrad. Time 97.39% enrichment (Target I) 99.01% enrichment (Target III) 0 h 2 h 8 h 12 h 24 h 0 h 2 h 8 h 12 h 24 h 16 MeV 3 h 0.57 0.57 0.81 1.12 3.54 7.20 6.87 9.23 12.22 34.78 6 h 0.58 0.61 0.90 1.26 4.07 7.15 7.24 10.10 13.58 39.58 12 h 0.64 0.70 1.11 1.58 5.24 7.73 8.19 12.07 16.61 50.06 19 MeV 3 h 0.65 0.65 0.91 1.24 3.80 8.33 7.86 9.97 12.83 34.11 6 h 0.66 0.69 1.01 1.40 4.34 8.21 8.17 10.81 14.15 38.39 12 h 0.73 0.79 1.23 1.74 5.49 8.70 9.07 12.71 17.02 47.53 24 MeV 3 h 4.02 4.91 8.86 13.18 40.81 11.59 11.15 13.84 17.51 41.76 6 h 4.60 5.61 10.15 15.08 45.87 11.49 11.54 14.92 19.17 46.11 12 h 5.86 7.14 12.94 19.12 55.63 12.14 12.68 17.34 22.72 54.32 Phosphonates Beam Energy Irrad. Time 97.39% enrichment (Target I) 99.01% enrichment (Target III) 0 h 2 h 8 h 12 h 24 h 0 h 2 h 8 h 12 h 24 h 16 MeV 3 h 0.52 0.46 0.57 0.75 2.14 7.10 6.13 7.49 9.59 25.96 6 h 0.50 0.47 0.62 0.83 2.45 6.71 6.29 8.10 10.57 29.47 12 h 0.52 0.52 0.74 1.01 3.13 6.89 6.89 9.50 12.75 37.15 19 MeV 3 h 0.60 0.53 0.65 0.83 2.31 8.34 7.18 8.24 10.19 25.47 6 h 0.57 0.54 0.70 0.92 2.62 7.84 7.27 8.81 11.12 28.63 12 h 0.59 0.60 0.83 1.12 3.29 7.91 7.79 10.14 13.18 35.31 24 MeV 3 h 3.23 3.76 6.59 9.74 29.95 11.54 10.22 11.47 13.93 31.27 6 h 3.59 4.25 7.53 11.13 33.65 10.97 10.31 12.19 15.09 34.43 12 h 4.47 5.36 9.56 14.08 40.78 11.05 10.94 13.85 17.61 40.41 Pertechnetate Beam Energy Irrad. Time 97.39% enrichment (Target I) 99.01% enrichment (Target III) 0 h 2 h 8 h 12 h 24 h 0 h 2 h 8 h 12 h 24 h 16 MeV 3 h 0.58 0.53 0.76 1.05 3.37 7.28 6.23 8.28 10.99 31.37 6 h 0.57 0.56 0.85 1.19 3.88 6.91 6.53 9.07 12.22 35.70 12 h 0.62 0.66 1.04 1.50 5.01 7.26 7.38 10.85 14.95 45.18 19 MeV 3 h 0.63 0.59 0.84 1.17 3.62 8.12 6.94 8.87 11.49 30.68 6 h 0.62 0.63 0.94 1.32 4.14 7.68 7.21 9.64 12.69 34.60 12 h 0.68 0.73 1.15 1.65 5.25 7.98 8.03 11.37 15.29 42.87 24 MeV 3 h 3.70 4.45 8.07 12.02 47.41 10.70 9.61 12.23 15.63 37.63 6 h 4.21 5.09 9.25 13.76 41.91 10.33 10.00 13.24 17.16 41.57 12 h 5.34 6.49 11.80 17.46 50.83 10.83 11.09 15.45 20.38 49.00     3. Theoretical Dosimetry Estimations  64  Figure 3–1 The percent difference (%) between the total effective doses following the injections of sestaMIBI™ labeled with technetium produced in a cyclotron and obtained from reactor. Cyclotron production corresponded to irradiation of a Target I (left) and Target III (right) with proton beams with energies equal to 16-10 MeV, 19-10 MeV, and 24-10 MeV for 3 h (red column), 6 h (blue column) and 12 h (yellow column) irradiation times. Dose differences resulting from injections performed at 0 h, 2 h, 8 h, 12 h and 24 h after EOB are compared (please note the difference in scale).  Percentage Difference Percentage Difference Percentage Difference Percentage Difference Percentage Difference Percentage Difference Percentage Difference Percentage Difference Percentage Difference Percentage Difference 3. Theoretical Dosimetry Estimations  65  Figure 3–2 The percent difference (%) between the total effective doses following the injections of sestaMIBI™ labeled with technetium produced in a cyclotron and obtained from reactor. Cyclotron production corresponded to 6 h irradiation of a Target I (left) and Target III (right) with proton beams. Doses resulting from target thicknesses leading to beam energy degradation from 16-, 19-, 24-10 MeV and from 16-, 19-, 24-6 MeV are compared for injection periods varying from 0 h-24 h after EOB. Dark color column bars represent the dose differences for beam energy decreasing to 6MeV, while the light color bars are for the energy decreasing to 10 MeV. In order to investigate the effect of target thickness on absorbed doses, calculations were performed for technetium products obtained when irradiating target thicknesses that would result in proton beam degradation from 16-, 19-, 24-10 MeV and from 16-, 19- and 24-6 MeV. An example of these data is presented in Figure 3–2. The percent difference between effective doses after the injections of sestaMIBI™ labeled with technetium produced in a cyclotron and in a reactor are analyzed. Cyclotron production corresponds to 6 h irradiations of enriched Target I and Target III by 200 A proton beam. Target thicknesses degrading beam energy from 16 MeV, 19 MeV and 24 MeV to 10 MeV and 6 MeV, respectively are compared Injection Time after EOB Injection Time after EOB Percentage Difference Percentage Difference 97.39% Enriched Target (Target I) 99.01% Enriched Target (Target III) 3. Theoretical Dosimetry Estimations  66 for injection periods of 0 h, 2 h, 8 h, 12 h and 24 h after EOB. Additionally, radiation-absorbed doses to specific organs were calculated for 6 h irradiations by a  beam with energy 19-10 MeV of enriched Target I and III. Table 3–4 shows the percent dose difference between radiopharmaceuticals labeled with mixture-Tc produced in a cyclotron when irradiating enriched Target I, and labeled with pure 99mTc obtained from a reactor. Table 3–5 shows similar results for enriched Target III. The ratio of absorbed doses corresponding to injection periods varying between 0 h and 24 h are compared. Additionally, the same data are presented in Figure 3–3, where the percent differences in radiation doses to organs with the most significant uptake after injection with technetium labeled sestaMIBITM, phosphonates and pertechnetate at 0-24 h after EOB are shown. The dashed lines in the figures represent the percent dose differences using enriched Target I (97.39% enrichment), while the solid lines represent the percent dose differences using Target III (99.01% enrichment). 3. Theoretical Dosimetry Estimations  67 Table 3–4 The percent (%) difference between absorbed doses following injections of radiopharmaceuticals labeled with a cyclotron–produced 99mTc and pure 99mTc obtained from a reactor. Cyclotron productions correspond to 6 h irradiation of the enriched Target I (97.39% enrichment) by a proton beam with energy 19-10 MeV. Doses corresponding to injection periods of 0 h, 2 h, 8 h, 12 h and 24 h after the EOB are compared.  Sestamibi™ Phosphonates Pertechnetate Organs 0 h 2 h 8 h 12 h 24 h 0 h 2 h 8 h 12 h 24 h 0 h 2 h 8 h 12 h 24 h Adrenals 0.66 0.66 0.86 1.11 3.07 0.94 0.98 1.41 1.95 5.86 0.68 0.7 1.01 1.38 4.10 Brain 0.68 0.70 0.97 1.31 3.85 1.01 1.06 1.56 2.17 6.6 0.68 0.7 1.04 1.45 4.46 Breasts 0.80 0.81 1.10 1.48 4.31 1.08 1.07 1.51 2.07 6.23 0.77 0.8 1.17 1.63 4.98 Gallbladder Wall 0.62 0.62 0.80 1.04 2.86 0.84 0.83 1.14 1.54 4.52 0.61 0.63 0.87 1.17 3.38 LLI Wall 0.74 0.85 1.44 2.12 7.21 0.67 0.66 0.84 1.08 2.96 0.73 0.84 1.44 2.13 7.27 Small Intestine 0.56 0.5 0.65 0.87 2.47 0.73 0.72 0.96 1.26 3.59 0.53 0.48 0.65 0.88 2.55 Stomach Wall 0.70 0.71 0.95 1.25 3.54 0.90 0.88 1.22 1.64 4.84 0.60 0.46 0.57 0.74 2.04 ULI Wall 0.47 0.49 0.68 0.92 2.77 0.77 0.76 1.01 1.33 3.81 0.45 0.47 0.67 0.93 2.82 Heart Wall 0.60 0.58 0.77 1.02 2.97 0.89 0.89 1.26 1.73 5.15 0.70 0.72 1.05 1.44 4.30 Kidneys 0.48 0.42 0.52 0.68 1.92 0.80 0.81 1.27 1.84 6.11 0.68 0.70 0.99 1.35 3.96 Liver 0.64 0.58 0.73 0.95 2.63 0.91 0.91 1.27 1.73 5.13 0.68 0.71 1.02 1.39 4.12 Lungs 0.69 0.70 0.94 1.25 3.59 0.93 0.95 1.36 1.87 5.63 0.69 0.71 1.04 1.43 4.32 Muscle 0.72 0.74 1.00 1.34 3.87 0.86 0.87 1.19 1.60 4.68 0.71 0.74 1.08 1.48 4.43 Ovaries 0.71 0.75 1.05 1.42 4.12 0.65 0.63 0.80 1.03 2.81 0.69 0.73 1.06 1.46 4.31 Pancreas 0.66 0.66 0.87 1.14 3.17 0.89 0.90 1.27 1.73 5.14 0.64 0.65 0.90 1.20 3.47 Red Marrow 0.73 0.75 1.02 1.35 3.86 0.65 0.65 0.92 1.27 3.85 0.72 0.76 1.10 1.50 4.44 Osteogenic Cells 0.35 0.36 0.49 0.65 1.88 0.27 0.29 0.44 0.63 2.02 0.33 0.34 0.50 0.68 2.04 Skin 0.79 0.81 1.10 1.48 4.33 1.09 1.10 1.55 2.12 6.31 0.77 0.79 1.17 1.62 4.96 Spleen 0.68 0.68 0.89 1.17 3.26 0.92 0.92 1.30 1.78 5.29 0.66 0.68 0.95 1.29 3.78 Testes 0.78 0.81 1.13 1.52 4.46 0.73 0.71 0.89 1.15 3.12 0.75 0.79 1.17 1.61 4.86 Thymus 0.72 0.74 1.01 1.35 3.90 0.94 0.93 1.32 1.80 5.39 0.72 0.75 1.10 1.52 4.59 Thyroid 0.57 0.46 0.56 0.73 2.04 0.94 0.96 1.38 1.90 5.74 0.50 0.33 0.41 0.55 1.63 Urinary Bladder 0.55 0.56 0.77 1.05 3.10 0.47 0.41 0.47 0.59 1.58 0.55 0.57 0.83 1.15 3.56 Uterus 0.66 0.67 0.91 1.20 3.41 0.59 0.57 0.68 0.85 2.17 0.62 0.65 0.92 1.24 3.58 Effective Dose 0.66 0.69 1.01 1.40 4.34 0.57 0.54 0.70 0.92 2.62 0.62 0.63 0.94 1.32 4.14    3. Theoretical Dosimetry Estimations  68 Table 3–5 The percent (%) difference between absorbed doses following injections of radiopharmaceuticals labeled with a cyclotron-produced 99mTc and pure 99mTc obtained from a reactor. Cyclotron productions correspond to 6h irradiation of the enriched Target III (99.01% enrichment) by a proton beam with energy 19-10 MeV. Doses corresponding to injection periods of 0 h, 2 h, 8 h, 12 h and 24 h after the EOB are compared.  SestaMIBI™ Phosphonates Pertechnetate Organs 0 h 2 h 8 h 12 h 24 h 0 h 2 h 8 h 12 h 24 h 0 h 2 h 8 h 12 h 24 h Adrenals 9.49 9.35 11.63 14.71 37.61 13.18 13.41 18.66 25.09 71.70 9.36 9.37 12.62 16.58 45.09 Brain 9.39 9.40 12.31 16.02 43.01 14.02 14.45 20.46 27.73 80.17 8.86 8.81 12.03 15.95 44.07 Breasts 10.97 10.88 14.03 18.12 48.10 14.96 14.32 19.41 25.86 72.91 10.10 9.97 13.51 17.85 48.98 Gallbladder Wall 8.89 8.81 11.00 13.94 35.72 11.87 11.43 15.09 19.83 54.65 8.58 8.68 11.48 14.92 39.72 LLI Wall 6.78 7.33 10.66 14.54 42.00 9.58 9.32 11.47 14.48 37.21 6.60 7.17 10.58 14.50 42.12 Small Intestine 7.85 6.83 8.40 10.71 27.79 10.43 10.10 12.88 16.59 44.25 7.45 6.44 8.17 10.55 27.79 Stomach Wall 9.87 9.91 12.73 16.38 43.11 12.56 12.04 15.94 20.98 58.03 8.62 6.17 7.12 8.82 21.58 ULI Wall 5.94 5.85 7.27 9.20 23.49 10.96 10.56 13.49 17.41 46.60 5.60 5.55 7.09 9.07 23.40 Heart Wall 8.20 7.51 9.27 11.78 30.41 12.51 12.18 16.52 22.00 61.92 9.52 9.53 12.89 16.98 46.42 Kidneys 6.50 5.25 5.85 7.10 16.73 8.54 7.81 10.49 13.99 39.48 9.36 9.39 12.57 16.46 44.43 Liver 8.97 7.87 9.36 11.68 29.17 12.72 12.36 16.63 22.05 61.70 9.41 9.48 12.76 16.75 45.47 Lungs 9.60 9.53 12.23 15.74 41.53 12.99 12.88 17.76 23.81 67.76 9.18 9.17 12.44 16.41 44.99 Muscle 10.04 10.07 13.07 16.93 45.09 12.06 11.94 15.81 20.77 57.19 9.72 9.83 13.38 17.67 48.43 Ovaries 10.13 10.50 14.18 18.70 51.25 9.27 8.96 10.96 13.80 35.31 9.73 10.19 14.15 18.84 52.25 Pancreas 9.41 9.35 11.78 15.01 38.87 12.45 12.29 16.70 22.22 62.52 9.04 8.85 11.56 14.94 39.52 Red Marrow 10.43 10.57 13.79 17.88 47.72 8.78 8.59 11.63 15.51 43.80 10.11 10.39 14.26 18.88 52.03 Osteogenic Cells 4.94 4.94 6.46 8.40 22.42 3.24 3.20 4.45 5.99 16.86 4.60 4.60 6.28 8.31 22.82 Skin 10.89 10.82 14.01 18.13 48.28 15.16 14.98 20.29 26.97 75.74 10.09 10.00 13.58 17.95 49.32 Spleen 9.63 9.57 12.04 15.33 39.65 12.86 12.63 17.11 22.75 63.91 9.22 9.08 12.02 15.64 41.89 Testes 10.82 11.02 14.66 19.20 52.14 10.47 10.04 12.18 15.28 38.84 10.21 10.44 14.41 19.17 53.20 Thymus 10.07 10.07 13.07 16.92 45.07 13.09 12.67 17.16 22.84 64.27 9.64 9.67 13.19 17.47 48.13 Thyroid 8.06 6.12 7.01 8.73 21.77 13.11 13.08 18.11 24.32 69.39 6.88 4.03 4.24 5.14 12.00 Urinary Bladder 7.26 7.23 9.25 11.90 31.33 6.28 5.31 5.52 6.43 14.09 6.75 6.57 8.48 10.96 29.05 Uterus 9.37 9.49 12.32 15.94 42.32 8.63 8.27 9.58 11.67 27.98 8.86 9.07 12.17 15.93 43.01 Effective Dose 8.21 8.17 10.81 14.15 38.39 7.84 7.27 8.81 11.12 28.63 7.68 7.21 9.64 12.69 34.60  3. Theoretical Dosimetry Estimations  69  Figure 3–3 The percent dose difference between injections of sestaMIBI™ (left), phosphonates (middle) and pertechnetate (right) labeled with cyclotron-produced technetium and reactor-produced pure 99mTc. Cyclotron production corresponds to 6 h irradiation by a proton beam with energy 19-10 MeV of Targets I and III. The dashed lines in the figures represent the percent dose differences using enriched Target I (97.39% enrichment), while the solid lines represent the percent dose differences using Target III (99.01% enrichment).  3. Theoretical Dosimetry Estimations  70 3.5 Discussion Based on the cross section and yield calculations presented in Chapter 2, the dosimetry calculations for natural and three different enriched molybdenum targets were performed. The data showed in Table 3–2 clearly demonstrate the unsuitability of natural molybdenum as the reaction target for 99mTc production for use in diagnostic studies. Large amounts of produced radioactive technetium isotopes other than 99mTc would result in dramatically increased patient doses relative to the doses from pure 99mTc-labeled agents.  When considering different target enrichments, the results prove the importance of two factors. It is clear that in order to optimize the 99mTc production conditions not only must the percentage of 100Mo enrichment be high, but also the relative amounts of other molybdenum isotopes, even if present in minute quantities, must be carefully considered. Although it may seem surprising, the results show that out of the three considered target enrichments, Target I which had lower 100Mo contents than Target III, showed a smaller difference between the dose from the cyclotron-produced 99mTc and reactor-produced 99mTc than Target III. This is because in the case of Target I the amount of all other molybdenum isotopes (except 98Mo) remains below 0.01%, while in Target III these amounts are at least one order of magnitude higher.  For example, a closer look at these data shows that 94gTc, 95gTc and 96gTc isotopes (dominantly produced by reactions on 95Mo, 96Mo, and 97Mo target 3. Theoretical Dosimetry Estimations  71 impurities) make the most significant contributions to the effective dose.  According to the isotope distribution in all targets (Table 2–1), 95-97Mo constitutes a relatively small part of Target I (0.02% in total), almost 15 times smaller than in Target III (0.29% in total). Meanwhile, Table 3–2 shows that 97mTc also contributed somewhat to the doses, because its reaction parent (98Mo) had 2.58% content in the 97.39% 100Mo target.  In summary, it is true that enrichment with a large content percentage of 100Mo is preferable for a target for cyclotron-produced 99mTc. However, contributions of isotopes other than 100Mo in the target affect the production of technetium impurities and influence the final doses to patients. In other words, to determine the optimum target for 99mTc production one should consider the relative content percentage of 100Mo compared to other molybdenum isotope contents (92Mo, 94Mo, 95Mo, 96Mo, 97Mo and 98Mo) rather than the absolute 100Mo enrichment in the target. The percent differences in total effective doses resulting from injections of sestaMIBITM, phosphonates and pertechnetate labeled with technetium obtained using different irradiation conditions for enriched Target I and III relative to doses resulting from injections of the same agents but labeled with reactor-produced 99mTc is presented in Table 3–3 and Figure 3–1. The analysis of these data fully confirms the advantage of using Target I enrichment with low 95Mo, 96Mo and 97Mo contents. The total effective doses in this case are about an order of magnitude lower than those corresponding to Target III irradiation. 3. Theoretical Dosimetry Estimations  72 Additionally, these results corroborate previous finding that the most favorable proton energy for cyclotron-produced 99mTc would be in the region between 16 MeV to 19 MeV because for higher proton energies the mixture of other technetium isotopes increases and the absorbed dose rises considerably compared to that obtained with a lower energy beam. This effect is particularly striking for Target I, because at higher energies (above 20 MeV) the cross section for 98Mo(p,3n) reaction leading to 96mTc (51.5 min) and 96gTc (4.28 d) is rapidly increasing. Further, according to these data, for cooling times 2-24 h after the EOB the doses slightly increase when longer irradiation times are used. Although these increases might not be significant, the results still suggest that from the dosimetry point of view, short irradiation times for cyclotron production of 99mTc would be beneficial. The only exception occurs for doses corresponding to irradiation of Target III (99.01% enrichment) and for injections at EOB. There the doses for 3 h irradiation are slightly higher than for 6 h. This is due to the fact that the short 3 h irradiation of Target III results in a relatively higher production of short-lived products (93mTc, 94mTc and 96mTc). This relative production gain disappears when longer irradiation times and/or longer cooling times are used.  As mentioned before, the cross sections for different (p,n) reaction channels dominate the 6-10 MeV energy range, while there is only a small contribution to the (p,2n) reaction cross section for 99mTc production in this low energy range. Therefore, target thickness optimized for 99mTc production would be such as to allow protons with energies lower than about 10 MeV to escape. Analysis of the 3. Theoretical Dosimetry Estimations  73 percent difference (%) between the total effective doses following the injections of sestaMIBI™ labeled with technetium produced in a cyclotron and obtained from the reactor confirms these findings.  The exception is enriched Target I (enrichment 97.39%) irradiated with a 24 MeV beam where a relatively high 98Mo target content is responsible for production of 96mTc, 96gTc and 97mTc. The cross section for 98Mo(p,2n)97mTc reaction begins only above 10 MeV, while the cross section for 98Mo(p,3n)96mTc and 98Mo(p,3n)96gTc - above 20 MeV. At the same time, because the content of other molybdenum isotopes in the target is relatively low, their contributions to the total dose are also low relative to 99mTc. As a result, the total absorbed dose of technetium mixture relative to that of a pure 99mTc is higher for target thicknesses leading to beam degradation 24-10 MeV than 24-6 MeV. Since for beam energies lower than 20 MeV (such as 16 MeV and 19 MeV investigated in this study) the 98Mo(p,3n) reaction does not occur, contributions from other radioactive technetium products, resulting from (p,n) reactions on other molybdenum isotopes, play a more important role here. In this case, the highest contributions to the total body dose come from 94gTc, 95gTc and 96gTc, all produced through (p,n) reactions on 94Mo, 95Mo and 96Mo, respectively.  Figure 3–3, Table 3–4 and Table 3–5 summarize the percentage dose differences between specific organs for the 6 h irradiation with 19-10 MeV beam for enriched Target I and III corresponding to 0-24 h injection times after EOB. All organ doses following the injection performed within 0-2 h after EOB would only increase by ≤1% for any of the three imaging agents considered in this study, if they 3. Theoretical Dosimetry Estimations  74 were labeled with technetium produced from enriched Target I, compared to the pure 99mTc dose. In some cases, this difference even decreases slightly over the first few hours after EOB as the shorter-lived isotopes decayed, and for up to 12 h remains below 2% for the majority of cases. Then, at 24 h after EOB, the dose resulting from the mixture of Tc isotopes exceeds the pure 99mTc dose by approximately 5%-8% for most organs. This late increase in the percent difference is due to the increased contribution from isotopes with half-lives longer than the 6.01 h half-life of 99mTc. However, when using Target III, the doses resulting from injections performed at 0-8 h after EOB with agents labeled with the mixture of Tc isotopes exceed the dose from pure 99mTc by about 10% or less. At 24 h after EOB, this percent difference further increases to about 50% for most organs. These results confirm the advantage of Target I and illustrate that in this case the injection time after EOB should be set below 12 h, whereas injections performed after 24 h would substantially increase patient doses. Although the doses for Tc isotopes produced from Target II irradiations were not presented in many details, it is obvious that this target would be the best target comparing with Target I and III because of its very small amounts of all other Mo isotope compositions in the target. Our theoretical estimations indicated that the increased patient doses at 24 hours after EOB would be below 10% when Target II is irradiated for 6 hours even using a 24 MeV proton beam.  3. Theoretical Dosimetry Estimations  75 3.6 Summary The objective of this chapter was to estimate the dosimetry and potential dose increases for 99mTc produced in a cyclotron using a proton induced reaction on a molybdenum target, relative to 99mTc obtained in a traditional way from a reactor. The increase of radiation dose received by patients due to other technetium radioisotopes produced in a cyclotron in parallel to 99mTc has been considered. Dose comparisons for the cyclotron-produced and traditional generator/reactor-produced 99mTc labeled agents allowed us to suggest optimized conditions for production and labeling procedures of 99mTc that minimize patient dose and radioactive waste. The results indicate that proton energies in the range of 16-19 MeV to 10 MeV with short irradiation times may correspond to the most advantageous energy region for 99mTc production procedures, which is consistent with the results of yield calculations. Additionally, the times below 12 hours after EOB were identified as the optimal period for injection into patients.  Moreover, the analysis indicates that target selection is one of the most important factors, which could largely influence the dosimetry results. The most favorable target for 99mTc production should not only hold a large percentage content of 100Mo, but it also needs to have a relatively small content of 94-97Mo, because presence of these isotopes will lead to production of significant amounts of radioactive technetium isotopes other than 99mTc.  4. Graphical User Interface-CYD  76 Chapter 4 Graphical User Interface-CYD This chapter describes the graphical user interface (GUI) that we developed in order to automate the theoretical production yield calculations and dosimetry estimations for cyclotron production of 99mTc.  4.1 Introduction The theoretical studies presented in Chapter 2 and 3 have shown that the amounts of stable and radioactive isotopes produced through different reaction channels and obtained from decays of radioactive reaction products depend heavily on the reaction conditions. These conditions can be controlled only to a certain degree, because in practice during every cyclotron run beam intensities and irradiation times may fluctuate. Additionally, a variety of molybdenum materials with different compositions can be used as targets with thicknesses that may vary. In principle, in order to predict 99mTc production yields, quantities of contaminants, and to evaluate resulting dosimetry for each particular situation, long series of very tedious and time consuming calculations need to be performed, and then repeated multiple times.  This ‘manual’ approach is not only difficult but also very inefficient. Therefore, in order to simplify the task, a graphical user interface (GUI) named Cyclotron production Yields and Dosimetry (CYD) estimator that allows us to automate these complex calculations was created. This GUI not only helps us to calculate yields (the number of produced nuclei or activity) for each potential 4. Graphical User Interface-CYD  77 reaction-decay product, but it can also help in gamma spectroscopy analysis by predicting intensities of different components that would be expected to be present in the measured spectrum. In addition, the effect of different technetium impurities on patient dosimetry can be evaluated as a function of post end-of-beam (EOB) injection time.   In this chapter, the principles of operation of the CYD and its main elements are described. The functionality of CYD is illustrated by several screen captures and tables showing examples of calculations that were performed for different reaction conditions. Such calculations can greatly facilitate analysis of the data obtained from 99mTc cyclotron production runs.  4.2 Description of the GUI functions CYD graphical user interface was created using the GUI design environment in Matlab 8.1.0®. It is organized into three different parts (layers): (a) production yield calculations, (b) gamma spectrum predictions and (c) dosimetry estimations. For better identification each layer uses a different color scheme, namely grey, blue and purple for estimating yields, gamma emissions and dosimetry, respectively. Accordingly, CYD can be used to calculate activities of the radioisotopes produced through all possible reaction-decay channels, predict intensities of their gamma emissions, and estimate organ doses in only few minutes. All the calculation results can be saved as .txt files. The structure of the CYD calculations is shown in Figure 4–1. The details of each of the three GUI layers are discussed in the following sections. 4. Graphical User Interface-CYD  78  Figure 4–1 Block diagram showing the main structure of CYD calculations. 4.2.1 CYD - yield calculation layer As already discussed, when protons irradiate molybdenum targets, isotopes may be created through a number of production-decay channels. In the Yield Calculation layer (see Figure 4–2), production yields of any reaction products (quantified in terms of the activity or number of produced nuclei) are determined using the approach described in Chapter 2 [70]. The Yield Calculation layer includes three panels: Reaction Inputs, Reaction Information Summary and Results of Yield Calculations. In order to initiate calculations, the user must enter information about the Reaction Conditions into the upper part of the Reaction Inputs panel. This information includes: proton beam current (μA), irradiation time (hours), time after EOB for which yields will be estimated (hours), and incident proton beam energy (MeV). Only integer values of the proton beam energy can be entered (MeV). Time 4. Graphical User Interface-CYD  79 after EOB provides the time range for which the calculations will be performed (in one-hour time intervals). Effective target thickness (the actual distance that the protons travel through the target) and the composition of molybdenum material need to be specified in the Target Information section of the Reaction Inputs panel. Figure 4–3 shows different enrichments of Mo target that are currently stored in the database of the Target Information section. The user can choose one of these targets or create a new target composition using this sub-GUI. When the effective thickness and composition of the Mo target are provided by the user, proton energy loss in the target is automatically estimated and the exiting beam energy is displayed under the Exit Energy tab. Alternatively, the user can input the target composition and exiting proton energy, and then target effective thickness will be calculated and displayed. Calculations of stopping power corresponding to different target thicknesses were performed using the SRIM software [56] and the results are stored in the database of CYD. Their values can be displayed by clicking the Display Target Stopping Power buttons. Reaction product(s) for which yield calculations will be performed have to be selected in the Calculate Yields for panel (see Figure 4–2). Options include selecting (a) all possible reaction products (All Products), (b) all technetium isotopes (All Technetium), or (c) all isotopes other than technetium (All Impurities). The user can select whether results are presented in terms of the activity of each final product or the number of produced nuclei in the Output Display section.  4. Graphical User Interface-CYD  80 Production yield calculations begin when the user clicks the Run button, and the results are shown in the Results of Yield Calculations panel. Reaction parameters used for the calculations are displayed in the Reaction Information Summary panel. This information and the results are saved in the output file (in .txt format).  The cross sections used for yield calculations were obtained from the EMPIRE-3 software [58] and are stored in the database of CYD. Tables of numerical values of the cross sections can be displayed by clicking the Display Cross Sections buttons. All values included in these tables can be modified, or replaced (for example, by experimental cross sections, if available). As discussed in Chapter 2, considering the large number of possible reaction channels and the corresponding cross sections, some limits had to be set. Accordingly, the current version of CYD includes reaction channels with up to five emitted neutrons and/or protons and considers proton energy range of 0-30 MeV. The half-lives, decay modes for all isotope products which potentially may be created directly through different reaction channels and for all their decay products (technetium, molybdenum, niobium and zirconium isotopes) have been incorporated manually into the GUI and are stored in its database. Isotopes with half-lives longer than 103 years are considered as stable. These conditions, however, can easily be changed if required. Table 4–1 provides a list of reaction channels that lead to technetium products included in the current version of CYD.  4. Graphical User Interface-CYD  81 Table 4–1 Reaction channels leading to different technetium products that are being considered by CYD. Isotope Half-life (hour) Reaction Channels Isotope Half-life (hour) Reaction Channels 91mTc 0.055 92Mo(p,2n) 96Tc 102.7 95Mo (p,ϒ) 91Tc 0.052 92Mo(p,2n) 96Mo (p,n) 92Tc 0.078 92Mo(p,n) 97Mo (p,2n) 94Mo(p,3n) 98Mo (p,3n)  93mTc 0.725 92Mo (p,ϒ) 95Mo (p,ϒ)96mTc decay (98%) 94Mo (p,2n) 96Mo (p,n)96mTc decay (98%) 95Mo (p,3n) 97Mo (p,2n)96mTc decay (98%) 93Tc 2.75 92Mo (p,ϒ) 98Mo (p,3n)96mTc decay (98%) 94Mo (p,2n) 97mTc 2194 96Mo (p,ϒ) 95Mo (p,3n)  97Mo (p,n) 92Mo (p,ϒ) 93mTc decay (77%) 98Mo (p,2n) 94Mo (p,2n) 93mTc decay (77%) 97Tc "stable" 96Mo (p,ϒ) 95Mo (p,3n) 93mTc decay (77%) 97Mo (p,n) 94mTc 0.867 94Mo (p,n) 98Mo (p,2n)  95Mo (p,2n) 96Mo (p,ϒ )97mTc (96%) 96Mo (p,3n) 97Mo (p,n)97mTc (96%) 94Tc 4.883 94Mo (p,n) 98Mo  (p,2n)97mTc (96%) 95Mo (p,2n) 98Tc "stable" 97Mo (p,ϒ) 96Mo (p,3n) 98Mo (p,n) 95mTc 1464 94Mo (p,ϒ) 100Mo (p,3n) 95Mo (p,n) 99mTc 6.01 98Mo (p,ϒ) 96Mo (p,2n) 100Mo (p,2n) 97Mo (p,3n) 100Mo (p,pn)99Mo decay (88%) 95Tc 20.0 94Mo (p,ϒ) 99Tc "stable" 98Mo (p,ϒ) 95Mo (p,n) 100Mo (p,2n) 96Mo (p,2n) 100Mo (p,2n)99Mo decay (12%) 97Mo (p,3n)  98Mo(p,ϒ)99mTc decay (100%) 94Mo (p,ϒ)95mTc  decay (4%) 100Mo (p,2n)99mTc decay (100%) 95Mo (p,n)95mTc  decay (4%) 100Mo (p,pn)99Mo decay(88%) 99mTc decay (100%) 96Mo (p,2n)95mTc decay (4%) 100Tc 0.004 100Mo (p,n) 97Mo (p,3n)95mTc  decay (4%) 101Tc 0.233 100Mo (p,ϒ) 96mTc 0.858 95Mo (p,ϒ)   96Mo (p,n) 97Mo (p,2n) 98Mo (p,3n)  Figure 4–2 shows a screenshot of yield calculations performed using this layer of CYD. In this example we used a 3 hours irradiation time, 18 MeV beam energy, 100 μA beam current, and 99.01% enriched 100Mo target. Yield calculations were performed for times ranging from EOB (0 h after EOB) to 10 h after EOB. The exit proton energy (Exit energy) was set to be 10 MeV, so the program was able to estimate target thickness as being 0.44 g/cm2. Activities (in GBq) for all technetium products were chosen to be calculated. 4. Graphical User Interface-CYD  82  Figure 4–2 Screenshot of Yield Calculation layer of CYD.  Figure 4–3 Screenshot of sub-GUI for Target Selection.  4. Graphical User Interface-CYD  83 The Yield Calculation layer of CYD is hyper-linked to another sub-GUI named Cyclotron products Yield Calculations-Single Reaction, which can be used to calculate yields of products from one specific reaction.  This sub-GUI can be reached by pressing the Single Reaction Calculation button in the Advanced Features panel; this opens a new window, which is shown in Figure 4–4. The left panel includes the input reaction information and displays the target stopping power. In the central panel the user needs to specify the reaction channel, decide if the ground state or isomeric state of the product is to be analyzed, and select the type of decays of the reaction product in the Reaction panel. From this sub-GUI, the activity or the number of product nuclei and decay products for the specified reaction are obtained. Figure 4–4 shows an example of the CYD-Single Reaction calculation for the 100Mo(p,2n)99mTc reaction. In this case, calculations were performed for a 100 μA proton current and 3 h irradiation time. Results correspond to yields that would be obtained at 10 h post EOB time. Incident and exit beam energies were 18 MeV and 10 MeV, respectively.  4. Graphical User Interface-CYD  84  Figure 4–4 Screenshot of sub-GUI for single reaction yields calculations. 4.2.2 CYD - gamma spectrum analysis layer The second layer of CYD generates information that is useful for experimental evaluation of reaction yields (Figure 4–5). With this purpose in mind, it provides estimates of the number of gamma photons that will be emitted by all radioisotopes produced in a given cyclotron irradiation experiment. Two parameters need to be considered for this estimation: (1) Radioisotope activities at the observation time and (2) the energies and intensities of all gamma emissions for each radioactive product. The activity of each radioisotope at the observation time is loaded from the Yield Calculation layer by pressing the button of Load Data from Yield Calculations. The gamma energies and intensities were obtained from the National Nuclear Data Centre website [6] and are stored in the CYD’s database. For each radioactive isotope, only intensities of the three or four strongest gamma lines 4. Graphical User Interface-CYD  85 are included in the results table, but the entire decay information can be shown in the Isotope Decay Information panel. Annihilation photons (511 keV) are not included in the analysis because many reaction products undergo positron decay and their 511 keV annihilation photons cannot be separated.  The results are shown in the table of Predict Number of Photons panel. Although photons at 511 keV are not included in the gamma analysis, but they are included in the dosimetry estimations. To facilitate comparisons of theoretical estimates with the experimental data, the list of gamma emissions can be sorted by energy or by emitting radioisotope. Figure 4–5 shows the list of predicted gamma emissions for all technetium isotopes that will be produced using the reaction conditions shown in Figure 4–2. In this case, the observation time was 3 h after EOB and the table provides estimates of the intensities (photons/sec) for the strongest gamma emissions (sorted by gamma lines). Information about detector efficiency and measurement dead-time would be required to estimate the actual observed photon counts.  4. Graphical User Interface-CYD  86  Figure 4–5 Screenshot of Gamma spectrum analysis of CYD.  4.2.3 CYD - dosimetry estimation layer The Dosimetry Estimation layer offers tools for dose calculations for nuclear medicine diagnostic imaging studies that would use cyclotron-produced 99mTc (Figure 4–7). It provides absolute absorbed doses that are due to each of the technetium radioisotopes as well as dose differences between radiotracers labeled with cyclotron-produced 99mTc and reactor-produced pure 99mTc. Since it is assumed that all other elements can be removed from the sample by chemical methods, only doses due to technetium isotopes are considered.  4. Graphical User Interface-CYD  87 Dosimetry follows the standard internal dose calculation scheme and was performed using methodology described Chapter 3. The workflow for dosimetry estimations based on equation (3-5) and (3-6) is presented in Figure 4–6.   Figure 4–6 The workflow of dosimetry estimations.  For cyclotron-produced 99mTc, patient absorbed doses in clinical studies will depend on the relative amounts of different technetium radioisotopes in the sample that will be used for radiotracer labeling which, in turn, depends on target composition and irradiation conditions. Therefore, to estimate doses, activities of all radioisotopes of interest must be obtained from the Yield Calculation layer. The current version of CYD predicts doses that are absorbed in different organs for the three main imaging agents (radiotracers): sestaMIBITM, phosphonates and pertechnetate. The residence times for these three tracers were obtained from ICRP Publication 53 [68] and the S-factors (standard male phantom) for each radioactive 4. Graphical User Interface-CYD  88 Tc are from the OLINDA software [69]. All these data are stored in the CYD database. The values of S-factors and the residence times for each technetium isotope and radiotracer combination can be displayed in two separate windows (shown in Figure 4–8 and Figure 4–9) by clicking the S-Factor and the Residence Time buttons, respectively, in the left part of the Dosimetry Estimation panel (Figure 4–7). All these values can be modified if needed.  To perform dosimetry calculations using CYD, the user needs to upload the activities of all radioactive technetium isotopes (estimated for a given injection time) from Yield Calculation layer and choose the radiopharmaceutical. Then, the doses from pure 99mTc (which could be considered as a reactor-produced 99mTc) and the mixture of technetium isotopes (as produced in the cyclotron) for different organs will be calculated. In addition, differences between doses resulting from pure 99mTc and the mixture will be displayed in the table of Dose Results panel. Moreover, by clicking All Results button, the user can calculate individual organ doses that are due to each radioactive technetium product. The results will be saved in the dosimetry output file. 4. Graphical User Interface-CYD  89  Figure 4–7 Screenshot of Dosimetry Estimation layer of CYD.  Figure 4–8 Screenshot of sub-GUI for S-factor. 4. Graphical User Interface-CYD  90   Figure 4–9 Screenshot of sub-GUI for residence time. 4.3. Results For each layer, there is an output file that includes all the results from the corresponding calculations. Here, the functionality of this CYD GUI is illustrated by examples of calculations performed using different reaction parameters. 4.3.1 Example of results from yield calculation layer This section presents examples of yield calculations performed for 3 h irradiations using five different proton beams with energies ranging from 16-10 MeV to 24-10 MeV. Three enriched 100Mo targets were employed (Target I-III in Table 2–1). The estimated activities of 99mTc, other radioactive Tc, and other elements are shown in Table 4–2.  4. Graphical User Interface-CYD  91 Table 4–2 Activities (GBq) at EOB calculated by the CYD Yield Calculation layer for all radioactive reaction products. These results correspond to 3 h irradiation using different proton beam energies and 100 μA current. Products with half-lives shorter than 5 min were considered as decaying directly to their daughters. Beam Energy (MeV) Reaction Product Target I Target II Target III 16-10 99mTc 80.50 82.27 81.83 Other radioactive Tc 0.33 0.32 1.08 Other radioactive elements 4.73 4.82 4.81 18-10 99mTc 108.46 110.85 110.26 Other radioactive Tc 0.43 0.41 1.55 Other radioactive elements 8.94 9.07 9.05 20-10 99mTc 133.11 136.05 135.33 Other radioactive Tc 0.51 0.49 2.06 Other radioactive elements 14.18 14.29 14.29 22-10 99mTc 151.94 155.29 154.47 Other radioactive Tc 0.77 0.59 2.61 Other radioactive elements 20.22 20.24 20.28 24-10 99mTc 165.70 169.35 168.45 Other radioactive Tc 1.50 0.75 3.26 Other radioactive elements 27.22 27.08 27.16  4.3.2 Example results from spectrum analysis layer Based on yield calculations, intensities of gamma emissions can be estimated by the CYD Gamma Spectrum Analysis layer. Table 4–3 presents an example of the results that can be obtained from this layer. In this example intensities (photons/sec) of the strongest gamma emissions for each radioactive product are displayed. The same three targets, which were used in the activity calculations, were also employed here. The beam energy was set as 18-10 MeV with 100 μA current intensity and 3 h irradiation time. The observation time was 3 h after EOB. To compare with the experimentally measured intensities, these theoretical values 4. Graphical User Interface-CYD  92 estimated by CYD must be combined with the efficiency of the detecting system and the measurement time.  Table 4–3 Absolute intensities of the strongest gamma emissions (photons/sec) of radioactive products estimated by CYD for three different targets. Results correspond to 3 h irradiation using 18-10 MeV proton beam energy and 100 μA current. The gamma observation time was set as 3 h after EOB. Only one gamma emission per isotope is listed and gammas’ intensities smaller than one photon per second are omitted. Isotope Isotope Half-life (hour) Gamma Energy (keV) Absolute Emission Intensity (Photons/sec) Target I Target II Target III 99mTc 6.0 140 6.83E10 6.98E10 6.95E10 101Tc 0.2 306.8 4.05E04 4.14E04 4.12E04 97mTc 2194.0 96.5 1.85E04 2.94E03 4.18E03 96mTc 0.9 778 4.03E04 7.44E03 4.92E05 96gTc 102.7 778.2 3.08E06 5.66E05 3.72E07 95mTc 1464 204.1 1.86E04 1.55E04 3.91E05 95gTc 20 765.8 6.24E06 5.84E06 1.30E08 94mTc 0.9 871.1 1.27E06 1.48E06 1.81E07 94gTc 4.9 871.1 1.53E07 1.85E07 2.30E08 93mTc 0.7 391.8 1.00E05 1.03E05 1.21E06 93gTc 2.8 1362.9 3.46E06 3.53E06 4.18E07 99Mo 65.9 739.5 4.58E07 4.68E07 4.66E07 93mMo 6.9 684.7 1.61E03 1.64E03 1.93E04 98gNb 0.9 787.4 1.02E03 1.04E03 1.04E03 97gNb 1.2 657.9 1.41E09 1.45E09 1.44E09 96Nb 23.4 778.2 3.35E08 3.42E08 3.41E08 95mNb 86.7 235.7 1.81E05 2.87E04 3.86E04 95gNb 840.0 765.8 1.03E06 1.64E05 2.21E05 92mNb 243.6 934.4 1.17E04 1.63E04 2.36E05 91mNb 1460.6 104.6 4.39E02 5.03E02 6.70E03 90gNb 14.6 1129.2 2.60E02 2.65E02 3.12E03 89mNb 1.1 588 1.26E04 1.52E04 2.27E05 89gNb 2.0 3092.7 5.06E03 6.07E03 9.11E04   4. Graphical User Interface-CYD  93 4.3.3 Example results from dosimetry estimation layer Table 4–4 shows an example of the results of dosimetry calculations. Activities of all radioactive Tc isotopes were calculated assuming 3 h irradiation of Target I with beam current of 100 μA, and 18-10 MeV proton energy. Internal absorbed dose for each organ from sestaMIBITM labeled technetium was estimated for an injection time of 3 h after EOB. 4.4 Discussion The developed GUI can be used to calculate yields and resulting doses for cyclotron-produced 99mTc for many different combinations of irradiation parameters. In addition, it will be useful in gamma spectroscopy analysis by predicting the intensities of the expected gamma emissions for comparison with the experimental results. Such comparison can be subsequently used to derive experimental reaction cross sections. If discrepancies are found, the theoretical cross sections present in CYD can be easily replaced by the experimental cross sections.  When performing such replacement, the experimental cross sections have to be known for each individual reaction channel. However, most of the published experimental results correspond to cumulated cross sections, this means they sum contributions from all reactions on all Mo isotopes present in the target. Also, these experiments were performed using various ranges of irradiation energies [71-73]. Therefore, at this point, it is difficult to make the replacement. 4. Graphical User Interface-CYD  94 Table 4–2 and Table 4–3 present examples of yields and gamma emission intensities. These calculations allow the user to compare different reaction conditions and targets. Such comparison could also be helpful when searching for optimal irradiation parameters that would maximize 99mTc production and minimize impurities. When performing such comparison manually, a long series of very time consuming calculations have to be done. Additionally, the procedure is prone to different types of mistakes and typing errors. When using CYD, the same calculations can be done orders of magnitude faster and potentially without mistakes, providing the production yields and much needed guidance for the experiments. The Dosimetry Estimation layer of CYD provides estimates of radiation doses, which may occur when cyclotron-produced 99mTc is used in clinical studies. An example of doses predicted from CYD is shown in Table 4–4. The obtained values are identical with those that would be calculated by the OLINDA program. The advantage of using this GUI instead of the original OLINDA is that, in addition to estimating organ doses for each individual technetium product, CYD also calculates combined doses corresponding to a mixture of cyclotron-produced technetium isotopes. Additionally, the differences between pure 99mTc from a reactor and the technetium mixture from a cyclotron are provided. Although the current version of CYD uses only S-values corresponding to an adult male model and only three imaging agents, this user-friendly MATLAB GUI can be easily customized to add other models and agents to meet specific user needs. 4. Graphical User Interface-CYD  95 Table 4–4 Results of absorbed dose calculations (mSv) for different organs from sestaMIBITM labled cyclotron-produced technetium radioisotopes. The doses were calculated assuming beam current of 100 μA for 18-10 MeV proton beam energy and 3 h irradiations of Target I. The injection time was 3 h after EOB. The differences between pure 99mTc and mixture of technetium produced by the cyclotron are listed in the last column.  Organs 93mTc 93Tc 94mTc 94Tc 95mTc 95Tc 96mTc 96Tc 97mTc 99mTc 101Tc 99mTc Mix-Tc Diff (%)     Adrenals 8.52E-04 1.51E-01 2.35E-02 1.22E+00 2.57E-03 3.54E-01 1.01E-03 8.06E-01 7.17E-02 4.02E+02 6.18E-05 4.02E+02 4.05E+02 0.65 Brain 2.79E-04 5.09E-02 9.69E-03 4.25E-01 1.30E-03 1.51E-01 5.05E-04 3.77E-01 7.11E-02 1.58E+02 5.01E-05 1.58E+02 1.59E+02 0.69 Breasts 3.08E-04 5.48E-02 1.03E-02 4.39E-01 1.19E-03 1.47E-01 5.16E-04 3.61E-01 6.94E-02 1.37E+02 3.86E-05 1.37E+02 1.38E+02 0.79 GB Wall 1.06E-03 1.90E-01 2.85E-02 1.58E+00 3.38E-03 4.69E-01 1.16E-03 1.06E+00 7.23E-02 5.56E+02 6.37E-05 5.56E+02 5.59E+02 0.61 LLI Wall 8.10E-04 2.14E-01 2.97E-02 2.22E+00 1.52E-02 1.23E+00 1.46E-03 3.37E+00 4.49E+00 1.41E+03 3.95E-05 1.41E+03 1.42E+03 0.82 Small Intestine 2.80E-03 3.00E-01 1.49E-01 2.32E+00 5.58E-03 7.25E-01 7.83E-03 1.67E+00 3.31E-01 1.12E+03 4.41E-05 1.12E+03 1.13E+03 0.49 Stom Wall 6.37E-04 1.22E-01 1.85E-02 1.03E+00 2.61E-03 3.37E-01 7.98E-04 8.09E-01 7.11E-02 3.44E+02 4.56E-05 3.44E+02 3.46E+02 0.70 ULI Wall 2.17E-03 4.33E-01 9.95E-02 3.62E+00 8.44E-03 1.14E+00 5.24E-03 2.34E+00 1.57E+00 1.94E+03 4.53E-05 1.94E+03 1.95E+03 0.47 Hrt Wall 9.72E-04 1.27E-01 4.41E-02 9.73E-01 2.33E-03 2.93E-01 2.31E-03 6.76E-01 2.23E-01 4.16E+02 1.22E-04 4.16E+02 4.19E+02 0.56 Kidneys 6.74E-03 6.95E-01 3.63E-01 4.80E+00 7.44E-03 1.18E+00 2.10E-02 2.07E+00 1.45E+00 2.61E+03 2.05E-03 2.61E+03 2.62E+03 0.41 Liver 1.75E-03 2.04E-01 7.24E-02 1.48E+00 2.86E-03 3.96E-01 3.80E-03 8.64E-01 1.99E-01 5.69E+02 4.29E-04 5.69E+02 5.72E+02 0.57 Lungs 4.23E-04 7.47E-02 1.31E-02 6.07E-01 1.61E-03 1.98E-01 6.32E-04 4.82E-01 7.11E-02 2.12E+02 5.22E-05 2.12E+02 2.13E+02 0.68 Muscle 4.44E-04 8.25E-02 1.42E-02 6.90E-01 1.91E-03 2.35E-01 6.64E-04 5.80E-01 7.98E-02 2.33E+02 8.35E-05 2.33E+02 2.35E+02 0.72 Ovaries 9.14E-04 1.94E-01 2.54E-02 1.76E+00 5.91E-03 6.85E-01 1.09E-03 1.80E+00 8.85E-02 6.20E+02 4.11E-05 6.20E+02 6.24E+02 0.74 Pancreas 7.78E-04 1.39E-01 2.20E-02 1.17E+00 2.68E-03 3.56E-01 9.12E-04 8.30E-01 7.05E-02 3.97E+02 5.69E-05 3.97E+02 4.00E+02 0.65 Red Mar. 5.11E-04 9.77E-02 1.46E-02 8.50E-01 2.35E-03 2.89E-01 6.64E-04 7.26E-01 4.57E-02 2.74E+02 4.38E-05 2.74E+02 2.76E+02 0.74 Osteogenic Cell 5.28E-04 9.30E-02 1.61E-02 7.60E-01 2.23E-03 2.92E-01 4.48E-03 6.58E-01 7.75E-02 5.44E+02 7.47E-05 5.44E+02 5.46E+02 0.35 Skin 2.82E-04 5.05E-02 9.75E-03 4.11E-01 1.13E-03 1.39E-01 4.65E-04 3.46E-01 6.59E-02 1.30E+02 3.94E-05 1.30E+02 1.31E+02 0.79 Spleen 6.95E-04 1.30E-01 1.98E-02 1.06E+00 2.41E-03 3.25E-01 8.72E-04 7.50E-01 7.17E-02 3.52E+02 5.17E-05 3.52E+02 3.55E+02 0.67 Testes 3.41E-04 6.74E-02 1.12E-02 5.78E-01 1.84E-03 2.14E-01 5.41E-04 5.53E-01 6.94E-02 1.89E+02 3.51E-05 1.89E+02 1.90E+02 0.79 Thymus 3.82E-04 6.90E-02 1.21E-02 5.72E-01 1.60E-03 1.94E-01 5.81E-04 4.82E-01 7.00E-02 1.93E+02 5.84E-05 1.93E+02 1.95E+02 0.72 Thyroid 1.50E-03 1.21E-01 8.09E-02 7.91E-01 1.57E-03 2.08E-01 4.79E-03 4.60E-01 1.30E-01 4.05E+02 1.84E-01 4.05E+02 4.07E+02 0.49 UB Wall 1.08E-03 2.10E-01 5.16E-02 1.76E+00 4.76E-03 5.94E-01 2.67E-03 1.37E+00 4.70E-01 8.14E+02 3.87E-05 8.14E+02 8.18E+02 0.55 Uterus 8.50E-04 1.68E-01 2.38E-02 1.45E+00 3.91E-03 4.87E-01 9.93E-04 1.20E+00 7.17E-02 5.14E+02 4.10E-05 5.14E+02 5.17E+02 0.66 TotBody 5.45E-04 9.14E-02 2.01E-02 7.48E-01 2.04E-03 2.49E-01 9.93E-04 6.05E-01 1.26E-01 2.88E+02 1.34E-04 2.88E+02 2.90E+02 0.64 4. Graphical User Interface-CYD  96 4.5 Summary A graphical user interface, CYD, designed to estimate characteristics of 99mTc cyclotron production was created. During the research and development stage of the 99mTc cyclotron production, this GUI can be used to estimate reaction yields and corresponding gamma emissions to be compared with the experimentally measured values. In addition, since it is anticipated that enriched molybdenum will be recycled for repeated use, the GUI may prove valuable in predicting the impurities profile for each subsequent irradiation in order to ensure that the resulting products meet the regulatory criteria. Most importantly however, it is expected that the main advantage of CYD will be at the clinical stage, where reaction parameters can be entered into the GUI to predict production yields and estimate radiation doses for each particular cyclotron run.   5. Quantitative Activity Measurements  97 Chapter 5 Quantitative Activity Measurements  Previous chapters discussed the theoretical yields calculations that can be considered as guidance for the cyclotron experiments. However, they always represent an approximate model of the truth. Therefore, it is critically important to validate these calculations in experimental studies. The objective of this chapter is to identify and quantify the radioisotopes presented in samples from real cyclotron experiments. In this chapter, the quantitative measurements for cyclotron-produced technetium and other radioisotope products from four cyclotron runs are described. From analyzing the gamma spectra from cyclotron-produced 99mTc samples, the absolute activities of radionuclides present in these samples are estimated. The experimental results and theoretical predictions are compared.  5.1 Gamma-ray spectrometry  As mentioned in Chapter 1, a radioactive decay of a radioisotope usually results in an excited state of its daughter. This excited state will decay to lower energy states by emitting gamma rays and conversion electrons. For example, in the process of 99Mo decay, multiple excited states of 99m+gTc could be involved by emitting gamma rays with different energies, as shown in Figure 5–1. Since absolute yields per decay of these gamma emissions are known[6], the absolute activity of radioisotopes in the sample can be determined by measuring their intensities. 5. Quantitative Activity Measurements  98  Figure 5–1 A simplified decay scheme of 99Mo and 99mTc including the main gamma emissions from their decays. The decay information was obtained from [6]. The detection of gamma rays is based on their interactions with detector material. Detectors are designed to collect and count electric charges produced during these interactions. In this section, the mechanisms of interactions of gamma radiation with detector materials are briefly described. The properties of gamma spectrum used for activity determination are discussed. 5.1.1 Mechanisms of gamma interaction In general, gamma rays interact with matter by elastic scattering (Rayleigh scattering) and inelastic processes (photoelectric absorption, Compton scattering and pair production). The elastic scattering, where gamma particles interact with the matter atom as a whole, the scattered gamma particles have the same energy as incident gammas so this process does not contribute to detection. On the other hand, 2.2 keV (7×10-9%) 99Mo, T1/2=65.9 h 920.6 keV  509.1keV  181.1keV 140.5 keV  0keV β- 16.4% β- 1.2% 40.5 keV  (1.1%) β- 82.2% 140.5 keV (89%) 99mTc, T1/2=6.01 h 99gTc, T1/2=2.1×105 year 366.4 keV  (1.2%) 739.5 keV  (12.3%) 777.9 keV  (4.3%) 142.7 keV  142.5 keV (0.02%) 5. Quantitative Activity Measurements  99 in inelastic processes the energies of gamma rays are absorbed and transferred to the counting system. These inelastic processes are discussed in Table 5–1. Table 5–1 Inelastic gamma interactions with material.  Photoelectric Absorption Compton Scattering Pair Production Interaction Procedure A photon interacts with a bound electron from the inner shell of an atom This interaction leads to the ejection of a photoelectron. A vacancy left in the atom leads to X-ray fluorescence or ejection of Auger electrons. A photon interaction with an outer shell electron of atom of material results in ejection of this outer shell electron (recoil electron) and a scattered photon. A photon, whose energy is larger than 1.02 MeV, interacts with an atom and creates an electron-positron pair. Scheme    Energy Transfer  Eγ is totally absorbed   The energy of the ejected electron:         𝐸𝑒 = 𝐸𝛾 − 𝐸𝑠ℎ𝑒𝑙𝑙 𝑏𝑖𝑛𝑑𝑖𝑛𝑔  Photon energy after scattering:        𝐸𝑓 =𝐸𝛾1 +𝐸𝛾0.511 (1 − 𝑐𝑜𝑠 𝜃)  The recoil electron energy:        𝐸𝑒 = 𝐸𝛾 − 𝐸𝑓  Eγ is totally absorbed.   The energy of electron-positron pair:          𝐸+ + 𝐸− = 𝐸𝛾-1.02 MeV  Regardless of elastic or inelastic interaction, the process of a gamma ray interacting with a material and depositing its energy is called attenuation. The fraction of gamma rays absorbed or scattered during these interactions is expressed by the attenuation coefficient, which depends on the incident gamma ray energy and the material. Its value, divided by the density of material, is called mass attenuation coefficient. Figure 5–2 shows the mass attenuation coefficient of germanium (Ge), which is a common detector material for gamma spectrum detection. 5. Quantitative Activity Measurements  100  Figure 5–2 Total mass attenuation coefficient and the attenuation coefficient corresponding to different types of gamma interaction of germanium (Ge). 5.1.2 Gamma spectrum  During different types of interactions, the deposited gamma energy varies, which leads to their different contributions to the gamma spectrum. As shown in Figure 5–2, the principle interactions are photoelectric absorption and Compton scattering when incident gamma energy is lower than 2 MeV. The photoelectric absorption, where gamma deposits its full energy in the detector, results in a single narrow line in the measured spectrum (photopeak) at the location corresponding to its total energy (𝐸γ). However, as shown in Table 5–1, in a Compton scattering event, only part of gamma energy is transferred to the detector. This deposited energy is less than 𝐸γ which shows in the detected gamma spectrum. According to the energy transfer equations in Table 5–1, the energy deposited (𝐸𝑒) in the detector from a 0.0001 0.001 0.01 0.1 1 10 100 50 100 200 400 800 1600 Mass Attenuation Coefficient (cm2/g) Incident Gamma Energy (keV) Total Photonelectric absorption Compton scattering Rayleigh scattering Pair production 5. Quantitative Activity Measurements  101 single Compton scattering event can range from near zero to a maximum value of Ece (when 𝜃=180 degree), which leads to a Compton region (when 𝐸𝑒<Ece) and a Compton edge (when 𝐸𝑒 = Ece) in the gamma spectrum. Moreover, it is possible that a gamma ray may experience more than one Compton scattering that shows in the gamma spectrum as a multiple Compton-scattering region. Figure 5–3 (left) gives an ideal gamma spectrum for 137Cs which has the photopeak energy 𝐸𝛾 of 662 keV. However, in the actual spectrum, instead of detecting a sharp line of photopeak and a sharp Compton edge, a broad peak and a rounded Compton edge are observed. This effect is caused by the imperfect energy resolution of the gamma detecting system. Moreover, a backscatter peak may appear in the spectrum. It is caused by the detection of gamma rays which are scattered toward the detector after undergoing a 180-degree scattering outside the detector. In addition, when lead shielding is employed, X-ray peaks can be created by interactions of gamma rays in lead. Figure 5–3 (right) gives an example of real-world gamma spectra of 137Cs with these various features[74].    5. Quantitative Activity Measurements  102  Figure 5–3 Schematic graphs of ideal (left) and real-world (right) gamma spectra of 137Cs. 5.1.3 Detection of gamma spectrum   In a gamma detection system, a detector produces output pulses whose magnitudes are proportional to the energy deposited in the detector. A multichannel analyzer (MCA) is used to assign different energies to small consecutive pulse-height channels. By counting the number of pulses in each channel, the gamma energy spectrum is created. Figure 5–4 gives a scheme of detected pulses used in MCA converted to its corresponding gamma spectrum.  Relative Gamma Counts  0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800 Gamma Energy (keV) Gamma Energy (keV) Ideal Spectrum Real-world  Spectrum Compton region Compton edge, Ece Multiple Compton scatterings Photopeak, Eγ Backscatter peak Lead X-rays Compton edge, Ece Multiple Compton scatterings Photopeak, Eγ 5. Quantitative Activity Measurements  103  Figure 5–4 A scheme of gamma spectrum formation from the detected electrical pulses using MCA. The horizontal blue lines represent the channels defined by MCA. The same color of vertical histograms represents the pulses fall into the same channel, which corresponds to the gamma energies in the spectrum. The number of photon counts detected at different energies in the spectrum is proportional to the number of pulses in the corresponding channels. In gamma spectroscopy measurements, it is important to accurately translate the channel numbers into gamma energies and to convert the number of pulses into intensities of incident gamma rays. Energy and efficiency calibrations have to be performed for such interpretations. These calibrations can be performed by measuring a standard source with well-known gamma peak energies and activities. In addition, energy resolution, which is represented by the peak width and varies with gamma energy, has to be determined.   Energy calibration:  The purpose of energy calibration is to derive the relationship between peak positions in the spectrum (channel numbers) and the corresponding gamma energies emitted from the sample. It is usually obtained by comparing the measured Photon Counts Time Pulse Amplitude (Channel) Gamma Energy 5. Quantitative Activity Measurements  104 gamma peak positions with precisely known energies acquired from a standard radioactive source sample. In general, the relationship between the peak position and gamma energy can be expressed by a linear (or polynomial) curve.    Efficiency calibration:  Detector efficiency, which is the ratio of detected photopeak counts to the gamma photons emitted by the sample, has to be obtained by measuring a calibration source consisting of a combination of radionuclides with well-known activities. Because the detection efficiency depends on the measurement geometry, it is very important to use the same sample volume and measurement configuration for the sample and the efficiency calibration measurements.  Energy resolution calibration As shown in Figure 5–3, due to limited resolution of the detector, each photopeak in the gamma spectrum spreads over several channels, which gives the peak an approximately Gaussian-curve shape instead of a sharp line.  The width of this curve, usually expressed as full-width-at-half-maximum (FWHM), increases with energy. During the energy calibration the characteristics of FWHM can be determined; its value is used as a quantitative indication of the expected resolution of a gamma detector. In general, a linear fit between FWHM and gamma energy is adequate over a wide energy range[75]. In the analysis of the measured spectrum, the information about FWHM is used in gamma ray’s intensity determinations. Substantial deviations of the peak 5. Quantitative Activity Measurements  105 width from the expected FWHM may indicate peak multiplet (more than one gamma line of the same or very similar energy).  In summary, these three calibrations are very important for gamma spectroscopy measurement. The gamma emissions from a standard source used for calibrations must span over the whole energy range of interest. Inappropriate energy calibrations could cause gamma energy shift which can lead to incorrect gamma peak identification, while inaccurate FWHM (energy resolution) and efficiency calibrations could provide large discrepancies in the detected gamma counts, leading to wrong activity determination results.  5.1.4 Activity determination  After performing all the calibrations, a radioactive sample can be measured. The activity of the measured sample is then determined by combining information about the detected gamma counts and the branching ratios of the corresponding gamma energies. However, in this determination processes, several additional factors need to be considered: a. Before measuring any radioactive samples, background measurements performed over a long period of time are required. These measurements set baseline signals which must be deducted from the radioactive sample measurement.  b. During the process of gamma counting, the radioactive isotopes in the sample decay, so the accumulated gamma counts need to be corrected for their decays. 5. Quantitative Activity Measurements  106 c. If EOB activity (i.e. the activity at end of beam) needs to be determined, a second decay correction for the time elapsed between EOB and the gamma measurement time must be applied. After considering the above factors, the sample EOB activity (in Bq) can be written as [76]:  𝐶 =𝑆𝜀𝑦𝑇1𝐾𝑐𝐾𝑊  (5-1) where 𝑆 is the net peak area, 𝜀 is the detector efficiency, 𝑦 is the normalized branching ratio of the peak energy, 𝑇1 is the live time of the measurement in seconds, 𝐾𝑐 is the correction factor accounting for the radionuclide decay during counting, namely,  𝐾𝐶 =𝑇1/2ln(2) 𝑡𝑐[1 −𝑒( −ln(2)𝑡𝑐𝑇1/2)] (5-2) where, 𝑇1/2 is the half-life of the radioisotope, 𝑡𝑐 is the elapsed real clock time during the measurement (in the same time units as 𝑇1/2).  In addition, the 𝐾𝑊 must be used for the nuclide decay correction from the cyclotron EOB time to the start time of gamma measurement (𝑡𝑊).  𝐾𝑊 = 𝑒( −ln(2)𝑡𝑊𝑇1/2) (5-3) It has to be noted that such calculations can only be used for the activity determination from a pure photopeak, i.e. the peak that originated entirely from a 5. Quantitative Activity Measurements  107 single isotope produced directly in a cyclotron irradiation. An example of such a peak would be the gamma peak of 181 keV from 99Mo decays. In cases, when the sample contains several radioisotopes, some of which are emitting photons with similar energies peak multiplets are created. For example, in the cyclotron-produced technetium samples, there might be four isotopes (96mTc, 96gTc, 96Nb and 99Mo) contributing to 778 keV. In such case, a multiplet separation needs to be performed by weighting count contributions from each isotope and taking into account data from different measurement times. The corrections are based on the differences of half-lives and branching ratios of peak contributors.  Moreover, when a sample contains both an isotope and its daughter, corrections for parent decay need to be performed when estimating the activities of the daughter nuclides. The activity created during the periods between EOB and the start of measurement, and during the measurement itself needs to be subtracted for the daughter activity determination.  5.2 Method In this chapter, the analysis of samples irradiated during four cyclotron runs at the BC Cancer Agency with proton beam energy of 18 MeV is reported. Two batches of 100Mo target, containing 97.39% and 99.01% 100Mo content (Target I and Target III in Table 2–1) respectively, were irradiated with proton beam currents ranging from 100 to 240 μA, for durations ranging from 85 min to 6.9 hours.  For gamma measurements, samples were taken from the dissolved target 5. Quantitative Activity Measurements  108 solution before purification (samples contained Tc, Mo, Nb isotopes). The measurements of gamma rays emitted from those samples were performed at 3 h, 24 h, 3 days, 7 days, and 21–30 days after EOB. These repeated measurements were necessary for separating peak contributions from different isotopes. The details of irradiation conditions and observation times are summarized in Table 5–2. Table 5–2 Irradiation and observation information for samples used for gamma spectrum analysis. Run Current (μA) Target (100Mo %) Proton Energy (MeV) Irradiation Time (hours) Observation Time (hours after EOB) 1 85 99.01 18-11 1.50 3, 527 2 159 99.01 18-12 1.32 3, 27, 168, 844 3 188 97.39 18-12 6.42 3, 27, 82, 218, 897 4 223 97.39 18-12 6.90 3, 26. 68, 268, 830  All the samples were measured using a high-resolution gamma-ray spectrometer equipped with a high-purity germanium (HPGe) detector. Before measuring cyclotron samples the energy, FWHM and the efficiency calibrations were performed using the National Institute of Standards and Technology traceable radioactive sources (Eckerd & Ziegler). The calibration curves are shown in Figure 5–5. The same sample volume and measurement configuration were used for both calibration measurements and sample measurements.   5. Quantitative Activity Measurements  109  Figure 5–5 The FWHM and efficiency curves used into the activity analysis. (Upper): FWHM curve. The green points are the photopeaks used for the calibration. (Lower): Efficiency curve. Different color points represent different isotopes. The red curves are the best-fit curves for the FWHM and efficiency calibrations. The curves besides best fittings represent the FWHM and efficiency uncertainties. Since the cyclotron-produced 99mTc samples have a large number of peak multiplets, gamma spectra were analyzed using HyperLabs 2009[77] computer program with the capability to recognize these multiplets. Following the measurement of peaks intensities, calculations according to equation (5-1) were performed (by HyperLabs software) and the experimental EOB activities of 99mTc and other isotopes were determined. Since the HyperLabs 2009 program has limited ability to perform parent-daughter corrections, when estimating products’ EOB activities all the parent-daughter corrections were performed manually. For the FWHM (Ch) Channel Efficiency Energy (keV) 5. Quantitative Activity Measurements  110 products with more than one gamma energy peak, the activity was calculated as the average of the activities obtained from each observed peak. The uncertainty of activity results includes uncertainties of determination of the net peak area, detection efficiency and calibration source. Moreover, theoretical calculations done for the same reactions and the same measurement conditions using CYD were compared with the results from this gamma spectrum analysis.  5.3 Results The first step in gamma analysis is to identify the observed gamma peaks. Table 5–3 summarizes the observed gamma peaks from the samples of four cyclotron runs, their corresponding radioisotope contributors and observation times. All of these peaks were used for activity determinations.  After peak identification, the activities of the observed isotopes for different observation times were obtained from the HyperLabs software. After performing parent-daughter corrections, the EOB activities were estimated. Table 5–4 compares the results of EOB activity of 99mTc estimated from the gamma analysis results and from CYD theoretical calculations. Table 5–5 shows similar activity results for other technetium and non-Tc isotopes. To analyze the consistency of cyclotron runs and test the accuracy of theoretical estimations, the ratios, defined as the experimental activity to theoretically predicted activity, are shown in Figure 5–6. The average ratio of the four cyclotron runs is shown as well. 5. Quantitative Activity Measurements  111 Table 5–3 Summary of main gamma peaks, corresponding isotope contributors and the times, when peaks were observed from gamma spectra of cyclotron samples. Gamma Peak  (keV) Potential Isotopes Detection Time ( after EOB) 96.5 97mTc 1 month 140.0 99mTc 3 h, 1 d, 7 d, 1 month 204.1 95mTc 1 month 181.1 99Mo 3 h, 1 d,7 d 314.3 96gTc 1 month 316.5 96gTc 1 month 366.4 99Mo 3 h, 1 d, 7 d, 1 month 459.8 96Nb 3 h, 1 d, 568.9 96Nb 3 h,1 d 582.0 95mTc 1 month 616.5 95mTc 1 month 658.0 97gNb 3 h 702.4 94gTc 3 h 739.3 99Mo 3 h, 1 d, 1 month 765.5 95gTc, 95gNb 3 h, 1 d, 1 month 777.9 96mTc, 96gTc,96Nb, 99Mo 3 h, 1 d, 7 d, 1 month 812.2 96mTc, 96gTc, 96gNb 3 h, 1 d, 7 d 786.2 95mTc 1 month 820.7 95mTc 1 month 835.1 95mTc 1 month 849.2 96mTc, 96gTc, 94gTc,96Nb 3 h,1 d,7 d, 1 month 870.8 94mTc, 94gTc 3 h, 1039.2 95mTc 1 month 1091.0 96mTc, 96gTc, 96gNb 3 h, 1 month 1126.5 96gTc 7 d, 1 month 1362.5 93gTc 3 h  Table 5–4 99mTc activities determined from four cyclotron runs and corresponding CYD estimations. The ratio of experimental to theoretical estimations are shown in the last column. Run Current (μA) Target (100Mo %) Proton  Energy  (MeV) Irradiation  Time  (hours) Activity at EOB (MBq) Exp./Theo. Ratio Exp. Theo. 1 85 99.01 18-11 1.50 8.47E04±3.41E03 4.74E04 1.80±0.07 2 159 99.01 18-12 1.32 8.06E04±2.89E03 7.15E04 1.13±0.04 3 188 97.39 18-12 6.42 2.32E05±9.34E03 3.08E05 0.75±0.03 4 223 97.39 18-12 6.90 4.34E05±1.74E04 3.83E05 1.13±0.05  5. Quantitative Activity Measurements  112 Table 5–5 Other radioisotopes activity results (MBq) from the four cyclotron runs and CYD estimations under different reaction conditions. The comparison of experimental results with theoretical estimations is shown in the last column of each cyclotron runs. The “- -“ in the cells indicate either that the corresponding gamma peaks were not observed or the detected activities were so small that the measurement cannot be trusted. Product Half-life (h) RUN1 RUN2 RUN3 RUN4 Exp. Theo. Exp./Theo. Exp. Theo. Exp./Theo. Exp. Theo. Exp./Theo. Exp. Theo. Exp./Theo. 97mTc 2194 -- 0.6 -- 1.2±0.1 0.9 1.35±0.07 31.2±1.4 22.1 1.42±0.06 35.5±1.5 28.1 1.26±0.05 96gTc 102.7 12.9±1.5 13.7 0.94±0.11 17.1±0.8 20.4 0.84±0.04 8.1±0.7 11.1 0.73±0.06 29.9±1.4 14.2 2.11±0.1 96mTc 0.9 -- 177.0 -- -- 279.0 -- -- 44.5 -- -- 52.9 -- 95mTc 1464 0.3±0.1 0.3 1.09±0.24 -- 0.4 -- 0.3±0.0 0.10 2.47±0.09 0.9±0.1 0.1 6.02±0.21 95gTc 20 79.8±2.8 63.3 1.26±0.06 -- 96.7 -- 29.8±2.2 24.3 1.23±0.09 162.8±7.5 30.6 5.31±0.24 94gTc 4.9 87.7±2.9 157.6 0.56±0.02 84.1±4.5 246.9 0.34±0.02 25.4±3.4 66.0 0.38±0.05 177.6±11.1 81.7 2.17±0.14 94mTc 0.9  127.0 -- -- 198.0 -- -- 24.1 -- -- 28.6 -- 93gTc 2.6 79.2±5.4 61.2 1.29±0.10 59.5±7.2 102.0 0.58±0.07 -- 30.1 -- 138.8±18.2 36.7 3.78±0.5 93mTc 0.7 -- 25.0 -- -- 43.7 -- -- 5.8 -- -- 7.1 -- 99Mo 65.9 1095.5±26.3 167.9 6.52±0.25 1033.5±33.4 277.0 3.73±0.12 4505.5±141.4 1526.4 2.95±0.09 8339.5±260.8 1938.1 4.30±0.13 97Nb 1.2 4265.1±102.4 4892.8 0.87±0.03 1837.6±77.1 8314.8 0.22±0.01 8838.5±344.0 17748.0 0.50±0.02 13660.1±537.0 21178.0 0.65±0.03  96Nb 23.4 64.4±2.3 167.7 0.38±0.01 37.8±2.0 276.7 0.14±0.01 262.5±9.3 1455.7 0.18±0.01 549.4±18.0 1840.4 0.30±0.01 95mNb 95g 86.4 -- 0.1  -- 0.1 -- 7.9±1.1 2.9 2.74±0.29 6.59±0.88 3.7 1.80±0.24 95gNb 840 -- 0.1  -- 0.2 -- 1.9±0.1 4.1 0.46±0.02 3.25±0.14 5.2 0.62±0.03 5. Quantitative Activity Measurements  113  Figure 5–6 Activity comparison ratio of experimental results over theoretical estimations for each cyclotron run. The average of ratio for each product is shown in black lines. The uncertainty of activity results includes uncertainties of determination of the net peak area, detection efficiency and calibration source. 5.4 Discussion The gamma spectra from the cyclotron-irradiated samples were studied using HPGe detector and HyperLab computer software. The absolute activity determinations of produced 99mTc and other radioactive isotopes were quantitatively estimated.  The peak information shown in Table 5–3 suggests that different observation times are necessary for quantitative estimations of cyclotron technetium samples. For example, for short half-life isotopes, such as 94gTc, 93gTc, 99mTc and 97gNb, early 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 99mTc 97mTc 96gTc 95mTc 95gTc 94gTc 93gTc 99Mo 97Nb 96Nb 95mNb 95Nb RUN1 RUN2 RUN3 RUN4 Average c  97c   96gTc  95mTc  95gTc  94gTc  93gc  99o  9    9  95  Observed Isotopes Activity Ratio (Expe./Theo.) 5. Quantitative Activity Measurements  114 observation time is better because of their fast decays; while for 97mTc and 95mTc, whose half-lives are relatively long, late observation (1 month) is the only time when their gamma-rays were detectable. In addition, it can be concluded that accurate estimation of activities cannot rely solely on automated computer programs, but careful (manual) analysis of the spectra has to be performed. In particular, parent-daughter corrections and multiplets separation corrections needed to be carefully performed for determination of the EOB activities.  In Table 5–4 and Table 5–5, the absolute activities of 99mTc and its contaminants are presented. However, gamma rays from 92Tc, 93mTc, 94mTc, 96mTc and 101Tc were barely observable. This was caused by either their very short half-lives or low gamma emission intensities. From Table 5–5, the main Tc-contaiminants produced with 99mTc are 94gTc, 95gTc and 96gTc. As discussed in Chapter 3, these isotopes have been identified as most significant impurities that may result in increase of patient doses.  By comparing activities of produced 99mTc and other technetium isotopes, it was found that for RUN 1 and RUN 2, the relative activity of 99mTc to the total technetium activity (~99.7%) was lower than those from RUN 3 and RUN 4 (~99.9%). These results highlight the fact that the isotopic composition of the target material is more important than the absolute enrichment level. In particular, 94-97Mo significantly contributed to the production of radionuclide impurities of 94g-96gTc. For the production of other elements, 99Mo and 96-97Nb are the ones observed with high activities in the cyclotron samples; they were mostly produced from 100Mo. For 5. Quantitative Activity Measurements  115 RUN 3 and RUN 4, 95m+gNb are detected because of relatively high contents of 98Mo in the target.  Additionally, theoretical calculations from CYD were compared with the experimental results, as shown in Table 5–4 and Table 5–5. The ratios (Experimental results/Theoretical results) for each observed isotope are summarized in Figure 5–6. The analysis of these data indicates that in most cases the mean activities of technetium isotopes produced in experiments are consistent with theoretical calculations. However, the agreement between the experimental measurements and theoretical prediction from different cyclotron runs vary. For example, as shown in Table 5–4, 99mTc results for RUN 1 and RUN 3 shows large discrepancies whereas RUN 2 and RUN 4 are consistent. There can be two explanations: (a) firstly, that the theoretical cross section of the main reaction of 100Mo(p,2n) used in the calculations reflect the true reaction probability (as indicated by the agreement of RUN 2 and RUN 4). The discrepancy between these RUN 1 and RUN 3 could be explained by experimental errors (related to, for example, the difficulty in handling highly radioactive samples to get diluted qualitative aliquots). (b) The other case could be the opposite in that our theoretical cross sections for 99mTc production do not represent the true reaction probabilities, and the agreement between Run 2 and RUN 4 is a mere coincidence. By comparing our theoretical cross sections with a similar work from Tárkány [51]and considering the consistence of experiment results, the former case is preferred.  Regarding other reaction products: the experimental production of 99Mo is 5. Quantitative Activity Measurements  116 around 4 times higher than predicted by the theoretical calculations, while it is 2-4 times lower for 95-97Nb for all four runs. These ratios are consistent for all four runs, which would indicate that the theoretical cross sections are consistently under and over estimating the true cross sections, respectively for these two cases, and may need to be modified to better represent experimental results.  5.4 Summary This chapter focused on the activity estimations based on the data from cyclotron experiments. By analyzing gamma spectra, quantitative activity measurements for cyclotron produced pre-purified 99mTc were investigated for four cyclotron runs. The results show that 350 GBq (~9 Ci) of 99mTc could be produced in just around 6 hours irradiations. In agreement with the theoretical calculations, besides 99mTc, such technetium isotopes as 94g-96gTc are the most significant contributors to the total technetium activity. Large amounts of 99Mo and 95-97Nb can also be produced during cyclotron irradiations. Although they can be eliminated from the technetium samples, problems of how to deal with radiation waste may arise.  The lack of consistency in experimentally determined production yields for some isotopes indicates that experimental conditions and potential sources of errors (target preparation, beam energy, dissolution, purification and dilution) must be carefully examined.  6. SPECT Imaging Studies of Cyclotron-produced 99mTc  117 Chapter 6 SPECT Imaging Studies of Cyclotron-produced 99mTc The results of our theoretical calculations and experimental analysis, the results demonstrated that when using cyclotron-produced 99mTc several other technetium isotopes could be produced simultaneously. As shown in Table 5–3, most of these technetium isotopes emit high-energy photons, which could degrade image quality by adding background counts to the photopeak window due to scattered photons from said high-energy photons. The aim of this chapter is to investigate the impact on the image quality due to those high-energy emitters using single photon imaging systems. The characteristics of images acquired using cyclotron and reactor/generator produced technetium samples are compared.  6.1 Single photon imaging system Single photon imaging is a nuclear medicine diagnostic technique that uses gamma cameras (also called Anger cameras [78, 79]) to detect photons emitted by radiotracers located in patient’s body. Radioisotopes used in single photon imaging systems are the gamma emitters with their emitting energies in the range of 70 keV to 400 keV. With the injection of 99mTc labeled radiotracers, 140 keV gamma rays emissions from the patient body are detected by gamma cameras and processed into images. In this section, the structure and the function of gamma camera are briefly discussed.  6. SPECT Imaging Studies of Cyclotron-produced 99mTc  118 6.1.1 Structure of gamma camera The major components of a gamma camera are the collimator, scintillation detector, photomultiplier tubes (PMTs), position & energy analysis electronics, and a computer system for data processing and displaying images. Figure 6–1 shows a simplified schematic of a gamma camera.  Figure 6–1 A simplified schematic of a gamma camera. Photons indicated in red are emitted from the patient and one of them interacts with scintillation detector by emitting scintillated light (yellow arrows) after traveling through the collimator. The light is converted to electric signals via photoelectric effect and is amplified by the photomultiplier tubes (shown in orange color). After analyzing the position and energy, a projection image can be stored and shown on the computer screen.  Computer for imaging display Position and energy  analysis electronics Photomultiplier tubes (PMTs) Light guide Scintillation detector Collimator Patient 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  119  The collimator After radiotracer is injected, photons are emitted randomly and isotropically from the patient body. In order to acquire the direction of detected photons, a collimator, which is a thick sheet of perforated material with long thin holes, needs to be positioned in front of the gamma detector [80]. Only photons travelling in certain directions can pass through the collimator holes and reach the detector; otherwise they would be absorbed by the collimator walls (septa). However, some photons may pass through the septal walls without being absorbed, this effect is known as septal penetration. The collimator shown in Figure 6–1 is a parallel hole collimator which ideally only accepts photons moving in directions that are parallel to the septa and perpendicular to the detector surface. The collimator usually is made of a heavy material with high attenuation coefficient, which increases the chances of the incoming photons at lower energies to be absorbed (e.g. lead).  The collimator provides information about photon direction. Its geometry, including the septal length, the thickness and the diameter of holes, is designed for each specific radiotracer and imaging applications since all of these parameters will influence the camera sensitivity and resolution. For example, if the diameter of holes is increased, it could result in higher camera sensitivity but lower spatial resolution.     6. SPECT Imaging Studies of Cyclotron-produced 99mTc  120  Scintillation detector and PMTs The detection system of a gamma camera consists of a scintillation material (scintillator) coupled to an array of PMTs [81], as shown in Figure 6–1. Scintillator is a material that can absorb incoming photons and re-emit their energies in the form of visible light. These light photons create secondary electrons via photoelectric absorption effect at the entrance to the PMTs. Each PMT is a cathode-electrode tube with many dynodes in between. It amplifies the secondary electrons to create stronger detectable electric signals, which are used for the position and energy analysis. For each light photon, 1 to 3 secondary electrons can be ejected by the photo-cathode in the PMTs; subsequently, 6-10 times more electrons can be produced from each dynode. A 10 dynode PMTs are able to achieve a gain of up to 106-107 times in electric signal [82].  Position & energy analysis  Electrical signals produced by the PMTs go through a series of electronic circuits in order to identify the location of the incident gamma and to determine its energy. The original position of incident gamma in the patient body can be identified by comparing and weighting signals from those circuits, while the gamma energy can be determined by summing up all the signals [83]. Thus, the acquired image is a 2D representation (projection) of activity distributions in the patient body, providing the position of radiotracer and measuring its intensity. In order to gather enough counting statistics, the data must be collected over a period of time. 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  121 As shown in Chapter 5, for each incident gamma ray, the detector detects a wide spectrum of energies instead of a single peak of primary photons due to inelastic scattering events. In order to minimize detecting scattered photons, an energy window needs to be defined. Usually, to compensate for limited energy resolution of a scintillator, energy window is set of ±10% of the radioisotope’s photopeak energy [84]. However, this window setting only blocks the scattered photons, whose energies are outside of the window. Scattered photons and photons penetrate collimator septals that fall into the window can still be detected and contaminate the image. In that case, scatter corrections need to be performed (for example, using analytical method [85, 86] or by employing dual or triple energy windows to estimate the scattered photons and subtract them from the photopeak window [87, 88]). Besides scattered photons, some photons can be totally absorbed by human body. This leads to a reduction in the number of detected counts relative to the truth. In such case, an attenuation map is required for performing attenuation corrections [89, 90]. 6.1.2 SPECT The gamma cameras can be used for planar imaging, in which cameras are static during the whole scan time. Alternatively, 3D tomographic imaging technique, i.e. SPECT (Single Photon Emission Computed Tomography), can be used. Detectors, mounted on a rotating gantry, rotate around the patient acquiring a number of 2D projection images with each projection collecting data in a 10-30 second static scan. After that, imaging reconstruction techniques transform those series of 2D 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  122 projections into a 3D image of activity distribution. Moreover, modern SPECT systems are often combined with a low dose X-ray computed tomography (CT) component. Such systems are known as SPECT/CT. The scans of SPECT and CT are acquired sequentially when the patient remains in the same position on the imaging couch. The implemented low-dose CT may provide poorer image quality compared to the standard diagnostic CT machines. However, it is very useful for lesion localization and is also used to generate tissue density maps for attenuation correction [91]. Figure 6–2 gives an example of a dual head SPECT/CT from GE Healthcare.   Figure 6–2 An example of a dual headed SPECT/CT system: GE Infinia Hawkeye. The two detector heads, CT component and other main part of the system are indicated with red arrows.   Tw  h ds (c r s) Patient bed CT 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  123 6.2 Phantom imaging experiments  For the cyclotron-produced technetium imaging studies, phantom scans were performed using Dual head Infinia Hawkeye SPECT/CT camera from GE Healthcare (shown in Figure 6–2). Images of technetium samples produced from both cyclotron and reactor were compared. Multiple scans were performed at various times, i.e. 2 hours, one day and four to five days after EOB, to investigate the effects of long-lived technetium contaminants. The experimental details are discussed below and summarized in Table 6–1:  Experiment round 1 In the first experimental round, a water filled Jaszczak phantom with four identical bottles (33 ml) was used, as shown in Figure 6–3. Cyclotron- and reactor- produced 99mTc were injected into two of the four bottles whereas the other two bottles were empty (filled with air) in order to investigate the imaging differences (potential scatter component) between air and water. A small marker source was put on one side of the phantom for identification purposes. The cyclotron-produced technetium used in these scans was obtained by 1 h irradiations of 99.01% enriched 100Mo target (Target III in Table 2–1) with 18-10 MeV protons. A standard photopeak window of 99mTc, i.e. 126 keV-154 keV (140 keV±10%), was set for scans. To investigate the images from other long-lived technetium contaminants, scans for both technetium samples and backgrounds were performed on Day 1, 2, and Day 5 (Day 1 means the day of cyclotron irradiation (in this case it is 2 hours after EOB); where Day 5 represents the fifth day after the irradiation). 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  124  Figure 6–3 Experiment setup for round 1. (Left): A water filled Jaszczak phantom with four identical bottles (33 ml) was used. Two bottles were filled with cyclotron-produced and reactor-produced 99mTc, two other bottles were filled with air. (Right): Configuration used in SPECT/CT acquisition.  Experiment round 2 To investigate the influence of higher energy photons emitted from long-lived technetium, in the second round of scans the data were acquired in three energy windows. Besides the photopeak window (126-154 keV), the upper energy window (168-312 keV) and lower energy window (89-120 keV) were added to detect the scattered photons originating from all the technetium isotopes present in sample. The cyclotron-produced 99mTc sample used in this round of scans were obtained by 1hour irradiations of 97.39% enriched 100Mo target (Target I in Table 2–1) using 18-10 MeV proton beam. Cyclotron-produced 99mTc and reactor-produced 99mTc were respectively injected into two 17 ml bottles, which were placed inside the Acrylic (thyroid) phantom. Figure 6–4 shows the phantom setup Reactor 99mTc Empty bottles Cyclotron 99mTc 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  125 and its co-registered SPECT/CT image. Photon counts and images from the reactor and cyclotron-produced 99mTc were evaluated.   Figure 6–4. (Left): Phantom configuration for experimental round 2. (Right): The co-registered SPECT/CT phantom image. Table 6–1 The summary of details of two rounds of scans. For each scan date, 5 min background scans were performed before sample scans. Scan Scan Date (Time relative to the cyclotron irradiation) Scan Time Scan Type Technetium Activity @ Day 1 (MBq) Phantom Round 1 #1-1 Day 1 30 min Tomography Cyclotron Sample:  49 MBq Reactor Sample:     62 MBq Jaszczak / water #1-2 Day 2 30 min Tomography #1-3 Day 2 5 min Planar #1-4 Day 5 5 min Planar #1-5 Day 5 5 min Planar Samples on camera Round 2 #2-1 Day 1 20 min Tomography Cyclotron Sample:  58 MBq Reactor Sample:     59 MBq Acrylic #2-2 Day 1 15 min Planar #2-3 Day 5 20 min Tomography #2-4 Day 5 15 min Planar 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  126 6.3 Results  In order to compare images obtained from the two types of technetium samples produced from the cyclotron and reactor, both imaging projections and image profiles were studied. In the first round of experiments, only 99mTc photopeak window (126-154 keV) was used in the scans. Figure 6–5 presents the sample projections corresponding to the tomographic scans of Day 1 and Day 2 (scan #1-1 and #1-2 in Table 6–1). The profiles were drawn as indicated by the lines shown in the projections. The upper bottle shown in the projection corresponds to the reactor-produced 99mTc; while the lower one corresponds to the technetium sample produced in the cyclotron (Figure 6–5). A small marker source visible in the upper right of the projection was used for sample identification. Figure 6–6 shows similar projections and corresponding profiles from the scans of Day 2 and Day 5 (scan #1-3 and #1-4 in Table 6–1). Additionally, the projections and profiles obtained from the scan #1-5 where the samples were directly put on the camera (without any absorbing material) are also shown in Figure 6–6.   6. SPECT Imaging Studies of Cyclotron-produced 99mTc  127  Figure 6–5 Sample projections corresponding to the tomographic scans of Day 1 and Day 2 (scan #1-1 and #1-2 in table 6-1). The profiles are drawn as indicated by the lines shown in the projections. The number on each profile corresponds the line numbers shown on the projection. Two technetium samples are shown in the projection, the upper one corresponds to the reactor-produced 99mTc; where the lower one corresponds to the technetium sample from the cyclotron.  Figure 6–6 Sample projections corresponding to the planar scans of Day 2 and Day 5 with and without phantom (scan #1-3, #1-4 and #1-5 in table 6-1). The profiles are drawn as indicated by the lines shown in the projections. The number on each profile corresponds to the line numbers shown on the projection. Two technetium samples are shown in the projection, the upper one corresponds to the reactor-based 99mTc; where the lower one corresponds to the technetium sample from cyclotron. 123 4 1 2 3 4121 2 3 443Day 2: Day 1: Day 2: Day 5: Day 5 Samples were on the camera: 123 4 1 2 3 413 4 1 2 3 4123 4 1 2 3 46. SPECT Imaging Studies of Cyclotron-produced 99mTc  128 In the second round of scans, three energy windows were used for detecting the scattered photons from the contaminant technetium. Figure 6–7 and Figure 6–8 show the sample projections from the photopeak, upper and lower windows and their horizontal and vertical profiles from second round scans of Day 1 (scan #2-2) and Day 5 (Scan #2-4). In the profiles, the red lines correspond to the cyclotron-produced technetium sample, where the black lines correspond to the reactor-produced 99mTc sample. Additionally, the counts measured in planar scans of #2-2 and #2-4 in three energy windows for both types of samples and for the background are summarized in Table 6-2. All scans were performed in 15 min.  Figure 6–7 Projections from the photopeak, upper and lower windows and their horizontal and vertical profiles. The data were acquired during the second round of scans on Day 1 (#2-2). In the profiles, the red line corresponds to the cyclotron technetium sample, the black line to the reactor 99mTc sample.  6. SPECT Imaging Studies of Cyclotron-produced 99mTc  129  Figure 6–8 The sample projections from photopeak, upper and lower windows and their horizontal and vertical profiles from second round scans of Day 5 (#2-4). In the profiles, the red line corresponds to the cyclotron technetium sample, the black line to the reactor 99mTc sample. Table 6–2 Photon counts measured in three energy windows for the technetium samples from cyclotron and reactor and background.  Sample Acquisition Day Photon Counts in the Energy Windows Photopeak Upper Lower Cyclotron-produced Tc Day 1 4.3E06 5.8E05 2.1E06 Day 5 5.0E04 1.8E05 5.5E04 Reactor-based Tc Day1 4.2E06 1.2E05 2.0E06 Day 5 3.4E04 1.2E05 3.9E04 Background Day 5 3.4E04 1.2E05 3.9E04  6.4 Discussion  The data from both rounds of scans clearly shows that the images corresponding to 99mTc photopeak and lower energy windows acquired on Day 1 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  130 and Day 2 are almost identical (see Figure 6–5, Figure 6–6 and Figure 6–7). There is no difference in the shapes of profiles drawn across the two sources. Similarly, there is no difference in the scatter tails for the data corresponding to these two windows. According to the photon counts shown in Table 6-2, there is only a 3-6% increase in the counts in the cyclotron sample as compared to the reactor sample.  However, the counts in the upper energy window from the cyclotron technetium sample are four times higher than those from the reactor. This is due to the fact that most important contaminants in the cyclotron technetium samples are 94gTc, 95gTc and 96gTc with emission energies mostly between 700 keV and 800 keV. Although these high energy photons could not be detected by the camera, their scatter photons have lower energies and can be detected. Although this scatter is present in all energy windows, its relative contribution to the upper energy is especially visible because reactor-produced 99mTc do not have any high energy component. For the images acquired on Day 5, the counts for the reactor sample are at the baseline background level which means that all the 99mTc decayed after 4-5 days; while the counts from the cyclotron technetium sample are 50% higher than the background (see Table 6–2, Figure 6–6 and Figure 6–8). Our theoretical yield estimations indicate that the cyclotron sample used on the second round Day 5 scans are composed of around 78% of 97mTc (half-life of 91.4 days), 20% of 96gTc (half-life of 4.28 days) and 2% of 95m+gTc (half-life of 20h for 95gTc and 61days for 95mTc). 6. SPECT Imaging Studies of Cyclotron-produced 99mTc  131 Based on above discussion, one would suggest that SPECT diagnostic scans using cyclotron-produced 99mTc should be done within the 24 hours after the cyclotron irradiations. 6.4 Summary The objective of this study was to investigate the quality of images of cyclotron-produced technetium. The SPECT/CT and planar scans were performed on different days after cyclotron irradiations. Images and corresponding profiles for both cyclotron- and reactor-produced technetium samples were compared. Three different energy windows were set during the scans in order to study the contaminants in the cyclotron technetium samples. The results indicate that images corresponding to the 99mTc photopeak window obtained from the cyclotron-produced technetium acquired up to 24 hours post cyclotron irradiations are basically identical to those from reactor technetium. In agreement with our theoretical predictions, the existence of long-lived 97mTc, 96gTc and 95m+gTc lead to the increase in counts, especially in the images from later scans acquired. 7. Conclusion and Future Work  132 Chapter 7 Conclusion and Future Work 7.1 Conclusions The objective of this thesis was to investigate the feasibility of the cyclotron-based production of 99mTc.  The first step towards meeting this objective was to theoretically predict the quantity and purity of cyclotron-produced 99mTc. From calculating the reaction cross sections and production yields, the amount of 99mTc and other radioactive and stable isotopes were estimated (Chapter 2). Due to the existence of other technetium in the cyclotron production samples, the radiation dose to the patient would be increased. Chapter 3 presented the estimation of the dosimetry and potential dose increases when cyclotron-produced 99mTc was used. In diagnostic procedures, the main contributors to the doses were 94g-96gTc. These results indicated that the Mo target used in cyclotron production should have relatively small content of 94-97Mo, which were the “reaction parents” for 94g-96gTc.  Comparisons of both yield and dosimetry estimations using different irradiation parameters suggested that proton energies in the range of 16-19 MeV with target thicknesses degrading beam energy to 10 MeV and relatively short irradiation times (3-6 hours) correspond to the most advantageous energy region for 99mTc production. Additionally, considering potential dose increases, the times below 12 hours after EOB were identified as the optimal time period for the patient injection. However, it has to be noted that these suggested reaction and injection 7. Conclusion and Future Work  133 conditions are based on the analysis of the target list on Table 2-1. The relative percentage of different Mo isotopes in the target is the most important parameter that will largely influence the yield and dosimetry results.  Recently, a new enriched target became available; it contains up to 99.82% of 100Mo isotope with small contributions from other Mo isotopes (0.003% of 92Mo, 0.003% of 94Mo, 0.003% of 95Mo, 0.003% of 96Mo, 0.003% of 97Mo, 0.17% of 98Mo). Our theoretical estimations indicate that, if this new target is irradiated for 6 hours using 24 MeV proton beam, the increased patient dose even at 24 hours after EOB would be only around 5% which may be acceptable. However, even in this case, if lower beam energy is used (e.g. 19 MeV), the dose increase would be smaller. Due to the complex and time-consuming yields and dosimetry calculations, a graphical user interface, named CYD, was developed allowing users to perform theoretical predictions in only a few seconds. CYD can be used to estimate reaction yields and corresponding gamma emissions to be compared with the experimentally measured values and predict patient doses. Moreover, we expect that it would be very useful in the future, at the clinical stage, where reaction parameters could be entered into this GUI to predict production yields and estimate radiation doses for each particular cyclotron run.  In Chapter 5, these theoretical predictions were compared with experimental data. By analyzing gamma spectra from different cyclotron runs, quantitative activity measurements for cyclotron-produced 99mTc samples were investigated. The results demonstrated that it was possible to create large amounts of 99mTc in a 7. Conclusion and Future Work  134 single cyclotron run. Consistent with our theoretical calculations, experiments showed that besides 99mTc, isotopes 94g-96gTc were the most significant contributors to the total technetium activity. When used in radiopharmaceuticals, these isotopes will also be responsible for creating extra radiation dose to the patients.  Since 99mTc is used in planar and SPECT imaging, investigation of image quality of cyclotron-produced technetium was of great importance (Chapter 6). Imaging scans for both cyclotron- and reactor-produced 99mTc at different times after EOB were performed. The results indicated that images from the cyclotron-produced technetium acquired up to 24 hours post cyclotron irradiations were of the same quality as those from reactors. However, the existences of long-lived 97mTc, 96gTc and 95m+gTc led to the increase in count rates, especially in the images from later scans. 7.2 Future work There are several possibilities for expanding on the work presented in this thesis: Firstly, there always could be new and useful functions to add to the yield and dosimetry calculation GUI. For example, information about detector efficiency and/or relative peak corrections could be added into the spectrum analysis layer. This could give the user the true detectable photon counts estimations. Moreover, in the current version of this GUI, only one adult male phantom model and three chemical injection agents can be used in dosimetry estimations. In the future, more 7. Conclusion and Future Work  135 models and agents could be added. Aslo, the reaction cross section preset in CYD are based on theoretical calculations, some of them might not reflect the true reaction probability, as discussed in Chapter 5. In the future, the theoretical cross sections stored in CYD could be replaced by the experimental cross sections. Secondly, although conditions that optimize production yields have been identified, variations in target composition and thickness, irradiation conditions and the dissolutions and dilutions procedures may dramatically affect the amounts of reaction products. In order to ensure the stability of 99mTc supply, the factors, which lead to such variability, need to be investigated. Thus, the procedures used in cyclotron runs can be improved to eliminate or at least decrease this variability. Moreover, in the future clinical applications of cyclotron-produced 99mTc, there may not be enough time to perform full gamma spectroscopy analysis to investigate the impurities in the sample. Therefore, it is important to develop a methodology, which would allow the user to examine the quality and purity of a cyclotron sample in a short and simple measurement. 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