High Energy Gamma Detection for Minimally Invasive Surgery

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By

Gregg J Chapman

Graduate Program in Electrical and Computer Engineering

The Ohio State University

2017

Dissertation Committee:

Dr. Robert Lee, Advisor

Dr. Marvin H. White

Dr. Edward Martin Jr.

Copyrighted by

Gregg James Chapman

2017

Abstract

Intraoperative detection of radio-labeled cancer has become a standard of care for some forms of cancer surgery. Most commercially available gamma detection probes are designed for use with low energy radioisotopes. Many new radiotracers exhibit positron emission which ultimately decays into two 511 kilo-electron volts (KeV) high energy gamma emissions. Gamma detection probes capable of capturing this energy require heavy side shielding to block off-axis radiation, making them both large and cumbersome for intraoperative use. Moreover, minimally invasive surgical procedures, performed either laparoscopically or robotically, are rapidly replacing open procedures in many areas of surgical oncology.

To detect high energy radioisotopes with a gamma detection probe capable of being introduced into the surgical field laparoscopically, a significant change to the approach of intraoperative gamma detection is required. Gamma detection probes must be re-designed with both increased sensitivity at high energy, and an alternative to the heavy metal shielding. The necessity for side shielding can be eliminated by using two detectors in combination with software to limit the field of view. To achieve increased sensitivity, the detection system can be configured to detect a broader energy range that includes gamma counts from Compton scattered radiation. Compton scattered radiation is the result of incomplete photoelectric absorption within the detection crystal. In currently marketed designs, it is excluded from the accumulation of gamma counts because it reduces the ii spatial resolution of the probe. A third methodology is required to recover this loss of spatial resolution associated with the expanded energy range. A statistical basis for probe positivity can be used to improve the spatial accuracy of the radiation source measurement.

This research investigates the viability of applying these three methodologies to reduce the diameter of gamma radiation probes while simultaneously increasing the sensitivity at an energy of 511 KeV. A positive outcome defines the parameters for a subsequent implementation of laparoscopic and robotic probes to be used for the detection of positron emitting radionuclides.

It is evident from the study that a detector pair can limit the field of view without the use of side shielding. The data also suggests that the depth of the source may be calculated using the count rates from the detector pair, under limited conditions. However, further development is needed. When the energy range is expanded to include Compton scattered radiation, probe sensitivity is increased by two orders of magnitude. A statistical criterion for probe positivity recovers the loss of spatial resolution associated with the use of a wider energy acceptance range. The statistical criterion is also capable of differentiating a radiation source from background at tumor-to-background ratios as low as 1.1-to-1 if the gamma counts are sufficiently high.

Surface mapping of the radioactivity emitted from phantom models demonstrates that the ratio of two detector counts is a more sensitive indicator of spatial differences in radioactivity compared to count rates from a single detector. This finding suggests that a new criterion for probe positivity based on count rate ratios may improve localization of radio-labeled tumors.

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Acknowledgements

I wish to dedicate this dissertation to the late Dr. Marlin O. Thurston, who’s contribution to radioguided surgery made this work possible, and to patients, families, and friends affected by cancer.

I would like to extend my gratitude to Dr. Robert Lee for his wisdom and extraordinary insight, Dr. Edward Martin Jr. for his motivation and undaunting support, and Dr. Marvin

H. White for his invaluable insight, expertise, and many kind words. I also wish to thank

Dr. Stephen Povoski and Dr. Douglas Murrey for creating many opportunities in both intraoperative research and journal publications. Most of all, I would like to honor my wife, Valerie, for her devotion, patience and many insightful reviews of this material.

Colossians 3:17 “And whatever you do in word or deed, do all in the name of the Lord

Jesus, giving thanks to God the Father through Him.”

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Vita

May 1974 ...... Olentangy High School

1983...... B.S. Biomedical Engineering, Case Western Reserve University

1995...... M.S. Electrical Engineering, Case Western Reserve University

1983-1989: Senior Research Engineer, Division of Surgical Research, St. Luke’s Hospital, Cleveland, Ohio

1989-1996: Director of Hardware Development, Cleveland F.E.S. Center, Technical Development Laboratory, Cleveland, Ohio

1996-2000: Senior Electronics Development Engineer Caterpillar Inc., Technical Systems Development, Mossville, Illinois

2001-2009: Manager of Instrument Development Programs Neoprobe Corporation, Dublin, Ohio

2009-2010: Consulting Engineer Dept. Surgical Oncology, The Ohio State University Medical Center, Columbus, Ohio

2010-Present: PhD Candidate ECE Department, The Ohio State University, Columbus, Ohio

2010 - 2014: Graduate Teaching Assistant. ECE Department, The Ohio State University, Columbus, Ohio

2014 - Present: Laboratory Supervisor, ECE Department, The Ohio State University

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Publications

1. Chapman, G.J., Povoski, S.P., et. al. (2014). Comparison of two threshold detection criteria methodologies for determination of probe positivity for intraoperative in situ identification of presumed abnormal 18F-FDG-avid tissue sites during radioguided oncologic surgery Cancer,14:667.

2. Povoski, S.P., Chapman, G.J., Murrey, D.A., Lee, R., Martin, E.W., Hall, N.C. (2013). Intraoperative detection of 18F-FDG-avid tissue sites using the increased probe counting efficiency of the K-alpha probe design and variance-based statistical analysis with the three-sigma criteria. BMC Cancer, 13: 98-10.1186/1471-2407-13- 98.

3. Martin, E.W., Chapman, G.J., et. al. (2010). Intraoperative detection of gamma emissions using K-alpha x-ray fluorescence. Expert Review of Medical Devices, 7(4), 431-434.

4. Crago, P.E., Usey, M., Memberg, W.D., Keith, M.W., Kirsch, R.F., Chapman, G.J., Katorgi, M.A., Perreault, E.J. (1996). An Elbow Extension Neuroprosthesis for Individuals with Tetraplegia., Proceedings of the First Annual Conference of the International Functional Electrical Stimulation Society, May 14-16.

5. Hines, A. E., Crago, P. E., Chapman, G. J., Billian, C. (1996). Stimulus Artifact Removal in EMG from Muscles Adjacent to Stimulated Muscles., Journal of Neuroscience Method, Vol. 64: 55-62.

6. Lemay, M.A., Crago, P.E., Katorgi, M.A., Chapman, G.J. (1993). Automated Tuning of a Closed Loop Hand Grasp Neuroprosthesis., IEEE Transactions on Biomedical Engineering, Vol. 40 (7): 675-685.

7. Lemay, M.A., Katorgi, M.A., Chapman, G.J., Crago, P.E. (1990). Addition of Closed Loop Stiffness Regulation to an Open Loop Hand Grasp Neuroprosthesis. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 12, No. 5, 2271-2272.

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8. Hutton, M., Rhodes R.J., Chapman G. (1982). The Lowering of Post-Ischemic Compartment Pressures with Mannitol. Journal of Surgical Research, Vol. 32: 239- 242.

Field of Study

Major Field: Electrical and Computer Engineering

Other Fields: Biomedical Engineering, Surgical Oncology

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Table of Contents

Abstract ...... ii

Acknowledgements ...... iv

Vita ...... v

Publications ...... vi

Field of Study ...... vii

Table of Contents ...... viii

List of Tables ...... xi

List of Figures ...... xiii

Chapter 1: Introduction and Rationale ...... 1

Chapter 2: History ...... 5

Chapter 3: Theoretical Framework ...... 11

3.1 Gamma Detection ...... 11

3.2 Radiation Types...... 12

3.3 Radiation Interactions ...... 15

3.4 The Detector ...... 23

3.5 Single Element Semiconductor Probe Design ...... 30 viii

3.6 Probe Characterization ...... 38

3.7 Inverse Squared Law ...... 43

3.8 Depth Detection...... 44

3.9 Electronic Collimation ...... 46

3.10 Radiation Counting ...... 52

3.11 The 3-Sigma Criteria for Probe Positivity...... 53

Chapter 4: Research and Development Methodology ...... 59

4.1 Dual Detector Probe Design ...... 59

4.2 The Open Energy Window ...... 62

4.3 Probe Characterization Studies ...... 67

4.4 Modelling, Simulations, and Software Analysis ...... 73

4.5 Experimental Design ...... 79

4.6 Experimental Protocols ...... 88

Chapter 5: Findings and Analysis ...... 114

5.1 NEMA NU3:2004 Standard Studies ...... 114

5.2 Source Detection in a 1.1-to-1 Target-to-background Ratio ...... 141

5.3 Limits of Detection...... 143

5.4 Depth Detection...... 146

5.5 Spatial Resolution ...... 153

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5.6 Intraoperative Phantoms ...... 161

Chapter 6: Discussion, Conclusions, and Future Research...... 176

6.1 Probe Design ...... 176

6.2 Laparoscopic and Robotic Probes ...... 178

6.3 Electronic Collimation ...... 181

6.4 Depth Detection...... 182

6.5 Background Rejection ...... 184

6.6 A Multiple Channel Pre-amplifier...... 184

6.7 Gamma Detection System Console ...... 185

Conclusions ...... 187

References ...... 189

Appendix A: Characteristics of Cadmium Zinc Telluride ...... 197

Appendix B: Design Plan...... 198

Appendix C: Derivation of the Hecht Equation ...... 211

Appendix D: Phantom Data ...... 217

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List of Tables

Table 1: Mass and linear attenuation coefficients and percentage of interaction...... 22

Table 2: Calculation of expected count rate ratios for angle and distance...... 50

Table 3: Preliminary study. 18F-FDG required for each object and volume...... 90

Table 4: Titrated radioactivity for 3 sizes of source spheres ...... 112

Table 5: Sensitivity in Air. Window is 50-600 KeV...... 115

Table 6: Sensitivity through side shielding in air. Window is 50-600 KeV...... 117

Table 7: Sensitivity of side and back shielding...... 118

Table 8: Energy resolution results from MCAs taken with a 22Na source...... 127

Table 9: Data and calculated values for sensitivity in a scatter medium...... 129

Table 10: Data and calculated values for sensitivity to scatter...... 130

Table 11: Spatial resolution data for open window setting (50-600 KeV)...... 132

Table 12: Spatial resolution data for a commercial window setting (409-600 KeV). .... 133

Table 13: Calculated values for spatial resolution in a scatter medium...... 134

Table 14: Angular resolution data. Energy Window is 50-600 KeV...... 136

Table 15: Angular resolution can be limited to 90⁰ at a count rate ratio of 1.35 ...... 139

Table 16: Volume sensitivity for the dual element probe...... 140

Table 17: Data results at low Target to Background ratios...... 141

Table 18: Limit of Detection sorted by calculated target-to-background...... 144

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Table 19: Depth detection data appended to Table 18...... 147

Table 20: Percentage of depth error under various constraints...... 152

Table 21: Spatial resolution data with count rate ratios...... 154

Table 22: Spatial Resolution at 1 cm. and 1:0 TBR ...... 155

Table 23: : Spatial Resolution at 3 cm. and 1:0 TBR ...... 155

Table 24: Spatial Resolution at 1 cm. and 5:1 TBR ...... 155

Table 25: Spatial Resolution at 3 cm. and 5:1 TBR ...... 156

Table 26: Spatial resolution of front detector ...... 157

Table 27: Spatial resolution of rear detector ...... 157

Table 28: Field of view at 3 cm. for 50-600 KeV energy window...... 160

Table 29: Imposed limitations for Gamma Detection Console ...... 185

Table 30: Characteristics of CZT and other semi-conductors ...... 197

Table 31: Design Plan ...... 201

Table 32: Design Reviews...... 204

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List of Figures

Figure 1: Mass attenuation due to various interactions in CZT ...... 21

Figure 2: Relationship between three major modalities of material interaction...... 22

Figure 3: Energy bands and bandgap model for a semiconductor ...... 24

Figure 4: An MCA showing hole tailing in CZT...... 27

Figure 5: Diagram of a semiconductor probe (bias voltage not shown) ...... 31

Figure 6: Charge migration in a semiconductor crystal...... 31

Figure 7: Semiconductor Gamma Detection Probe. Neoprobe, Model 1017...... 32

Figure 8: A typical RC charge preamplifier and shaper circuit...... 34

Figure 9: The Field of View imposed by heavy metal shielding ...... 37

Figure 10: Multichannel Analysis of a monoenergetic radioisotope ...... 39

Figure 11: The Full Width Half Maximum value ...... 41

Figure 12: Geometry of off-axis radiation source ...... 47

Figure 13: Depth detection using a reduction in field of view...... 51

Figure 14: Background, Target, and Source count distributions ...... 57

Figure 15: Background and Target count distributions when Source is zero ...... 57

Figure 16: Target count distribution is at the minimum detectable level ...... 58

Figure 17: Dual detector probe design for electronic collimation and depth detection. ... 60

Figure 18: Disassembled Dual Detector Probe ...... 60

Figure 19: Assembled Dual Detector Probe, 15mm diameter...... 61

Figure 20: Efficiency as a function of gamma energy ...... 63 xiii

Figure 21: MCA showing a standard commercial energy window ...... 65

Figure 22: MCA showing an open energy window ...... 65

Figure 23: MCAs for three source activities...... 66

Figure 24: MCAs normalized to source activities...... 66

Figure 25: MCAs showing MCNP output, Hecht equationand GEB Filter ...... 77

Figure 26: MCAs comparing model to actual probe response ...... 78

Figure 27: CNC manipulator, probe, and NEMA NU3 standard water bath...... 82

Figure 28: Two gamma detection systems, probe, and patch box...... 84

Figure 29: MCA Set-up...... 86

Figure 30: Phantom sphere set ...... 92

Figure 31: Large phantom sphere...... 92

Figure 32: Specifications for spheres used in the studies ...... 93

Figure 33: Cylindrical source detail prior to glueing ...... 93

Figure 34: Phantom set-up #1 ...... 94

Figure 35: Phantom setup #2 ...... 94

Figure 36: Phantom setup #3 ...... 95

Figure 37: Phantom setup #4 ...... 95

Figure 38: Phantom setup #5 ...... 96

Figure 39: Angle adapter...... 105

Figure 40: The ratiometric basis for electronic collimation ...... 119

Figure 41: Field of view at a ratio of 1.30...... 121

Figure 42: Field of view at a ratio of 1.50...... 122

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Figure 43: Field of view at a ratio of 2.50 ...... 123

Figure 44: Field of view at a ratio of 3.50...... 124

Figure 45: MCA from front detector. Source is 18F-FDG. Two-minute record...... 126

Figure 46: MCA from rear detector. Source is 18F-FDG. Two-minute record...... 126

Figure 47: MCA repeated with 22Na source...... 127

Figure 48: Field of view for count rate ratios:1.3, 1.36, 1.56, 2.25, and 3.36 ...... 138

Figure 49: MCNP probe model of the electronically collimated probe...... 149

Figure 50: MCNP simulation results for near and far field of dual detector probe ...... 150

Figure 51: Interpolation of the source depth from 4 count rate ratios ...... 152

Figure 52: FWHM for front detector...... 159

Figure 53: FWHM for rear detector...... 159

Figure 54: FWHM for count rate ratio...... 160

Figure 55: 3-D contour of the count rate ratio. phantom #1. Threshold is 1.1...... 163

Figure 56: 3-D contour of the count rate ratio, phantom #1. Threshold is 1.68...... 163

Figure 57: PET/CT scan of phantom #1, axial and coronal views...... 164

Figure 58: MCNP computer model for phantom #1, axial view...... 164

Figure 59: 3-D contours of the count rate ratio, phantom #2. Threshold is 1.14 ...... 166

Figure 60: 3-D contours of the count rate ratio, phantom #2. Threshold is 1.36...... 166

Figure 61: PET/CT scan of phantom #2, axial, sagittal, and coronal views...... 167

Figure 62: MCNP computer model for phantom #2, sagittal view...... 167

Figure 63: 3-D contour of the front detector, phantom #3. Threshold is 1836...... 169

Figure 64: 3-D contour of the rear detector, phantom #3. Threshold is 1100...... 169

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Figure 65: 3-D contour of the count rate ratio of phantom #3. Threshold is 1.27...... 170

Figure 66: PET/CT scan of phantom #3, axial and coronal views at two depths...... 170

Figure 67: MCNP computer model for phantom #3, coronal view...... 171

Figure 68: 3-D contour of the count rate ratio of phantom #4...... 174

Figure 69: PET/CT scan of phantom #4, sagittal, axial, and coronal views...... 174

Figure 70: 3-D contour of the count rate ratio of phantom #5...... 175

Figure 71: PET/CT scan pf phantom #5, axial and coronal views...... 175

Figure 72: Robotic probe with articulating head...... 179

Figure 73: Standard da Vinci instrument, Intuitive Surgical Inc...... 179

Figure 74: Isolation Diagram for a gamma detection system...... 210

Figure 75: Charge migration for Hecht calculation ...... 212

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Chapter 1: Introduction and Rationale

This research investigates solutions to ultimately provide the surgeon with probes capable of detecting high energy gamma radiation (350 KeV – 1.22 MeV). The detection efficiency of these devices must be sufficient to localize radio-labeled agents concentrated in metastatic tissue. As these devices will be used intraoperatively, and in conjunction with state of the art surgical techniques, high energy gamma detection probes should be implemented in both a laparoscopic and robotic form factors. This will require an original approach to the design of gamma detection probes in order to limit the size of the probe, and concurrently provide increased counting efficiency at high energies.

The detector efficiency of commercially available probes is not sufficient to detect 511

KeV gamma energy intraoperatively where tumor-to-background ratios encountered are often less than 1.5-to-1. Moreover, the side shielding required for gamma energies of this magnitude make commercial devices too large and heavy to be used in laparoscopic or robotic applications.

Probe efficiency can be increased dramatically at 511 KeV by implementing a wider energy acceptance window than is currently used in commercial products. Since all counts ultimately arise from the 511 KeV source, Compton scatter can be included when only a single radionuclide is present.

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The application of statistical confidence intervals as criteria for probe positivity is superior to the more commonly used ratiometric criterion [1]. If the measured count rates are greater than approximately 1000 counts per seconds, target count rates of less than 1.1 times the background count can be detected as probe positive using a three-standard deviation statistical criterion for probe positivity.

To limit the tissue volume contributing to the count rate measurement, a limited field of view must be designed into the probe. This is traditionally done by recessing the detection crystal in lead or tungsten shielding of a sufficient thickness to attenuate the gamma energy by 90-95%. This collimation improves the tumor-to-background ratio by decreasing the spatial resolution of the probe.

To reduce the size of high energy gamma probes to a suitable size for laparoscopic and robotic applications an alternative to conventional shielding materials is needed. Multiple element detectors can be used to eliminate the need for side or rear shielding materials.

To address the issues of reduced probe size and increased efficiency at high energies, conventional probe design practices must be challenged. The success or failure of the proposed research can be summarized in the following three hypotheses.

Hypothesis #1: The Open Energy Discrimination Window Hypothesis

The sensitivity of the probe can be increased, without increasing detector volume, by expanding the energy range of the detector to include Compton scattered radiation. In an environment that contains only one radionuclide, the number of counts detected in a fixed period is proportional to the source activity. If two or more radionuclides are present, it is 2

impossible to differentiate between the lower energy radionuclides and photons originating from a higher energy radionuclide that have lost energy from interactions with the detector material (Compton scatter). Expanding the energy range of the detector to include

Compton scatter increases the probe sensitivity. Probe sensitivity is typically improved by increasing the volume of the detection crystal. An alternative method, proposed here, increases the sensitivity by expanding the energy acceptance range.

Hypothesis 2: The 3-sigma Hypothesis

Increases in count rate above the background radiation measurement can be defined as a probe positive finding for cancerous tissue based on a statistical criterion for a predefined confidence level. This method provides an increase in the accuracy of localization in the spatial sense when compared to other methods. Application of the statistical criterion is required to recover the loss of spatial resolution associated with increasing the energy acceptance range of the probe to include Compton scattered counts described in the first hypothesis. It should also be noted that the statistical criterion can detect areas of positivity in environments where the tumor-to-background ratio of radioactivity is as low as 1.1-to-

1. This is not possible with the ratio based method, commonly referred to in current publications [2 - 4] that address the topic of probe positivity, and is only possible if the count rate is sufficiently high.

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Hypothesis 3: The Electronic Collimation Hypothesis

The difference in the count rate from two detectors can be used to define the field of view. This will allow high energy gamma detection probes to be designed in a small form factor by eliminating side and rear shielding. Multiple detectors and software algorithms can impose a limit on the field of view by disabling probe counting when the relationship between 2 (or more) detectors counts exceeds specified limits. This method of limiting the field of view is referred to as electronic collimation throughout the dissertation.

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Chapter 2: History

The history of intraoperative gamma detection correctly begins with the discovery of x-rays in by Roentgen in 1895 [5]. Henry Becquerel discovered naturally occurring radiation in uranium one year later in 1896 [6]. The term “radioactivity” was first introduced by Madam Marie Curie in her publication which also announced the discovery of the element radium [7]. Using an electrometer developed by her husband, Pierre,

Madam Curie was the first scientist to document that the radioactivity of the element uranium was proportional to the amount of the element present, even in compound form.

The Curies also developed the mathematical relationship for radioactive half-life. It is significant that Madam Curie, a physicist, devoted most of her research to medical applications. By 1914 her fine work resulted in both X-ray imaging and the use of radioactive elements to destroy tumor tissue make her the founder of radiation oncology.

In 1913 Henry Mosely, a brilliant British physicist, verified the Bohr model of the atom by investigating the x-ray spectra of various elements. He recognized in what later became referred to as Mosely’s Law that the characteristic x-ray (K-alpha) produced by an element exposed to radiation occurred at discrete and predictable levels [8]. This work formed the basis of the current periodic table and the atomic number of elements. When WWI broke out, Henry Mosely became a telecommunications officer and, sadly, was killed by a sniper

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in 1915. He was 27 years old. It is speculated that he would have been awarded the Nobel

Prize in 1916 had he not died. This profound loss to the scientific community lead to

British laws limiting the eligibility of scientists for combat duty.

Based on Mosely’s work, George de Hevesy discovered the element hafnium by recognizing that there were large gaps in documented characteristic x-rays. George de

Hevesy was later awarded the Nobel Prize for his work in radiotracers. He first used radiotracers as early as 1913 [9]. Although he went on to use an isotope of lead as a radiotracer to map metabolic activity in plants in 1923 he never published the work. De

Hevesy would later apply these techniques to the measurements of metabolic rate in animals [10]. The PET scan of today images the increased metabolic activity of cancerous tissue using an 18F radio-labeled sugar analog as a radiotracer and is based on the methodology developed by George de Hevesy.

But to measure radioactivity in humans, instruments more sophisticated than the electrometer of Pierre Curie were required. The first gamma radiation detector was developed by Hans Geiger and Walther Muller in 1928 consisting of a gas filled vacuum tube, anode, and cathode [11]. Marinelli and Goldschmidt are recognized as the first to apply gamma detection to a clinical application [12]. In 1942, this group examined

Phosphorus-32 uptake in skin lesions using a GM tube. Beer, et al., differentiated benign and malignant breast lesions using the same technique in 1946 [13]. The first intraoperative use of gamma detection was conducted by Selverstone, et al. in 1949, when this group identified Phosphorus-32 uptake in brain tumors [14]. The first gamma detection probe

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designed for intraoperative use was developed by Harris, et al. in 1956 and consisted of a thallium doped cesium iodide (CsI:Tl) scintillation detector connected to a photomultiplier tube [15]. This device was used to detect 131I in patients undergoing surgery for thyroid carcinoma. Semiconductor detectors became available in the mid-1970s but were not used intraoperatively until 1984 when Aitkin and Thurston applied the art using 131I labeled anti-

CEA antibody as a tumor targeting agent [16], [17].

Sentinel Lymph Node Biopsy, first described by Gould et al. in 1960 [18], and first performed intraoperatively by Krag in 1993 [19], has become the most common application of intraoperative gamma detection in the past twenty years. In more recent years, and of primary interest to the current study, intraoperative detection of 18F-FDG has gained interest among surgical oncologists [4, 20-22, 24-32]. Essner et al. first proposed detection of this residual radiation from the preoperative PET scan in 2001 using an adaptation of a commercially available probe [22].

In vivo detection of 18F-FDG is challenging [23]. The tumor-to-background ratio of radioactivity is often less than 1.5 to 1 [24-32]. Moreover, as 18F-FDG is an indicator of increased metabolic rate, non-cancerous tissues that exhibit a normally elevated metabolism such as brain, heart tissue, and acute inflammatory response often confound the measurement process.

Tumor-to-background ratios can be dramatically improved by using radio-labeled

Monoclonal Antibodies (MABs) as a cancer specific targeting agent [32], [33], [34]. The appropriate MAB will bind to tumor or tumor expressed antigens, such as TAG-72, with a

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high affinity, and at the same time, clears rapidly from the normal tissue. The radionuclide half-life must be sufficiently long compared to the biological half-lives for uptake and clearance of the targeting agent (about 5 times longer) in order to provide a detectable signal when the tumor-to-background ratio is optimal in the tissue [34].

Radioimmunoguided Surgery (RIGS) uses monoclonal antibodies or antibody fragments to concentrate radioisotopes on cancer produced antigens [32], [34]. The tumor- to-background ratio of radioactivity is a function of the binding efficiency of the radioisotope to the antibody, the pharmacokinetic half-life of the antibody, and the radioactive half-life of the isotope. RIGS was originally developed with relatively low energy radionuclides including 131I,111In, 99mTc, and 125I. Recent developments in RIGS include the use of higher energy radionuclides such as 124I and 89Z [35] [36] [37], [38].

The clear majority of intraoperative gamma detection performed currently is intraoperative lymphatic mapping (ILM) [33]. ILM consists of radio-labeled molecules, such as sulphur colloid, of sufficient size to be trapped in the nodes of the lymphatic system.

By injecting this carrier near the tumor, the lymphatic drainage basin of the tumor can be identified and removed, since this will be a likely source of metastasis. The first lymph node in the drainage basin that exhibits a concentration of the radio-labeled carrier is identified as the sentinel lymph node. Commercially available probes are, for the most part, optimized for ILM. High energy probes that apply the same technology and techniques to try to capture gamma energies of greater than 350 KeV, are inefficient and prohibitively large.

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More recently, lower energy radionuclides have been attached to ligands injected into the bloodstream that concentrate in areas of specific biological activity or track the perfusion of blood in capillary beds of tissue structures. While this mechanism is similar to PET imaging, a wider range of radioisotopes with longer half-lives and lower cost to produce can be used for single photon emission computer tomography (SPECT/CT) [40]

[41]. While 3-D imaging is possible with SPECT/CT, the coincident emissions of 511

KeV gamma photons following positron annihilation used in PET scans results in a better resolution image when the two methodologies are compared (about 1 cm for SPECT/CT, compared to <4mm for PET/CT images).

Because of the superior resolution associated with positron emission tomography, instrumentation that can be used in conjunction with positron emitting radionuclides should be developed for the foreseeable future. These devices should include gamma detection probes in smaller form factors to allow for laparoscopic procedures. While these devices will have some diagnostic utility in the laboratory, intraoperative applications remain the primary focus of such development.

The detection of gamma radiation has a rich history of its own. All materials are capable of electrical ionization from incident radiation of photons. The term photon was first applied by Albert Einstein, in 1905 to explain the quantum nature of the relationship between energy transferred from a photon of a specific wavelength to a proportional amount of electron ionization within a material [42]. If the material is conductive, such

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ionization can be measured as charge or current. This quantum nature of “light” fully explained the photoelectric effect observed by Max Plank in 1900[43].

E - The energy measured

h - Plank's constant (4.135x10-15 eV▪s)

ν - The frequency of the incident radiation

Dr. Einstein was ultimately awarded the Nobel Prize in 1921 for this law of photoelectric effect. This same work was the foundation of quantum mechanics.

As gamma rays are photons at higher frequencies than visible light, the photoelectric effect can be used to indirectly measure photon energy by capturing the charge induced in a conductive or semi-conductive material.

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Chapter 3: Theoretical Framework

3.1 Gamma Detection

Most intraoperative radiation detection probes have been designed to detect gamma radiation. Gamma detection probes use either a semiconductor or scintillating materials to capture gamma photon energy. The two most common materials are CZT (Cadmium Zinc

Telluride), a semiconductor, and NaI (Tl) (Thallium-doped Sodium Iodide), a scintillator.

The NaI(Tl) material has become the industry standard to which all other gamma detectors are compared [44]. For energy applications between 200 KeV and 1 MeV both detector materials lose a significant amount of detection efficiency [45], [46].

Probes designed for the direct detection of positron emissions (beta-plus) have met with only limited success and proven to be impractical for intraoperative applications. For this reason, this work is constrained to gamma radiation detection. CZT detectors were chosen as the material for subsequent probe designs as they require less expertise to assemble and use.

Many nuclear reactions produce gamma emissions. This chapter reviews the various types of radiation, radiation interaction, the principles of single detector probe design, methods of evaluating probe design, and a brief overview of radiation counting. In the last section of the chapter, a statistical criterion for comparing background radiation counts to elevated counts associated with a radio-labeled cancerous tissue is derived. 11

3.2 Radiation Types

Radiation sources may be divided into two main groups, charged particle radiation, consisting of fast electrons, and heavy charged particles; and uncharged radiation consisting of electromagnetic radiation and neutrons.

3.2.1 Fast Electron Sources

Nuclear reactions that result in a neutron to positron conversion, cause the emission of a free electron and an anti-neutrino. Because the electron is nuclear in origin, it is referred to as a negative beta particle. The beta-minus emission occurs over a broad range of energy.

Positron emission, or beta-plus decay, occurs when a nuclear proton is converted to a neutron resulting in the emission of a positively charged particle with the same mass as an electron, and a neutrino. Positrons travel only a few millimeters in most materials before they are annihilated by combining with a free electron creating two 511 KeV gamma photons at trajectories separated by 180 degrees of arc.

Internal conversion occurs when a nucleus in an excited state transfers energy directly to an electron in one of the orbitals. If the energy transfer exceeds the binding energy of the orbital, a free electron at the binding energy of the orbital of origin is produced. Thus, monoenergetic sources are possible. Several discrete energies of electrons can occur corresponding to the various orbitals of origin. 12

Auger electrons may result from energy transferred from internal orbitals to outer orbitals, freeing an electron with the energy of the difference between the two orbitals. The original energy is often the result of electron capture, where the nucleus captures an electron from one of the two inner most shells and forms a neutron from a positron and the electron. Electron capture may produce a gamma ray, usually a characteristic x-ray, or an

Auger electron.

Characteristic X-rays are gamma rays that are emitted with the binding energy of the orbital vacated and are distinct for different atomic masses. This can be useful in identifying elements present in an energy spectrum. Characteristic x-rays can also be produced by exposing elements to electromagnetic radiation (usually gamma) of energies in excess of the binding energy of the inner-most orbital, the K-shell.

3.2.2 Heavy Charged Particles

Alpha decay occurs in energetically unstable elements of high atomic mass. Alpha particles consist of two neutrons and two protons. Emissions occur at discrete energies.

Spontaneous fission of charged particles can also occur in heavy elements. Here the nucleus is fragmented into two fragments larger than alpha particles.

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3.2.3 Neutrons

Spontaneous fission can also produce free neutrons. For the most part, however neutron sources must be created by combining alpha emitters with certain elements or bombarding low atomic mass elements with electromagnetic radiation.

3.2.4 Electromagnetic Radiation

Intraoperative detection probes are designed to detect electromagnetic radiation. 511

KeV gamma radiation following positron annihilation and Characteristic X-rays has already been introduced. Gamma emissions are also produced in most nuclear reactions.

One or more discrete gamma emissions often follow a beta-minus decay which leaves the nucleus in an excited state. Electron capture can also lead to subsequent gamma emissions as the element changes from the parent nucleus to the daughter nucleus.

Bremsstrahlung radiation occurs as free electrons pass close to the atoms of an absorbing material. The electron slows and is deflected by the energy loss. The difference in energy is emitted as gamma radiation, and if greater than the binding energy of the atom electrons, may result in subsequent Characteristic X-rays. This process is similar to energy loss of synchrotron radiation, where a beam of electrons is bent into a circular path and exhibits gamma energy losses every cycle of the process.

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3.3 Radiation Interactions

In the discussion that follows the material of interaction is assumed to be a semiconductor material, cadmium zinc telluride (CZT), with a plated anode and cathode on opposing surfaces, and an applied electric field between the anode and cathode. The modes of interaction occur in all materials and are not unique to the assumed semiconductor.

When a gamma photon interacts with a detector material, four primary forms of energy transfer may occur. These are photoelectric absorption, Compton scattering, Coherent scattering and pair production. Other interactions of negligible contribution to total energy transfer are not considered within the scope of this discussion.

3.3.1 Photoelectric Effect

In photoelectric absorption, all of the photon energy is transferred to a bound atomic electron and the photon ceases to exist. If the energy transferred is greater than the binding energy of the electron, a free electron is created.

15

The free electron energy is:

퐸푒− = 퐸훾 − 퐸푏

where 퐸푒− is the photo-electron (free) energy,퐸훾 is the original energy of the gamma photon, and 퐸푏 is the binding energy of the bound atomic electron. The initial energy of the electron is equal to the energy of the gamma photon minus the binding energy of the electron in the original atom. The free electron is usually ejected from the K-shell, closest to the nucleus, which has the greatest binding energy for the given atom [47]. When the electron is freed from the atom or molecule, a net positive atomic charge is also created in the crystal structure, hereafter referred to as a “hole”. The electron-hole pair is free to propagate through the material. The velocity of propagation is proportional to the applied electric field between the anode and cathode of the detector. The freed electron may transfer part of the energy to other electrons, or recombine with any hole in the crystal lattice. The latter process, referred to as trapping, will be discussed in detail.

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3.3.2 Compton Scattering

Compton scattering (or inelastic scattering) occurs when a gamma photon interaction results in a partial energy transfer to a free or weakly bound atomic electron. The gamma photon is reduced in energy and deflected in trajectory (scattered). The recoil electron is increased in kinetic energy and deflected as well. The reduced energy of the scattered gamma photon is given by:

′ 퐸훾

퐸훾 = 퐸훾 1+ 2(1−cos 휃) 푚0푐

′ where 퐸훾 is the scattered gamma photon energy,퐸훾is the original gamma photon energy,

2 푚0푐 is the resting mass energy of an electron (0.511 MeV), and 휃is the scatter angle of the new photon. The scattered photon of reduced energy may interact with the detector material again or escape the material altogether.

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3.3.3 Pair Production

Pair production cannot occur unless the incident gamma photon energy exceeds 1.022

MeV, twice the resting mass energy if an electron, 511 KeV. In this interaction, the photon energy is transferred to an electron-positron pair in a nuclear reaction. Energy more than

1.022 MeV is shared in the kinetic energy of the electron-positron pair. When these particles lose sufficient energy, the positron combines with an electron in the material and is annihilated to form two 511 KeV gamma photons with trajectories 180 degrees apart.

3.3.4 Coherent Scattering

In coherent scattering (also referred to as elastic or Rayleigh scattering) the direction of the gamma photon is changed by interaction with all of the electrons in an atom without any loss of original energy. This only occurs at low photon energies in high Z (atomic number) materials.

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3.3.5 Mass and Linear Attenuation

The percentage of a photon flux that is absorbed by the material is a function of the material properties and can be calculated using probabilistic cross sections for the material.

The mass attenuation coefficient is the probability of gamma interactions per unit length within a material. The mass attenuation can be expressed separately or in combination for each of the four interactions described, and varies with gamma energy [48]. The National

Institute for Standards and Technology (NIST) provides a complete database of these coefficients and an online resource for calculating mass attenuation coefficients for elements or user defined compounds (NIST XCOM) [49]. The percentage of absorption in a material may be calculated as:

흁 % 퐴푏푠표푟푝푡𝑖표푛 = 100 ∗ (ퟏ − 풆− ⁄흆∗흆∗푻)

T - The material thickness (cm).

흁 2 ⁄흆 - The mass attenuation coefficient (cm /g).

흆 - The density of the material (g/cm3).

The density and mass attenuation coefficient are often combined and referred to as the linear attenuation coefficient 흁풍, such that

% 퐴푏푠표푟푝푡𝑖표푛 = 100 ∗ (ퟏ − 풆−흁풍∗푻) 19

For gamma energies below 1.022 KeV, the total absorption is a function of photoelectric effect and Compton scattering. Coherent scattering can be ignored as there is no net transfer of energy to charged particles. In subsequent analysis, the linear attenuation coefficients for total absorption consist of:

흁풍풕풐풕풂풍 = 흁풍푷풉풐풕풐풆풍풆풄풕풓풊풄 + 흁풍푪풐풎풑풕풐풏

The contribution from each of the four interactions changes as gamma energy increases.

Figure 1 illustrates the proportion of each interaction for CZT. Table 1 lists the density, attenuation coefficients and percentage of total absorption for CZT at 122KeV and 511

KeV for a material thickness of 4 millimeters. The percentage of attenuation due to photoelectric effect and percentage of Compton scatter for CZT are also listed in Table 1.

In 4 millimeters of crystal, a 511 KeV gamma ray is 4.33 times more likely to interact in

Compton scatter than photoelectric absorption. It is not necessary that these percentages sum to the total absorption. It is only necessary that the linear attenuation coefficients sum to the 흁풍 value given for total absorption.

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Figure 1: Mass attenuation due to various interactions in CZT [49] 21

Table 1: Mass and linear attenuation coefficients and percentage of interaction for two energy levels in 4mm thickness of CZT.

The Figure 2 diagram can be used to predict which type of interaction will dominate the energy transfer process as a function of atomic number and gamma energy.

Figure 2: Relationship between atomic number, photon energy and the three major modalities of material interaction. The 511 KeV photons are dominated by Compton effect for CZT which consists primarily of elements at an atomic number of 54 and 52. [50]

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3.4 The Detector

3.4.1 Conduction and Valance Bands

Once the gamma photon has transferred energy to electron-hole pairs through photoelectric absorption, charge is both induced and collected on the anode (as well as the cathode). Photoelectric absorption may follow Compton scatter and therefore occur at a reduced energy, or the energy transfer may be a complete photoelectric conversion to the charged particle.

Whenever gamma energy exceeding the semiconductor bandgap energy (Eg = 1.6 eV for CZT) is transferred to an outer shell electron in the material, it is free to migrate through the crystal lattice, leaving a net positive charge in the lattice. If these electron-hole pairs are created in the semiconductor, the electron energy is said to be elevated from the valance energy band to the conduction band. An abstraction of the energy bands is illustrated in

Figure 3. This model is convenient to discuss discrete energy levels associated with the photoelectric process.

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Figure 3: Energy bands and bandgap model for a semiconductor. Photoelectric ionization elevates the electron energy from the valance band to the conduction band. Charge trapping occurs at intermediate levels in the forbidden band called trapping sites.

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3.4.2 Charge Collection

Both the hole and the electron propagate through the material due to the applied electric field. Holes migrate to the cathode, and electrons migrate to the anode. The charges in motion cause an induce charge, 푄, in the respective electrodes according to the Shockley-

Ramo equation [51], [52]:

푄 = 푞 ∗ ∆푉푤(푟)

푞 - The particle charge

∆푉푤(푟) - The difference in the weighting potential from the beginning to the end of the charge path in the material.

The weighting potential, 푉푤(푟) , is a function of position and can be defined by solving the Laplace equation for the detector geometry. A time integration of equation of the

Shockley-Ramo equation also allows this relationship to be expressed as an induced current:

𝑖 = 푞 ∗ 푣⃗•퐸⃗⃗푣

푞 - The particle charge

𝑖 - The instantaneous current in the electrode

푣⃗ - The instantaneous velocity of the charge

퐸⃗⃗푣 - The electric field in the direction of the velocity

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3.4.3 Trapping and De-trapping

Either charge may be completely collected on the electrode, or may recombine within the lattice or become “trapped” at an intermediate energy level in the bandgap (refer to

Figure 3). These trapping centers are caused by crystal impurities or irregularities [47].

Doping can be used to intentionally create trapping energy levels in the forbidden band as well. Such is the case with zinc in CZT and thallium in NaI(Tl). This is advantageous to charge collection because the lifetime of the charge is effectively extended by trapping and de-trapping.

The charge mobility, a characteristic of the semiconductor material, is much lower for holes than electrons in CZT [34], [47]. Unless electron-hole pairs are produced near the cathode, nearly all of the holes are trapped in the semiconductor, resulting in incomplete charge collection. Hole trapping is the most problematic aspect of the CZT material [48],

[53]. Incomplete charge collection results in integrated pulse outputs of lower amplitude compared to complete charge collection. In this case, the energy spectrum for a monoenergetic gamma source will exhibit “hole tailing” as shown in Figure 4. The magnitude of hole tailing is also a function of the distance between the cathode and the initial charge location within the crystal. An increase in the electric field can reduce hole tailing [55].

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Figure 4: An MCA showing hole tailing in CZT for various levels of the applied field. A higher voltage field can reduce hole tailing. [54].

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3.4.3.1 The Hecht Equation

The total charge on the anode with charge trapping taken into account is quantified by the

Hecht equation [56], [57], [58]:

푄0 - The initial electron charge

퐸 - The magnitude of the uniform electric field (300 V/ cm)

퐿 - The thickness of the detector (0.4 cm)

휇푒 - The charge mobility of electrons for the material (1000 cm/(V*s))

-6 휏푒 - The electron lifetime (or trapping time) (3 x 10 s)

휇ℎ - The charge mobility of holes for the material (80 cm/(V*s))

-6 휏ℎ - The hole lifetime (1 x 10 s)

x0 - The distance of the initial gamma event from the cathode

(See Appendix A for parameter values)

The Hecht equation is a function of the distance from the electron-hole pair origin to both the anode and the cathode. This, and the initial charge, must be known to solve the equation. In many applications, also assumed here, the E field is assumed to be static, constant, and uniform between the two electrodes [59]. Some models include a mapping

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of the electric field and correction of the Hecht equation distances to follow flux line paths from the origin to the electrode [58].

The Hecht equation includes both collected and induced charge on the anode. The term for collected charge on the anode is not evident in the equation as it cancels with one term for the induced charge [60] (This reference contains an elegant derivation presented in the

Appendix C).

Although the Hecht equation takes trapping into account, it does not include the effect of de-trapping. Trapped charges eventually become de-trapped and return to the valance band by recombination. For some modeling applications, the effect of both trapping and de-trapping must be considered [61]. Because de-trapping may occur over the period on the order of seconds, it is usually ignored in calculations of brief time duration [59].

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3.5 Single Element Semiconductor Probe Design

Before addressing the dual detector probe design, probe characteristics are best presented in the context of a single element detection probe. All aspects of the single element probe presented in the following sections are incorporated in the dual element probe design. Any additional considerations are discussed in the following chapter.

3.5.1 The Semiconductor Probe

The semiconductor gamma detection probe consists of a detection crystal (e.g. CZT), a charge pre-amplifier and shaper, and a high voltage power supply (See Figure 5). The conversion from gamma energy to a proportional voltage pulse is performed in two steps.

The conversion of photon energy to charge discussed previously occurs in the crystal.

Charge migration in the electric field induces charge at the anode (Figure 6). A charge pulse begins with charge induction and ends when charge is collected at the anode. Charge integration in the first stage of the pre-amplifier converts the signal to a voltage pulse.

Additional gain and pulse shaping are required prior to signal processing by the multi- channel analyzer or gamma detection system. A crucial aspect of probe performance, the aluminum end cap must be thin to prevent absorption of the gamma energy and to minimize backscatter in the crystal. The single element CZT probe used in the study is illustrated in

Figure 7.

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Figure 5: Diagram of a semiconductor probe (bias voltage not shown) illustrates the steps in generating a pulse signal. [54]

Figure 6: Charge migration in a semiconductor crystal. The gamma creates a hole- electron pair. Electrons migrate to the anode in an electric field. Holes migrate to the cathode.

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Figure 7: Semiconductor Gamma Detection Probe. Neoprobe, Model 1017.

3.5.2 Cadmium Zinc Telluride

Cadmium Zinc Telluride (CZT) is the most commonly used semiconductor for gamma detection. The high resistivity and large bandgap (1.4 -2.2 eV) allow this semiconductor to be operated at room temperature. Energy resolution is superior to most scintillator materials, but not as good as cooled semiconductors such as high purity germanium

(HPGe) detectors.

A Cadmium Telluride crystal consists of four double bonds between cadmium and telluride atoms. In CZT, 10% of the cadmium sites are replaced by zinc. This increases the resistivity of the material which reduces leakage current and therefore electronic noise.

Zinc also reduces the density of Cd-Te crystal irregularities called “anti-sites” that can increase charge trapping [62]. CZT crystals are fabricated using a modified Bridgeman technique [58], [62]. The best CZT ingots still contain many inclusions. For this reason,

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it is difficult to fabricate a CZT crystal of large volume. Compared to many scintillators,

CZT is expensive.

3.5.3 Bias Voltage

The CZT detector is typically cylindrical with a planar anode and cathode of sputter deposited platinum or gold on the end surfaces [63]. An electric field is applied to the crystal and may vary from 10-150 V per millimeter of crystal thickness. Increasing the bias voltage reduces charge trapping by increasing charge velocity. This can reduce hole tailing and improve energy resolution. Electronic noise will increase with bias voltage due to leakage current.

3.5.4 Probe Construction and Function

The output signal from a gamma detection probe is a voltage pulse with amplitude proportional to the energy of the original gamma photon. As such, the probe gain is usually expressed in millivolts/KeV. The process of energy detection and transfer is quite different for semiconductor and scintillation detectors. To understand these processes some detail of the probe construction and underlying theory must be given.

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3.5.5 The Pre-amplifier and Shaper

A typical pre-amplifier design is shown in Figure 8. Parasitic capacitance between the anode and the first input stage is the most difficult aspect to control in this electronic application. The purpose of each stage is discussed briefly in the following sections.

VBIAS 60 – 300 V

Shaper

Anode

Cathode

Charge Integrator HPF LPF Gain/Driver

Figure 8: A typical RC charge preamplifier and shaper circuit. Charge collected at the anode is integrated into a voltage pulse in the first stage. The rise and fall time are set by the two time constants in the shaper circuit. Additional gain and buffering are required to send the signal through a 20 foot cable.

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3.5.5.1 Charge Integration

The total charge on the anode is integrated by the first stage of the charge pre-amplifier to generate a low-level voltage pulse. The voltage is produced in the feedback capacitor of the amplifier which follows the relationship:

푄 푉푚푎푥 = − 퐶푓

Where Q is the charge collected at the anode, Cf is the feedback capacitance and Vmax is the peak voltage pulse height. A parallel resistance in the feedback is required to slowly discharge the capacitor to a baseline voltage prior to the next charge pulse integration. This places a limit on the maximum count rate that the preamplifier can correctly condition due to the limitation imposed on pulse rise time. The reduction in the peak voltage due to this limitation is referred to as "ballistic deficit" [48]. The maximum count rate for an AC coupled preamplifier is given by [64]:

2 2 25 1.2 ∗ Vmax ∗ ϵ ∗ Cf ∗ 10 Rmax = Rf ∗ E

푉푚푎푥 – The maximum allowable output voltage from the pre-amp stage

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휖 – The number of electron-hole pairs created/eV

퐶푓 – Feedback capacitance in Farads

푅푓 - Feedback resistor in Ohms

퐸 - Maximum gamma energy in MeV

Alternatives to resistive-capacitive charge integration are currently available, but not discussed here since they do not apply to the current design [48].

3.5.5.2 Pulse Shaping

The rise and fall time of the pulse are optimized by the pulse shaper. The high pass filter is used to cancel the integrator pole which causes a voltage undershoot at high gamma energies [48]. The low pass filter insures that the pulse duration is sufficiently long to be processed by the digital circuitry in the analyzer or control unit, and eliminate high frequency noise.

3.5.6 Side and Rear Shielding

Density and mass attenuation coefficients described previously can be applied to calculate the percentage of absorption of incident gamma radiation of various heavy metals such as lead or tungsten used to attenuate off axis radiation as a function of energy. The linear attenuation coefficients of Tungsten and Lead respectively for an energy of 511 KeV are 2.67 and 1.83 respectively. A probe requiring 90% absorption of photon energy would

36

require 12.6 mm of Lead. The same 90% attenuation with Tungsten only requires 8.6mm of shielding.

3.5.6.1 Collimation and Field of View

By recessing the detector within a side shielding an angular field of view is imposed as shown in Figure 9. This is generally a conical volume. Gamma emissions originating from within the conical volume will contribute to the count rate in counts per seconds.

Figure 9: The field of view is imposed by recessing the detector in heavy metal shielding. This method is referred to as collimation.

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3.6 Probe Characterization

A number of metrics used to characterize probe performance are presented in this section.

Where applicable, the instrumentation and methods used to measure these parameters are described.

3.6.1 Multichannel Analysis

The multichannel analyzer (MCA) is the standard method of recording the energy spectrum from a probe detector. In brief, each voltage pulse from the probe preamplifier is digitized and processed by a pulse height analyzer. The instrument is calibrated to convert the voltage pulse amplitude to the energy of the original gamma ray in KeV. The

MCA displays a running tally of pulse counts at each energy level. The resolution of the energy levels, referred to as energy “bins”, is set by the user. The resolution is 1 KeV for the MCA results presented in this work. Although the MCA energy spectrum is a histogram of discrete energy levels verses counts, the resolution is sufficiently small for the final energy spectrum to appear as a continuum. A typical MCA is shown in Figure 10 for a monoenergetic radioisotope.

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Figure 10: Multichannel Analysis of a monoenergetic radioisotope. This energy spectrum is the standard method for characterizing the performance of a gamma detection probe.

The primary features include the photopeak for the radioisotope and the Compton plateau. The energy difference between the photopeak to the edge of the Compton plateau energy can be calculated by setting 휃 = 0 : into the Compton equation introduced previously.

퐸훾 퐸 = 푐 2퐸훾 1 + 2 푚0푐

It can also be shown that the 180-degree backscatter peak (휃 = 휋)will occur at the energy equivalent to 퐸푐 [48]. For 511 KeV, the backscatter peak will occur 170 KeV, and

39

the Compton edge would begin at 511 KeV minus 170 KeV, i.e. 341 KeV, and extend to lower energies.

The photopeak corresponds to the radioisotope emission energy that is not scattered in the detector or other materials, but is Gaussian in shape due to random variation in carrier generation, system electronic noise and inefficiencies in the detection process [57]. By convention, the photopeak includes the energy range defined by the full-width-half- maximum (FWHM) values, the two energy levels above and below the peak value where the energy spectrum is reduced to one half of the peak value.

3.6.2 Energy Resolution and Probe Efficiency

The FWHM is also considered a measurement of the energy resolution of the detector

(See Figure 11). This is often expressed as a percentage when the half maximum energy range is divided by the peak energy and multiplied by 100:

퐸 − 퐸 % 퐹푊퐻푀 = 100 ∗ 2 1 Epeak

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E1 EPEAK E2

Figure 11: The Full Width Half Maximum value is the energy difference between the two locations on the photopeak that correspond to one half of the maximum value.

41

The number of counts between the upper and lower half maximum values can be used to calculate the peak efficiency of the detector. Intrinsic peak efficiency (or sensitivity) is calculated as:

푛푢푚푏푒푟 표푓 푐표푢푛푡푠 푤𝑖푡ℎ𝑖푛 퐹푊퐻푀 표푓 푝푒푎푘 휖 = 𝑖푝 푛푢푚푏푒푟 표푓 푐표푢푛푡푠 𝑖푛푐𝑖푑푒푛푡 푡표 푡ℎ푒 푑푒푡푒푐푡표푟

Two additional definitions of efficiency are encountered in literature [48], [64].

Absolute efficiency is independent of probe geometry and distance to the source and is expressed as:

푛푢푚푏푒푟 표푓 푐표푢푛푡푠 푟푒푐표푟푑푒푑 휖 = 푎푏푠 푛푢푚푏푒푟 표푓 푐표푢푛푡푠 푒푚𝑖푡푡푒푑 푓푟표푚 푡ℎ푒 푠표푢푟푐푒

Intrinsic efficiency provides a metric for probe performance that takes geometry into account and is expressed as:

푛푢푚푏푒푟 표푓 푐표푢푛푡푠 푟푒푐표푟푑푒푑 휖 = 𝑖푛푡 푛푢푚푏푒푟 표푓 푐표푢푛푡푠 𝑖푛푐𝑖푑푒푛푡 푡표 푡ℎ푒 푑푒푡푒푐푡표푟

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3.6.3 Spatial Resolution

The same FWHM technique can be used as a measure of spatial resolution. Spatial resolution is defined as the distance between the two locations where the count rate is one half the peak value of counts per second [48], [65].

3.6.4 Angular Resolution

In probes with collimation and side shielding, the angular resolution is the standard method of measuring the field of view. The angle between the two angles where the count rate drops from the peak on-axis value to one half of that value is defined as the angular resolution, also referred to as the field of view of the probe.

3.7 Inverse Squared Law

With probe efficiency defined, it is possible to define N, the number of gamma counts recorded, as a function of S, the gamma source activity in Becquerels (emissions per second); A, the area of the detector; 휖𝑖푝, the intrinsic peak efficiency of the probe; and d, the distance from the gamma emission source to the detector.

퐴휖𝑖푝 푁 = 푆 ∗ 4휋푑2

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Note that in the preceding formula, all factors are constant except S and d. So, N is proportional to the inverse square of the distance to the source or:

푁 1 ∝ 푆 푑2

This proportionality is often referred to as the Inverse Squared Law.

3.8 Depth Detection

Consider two .5 x .5 x .5 cm CZT detectors, separated by a distance of x centimeters.

With these detectors energized by a biasing voltage and interfaced to a charge integrating pre-amplifier, they are placed such that the surface of the front detector is at a distance, d, from a gamma radiation source of strength S. The front detector will record counts according to the Inverse Squared Law:

퐴휖𝑖푝 푁 = 푆 ∗ 퐹 4휋푑2

The rear detector will accumulate counts as:

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퐴휖𝑖푝 푁 = 푆 ∗ 푅 4휋(푑 + 푥)2

If the ratio of the front to rear counts is calculated, all terms except d and x cancel and the relationship is reduced to:

2 푁 (푑 + 푥) 퐹 = ( ) 푁푅 푑

The ratio is largest near the detector and drops of rapidly. The depth can be calculated by solving the previous equation for d. The N values are measured in counts per second and x is fixed. 푥 푑 = 푁 (√ 퐹 − 1) 푁푅

Therefore, using the ratio of the two detector count rates, the depth of the source can be calculated. It should be noted that the inverse squared law is only valid for distances between the source and detector that are greater than the diameter or width of the detector.

Smaller distances are in the near field of the detector where interference from the detector is dominate and the inverse squared law is not valid.

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3.9 Electronic Collimation

The Inverse Squared Law can also be applied to two CZT detectors to implement

Electronic Collimation. The field of view for a gamma detection probe can be limited in software by disabling counts when the ratio of the front to rear detector count rates falls below a set threshold. The previously derived expression for the count rate ratio assumes that the radiation source, at a distance of d from the front of the probe, shares a common axis with the centerline of the two detectors. The following derivation expands the previous relationship to include an angle between the forward surface of the front detector and the radiation source.

Consider the illustrated in Figure 12. As the angle φ is increased, the distance to the front detector remains at the value d, but the distance to the rear detector, z, is reduced.

46

Figure 12: Geometry of off-axis radiation source with respect to front and rear detector. The extent of the electronically collimated field of view varies with angle.

Using the Law of Cosines, the distance to the rear detector is calculated as:

푧 = √푥2 + 푑2 − 2푥푑 ∗ cos (180 − 휑)

푧 = √푥2 + 푑2 + 2푥푑 ∗ cos (휑)

Substituting this expression for the value of (d+x) in the previous ratio equation, defines

the angle dependent relationship for the ratio of the front to rear detector count.

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2 2 푁퐹 푥 + 푑 + 2푥푑 ∗ cos (휑) = 2 푁푅 푑

푁 푥 2 2푥 퐹 = ( ) + 1 + cos (휑) 푁푅 푑 푑

As the angle is increased the ratio is reduced from the on-axis value to a value of unity when the angle places the source at an equal distance from the front and rear detector surfaces. The Law of Sines can be used to define this angle, which must be slightly greater than 90 degrees (99.6 degrees for a source at 3 cm. in the current design).

푥 휑 = cos−1 (− ) 2푑

Substituting this value for the angle in the generalized ratio equation, does indeed result in a count ratio of one. A further increase in angle will result in a ratio of less than unity.

By comparing the ratio calculated from the angle dependent ratio equation to a fixed value greater or equal to unity, the effective field of view of the probe can be limited by disabling counting whenever the counts ratio falls below the selected fixed value. Changing the threshold value for counting modulates the size of the field of view.

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As an example, consider the fixed value of 1.416. Assume that x is 1 centimeter and d is 4 centimeters, the angle dependent ratio equation is equal to 1.416 when φ is equal to ±

45 degrees. This results in a theoretical field of view of 90 degrees at a distance of 4 centimeters.

It is also important to consider the change in the depth of the field of view. Unlike collimation form shielding, electronic collimation limits the field of view to a depth, in addition to an angle. For the previous example, counting will be inhibited whenever the ratio drops below a value of 1.416. For an on-axis source, this occurs at a depth given by or 5.30 centimeters. The following table illustrates the value of the count rate ratio, as a function of source distance and source angle.

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Table 2: Mathematical calculation of expected count rate ratios as a function of both angle and distance from the front detector to the radiation source.

Instead of calculating the depth, varying the depth of the field of view provides an alternate approach to measure the distance to a radioactive source. By reducing the depth of the field of view gradually until the counts from the gamma source drop out, it is apparent that the source depth is just below the depth limit for the field of view at that threshold (See Figure 13).

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Figure 13: Depth detection using a reduction in field of view. The field of view is slowly expanded until an abrupt rise in the count rate is detected. The filed is contracted to verify that the source counts drop out at the same depth.

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3.10 Radiation Counting

This section provides a brief overview of counting statistics used in radiation. By addressing radioactive counts as a stochastic process, a statistic for evaluating activity in excess of background radiation can be calculated at a specified confidence level.

3.10.1 Poisson Processes

Radioactive decay is a Poisson distributed discrete random process since each event is independent of the preceding event. The Poisson distribution is the probability that k takes on a specific value, and is given by the formula:

푘 휆 −휆 푃(푘) = 푒 푘!

휆 - The mean value of all events.

휆 - Also the variance of all events, making the standard deviation, σ, equal to √휆.

k - The set of discrete positive integer values: 0, 1, 2, 3, . . .

If the number of counts in a Poisson distribution exceeds approximately 30, the distribution is nearly identical to a continuous Normal distribution, also called a Gaussian

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distribution provides a close approximation [48]. However, the value for standard deviation used in the Gaussian approximation must be equal to the square root of the mean value since this is a characteristic of the original Poisson distribution. If this condition is imposed, the two distributions can be used interchangeably and one-sided Z-score statistics can be applied using the Gaussian approximation.

3.11 The 3-Sigma Criteria for Probe Positivity

A statistical test of the hypothesis that the true source count exceeds the background count can be performed using a microprocessor located in the control unit for a gamma detection probe. Statistical hypothesis tests must be performed at a pre-defined confidence level. For a Gaussian distribution, the standardized Z-test can be performed. Since the hypothesis in question is whether to not the source distribution is significantly greater than the background (as opposed to different, or lower than the background), a one-sided Z-test is the statistic of choice. The confidence level chosen for whether the target is greater than background is 85.56%. The Z value for this confidence level is equal to 1.0607 [66].

Consider the two probability distributions of gamma detection probe counts illustrated in Figure 14, with one count distribution representing the background measurement, and the second count distribution representing the target measurement. Since the target measurement contains counts from both the background and the true source of the increase in radiation, there is a third distribution of the true source that must be determined mathematically. Since the number of counts in the true source is the difference between 53

the target count and the background count, the variance of the true source is equal to the sum of the target source variance and background source variance [48]:

2 2 2 휎푆 = 휎푇 + 휎퐵

Where subscripts S, T, and B represent the true source, target, and background distributions respectively. Also let the mean value of the distributions be indicated as:

휇푆, 휇푇, 푎푛푑 휇푩

The threshold for the minimum detectable count at the given confidence level can be used as the criterion for a true source count that is consistent with the hypothesis that the counts exceed the background to the extent that the true source count can be considered as a probe positive finding for radio-labeled cancerous tissue. This threshold is a function of the critical limit often referred to in statistics [48]. Using characteristics of the Poisson distribution of radioactive count measurements, it is possible to derive a mathematical relationship for the critical limit at the desired confidence level, 85.56%.

Consider Figure 15, depicting the relationship between the background distribution and the target distribution when no source activity is present. The two distributions are superimposed. Since no source activity is present:

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2 2 휎푇 = 휎퐵

Substituting this into the previous expression for the true source variance, the standard deviation of the true source is:

2 휎푆 = √2휎퐵

The critical limit is:

퐿푐푟𝑖푡𝑖푐푎푙 = 휇퐵 + 1.0607휎푆

2 = 휇퐵 + 1.0607 ∗ √2휎퐵

= 휇퐵 + 1.0607 ∗ √2휎퐵

= 휇퐵 + 1.0607 ∗ √2 ∗ √휇퐵

= 휇퐵 + 1.5 ∗ √휇퐵

Now consider the situation when the true source is equal to the minimum detectible count. If the probability for true positives is set equal to the probability for true negatives

(85.56%), the relationship between the background count distribution and the target count 55

distribution is shown for this case in Figure 16. In this circumstance, the target mean value occurs at the background count plus twice the critical limit by symmetry [67]:

휇푇 = 휇퐵 + 2 ∗ ( 1.5 ∗ √휇퐵)

휇푇 = 휇퐵 + 3√휇퐵

휇푇 = 휇퐵 + 3휎퐵

For the Z-value chosen, corresponding to a confidence level of 85.56%, the threshold for the minimum detectable target count is 3 times the standard deviation of the background count, above the mean value of the same background count. This threshold is referred to as the 3-sigma criteria for probe positivity. Note that the threshold is completely defined by the background count because the probability function for radioactivity retains the standard deviation and mean value of the Poisson distribution.

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Figure 14: Background, Target, and Source count distributions. The target is the sum of the background distribution and the true source distribution.

Figure 15:Background and Target count distributions when Source is zero. Probabilities for false positive and true negative are chosen. This defines the critical limit. 57

Figure 16: Target count distribution is at the minimum detectable level assumig that the probabilities of false positive and true positive are equal to the probablities for false negative and true negative respectively. In this case, the minimum detectable level will occur at 3 standard deviations abouve the mean background count.

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Chapter 4: Research and Development Methodology

4.1 Dual Detector Probe Design

The two detectors chosen for the electronically collimated probe are 5 x 5 x 5 millimeter

Cadmium Zinc Telluride crystals (eV Products, Saxonburg, PA), with sputter deposited platinum anode and cathode on opposing surfaces. The cathode is extended past the corners of the crystal by 1 mm down each side of the cube. This design greatly reduces the edge effect in the electronic field of the CZT volume, a condition that reduces the efficiency of charge collection. Each detector is enclosed in a Teflon insulator of sufficient thickness to allow the anode and cathode of the crystal to protrude past both ends, making contact with the anode and cathode contacts wired to the pre-amplifier. Each anode is energized to 120 volts by either the multichannel analyzer, or an external supply when connected to the Neoprobe Gamma Detection Systems. Thirty-gauge silver wire from each anode-cathode pair is twisted together and routed through slots in the Teflon insulators. A

5mm Teflon spacer between the two crystals sets the point to point crystal distance, x, to 1 centimeter. Both twisted pair are passed through apertures in a threaded brass mounting bracket and soldered to the input terminals of two separate charge integrating pre-amplifier and pulse shaper circuit boards (See Figures 17-19).

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Figure 17: Dual detector probe design for electronic collimation and depth detection.

Figure 18: Disassembled Dual Detector Probe.

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Figure 19: Assembled Dual Detector Probe, 15mm diameter.

At this point in the design process it became apparent that two pre-amplifiers could not be adequately separated for proper function without increasing the diameter of the prototype probe. In the envisioned embodiment of the probe, the two PC board pre- amplifiers, constructed of discrete surface mount components, were to be replaced by a functionally equivalent, multichannel ASIC. The ASIC design did not progress to the extent that it could be used in the current design. For this reason, the outside diameter of the dual detector probe was increased from 12 millimeters to 15 millimeters. The two pre- amplifiers were mounted on a single brass bracket which threads into the aluminum probe cap, and stainless steel probe handle. A six pin LEMO™ connector threads into the opposite end of the probe handle, and attaches to a cable, 20 feet in length, which passes the probe signals to two separate Neoprobe Control Units. A separate power supply module was patched into the cable to provide sufficient +12 volts, ground, and 120 volts biasing voltage to the probe pre-amplifiers and detector crystals. 61

4.2 The Open Energy Window

Not all gamma pulses from a pre-amplified pulse signal are included in the calculation of count rate. A range of gamma energies are selected by signal processing hardware or software within the control unit of the gamma detection system. The energy widow extends from a lower threshold to an upper threshold. In commercial practice, this energy window is typically ± 20% of the photopeak energy of the radionuclide selected. For 511 KeV, the lower threshold, at 80% of 511 KeV, is set to 409 KeV. The upper threshold is not as critical if no other radionuclides are present. For 511 KeV, the upper threshold is nominally

600 KeV. The low threshold is intended to eliminate Compton scattered radiation which reduces the spatial resolution of the measurement.

Scatter is produced in both the medium surrounding the source of activity, and in the detector material. Scatter occurring at gamma radiation energies, can be compared to a similar phenomenon in visible light. Just as it is more difficult to see the location of a street lamp in dense fog, a gamma detection probe becomes less precise, spatially, in the presence of a scatter medium.

Limiting the energy window reduces the sensitivity of the probe to a great extent.

Additional loss is incurred as the efficiency of photoelectric absorption diminishes with increasing photon energy. Figure 20 illustrates a CZT detector efficiency as a function of the energy of incident gamma radiation. At 511 KeV the theoretical efficiency is less than

20%. The actual efficiency may be much lower.

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Figure 20: Efficiency as a function of gamma energy. Note that the theoretical efficiency at 511 KeV is under 20%.

Opening the energy window to include the Compton scattered radiation, improves probe sensitivity. If the lower threshold of the energy window is reduced to include

Compton scattered radiation, the count rate increases by more than two orders of magnitude for the CZT crystals incorporated in the both the single and dual detector probes used in this study when the energy window is increased from 409-600 KeV, to 50-600 KeV.

Since a single high energy photon can lose energy in the detector by more than one occurrence of Compton scatter, a preliminary study was performed to determine whether

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or not the measured energy of a broad energy window, including Compton scatter, is still proportional to the activity of the measured source. Figure 21 illustrates the 409-600 KeV energy window. The open energy widow of 50-600 KeV is shown in Figure 22. Figures

23 and 24 show multichannel analysis of three levels of 511 KeV radioactivity. In Figure

24, each MCA plot is normalized to match the 95 millicurie trace. The only apparent difference is the increase in the signal-to-noise ratio associated with the plots acquired at lower activity. These results verify that the summation of counts from 50-600 KeV are proportional to the activity of the source. Increasing the energy window provides the increase in sensitivity required to implement high energy probes using small crystals, essential for small diameter probe designs. The associated loss in spatial resolution can be recovered by using a combination of electronic collimation, and a statistical criterion to limiting the area of probe positivity.

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Figure 21: MCA showing a standard commercial energy window in blue.

Figure 22: MCA showing an open energy window in blue. 65

Figure 23: MCAs for three source activities.

Figure 24: MCAs normalized to source activities demonstrate that the area under the curve is approximately proportional the source activity present.

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4.3 Probe Characterization Studies

The electronically collimated gamma detection probe is characterized by performing experiments to measure the various sensitivities and resolutions discussed in the previous chapter. A portion of these measurements are performed in accordance with the National

Electrical Manufacturers Association Guidelines for Non-Imaging Intraoperative Gamma

Probes (NU 3:2004, hereafter referred to as NEMA NU3).

4.3.1 NEMA NU3 Studies

Using measurements defined in the NEMA NU-3:2004 [73] as a benchmark for intraoperative gamma probes, this study will illustrate that electronic collimation represents a significant departure from current technology to the extent that the some of the standard measurements no longer apply. Please note that reproduction of the standard in total or in part is prohibited by the publisher and will be described here as accurately as possible without infringing on the license agreed to when the standard was purchased by the OSU Medical Center, Department of Surgical Oncology. The entire document was available for reference during the experimental procedure. Each of the 9 tests performed is described in the following chapter.

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4.3.2 Multi-channel Analysis

Multichannel Analysis is performed on the front and rear detectors of the electronically collimated gamma detection probe in part 4 of the NEMA NU3 test protocol in order to measure the energy resolution of the detectors. The Canberra DSA 1000 Multichannel

Analyzer (Canberra, Australia) is connected to the probe using an adapter box constructed for that purpose. The bias voltage and other aspects of data collection are controlled from a laptop computer running the Genie 2000™ software interface (Canberra, Australia) to the DSA 1000.

4.3.3 Spatial Resolution

Although the spatial resolution of the probe is measured as part of the NEMA NU3 study, a second set of experiments investigates how spatial resolution changes with the size, depth, and activity of the radiation source in various levels of background radiation.

Hardware set-ups for each type of test are discussed in detail later in the chapter.

4.3.4 Target-to-background Ratio

When any gamma detection probe is used intraoperatively, the radioactivity of the target can be obscured by the residual radioactivity of the surrounding tissue. The relationship between the magnitude of the target and background radiation values are often referred to as the target-to-background ratio or tumor-to-background ratio [74], [75], [76].

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Since the target measurement is the sum of the true source activity plus the background activity, a target-to-background ratio of 2-to-1 implies that the source activity is equal to the background activity. A target-to-background ratio of 1.1-to-1 means that the source activity is 10% of the background activity. Target-to-background ratio values of 1.25-to-

1 are routinely encountered in surgery where 18F-FDG is the radiopharmaceutical to be detected [25-31]. A low target-to-background ratio may adversely affect the possibility of detecting a small radio-labeled tumor. For this reason, most of the experiments are repeated at target-to-background values of 1.25, 1.5, and 2. These results are compared to the same measurements of the target when no background activity is present.

4.3.5 Electronic Collimation

Since a microprocessor based control unit for the electronically collimated gamma detection probe does not exist at this time, much of the testing will require manual calculations from raw data. The 3-sigma criterion for probe positivity is calculated automatically by the Neoprobe Gamma Detection System.

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4.3.6 Depth Detection

In a third assay, count rates are acquired from both detectors for a source at a known depth. This value is compared to the depth calculation based on the ratio of the probe count rates described previously. Depth detection relies on the same two count rates as electronic collimation.

4.3.7 Limits of Detection

A fourth set of tests defines the limits of detection for the electronically collimated probe. The size, depth, source activity, and target-to-background ratio of activity are varied in order to verify the detection of the source for each combination of these four parameters.

4.3.8 Spatial Resolution and the Effect of the Expanded Energy Range

Spatial resolution can be improved by limiting the area of probe positivity surrounding the target source. This is implemented by requiring a high threshold for probe positivity.

The surgeon must identify and select a squelch site, the location at which the 3 second average background count is recorded, close to the target area. An increase in the background count reduces the area of probe positivity around an isolated radiation source.

The 3-sigma criterion can be applied to the front and rear detector count rate independently.

It may be advantageous to apply the 3-sigma criterion to the ratio of the front and rear count rates since this is the same number used for the field of view and depth detection.

Alternatively, the combined count rate from both detectors will result in a greater count per 70

unit of time. This reduces the percentage of increase in count rate that is required to exceed the 3-sigma threshold for probe positivity. As a final consideration for application of the

3-sigma criterion, there are advantages to using the count rates from the rear detector alone.

Since the rear crystal is recessed from the front of the probe by a distance of twice the width of the detector, the radiation source can never be located in the near field. This guarantees that the count rates from the rear detector are produced in the linear operating region of the detector response. However, the additional distance to the detector greatly reduces the count rate due to the inverse squared relationship discussed previously.

Regardless of the method chosen, the required background count to limit the area of probe positivity can be determined retroactively from the data acquired. The goal of this process is to use the 3-sigma criterion to limit the diameter of probe positivity to a distance smaller than the spatial FWHM value of the peak count rate. The location that produces the peak count rate in the detectors is assumed to be the centroid of the target source. This method of limiting the diameter of probe positivity is intended to recover the loss of spatial resolution associated with increasing the energy window from 409-600 KeV to 50-600

KeV. Note that the electronic collimation can also be used to limit the spatial resolution.

For the studies investigating spatial resolution, depth detection, the limits of detection, and angular resolution, the data required can be calculated from the 3 or 10 second average values for count rates recorded for the front and rear detector of the electronically collimated probe. 10 second counts were used whenever possible.

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4.3.9 Phantom Testing

Five radiation phantoms have been constructed to simulate the distribution of radioactive sources and background radiation commonly encountered intraoperatively during cancer surgery. These were chosen and defined after an extensive review of pre- operative PET/CT images. In PET scans, the physiology is not well defined since the PET scan is imaging an indicator of metabolic activity. By overlaying a simultaneous CT

(Computer-aided Tomography) scan, both the physiology and metabolic activity are imaged.

To construct the experimental targets, a set of hollow spheres, ranging from 0.5 cc. to

90 cc. are injected with a radioactive sugar analog (18F-Fluorodeoxyglucose, the same radiotracer used in PET scans), and titrated to the 511 KeV activity required for the experiment. The source is supported by threaded rods, fastened to a threaded Lucite plate, and submerged in an 8"x8"x8" Lucite cube containing a 0.9% saline solution. This container was chosen as it complies with the NEMA NU3 standard. The probe under test is suspended above the saline bath and clamped to a four degree of freedom manipulator arm (Sherline Model 5430 XYZ CNC Base/8730 Rotary Table/8761 EMC Computer and

Driver Board. Vista, CA). Computer software is used to control the X, Y and Z axis position, and angle of the probe, in order to change the location and angle of the probe in a repeatable and precise manner.

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4.4 Modelling, Simulations, and Software Analysis

As it was not practical to build multiple prototypes of the dual detector probe, computer simulations to test various orientations and separations of the detectors were performed. A complete model of the probe response required post processing of the simulated data. The following is a summary of these processes for a single element detector. The response of multiple detector systems incorporated multiple incidents of this single element model.

4.4.1 MCNP and Simulations

Radiation detection and interaction can be accurately modeled using the Monte Carlo

N Particle software code. Originally developed for the Manhattan Project [77], this code is updated and maintained by the Oak Ridge and Los Alamos National Laboratories. It is available, by permission, to students and other researchers through the Radiation Safety

Information Computational Center (RISCC), US Department of Energy, Oak Ridge, TN.

The Monte Carlo method simulates (but does not solve) the transport (Boltzmann) equation for a large number of particles in complex geometries [81]. For all but the most trivial cases, a closed form solution of the transport equation is not possible. Briefly, the transport equation describes four radiation transport processes within a defined volume where:

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Expressed mathematically (same order of terms), the transport equation is:

The Monte Carlo algorithm generates each particle history in sequence, often described as a “random walk” [78]. The particle history begins with the particle production and ends when the particle energy reaches a minimum threshold energy value, is transferred to a secondary particle, or the particle exits the defined geometry for the model. The algorithms consist of a series of random selections, repeated at each iteration, to determine the particle interaction type, track length between interactions (푟⃗), the new direction (⃗⃗⃗⃗), the new energy (퐸), and the production of additional particles.

To simulate the dual CZT semiconductor detection probe, MCNP5 code is used to define all detector probe materials and geometries, and a source or sources of 511 KeV gamma radiation. For the present application, the MCNP5 software is sufficient for modeling energy distribution of photon and electron particles in a volume or on a surface

[77-80].

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4.4.1.1 F8 Tally

One of the options in MCNP5 is the Pulse Height Tally (F8). In addition to the regular flux accumulation, the photons and electrons can be sorted into bin counts at predefined energy increments (pulse heights) and energy range, much like the multi-channel analyzer

[77-80].

4.4.1.2 PTRAC Output File and Post Processing

To model charge trapping, each particle history must be extracted from the enormous output file requested with the PTRAC card (command). A special editor is required to search and extract the desired data from this file. EM Editor (EmuraSoft Inc., Redmond,

WA). MATLAB™ is used to reformat the file into a searchable format, and extract all incidence of photoelectric absorption or Compton scattering that has occurred within the volume of the CZT detector crystal. Once extracted, the Hecht equation can be applied to each event to reduce the charge collected at the anode (electrons) due to trapping. The collected charge is modified based on the original value of the charge, the distance between the interaction location and the anode, the crystal thickness, and the E field strength within the detection crystal. These parameters, along with the charge mobility and trapping time for electrons and holes are used to calculate the Hecht Equation. The modified data is stored as a function of final energy.

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4.4.1.3 Gaussian Energy Broadening

The pulse shaping filter and other band limited electronics of the pre-amplifier broaden the photopeaks in the MCA. MCNP provides a Gaussian Energy Broadening (GEB) function to allow the experienced programmer to heuristically match the final energy spectrum to actual probe MCAs by setting the parameters of the GEB filter [77-80].

Figure 25 illustrates the MCNP model output of the Neoprobe 1017 probe before applying the Hecht equation (blue), and after the Hecht equation and GEB filtering processing are applied (black). Figure 26 compares the model output (orange) for a 511

KeV source, to actual probe data taken in the lab. The counts have been normalized at 511

KeV for purposes of comparison. While the model captures most aspects of the energy spectrum, it tends to underestimate the down-scattered energy, and slightly broaden the photopeak. This is not consistent, but may be improved by further tuning of the GEB filter.

Since the model lacks the effect of de-trapping, some underestimation of Compton scatter is expected. Impurities and inclusions in the CZT crystal cannot be incorporated in the model and may lead to additional underestimation of the down-scattered energy spectrum.

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Figure 25: MCAs showing MCNP output for a single element detector (blue). The black line is same data after applying the Hecht equation to take charge trapping is taken into account and filtering using a Gaussian Energy Broadening routine to model the effect of the pre-amplifier electronics.

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Model to Probe Comparison

5

4.5 Probe 4 Model 3.5

3

2.5

2

Normalized Counts 1.5

1

0.5

0 50 150 250 350 450 550 KeV

Figure 26: MCAs comparing final single element model to actual probe response (Neoprobe 1017), using a 22Na source. The counts have been normalized at 511 KeV.

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4.5 Experimental Design

Six series of experiments were designed to characterize the probe. The first study includes elements from the National Electronics Manufacturer’s Association NU-3 standard tests for intraoperative gamma detection probes (NU-3:2004). Three subsequent experiments examine the accuracy of depth detection, limits of detection, and changes in spatial resolution under various conditions. A fifth experiment was conducted to test the probes capability to detect sources in a low (1.1-to-1) target-to-background ratio of radioactivity. This is mathematically possible according to the three-sigma criterion for probe positivity, but should be documented with a physical assay. The sixth experiment incorporates five phantom models to simulate the background activity and radioactive sources often encountered intraoperatively. The probe’s capacity to discriminate these radioactive sources in either a scatter medium, or a scatter medium containing background radiation provides evidence that the probe will perform well in clinical use.

4.5.1 Experimental Set-ups

In this section, the physical set-ups used to measure the dual detection probe performance are introduced. Protocols for the experiments are covered in the following section.

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4.5.1.1 NEMA NU3 Standard Bath

To provide a scatter medium, the NEMA NU3 standard specifies an 8" x 8" x 6" minimum size for the container. Whereas the standard recommends water as a scatter medium, a 0.9% saline solution (normal saline) is more commonly used to approximate the radiation scattering properties of most human tissues. Water is used for all NEMA standard studies. All other experiments use normal saline.

For NEMA experimental setups requiring a scatter medium, an 8" x 8" x 8" Lucite cube with an optional cover was selected (MisterPlexi, Wexford, PA). A 0.5” Lucite sheet was drilled and tapped at the locations required for hollow spherical targets to be mounted on posts (Figure 27). Nuclear medicine phantoms use the same spheres to calibrate PET scanners and SPECT imaging systems. Two sets of six spheres: 0.5 cc, 1.0 cc, 2.0 cc, 4.0 cc, 8.0 cc. and 16.0 cc. were acquired for the study. An additional 90 cc. sphere was purchased from the same company (Models ECT/HS/SET-6 and ECT-HS-60/A, Data

Spectrum Corp., Durham, NC, See Figures 30 and 31). The spheres are injected with a mixture of normal saline and concentrated 18F-FDG solution to produce a target with the desired activity and size. Radioactivity is measured with a standard laboratory well counter in units of microcuries, and verified to match the required activity in becquerels (counts per second), using the Neoprobe Gamma Detection System (Models 2300 and 2200,

Neoprobe Corporation, Dublin, OH).

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4.5.1.2 Robotic Manipulator

To perform the set of experiments defined, it is essential to position the electronically collimated probe at a precise location and orientation with respect to the spherical sources, and have the capability to do so in a repeatable way. To this end, a Miniature CNC milling system was modified to provide movement in the X, Y, and Z directions of a 3-dimensional coordinate system (Sherline Model 5430 XYZ CNC Base/8730 Rotary Table/8761 EMC

Computer and Driver Board. Vista, CA, Figure 27). An additional rotary table was mounted to the vertical upright track to allow the probe to be placed at a known angle. To reach the saline bath, a Plexiglass C-arm with a probe clamp attachment was machined and constructed. This is attached to the rotary table and suspended above the saline bath. A

Linux computer system using EMC2 software (Sherline Inc.) to control the manipulator provides the operator feedback for the position and orientation of the manipulator in space, and the capacity to change locations and angle at an adjustable rate. Although this device is capable of running a full CNC program, the CNC manipulator was operated in the manual mode using the “jog” command.

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Figure 27: CNC manipulator, probe, and NEMA NU3 standard water bath. This set-up was used for the majority of the experiments conducted. The manipulator allows the probe placement and angle to be accurately repeated.

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4.5.1.3 Neoprobe Gamma Detection Systems

Neoprobe Gamma Detection Systems are commonly used in intraoperative procedures to locate radio-labeled agents. As the gamma detection system for a multi-detector probe does not yet exist, two Neoprobe control units were used to monitor the front and rear detectors of the electronically collimated probe independently (Figure 28). Two main modalities of operation are implemented in the Neoprobe control unit, Dynamic Pitch mode and Binary Pitch mode. To detect the area of probe positivity, the Binary Pitch mode is selected. The audio output of the Neoprobe control unit emits a constant tone whenever the average count rate exceeds the 3-sigma criterion for the current background level that was measured and saved during the squelch process. As standard settings for these units have been modified by Neoprobe, care was taken to match the settings prior to performing all studies. The control unit has 6 radionuclide settings, but the parameters for each of these settings can be modified by the user. The 18F settings on both units was manually set to an energy range of 50 – 600 KeV. Whenever this was to be compared to the standard commercial setting, the window was changed to 409-600 KeV. The 409 KeV value is 80% of the 511 KeV photopeak. The 80% value is commonly used as the lower threshold of the energy range, throughout the gamma detection industry.

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Figure 28: Two gamma detection systems, probe, and patch box. The +12V supply and filter module supplying bias voltage is to the right of the photograph.

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4.5.1.4 Multi-channel Analysis

To measure the energy resolution of the detectors a multichannel analysis is performed.

The FWHM of the peak at 511 KeV is the parameter used in this study. Because the

Neoprobe gamma detection systems do not provide enough isolated power for two pre- amplifiers, an external power supply is used. Moreover, the 8-channel custom anti-aliasing filters originally designed for data acquisition, provide an adjustable bias voltage capable of 0-500 VDC. The configuration for Multichannel Analysis is shown in Figure 29.

The custom +12/-12 V supply provides power to the custom anti-aliasing filter module.

This module provides +12V, 120VDC Vbias, and ground to both preamplifiers through the custom patch box. The probe connects to the patch-box through the 12-pin LEMO™ connector and cable. The left and right cable connections are wired to the pre-amplifier of the front and rear detector output respectively. To perform an MCA, each cable is connected to the Canberra DSA 1000 multichannel analyzer through another custom interface box. The interface box is capable of scaling down the pre-amp signal, and can select The Neoprobe input cable for +12V and Vbias, or select the Canberra system +12V supply and Programmable Vbias. However, since these two voltages are on separate cables in the first patch box, the external sources must be used. This is to prevent an inadvertent connection of +12V supplies or Vbias voltages when the systems are configured. A small laptop computer is running the Genie2000 software required to interface to the Canberra

DSA 1000 multichannel analyzer. 85

Figure 29: MCA Set-up. Laptop running Genie2000 software, Interface box, DSA 1000 MCA, Patch box. Neoprobe 2300 GDS, Filter module (Vbias), and +12V linear supply.

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4.5.1.5 Intraoperative Phantoms

Five phantom models have been developed to simulate the distribution of 18F-FDG radioactivity that would be encountered by the surgeon intraoperatively. The first of five models consist of a single 2 cc. sphere, mounted on a post which holds the target at a height of 7 cm from the bottom of the NEMA standard tank previously described. The second phantom consists of the same configuration with the addition of a 90-cc. secondary source located at a distance of 5 centimeters from the center of the primary source (target). Three secondary sources are incorporated in the third phantom consisting of a 0.5 cc, 2.0 cc, and

8.0 cc. spheres in locations specified in the experimental section. In the fourth phantom, the secondary object is a 250 cc. IV bag of normal saline chosen to provide a large irregular distribution. This is placed at the bottom corner of the bath container using double stick tape to prevent the object from floating to the surface when the normal saline solution is added. The fifth phantom consists of the same target and background, but the secondary source is a cylindrical volume of approximately 70 cubic centimeters. As before, the object is placed at the bottom corner of the bath container using double stick tape to prevent the object from floating to the surface when the normal saline solution is added.

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4.6 Experimental Protocols

Having presented the experimental set-ups, the procedures for each study are outlined in the following sections. Tables of the experimental results appear in the following chapter on Findings and Analysis.

4.6.1 Radioactive Sources

On the morning of each experiment, a 20 millicurie dose in a 10 cc. syringe was provided by the OSU Medical Center, Department of Nuclear Medicine. Since the half- life of 18F is 110 minutes, this amount was drastically reduced throughout the day, but provided enough concentrated 18F-FDG to titrate the sources and background solution to the desired level. Care was taken to return the concentrated source to a shielded area prior to taking any count rate measurements.

4.6.2 Preliminary Experiment

The purpose of this experiment is to establish the quantity and concentration of 18F-

FDG required to bring each object and volume used in subsequent experiments up to the activity, in Becquerels, required for the experiments. All activities are relative to the sensitivity of the measuring device, in this instance the electronically collimated gamma detection probe.

The probe is operated in conjunction with two Neo2000 Gamma Detection Systems.

The distal end of the probe is placed at the distance from the radiation source indicated in 88

the protocol spreadsheet. Counts consisting of 10 second averages are taken with an energy acceptance window of 50-600 KeV. For the preliminary experiment, only counts from the front detector need to be recorded. Table 3 contains a list of objects and volumes with the required activity at specified distances.

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Table 3: Preliminary study. 18F-FDG required for each object and volume.

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Each measurement in the procedure consists of the following steps:

1. A concentration of 18F-FDG at an activity of at least five times the required Bq. per volume listed for the step should be available. Note that this activity assumes that the detection efficiency of the electronically collimated gamma detection probe is likely less than the efficiency of the well counter used to measure the 18F-FDG activity. The number of counts detected by the probe for every microcurie detected by the well counter should be established at the onset of the study.

2. The 18F-FDG shall be titrated into the volume under test until the activity is documented to be equal to of the required activity listed for this device +20% / -0%. An additional 20% provides enough time to incorporate the object in the experimental set-up before making a measurement before the 110-minute half-life reduces the activity to below the required level.

3. The remaining volume of any object should be filled with normal saline and the activity re-evaluated prior to placing the source in the experimental set-up.

4. The device, volume, distance from the probe when measured, and 18F-FDG activity in Bq. are recorded.

5. In the event that the final activity is less than 100% of the activity listed. The titration step is repeated.

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The following devices are included in the studies:

Figure 30: Phantom sphere set. 0.5 cc, 2.0 cc, and 8.0 cc. are used to model tumors.

Figure 31: Large phantom sphere used to model injection site.

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Figure 32: Specifications for spheres used in the studies

Figure 33: Cylindrical source detail prior to glueing

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Figure 34: Phantom set-up #1

Figure 35: Phantom setup #2

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Figure 36: Phantom setup #3

Figure 37: Phantom setup #4

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Figure 38: Phantom setup #5

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4.6.3 NEMA NU3:2004 Standard Study

The study is intended to evaluate the performance of the prototype probe incorporating electronic collimation. Using measurements defined in the NEMA NU-3:2004 [73] standard as a benchmark for intraoperative gamma probes, this study illustrates that electronic collimation represents a significant change when compared to current technology to the extent that some of the standard measurements no longer apply.

Whenever possible, an alternative approach to quantify the same parameter for an electronically collimated probe is proposed.

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4.6.3.1 Sensitivity in Air

This assay requires source measurements in air at distance of 1, 3, and 5 centimeters from the source to the probe tip. The 0.5 cc. sphere mounted in the middle location of the

NEMA standard water bath (empty) contains the source activity. The probe is mounted in the Sherline CNC manipulator fixture in order to control the source to probe distance with precision.

The test requires that at least 10,000 counts are recorded for each measurement. The

Preliminary Study included the quantity of 18F-FDG required for 1500 cps @ 5cm in a 0.5 cc. volume which is used for this particular assay. The exact amount of 18F-FDG used, is documented using a well counter in order to calculate the probe sensitivity.

The probe under test is always operated with an open energy window (50-600 KeV), so it is not necessary to repeat the measurements in two window settings as described in the standard. Counts from both the front and rear detector are recorded separately. A 10 second accumulation of counts is performed at each of the three distances, then averaged to counts per second.

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4.6.3.2 Sensitivity Through Side Shielding in Air

The probe is mounted in the Sherline CNC Manipulator fixture. A 20 cm. (8”) clearance is required both laterally and beneath the probe tip, with the exception of the radiation source. The NEMA standard water bath is not used for this assay. For this reason, this portion of the experiment is performed before the sections that require a scatter medium.

The radiation source is mounted on one of the three Lucite mounting plates for this part of the study. The 0.5 cc. source is injected with 18F-FDG and normal saline according to the quantities listed in the results of the Preliminary Study for a 0.5 cc. sphere, 1500 Bq. activity, and a distance of 5 centimeters. A 10 second accumulation of counts is required for each of the Neo2000 Gamma Detection Systems which are recording the front and rear detector in the dual detector probe. The numbers are recorded at a lateral distance of 1.0,

3.0, and 5.0 centimeters from the center of the probe tip.

NOTE: This part of the standard is originally intended to document the attenuation of radioactivity that the side shielding introduces, and assumes that a high-Z material is present. Electronic collimation inhibits counting altogether when the source is outside of the calculated field of view. This part of the study is now intended to document the difference between the count rates recorded from the front and rear detectors of the electronically collimated probe. This part of the study was expanded to include count rates at 1.0, 3.0, and 5.0 centimeters from the center of the probe tip as opposed to the single

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distance of 5.0 cm stated in the original standard. The count rate ratio, the count rate of the front detector divided by the count rate of the rear detector, is calculated at each distance.

This value documents the ratio that must be exceeded in order to enable counting at the corresponding distance.

4.6.3.3 Side and Back Shielding

The original intent of this section is to measure the attenuation of the high-Z shielding material on the side and rear aspects of the gamma detection probe. Electronic collimation will disable all counting, resulting in an effective 100% attenuation whenever the ratiometric condition for limiting the field of view is met (CPSFRONT/CPSREAR≤

THRESHOLD). A functionally equivalent test for count rate ratios, would consist of recording the pair of count rates that results in the maximum and minimum count rates ratios as the source is moved over the surface of the probe as described in the NEMA standard.

For the present test, a 0.5 cc. source is injected with 18F-FDG and normal saline according to the quantities listed in the results of the Preliminary Study for 0.5 cc, 1500

Bq. @ 5 cm. The protocol for this part of the study follows.

1. Cover the probe with a probe sleeve or rubber glove to prevent contamination.

2. Move the source over the probe surface as described in the NEMA standard.

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3. At the location deemed to exhibit the minimum difference in front and rear probe counts, record the count rates for the front and rear detectors. 3 second averages of front and rear counts are adequate for this assay due to the close proximity of the source.

4. Locate the position on the probe surface that exhibits the maximum difference in the probe count rates and, again record the pair of count rates.

4.6.3.4 Energy Resolution

The Full-Width-Half-Maximum value for the for the front and rear detector shall be measured independently using the Canberra DSA 1000 Multichannel Analyzer. At least

5000 counts shall be contained in the 511 KeV energy peak of each record. The source activity should be adequate to record the 5000 counts in the 511 KeV energy peak in the less time than the radionuclide can decay by 5% (8 minutes for 18F). 5000 CPS @ 5 cm is likely to be adequate for this assay. The exact activity of the source is not critical for this study.

4.6.3.5 Sensitivity in a Scatter Medium

The experimental set-up is identical to Part 1 with the addition of water to the NEMA standard water bath. The 0.5 cc. sphere is again mounted in the middle location of the bath.

Lucite posts of custom height have been constructed for this study. A custom post that elevates the centroid of the sphere at 10 cm from the base of the water bath is used. Water

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(not normal saline) is added until the centroid of the sphere is at a depth of 5.0 cm relative to the surface of the water. The probe is positioned to just contact the water surface.

Measurements are taken with the source at a depth of 1.0, 3.0, and 5.0 cm. In between each measurement,760 cc. of water is removed from the bath, and the probe is advanced 2.0 cm.

The energy window is again 50-600 KeV. The source used in Part 1 is sufficient for this part as well. If the activity is not increased with additional 18F-FDG following Part 1 the activity should be time corrected. The activity must be sufficient to generate at least

1000 CPS @ 5cm in scatter. Document the actual activity at the beginning of each part.

4.6.3.6 Sensitivity to Scatter

The geometry described in the NEMA standard requires that both the probe and source are to be positioned in contact with one side of the water bath in order to provide a scattering medium into the field of view of the probe. This same geometry can be achieved vertically by placing the 0.5 cc. sphere at the mounting location that is 5.0 cm from the center of the water bath and filling the bath to the bottom of the sphere. The probe is then placed in contact with the surface of the water. Because the field of view can be modified with electronic collimation the data for this section consists of the counts recorded from both the front and rear detector for count rate ratio calculations. This will identify the minimum ratio necessary to disable counting when the source is lateral to the probe head.

How the effect of scatter will vary with the size of the field of view is not known. For this

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reason, the measurements are repeated at four different distances to the source. The 0.5 cc. source is injected with 18F-FDG and normal saline according to the quantities listed in the results of the Preliminary Study for 0.5 cc, 1500 Bq. @ 5 cm. A 10 second accumulation of counts is required for each of the Neo2000 Gamma Detection Systems which are recording the front and rear detector in the electronically collimated probe.

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4.6.3.7 Spatial Resolution in a Scatter Medium

The 0.5 cc. source is injected with 18F-FDG and normal saline according to the

quantities listed in the results of the Preliminary Study for 0.5 cc, 1500 Bq. @ 3 cm. The

source is placed in the center position of the mountings in the water bath using the post that

elevates the centroid of the sphere to 12 cm above the bottom of the bath. The bath is filled

with water until the centroid of the sphere is submerged 3.0 cm. The probe is positioned

on the CNC manipulator arm with the probe tip just contacting the surface of the water.

The lateral position of the probe begins at 5 cm off axis from the source. Counts are

calculated by averaging the accumulated 10 second counts, and recorded for each position

listed in the table (see Table 11). NOTE: This assay is repeated using the energy window

commonly used for 18F in commercially available probes, 409-600 KeV (Table 12).

4.6.3.8 Angular Resolution on a Scatter Medium

The 0.5 cc. source is injected with 18F-FDG and normal saline according to the

quantities listed in the results of the Preliminary Study for 0.5 cc, 1500 Bq. @ 3 cm. The

source is placed in the center position of the mountings in the water bath using the post that

elevates the centroid of the sphere to 12 cm above the bottom of the bath. The bath shall

be filled with water until the centroid of the sphere is submerged 3.0 cm. The probe is

positioned on the CNC manipulator arm with the probe tip just contacting the surface of

the water. Ten second counts are recorded for both the front and rear detector at each angle

indicated (See Table 14). 104

NOTE: It is likely that the manipulator will not be able to assume the more acute angles without repositioning the probe. A special fixture (Figure 39) has been implemented to allow for the additional angle.

Figure 39: Angle adapter.

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4.6.3.9 Volume Sensitivity to Distributed Activity in a Scatter Medium

This assay requires activity evenly distributed throughout the water bath. the bath is filled with water and injected with the amount of 18F-FDG determined in the Preliminary

Study to bring the activity in the center of the bath at the surface to between 1000 and 3500

Bq. The amount of isotope is measured using a well count prior to mixing and corrected for decay prior to the calculation for Volume Sensitivity.

NEMA NU3 tests that were not performed include Short Term Sensitivity Stability and

Count Rate Capability in a Scatter Medium. These tests are designed to characterize the gamma detection system performance overall and are not specific to probe performance.

Although they are part of the NEMA NU3 standard, they were not conducted.

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4.6.4 Source Detection in a 1.1-to-1 Target-to-background Ratio

The purpose of this study is to support a statement in a recent publication that, mathematically, it should be possible for the 3-sigma statistical criteria for probe positivity to detect sources at a target-to-background ratio of 1.1-to-1 if the background count rate exceeded 900 counts per second. This statement was based on a theoretical calculation and should be born out experimentally. The 1.1-to-1 target-to-background ratio may be considered as an additional case of the Limits of Detection Protocol. Each of two spherical targets, 0.5 and 8.0 cc. are tested for detection limit when the target is titrated to 100 Bq. at 3 cm. Background plus target activity is titrated to 1000 Bq. measured at surface in the center of the tank when the target is submerged by 7 cm. The squelch level is set to a value of 1000 CPS. Measurements for the front and rear detectors are the average of 10 second accumulated counts, and performed with the target submerged at depths of 7, 5, 3, and 1 centimeter, using the following technique.

Following each set of measurements perform the following steps:

1. Decrease the target depth in the background solution by 2 centimeters by

removing 760 cc. of normal saline.

2. Advance the probe by 2 centimeters using the CNC Manipulator software.

3. Record 10 second average counts for the front and rear detector.

4. Calculate the target-to-background ratio of the two counts.

5. Proceed with the next measurements until one centimeter.

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4.6.5 Limits of Detection

The purpose of the detection limit experiment is to identify the depth of the target in the scattering medium that allows the target to be identified as significantly different from the background media using the three-sigma criterion for probe positivity. This critical distance is to be identified for 3 target-to-background ratios, and with 3 different volumes of the spherical targets. For the 1:0 target-to-background ratio, the target activity shall be

1000 Bq. at a distance of 3 cm in air. The post will support the sphere so that the centroid is fixed at 7 centimeters from the bottom of the saline bath. Normal saline is added until the sphere is submerged at the maximum depth, 7 centimeters.

To achieve the desired target-to-background ratio for the remaining assays, the target sphere is injected with sufficient 18F-FDG to measure 250, 500, or 1000 Becquerel at a distance of 3 centimeters in air. The source is then mounted in the tank at a depth of 7 centimeters in normal saline solution. The normal saline contains a pre-injected amount of 18F-FDG to raise the activity to 1000 Bq. as measured at the surface in the center of the tank.

After each set of measurements, perform the following steps:

1. Decrease the target depth in the background solution by 2 centimeters by removing

760 cc. of normal saline.

2. Advance the probe by 2 centimeters using the CNC manipulator software.

3. Record 10 second average counts for the front and rear detector.

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4. Calculate the and record the count rate ratio. (Used later for calculated depth.)

5. Proceed with the next measurements until one centimeter.

4.6.6 Depth Detection

The data recorded for the limits of detection study can be used to calculate the depth from the count rate ratios as described in the theoretical framework. Since the true depth is known, the associated error can also be calculated. The additional calculations are added to the results for limits of detection.

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4.6.7 Spatial Resolution

Spatial resolution measurements are all conducted using a 0.5, 2.0 or 8.0 cc. targets titrated to an activity of 1000 Bq. at a distance of 3.0 cm. in air, and subsequently submerged in the scatter medium by 3.0 centimeters. The 2.0 cc. sphere is suspended on the top of a 7.0 cm post in the center of the water bath defined for this series of studies.

Only the two cases of target-to-background conditions are tested: 1.25:1, and 1.0:0. For each target-to-background and each target volume the probe is position just in contact with the surface of the scatter medium and on axis with the centroid of the target. The optics of the tank make this difficult to perform visually. The center is determined by the location that results in the maximum count rate recorded on the front detector of the electronically collimated probe. Perform the following steps for each set of conditions.

1. Record 10 second count averages for both the front and rear detector at the center

of the target as described previously.

2. Using the CNC Manipulator software interface advance the position of the probe

laterally until count rate has dropped to one half of the average value recorded in part

one. Record the 10 second counts at this location.

3. Record the distance of the off-axis lateral movement that results in the half

maximum count. If the CNC Software is zeroed at the center, this number can be read

from the computer interface.

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4. Calculate the spatial resolution for this target as two times the off-axis distance

recorded in step 3.

4.6.8 Intraoperative Phantoms

Five phantom models have been developed to simulate the distribution of 18F-FDG radioactivity that would be encountered by the surgeon intraoperatively. For each model, the person performing the test must use the electronically collimated gamma detection to localize the target sphere in environments where other activity is present. PET/CT imaging is performed on each of the phantom models to document the actual distribution of radioactivity. A computerized model for the first three phantoms will also be developed.

The first of five models consist of a single 2 cc. sphere, with an activity of 1500 Bq. as measured at a distance of 3 centimeters in air. The sphere is mounted on a post which holds the target at a height of 7 cm from the bottom of the tank. The target sphere is submerged in normal saline as a scatter medium. No activity is added to the background medium.

The second phantom consists of the configuration described previously with the addition of a 90 cc. secondary source located at a distance of 5 centimeters from the center of the primary source (target). The activity of the secondary source measures 1000 Bq. at the surface of the sphere. This large source is intended to model an injection site, after a significant amount of radioactive decay, in an intraoperative lymphatic mapping scenario.

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It may also model an organ exhibiting a higher metabolic rate than the surrounding tissue which results in an increased uptake of 18F-FDG, such as the heart.

Three secondary sources are incorporated in the third phantom and represent additional lesions exhibiting 18F-FDG uptake. The parameter associated with each of the secondary sources are:

Volume Activity Distance 0.5 cc 1500 Bq @ 3cm 10 cm 2.0 cc 1000 Bq @ 3cm 10 cm 8.0 cc 500 Bq @ 3cm 10 cm Table 4: Titrated radioactivity for 3 sizes of source spheres

In the fourth phantom, the secondary object is a 250 cc. IV bag of normal saline titrated with 18F-FDG to 1500 Bq. as measured at the surface near the middle of the flattened bag.

This is placed at the bottom corner of the bath container using double stick tape to prevent the object from floating to the surface when the normal saline solution is added. The object is intended to represent an area of increased 18F-FDG uptake associated with an acute inflammatory response. Alternatively, this could represent a distributed mass of malignancy, but it is likely that such a lesion would be excised prior to surveying the surgical bed with a probe.

The fifth phantom consists of the same target and background. The secondary source is a cylindrical volume of approximately 70 cubic centimeters. The activity is 1000 Bq. of

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18F-FDG as measured at the surface in the middle of the phantom. As before, the object is placed at the bottom corner of the bath container using double stick tape to prevent the object from floating to the surface when the normal saline solution is added. This secondary object is modeling the approximate dimensions of a section of colon with an increase in18F-

FDG uptake due to inflammatory response. The secondary activity could also represent blood pool background emitted from a major blood vessel in close proximity. The ureters of the kidneys are also similar in activity and distribution.

In order to analyze the effect of different levels of squelch on the area of probe positivity after the data has been taken, 10 second counts were recorded for the front and rear detector at evenly spaced locations at the surface of the phantom bath. The surface is divided into a 9 by 9 point grid with a distance of 2.0 cm between each vertical and horizontal position. Each phantom data set consist of an 81-point array of raw data for both the front and rear detector; Two additional arrays were generated for the decay corrected data. The final data set consists of an 81-point array of the front to rear count rate ratios, calculated from the decay corrected data.

Following the data measurements for each phantom the phantoms were transported to the PET/CT scanner and a full set of images to document the true geography of the radioactive distributions was acquired.

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Chapter 5: Findings and Analysis

5.1 NEMA NU3:2004 Standard Studies

Results for the sections of the NEMA NU3 standard performed using the electronically collimated gamma detection probe are presented in the following sections. All data measurements are tabulated in the appropriate section of the text.

5.1.1 Sensitivity in Air

When used intraoperatively, gamma detection probes are measuring radiation from three origins. Background radiation, present throughout the surgical field, is primarily residual labeling agent in the blood pool background. The source radiation is presumed to originate from the radio-labeled tumor. A third, and significant, source of radiation is scattered radiation from the tissue surrounding the tumor. A measurement of the gamma probes sensitivity in air is intended to establish a baseline, or best-case scenario for detection, in the absence of background radiation and scattering, for purposes of comparison. A periodic re-evaluation of the probe sensitivity in air can also be used to verify that the performance of the probe has not degraded.

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Table 5: Sensitivity in Air. Source is 18F-FDG; Energy Window is 50-600 KeV.

The sensitivity in air measured for the front detector of the electronically collimated gamma detection probe was 441 counts per second, per mega-Becquerel, when measured at a distance of 3 centimeters. This was performed with the energy window at 50-600 KeV.

The intrinsic efficiency of the probe is 20.05% at 511 KeV. This statistic requires an estimation of the percentage of radioactive emissions that are incident to the front detector.

The front surface area of the cubical detector is 0.25 cm2. This area is equivalent to a round detector of 0.564 cm diameter. At a distance of 3 centimeters this area can be approximated by:

2휋푟ℎ

where r is the radius of the spherical surface surrounding the omnidirectional source, and h is the height of the spherical section intersected by a plane at distance (r-h). The value of h is: 115

0.564 푐푚 ℎ = 푟 − 3 ∗ cos (arcsin (0.5 ∗ )) = 0.0133 푐푚 3

and the value of the portion of the spherical surface that the detector intersects is approximately:

2휋푟ℎ ℎ = = .0022 4휋푟2 2푟

Therefore, the intrinsic sensitivity is:

441 퐶푃푆 441 100 ∗ = ∗ 100 = 20.05 % 106 퐵푞 ∗ 0.0022 2200

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5.1.2 Sensitivity Through Side Shielding in Air

This test illustrates the fundamental difference between electronic collimation and conventional heavy metal side shielding. The numeric results of this assay indicate that virtually no shielding exists in the probe, and in fact that is the case.

Table 6: Sensitivity through side shielding in air. Conditions: Source is 18F-FDG; Energy Window is 50-600 KeV.

A calculation of the ratio of the front to rear detector count rates is listed for each measurement in Table 6. These measurements indicate that a ratio threshold of 1.35 would theoretically be sufficient to disable counting from sources orthogonal to the axis of the probe as long as the distance is greater than 1 centimeter. With counting disabled, 100% side shielding is effectively achieved. Moreover, this method of eliminating counts from peripheral sources is equally effective at all energy levels.

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5.1.3 Side and Back Shielding

The leakage sensitivity for the dual detector probe is 48% for the front crystal and

18.7% for the rear crystal. These results, again, demonstrate that the absence of a physical shielding material obviates the need for this measurement as it does not apply to electronic collimation.

Table 7: Data and results for the effectiveness and sensitivity of side and back shielding.

Considering the count rate ratio over the entire surface of the probe reveals that a count rate threshold of 1.34 or greater would result in a sensitivity to leakage of 0 % and a shielding effectiveness of 100 %. The minimum count rate ratio of 0.74 is measured behind the head of the probe. This presents further evidence that electronic collimation can be implemented in software for both peripheral and posterior aspects of the probe. If counting is disabled wherever the count rate ratio greater than 1.34, active counting is limited to the area forward of the front surface of the probe. The extent of this volume is expanded or

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limited by setting the numerical value that the count rate ratio must exceed before counting is activated in the control unit.

Since this function is performed by a microcontroller which continually monitors the count rate ratio of the front and rear detectors in a software program, the term electronic collimation may be misleading. The collimation is not implemented purely in electronic hardware, but is a combination of the electronic signals from two detectors and an embedded software process executed in the microcontroller of the gamma detection system control unit. Therefore, the probe is not electronically collimated unless it is used in conjunction with the control unit designed for this purpose.

Consider the four locations of a gamma radiation source relative to the electronically collimated probe in Figure 40.

Ratio F/R < 1

Ratio F/R ≈ 1 Ratio Ratio F/R > 1 Ratio F/R > 1 Ratio F/R ≈ 1

F/R ≈ 1

Figure 40: The ratiometric basis for electronic collimation. The count rate ratio is nearly one at positions lateral to the probe and when the source is at a distance that is large compared to the distance separating the two CZT detection crystals.

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The dashed line represents a plane that is at an equal distance from the front and rear detectors. If a gamma source is located anywhere behind this plane, the count rate on the rear detector will exceed the count rate on the front detector, and the count rate ratio will be less than one. If the source is located anywhere on this imaginary plane, the count rate ratio is equal to one. As the source location is moved forward of the plane, the count rate ratio will always be greater than one. The magnitude of the count rate forward of the equidistant plane is a function of both the angle to the center-line axis of the two detectors, and the distance from the detectors. The count rate ratio is maximized directly in front of the front detector, at the surface of the probe. At this location, the ratio of the distances to the surface of the front and rear detectors is also maximized. As the distance from the source to the front aspect of the probe is increased, the distances become more closely matched. As this occurs the count rate ratio is also reduced, and eventually drops below the threshold value required to enable counting. This approach to limiting the field of view constrains both the angle and the extent of the active volume in front of the probe.

Changing the threshold value to enable counting, modulates both the angle of the field of view and the depth of the field of view. Both must be taken into account in the probe design. The included angle of the field of view imposed using electronic collimation varies with depth. This is a significant difference from the constant angle of collimation in probes with heavy metal shielding.

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The following four figures illustrate the change in the field of view at four levels of the count rate threshold (See Figures 41-44). These plots were constructed from the mathematical equations derived in Chapter 3. The angle of the field of view is nearly 120 degrees at the greatest value regardless of the change in radius. The included angle is reduced as the distance from the front of the detector increases. It is apparent that the radius of the field of view changes to a much greater extent than the included angle as the count rate ratio is decreased.

Figure 41: Field of view at a ratio of 1.30.

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Figure 42: Field of view at a ratio of 1.50.

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Figure 43: Field of view at a ratio of 2.50

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Figure 44: Field of view at a ratio of 3.50.

Having demonstrated that the count rate ratio of the two detectors decreases with increasing depth (from the sensitivity in air study), and is reduced to less than or equal to unity for all positions proximal to an equidistant plane which passes between the two detectors (side and rear shielding, and sensitivity through side shielding in air studies), it is possible to implement electronic collimation using a dual detector probe design.

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5.1.4 Energy Resolution

The energy resolutions for the forward and rear detection crystals are measured by calculating the FWHM value of the 511 KeV photopeak identified in the spectral response plot of a multi-channel analysis. The studies performed with 18F-FDG in the laboratory demonstrated a 511KeV photopeak that was well defined on the high-energy side, but obscured by the down-scattered radiation and the Compton plateau at lower energies (See

Figures 45 and 46). In these circumstances, it is acceptable to measure the half maximum value at energies greater than the photopeak and double the energy difference to approximate the full width value. Applying this the two records for the front and rear detector indicated that the FWHM energy resolution was 27% for the front detector, and

26% for the rear detector.

However, as it was questionable as the whether or not there were 1000 counts incorporated in the FWHM range of the photopeak, as required by the NEMA NU3 standard, the MCAs were repeated using a 22Na check source (also a positron emitter) over a two-hour period of time. The records did result in over 1000 pulses in the photopeak, and the energy resolution was measured at 22% for both the front and rear detectors (See

Figure 47).

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Figure 45: MCA from front detector. Source is 18F-FDG. Two-minute record.

Figure 46: MCA from rear detector. Source is 18F-FDG. Two-minute record.

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Figure 47: MCA repeated with 22Na source to generate more than 1000 counts in photopeak as require by the NEMA NU3 standard. Little difference was observed in the MCAs acquired for both detectors.

Part 4: Energy Resolution Detector Energy Resolution Front 22 % @ 511 KeV Rear 22% @ 511 KeV Table 8: Energy resolution results from MCAs taken with a 22Na source.

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5.1.5 Sensitivity in a Scatter Medium

One of the best assessments of a gamma detection probe for intraoperative use is the evaluation of sensitivity in a scatter medium. A normal saline solution provides an excellent approximation to the radiation scattering produced by human soft tissue. It is not surprising that the effect of scatter increases with the depth of the tissue or any other scatter medium. Comparing the probe sensitivity in a scatter medium (Table 9) to the same measurements taken in air (Table 3), it is evident that the scatter medium has little effect at small depths, but progressively reduces sensitivity as the depth of the source is increased.

Demonstrated in subsequent testing, the loss of spatial resolution associated with scatter is more problematic than the reduction of sensitivity.

It should be noted again, that much of the sensitivity can be recovered by including

Compton scattered radiation in the accumulation of pulse counts. While expanding the energy range of the probe greatly increases the sensitivity, doing so further degrades the spatial resolution of the probe. Discussed in more detail later, either electronic collimation or the 3-sigma criterion for probe positivity can recover most of the loss in spatial resolution associated with increasing the energy bandwidth included in the accumulation of gamma counts.

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Table 9: Data and calculated values for sensitivity in a scatter medium.

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5.1.6 Sensitivity to Scatter

This test is intended to measure the amount of radiation scattered into the field of view by a peripheral radiation source. This is often referred to as "in-scatter". In the present application, it is not possible to measure sensitivity to scatter without fully implementing electronic collimation in software. Since the dual detector probe is not shielded from a radiation source when it is lateral to the probe, sensitivities to scatter (Table 10) were not significantly different than sensitivities measured in air, or directly in front of the probe.

Table 10: Data and calculated values for sensitivity to scatter.

To conduct the NEMA NU3 test for sensitivity to scatter, the source is located just proximal the front surface of the probe, and at a distance of 5.0 centimeters. This condition, typical of conditions leading to in-scatter, will result in low count rate ratios in the dual detectors. It is evident from the count rate ratios calculated from the same data, that

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electronic collimation could be used to disable counting from in-scatter at a ratio of less than 1.2. It is safe to assume that no sensitivity to in-scattering alone would be measured if this methodology is applied. However, in-scatter would contribute to the counting if a more active source within the electronically collimated field of view is enabling counting.

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5.1.7 Spatial Resolution in a Scatter Medium

The data acquired for the standard NEMA NU3 study of spatial resolution is listed in

Tables 11 and 12.

Table 11: Spatial resolution data for open window setting (50-600 KeV).

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Table 12: Spatial resolution data for a commercial window setting (409-600 KeV).

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A summary of the results is presented here.

Summary of Spatial Resolution in a Scatter Medium 409-600 KeV Energy Window Spatial Resolution @ 511 KeV (Front) 7 Spatial Resolution @ 511 KeV (Rear) 8 50-600 KeV Energy Window Spatial Resolution @ 511 KeV (Front) 10 Spatial Resolution @ 511 KeV (Rear) > 10 Table 13: Calculated values for spatial resolution in a scatter medium.

Because the dual element probe lacks side shielding, the spatial resolution in the absence of electronic collimation is very high (See Table 13). The Full Width Tenth

Maximum values described in the NEMA NU3 standard could not be achieved with the limited size of the NEMA NU3 standard water bath. The FWHM for the rear detector in the 50-600 KeV energy window setting was also not achieved. The front detector demonstrated an increase in spatial resolution from 7 to 10 cm when the energy widow was increased from 409-600 KeV to 50-600 KeV.

It is clear from the count rate ratios associated with each position in the study (Table

11) that electronic collimation can limit the spatial resolution to less than 10 centimeters.

The spatial resolution is limited to 7.7 centimeters (for a source depth of 3 cm.), if counting is disabled whenever the count rate ratio drops below 1.35. This value was interpolated from the spatial resolution data taken using a 50-600 KeV window (Table 11). There is a

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slight asymmetry to the table due to an offset in the distance measurement from the true maximum count value.

The low count rates recorded for the 409-600 KeV window setting (Table 12) resulted in a great deal of variability on the calculations for count rate ratio. It is not possible to draw a conclusion concerning spatial for this data set. It is evident, however, that the open window setting of 50-600 KeV results in a two order of magnitude increase in the probe sensitivity when compared to the same activity recorded with an energy window of 409-

600 KeV.

5.1.8 Angular Resolution in a Scatter Medium

This test is intended to measure the angular field of view of the probe under test.

Conventional side shielding and collimation limits the field of view to a conical volume that is assumed to extend to the detectable limit of the probe. Measurements taken for this test (Table 14) demonstrate that the absence of side and rear shielding make the detectors nearly omnidirectional at a fixed distance. The full width half maximum value cannot be measured for the dual detector probe at any angle. Therefore, the test cannot be applied.

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Table 14: Angular resolution data. Source is 18F-FDG; Energy Window is 50-600 KeV.

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Count rate ratios were calculated for the range of data taken. More acute angles could not be achieved using the test apparatus. It was apparent from the data taken that a FWHM value would not lie within a 180 degree angle field of view for the probe. As demonstrated, both mathematically and graphically (See Figure 48), the subtended angle of the field of view changes with depth when electronic collimation is applied. The angle is broad near the probe, becomes slightly broader at superficial depths, and then gradually narrows in deeper tissue until the depth limit is reached. At the depth limit, the field of view ends abruptly. This dependency of the angular resolution on depth would require multiple measurements with the source at different depths to completely characterize the angular field of view using electronic collimation.

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Figure 48: Field of view for count rate ratios:1.3, 1.36, 1.56, 2.25, and 3.36. The corresponding depths are 7.14, 6, 4, 2, and 1.2 centimeters respectively. Angular resolution is depth dependent.

Once the proposed software for electronic collimation is implemented, setting a lower limit for the count rate ratio will effectively limit the field of view. The angular resolution can be reduced by disabling counting when the count rate ratio falls below a specified value. In the data set presented here, it is clear that the angular resolution would be limited to approximately 90 degrees at a depth of 3 centimeters, if counting is disabled when the count rate ratio of falls below a value of 1.35 (See Tables 14 and 15).

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Table 15: Angular resolution can be limited to 90⁰ by applying a limitation of count rate ratio of 1.35 for the active counting region.

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5.1.9 Volume Sensitivity to Distributed Activity in Scatter

The volume sensitivities for the front and rear detector were taken with the probe in contact with the surface of the water bath. Since the radioactivity is distributed throughout the scatter medium, a direct comparison to source activity in air or scatter is not appropriate.

For a probe collimated by metallic shielding, the volume sensitivity is reduced by limiting the field of view. In contrast, the field of view was not limited during this measurement, and the measured volume sensitivity is high as a result (Table 16).

Table 16: Volume sensitivity for the dual element probe. Note that electronic collimation is not applied.

The count rate ratio calculated from the volume sensitivity data is 1.72. It is a significant finding that a distributed radiation source will produce a high count rate ratio.

In this circumstance, increasing the count rate ratio threshold to disable active counting would likely limit the field of view to the extent that the target source is no longer within the field. In this case, the operator would be required to expand the field of view 140

significantly in order to activate counts. It is possible that a concentrated radio-labeled source within the field of view would reduce the count rate ratio regardless of the high background activity.

5.2 Source Detection in a 1.1-to-1 Target-to-background Ratio

The first of the original experiments to be conducted, this study provides evidence to support a theoretical statement put forth in the article Comparison of two threshold detection criteria methodologies for determination of probe positivity for intraoperative in situ identification of presumed abnormal F-FDG-avid tissue sites during radioguided oncologic surgery, published in September of 2014 [1].

Table 17: Data results at low Target to Background ratios.

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As stated in the paper, the 3-sigma criterion for probe positivity can theoretically detect a radiation source in a target-to-background ratio as low as 1.1-to-1, if the background activity exceeds 900 CPS.

The source radiation level for this study had to be increased to guarantee that a target- to-background of 1.1:1 existed when the source was measured at a depth of 7 centimeters.

Moreover, in the interest of time, only the smallest (0.5 cc.) and largest (8.0 cc.) source spheres were included in the study.

The results demonstrated that, at a depth of 7 centimeters, both the 0.5 cc. and 8.0 cc. sources could be detected at a target-to-background of 1.1-to-1, but were intermittent at

1.09-to-1 (See Table 17). Since the conditions would be more favorable for positive detection at 1, 3, and 5 centimeters (where the target-to-background ratios are greater), it is evident that a source embedded in a target-to-background ratio of 1.1-to-1 can be detected using the 3-sigma criterion. While the conditions could not be controlled with enough precision to perform the study with a background count of 900 Bq., this study supports the claim that large sources (8.0 cc.) at a target-to-background of 1.1:1 can be detected as deep as 7 centimeters when the background level is in excess of 1000 CPS.

Small sources (0.5 cc.) can be detected at a target-to-background of 1.1:1 as deep as 5 centimeters when the background radiation level exceeds 1000 counts per second

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5.3 Limits of Detection

The studies in limits of detection investigate the effect of source size, depth, and target- to-background ratio on the capacity of the probe to detect target radiation using the 3-sigma criterion for probe positivity. The location for background count was standardized across all tests. This measurement was performed on the surface of the scatter medium, and half- way between the location of the maximum count rate and one corner of the N

A NU3 standard water bath. The target-to-background ratios of 1.25:1, 1.5:1, and 2:1 were originally specified for the three centimeter depth. During the experiment, the target- to-background ratios were observed to vary considerably with depth. Moreover, due to the short half-life of 18F, it was difficult to control the relative amounts of radioactivity necessary to maintain the desired target-to-background ratios, or anticipate the amount required at a given time. For this reason, the target-to-background ratios were calculated from the count rate values of the front detector and the corresponding background count measurement performed at the beginning of each step. It should be stated that this finding underscores the need to implement real-time measurement of the background radiation.

Target-to-background ratios are listed in increasing order in the second to last column of

Table 18.

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Table 18: Limit of Detection sorted by calculated target-to-background. Probe negative or intermittent readings are highlighted. All targets are detectable to a depth of 5 centimeters. All targets are detectable at a target-to-background ratio of greater than 1.52. Eight out of 10 failures occur at target-to-background ratios of less than 1.27.

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The 3-sigma criterion successfully identified probe positive targets of all sizes and depths of 5 centimeters or less, regardless of the target-to-background ratio. At a depth of

7 centimeters, and target-to-background ratios less than or equal to 1.52:1, sources of all sizes were intermittently probe positive, or probe negative. All of the probe negative sources were probe negative on the rear detector only, and probe positive on the front detector (6 out of 10 failures). Eight of the ten intermittent or probe negative measurements occurred at target-to-background ratios less than 1.27:1.

Referring to the Design Plan (See Appendix B: Design Plan), the limits of detection tests verify that the Design Output meets the Design Input requirements described in steps

9.1, 9.2, and 9.3

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5.4 Depth Detection

The same data taken for the limits of detection experiments was evaluated mathematically for the accuracy of the depth detection calculation using the count rate ratio. Since the target-to-background ratios for this data were not well controlled, the calculated values from the limits of detection study were also used to evaluate the effect of target-to-background, as opposed to using the 1:0, 2:1, 1.5:1, and 1.25:1 categories that were originally specified. The depth calculation and error have been appended to Table 18 and appear in Table 19.

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Table 19: Depth detection data appended to Table 18. Probe negative or intermittent readings are highlighted.

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The errors associated with the depth calculations from the count rate ratios were greater than anticipated for most measurements. Attempts to reduce the errors by applying mathematical offset and scaling, and other interpolation techniques, resulted in no improvement in the error statistics.

By limiting the conditions of the measurements that are considered to be valid, an improved percentage of error can be achieved. However, the standard deviation for the error is still large when compared to the mean value. It is also not possible to constrain depth detection to a certain range as the actual depth is not known a priori. Only the ranges of target-to-background ratio, count rate ratio, and probe positivity based on the 3-sigma criterion, are metrics that can be limited in range of depth detection.

The calculation does not appear to work well for measurements taken at 1 centimeter in depth. This is the result of the source distance lying within the near field of the detector.

Simulations of the front and rear detector were conducted prior to implementing the probe to document the near and far field of the probe, as well as the linearity and extent of the useful range. Using an MCNP model to simulate the dual detector probe (Figure 49), the effect of the near field was observed to begin between 1.5-to-1 centimeters from the probe surface (See Figure 50). At four centimeters from the probe surface, it was also observed that the count loss associated with shielding of the rear detector by the front detector becomes a significant percentage of the counts accumulated. This increases the

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count rate ratio and underestimates the target depth. At greater depth, the count rate ratios become redundant with values simulated at more superficial distances.

Figure 49: MCNP probe model of the electronically collimated probe.

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Figure 50: MCNP simulation results showing the near and far field of dual detector probe.

The effect of the near field can also be seen in the comparison of the count rate ratio and depth plotted in Figure 51. Average values form all data taken at, 1, 3, 5, and 7 centimeters were plotted. A piecewise cubic spine interpolation was performed in

MATLAB to approximate the continuous curve between the four discrete points. At small depths, small changes in count rate ratio result in large changes in the calculated depth compared to the same calculations for depth when the count rate ratio is greater. It is also

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evident from the data that errors are lower for higher count rate ratios. Errors do not exhibit a correlation to the size of the target.

The percentage of error for all data is 59 ± 67 % indicating that the method is useless if applied over the entire range. While eliminating the data from 1 and 7 improves the error, this is not possible to do a priori in a control unit. For this reason, the error can only be reduced by limiting depth detection to specific ranges of target-to-background ratios and count rate ratios. Requiring a target-to-background ratio of 1.07 to 2.08 reduces the error to 33 ± 50%. This limitation removes all but one of the 1-centimeter data points from the data set used in the error calculation. If the remaining 1-centimeter data point is removed

(this data point appears to be an outlier as the depth error is 275%), the average error is 24

± 16%. The percentages of error for different conditions are listed in Table 20.

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Figure 51: Interpolation of the source depth from 4 count rate ratios demonstrates that small changes in count rate ratio correspond to large changes in depth at superficial levels (1-4 centimeters).

Table 20: Percentage of depth error under various constraints.

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5.5 Spatial Resolution

The study was modified to limit the activity of the background. It was discovered that the volume of the bath was not sufficiently large to guarantee a uniform background count as the probe was moved laterally to find the half maximum value of counts per second.

Indeed, in the absence of a source the count rate dropped significantly as the probe passed

5 centimeters from the center point. This corresponds to half way to the edge of the container. Therefore, any FWHM values exceeding 10 cm are not entirely accurate. The data collection was limited to a background activity of 25% of the source activity. The target-to-background of this condition is 5:1. Although this is higher than conditions encountered intraoperatively, it is sufficient to demonstrate the effect of an elevated background activity on spatial resolution as it applies to the electronically collimated gamma detection probe.

The initial study (See Table 21) consisted of measuring the FWHM spatial resolution of a 0.5 cc, 2.0 cc, and 8.0 cc. source, at depths of 1, 3, 5, and 7 centimeters. All three sources were titrated to 1000 Bq. and initially submerged in normal saline without the addition of any background activity. Following the acquisition of a full data set at a target- to-background of 1:0, the normal saline was injected with 18F-FDG to raise the target-to- background to 5:1. The measurements were then repeated. The FWHM for the 8 cc. source in the 5:1 target-to-background could not be measured as it exceeded the dimensions of the tank.

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Table 21: Spatial resolution data with count rate ratios.

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Table 22: Spatial Resolution at 1 cm. and 1:0 TBR

Table 23: : Spatial Resolution at 3 cm. and 1:0 TBR

Table 24: Spatial Resolution at 1 cm. and 5:1 TBR

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Table 25: Spatial Resolution at 3 cm. and 5:1 TBR

It is clear from the data (Tables 28-31) that the spatial resolution increases significantly with the depth of the source. The FWHM at 7 cm depth compared to 1 cm depth increases by an average value of 197%. The size of the source also increases the spatial resolution, but to a far less degree. In 9 out of 11 measurements, the background activity increased the spatial resolution by an average value of 16% comparing the 0.5 cc. source to the 8 cc. source.

To investigate changes in spatial resolution with variations in energy bandwidth, and background media, an additional study was performed. The studies were limited to a source volume of 0.5 cc. and a depth of 3 centimeters (See Tables 32 and 33).

The open bandwidth of 50-600 KeV was compared to two bandwidths for 18F in commercial use, 409-600 KeV, and 350-600 KeV. These comparisons were performed with background media of air, normal saline and normal saline with sufficient 18F-FDG to raise the target-to-background to intended to be 1.25:1. Again, when 18F-FDG was titrated into the saline, the count rate at 3 cm. over the target increased from 2336 CPS in normal

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saline, to 2647 CPS, a target-to-background of 7.5:1. Although this is quite high, this is a significant difference based on the 3-sigma criteria. The high target-to-background also reduced the effect of the limited volume on the FWHM measurements. It is likely, however, that a lower target-to-background would increase the FWHM value to a much greater extent. The 0.5 cc. source activity remained above 1000 Bq. for the duration of the study.

Energy Range FWHM (cm) FWHM (cm) FWHM (cm) in Air in Saline In Saline+ 18F-FDG 409-600 KeV 6 7 8 350-600 KeV 8 7 9 50-600 KeV 7 8 11

Table 26: Spatial resolution of front detector at 3 bandwidths and 3 background media.

Energy Range FWHM (cm) FWHM (cm) FWHM (cm) in Air in Saline In Saline+ 18F-FDG 409-600 KeV 7 7 9.5 350-600 KeV 8 6.8 8 50-600 KeV 7.8 9 10.8 Table 27: Spatial resolution of rear detector at 3 bandwidths and 3 background media.

When the background media was changed from air, to saline, and to saline with 18F-

FDG, some increase in spatial resolution was observed for all three bandwidths. The increase was greater for the 50-600 KeV bandwidth, and more pronounced in the front detector than the rear detector. The front detector also exhibited an increase in spatial resolution as the width of the energy windows were increased from 409-600 KeV, to 350- 157

600 KeV, and finally to 50-600 KeV. The rear detector was inconsistent in changes to spatial resolution as the bandwidth was increased.

At a 50-600 KeV bandwidth, the normal saline with 18F-FDG was sufficient to demonstrate a 38% increase in FWHM as compared to a background of normal saline alone, and a 57% increase when compared to the FWHM measured in air. A previous study performed with probes housed in tungsten, did not demonstrate more than a few percent difference between any of the changes in background media. The difference here is likely the omnidirectional nature of the unshielded detectors in the dual element probe.

Electronic collimation eliminates the loss of spatial resolution by limiting the field of view with an effective shielding efficiency of 100%. Consider the FWHM plots of the front detector, rear detector, and count rate ratios for three background media: air, saline, and saline with 18F-FDG added (Figures 52-54). The same data for FWHM values (Table

27) was used to generate these curves. In the first two plots, the count rates are normalized to the maximum (on axis) value. Figure 54 illustrates the count rate ratio of the two detectors as a function of lateral displacement from the axis of the source. This plot demonstrates that electronic collimation software could limit the spatial resolution to 8 cm at a distance of 3 cm by inhibiting counting at the ratio value of 1.42 or greater.

Functionally, the count rate would drop to zero at a lateral distance of 4 centimeters from the source axis in background media of either saline or saline with 18F-FDG. For the front detector, this would limit the spatial resolution in a background of saline with 18F-FDG to

8 cm. as compared to 11 cm. without electronic collimation (See Table 28).

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Figure 52: FWHM for front detector.

Figure 53: FWHM for rear detector.

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Figure 54: FWHM for count rate ratio. Ratio of count rates could be electronically collimated to limit FOV to 8cm.

Table 28: Field of view at 3 cm. in various backgrounds for 50-600 KeV energy window.

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5.6 Intraoperative Phantoms

Phantoms, constructed as an approximation to the distributions of radioactivity encountered intraoperatively, were utilized to evaluate the effectiveness of the electronically collimated gamma detection probe. Measurements at 2 centimeter intervals, in 2 dimensions, were performed over the surface of each phantom bath. Data was recorded for the front and rear detector counts. The time of each measurement was recorded and the count rates were corrected for decay. The count rate ratio at each location was calculated.

All raw data is contained in Appendix D.

Three-dimensional surface plots were generated in MATLAB to illustrate of the contour of radioactive counts as measured at the surface. To model the extent of probe positive areas in the contour, a second plot is generated showing only the areas exceeding the threshold level. The threshold levels are represented as horizontal planes at the base the probe positive regions.

The count rate ratio threshold levels chosen for each phantom represent the best discrimination of the objects for each set of phantom measurements. Note that these are not based on the 3-sigma criterion, but were chosen subjectively for purposes of illustration.

For each phantom, the PET/CT scans provide documentation of the actual geometry of the various radiation sources and scatter medium distributed throughout the NEMA NU3 standard water bath. Data from the study are also used to validate MCNP models of the

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first three phantoms. This will enable computer simulations in future work. Use of these models is beyond the scope of this study. Each of the three models to be verified are illustrated with the PET/CT scans for further clarity.

5.6.1 A Single Source

The first phantom provides a fundamental case of a single target in normal saline. No background radiation was included in this model. The contour plot for this phantom demonstrates that a single source in no background can be localized to an area of a few centimeters at a high threshold level, in this instance 1.68.

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Figure 55: 3-D contour of the count rate ratio of phantom #1. Threshold for probe positivity is set to 1.1.

Figure 56: 3-D contour of the count rate ratio of phantom #1. Threshold for probe positivity is set to 1.68.

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Figure 57: PET/CT scan of phantom #1, axial and coronal views.

Figure 58: MCNP computer model for phantom #1, axial view.

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5.6.2 A Single Source with Large Secondary Source

The second phantom represents a common intraoperative scenario. The target is partially obscured by a larger more active secondary source. This is often the case in intraoperative lymphatic mapping where the injection site for the radiotracer contains far more radioactivity than the sentinel lymph node requiring resection.

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Figure 59: 3-D contours of the count rate ratio of phantom #2. Threshold for probe positivity set to 1.14.

Figure 60:3-D contours of the count rate ratio of phantom #2. Threshold for probe positivity is set to 1.36.

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Figure 61: PET/CT scan of phantom #2, axial, sagittal, and coronal views.

Figure 62: MCNP computer model for phantom #2, sagittal view.

The activity of the secondary source compared to the target source was less than anticipated. While the target was not initially obscured, the study was sufficient to document the capability of the probe to differentiate the two sources at different thresholds for probe positivity.

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5.6.3 Multiple Sources

The third phantom demonstrates the superiority of measuring the ratio of count rates compared to the individual count rate measurements of either the front or rear detector.

Figure 63 shows the distribution of front detector count rates over the entire surface of the scatter medium. Separation of all 4 targets is apparent and are not isolated as separate areas of probe positivity. The rear detector exhibits no distinct features of the multiple sources

(Figure 64). Taking the ratio of the front divided by the rear detector count rate measurements at each position results in a separately resolved area of probe positivity for each of the four spheres included in the phantom (See Figure 65). The lower left-hand corner corresponds to a larger (8cc) sphere with a low concentration of 18F-FDG activity, compared to the other spheres. It is evident that the spatial resolution of the count rate ratio mapping is superior to the count rate ratios of either detector alone.

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Figure 63: 3-D contour of the front detector count rate of phantom #3. Threshold for probe positivity is set to 1836.

Figure 64: 3-D contour of the rear detector count rate of phantom #3. Threshold for probe positivity is set to 1100.

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Figure 65: 3-D contour of the count rate ratio of phantom #3. Threshold for probe positivity is set to 1.27. This demonstrate that the count rate ratio mapping is a more sensitive indicator of differences in the spatial distribution of radioactivity, when compared to either of the detector count rate mappings alone (See Figures 63 and 64).

Figure 66: PET/CT scan of phantom #3, axial and coronal views at two depths.

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Figure 67: MCNP computer model for phantom #3, coronal view.

5.6.3.1 A Probe Positive Criterion for Count Rate Ratios

To take advantage of the improvement is spatial resolution associated with the count rate ratio, a new criterion for probe positivity is required. The probability density function of the count rate ratio is Gaussian since the two count rate distributions were Gaussian approximations [50]. It is therefore possible to define a metric for probe positivity with a known confidence level using this new statistic.

When two distributions are multiplied, or divided, the standard deviation of the result is different than the standard deviations of the separate distributions [previous]. The relationship is as follows:

2 2 2 휎푇 휎퐹 휎푅 (휇 ) = ( ) + ( ) 퐹⁄ 휇퐹 휇푅 휇푅

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where T refers to the distribution of the count rate ratio threshold for probe positivity, F is the count rate distribution for the front detector, and R is the count rate distribution for the rear detector. The symbols μ and σ are mean value and standard deviation respectively.

Substituting the square root of the mean values for the standard deviations and reducing the equation:

2 2 휇 휇 휇 퐹 √ √ 퐹 √ 푅 휎푇 = ( ) + ( ) 휇푅 휇퐹 휇푅

휇퐹 1 1 휎푇 = √ + 휇푅 휇퐹 휇푅

휇 1 1 3 − 푠𝑖푔푚푎 푡ℎ푟푒푠ℎ표푙푑 = 퐹 (1 + 3√ + ) 휇푅 휇퐹 휇푅

Therefore, the mean values for the front and rear background count rates can be used to find the count rate ratio that must be exceeded for probe positivity based on the original

3-sigma criterion.

How this new metric relates to the elevated activity of the target tissue is not altogether clear at this time. Evaluation of this methodology in intraoperative testing is recommended.

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5.6.4 A Single Source with an Irregular or Cylindrical Second Source

The last two phantoms were intended to model large distributions of radioactivity that can cause the localization of the target source to be more difficult. Unfortunately, the concentration of 18F-FDG in these secondary sources was too low to affect the level of activity at the target source. In both cases, the secondary objects were located at the bottom of the tanks, well below the level of the target. This distance also reduced the radioactivity measured at the surface. The following sets of figures illustrate the best resolution for each of the two phantoms. The corresponding PET/CT scans verify that the radioactivity in the secondary sources was not significant compared to the concentration of the spherical source. MCNP computer models were not constructed at this time as the geometries of the secondary sources are quite complex.

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Figure 68:3-D contour of the count rate ratio of phantom #4.

Figure 69: PET/CT scan of phantom #4, sagittal, axial, and coronal views.

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Figure 70: 3-D contour of the count rate ratio of phantom #5.

Figure 71: PET/CT scan of phantom #5, axial and coronal views.

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Chapter 6: Discussion, Conclusions, and Future Research

6.1 Probe Design

The probe construction was sufficient to demonstrate the advantages and disadvantages of both electronic collimation and depth detection. It is obvious from the NEMA NU3 standard that the probe performance of an electronically collimated probe requires a unique set of tests as it does not conform to the test procedures established for a probe using heavy metal side shielding. The MCA studies indicate a low signal to noise characteristic. The greatest improvement is signal to noise can be achieved by changing the capacitance of the

CZT or the feedback capacitance of the charge integrator in the pre-amplifier.

∆푉푂푈푇 퐶퐶푍푇 = ∆푉퐼푁 퐶퐹

∆푉푂푈푇 is signal amplitude following the pre-amp integration stage

∆푉퐼푁is signal amplitude from the CZT crystal.

퐶퐹 = 10.9 is the feedback capacitance of the pre-amp integration stage

퐶퐶푍푇 = 1.4 푝퐹 is the capacitance of the CZT crystal

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Detection crystals of a different geometry would greatly improve this performance.

CZT crystals 8.7 millimeters in diameter are readily available at a thickness of 4 millimeters. The capacitance of these crystals is calculated as:

퐾푠휖0퐴 퐶 = 퐶푍푇 푑

-12 휖0 is 8.854 x 10 Farads/meter

퐴 = 휋푟2 = 5.81 푥 10−5푚푒푡푒푟푠2

푑 = 4 푚푚 = .004 푚푒푡푒푟푠

퐾푠 = 10.9 for CZT

퐶퐶푍푇 = 1.4 푝퐹

compared to the 0.48 pF capacitance of the 5-millimeter CZT cubes used in the current design. The alternative crystals would improve the signal to noise ratio by a factor of 2.9.

Moreover, these crystals would be sufficiently small to allow the diameter of 12 millimeters required for laparoscopic or robotic probes.

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It has been demonstrated that the inverse squared relationship between gamma emissions and recorded counts is not valid in the near field of the front detector. Since the rear detector is recessed beyond the range of the near field for that detector, the count rate from this detector is more reliable than the front detector at distances of less than 1 centimeter. Since the sensitivity of the detector is reduced as the inverse of the distance squared, the improved linearity of response may be offset by a loss in sensitivity. By using the rear detector as the primary indicator of count rate, the near field effect of the probe on count rate could be eliminated. As the front detector is still effected by sources located in the near field, this advantage does not apply to the count rate ratio, or the modified 3-sigma criterion for probe positivity developed for application to the count rate ratio measurements.

6.2 Laparoscopic and Robotic Probes

Incorporating detectors of larger area and nearly equal thickness will improve the signal- to-noise ratio of the probe design. If a dual detector configuration is mounted on an articulating probe handle, and reduced to a diameter of 12 millimeters, the electronically collimated probe can be used in robotic applications, provided that the standardized gear mechanism for the robotic manipulator is included to control the angle of the articulation

(See Figures 72 and 73).

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Figure 72: Robotic probe with articulating head.

Figure 73: Standard da Vinci instrument from Intuitive Surgical Inc., Sunnyvale, CA.

A completely rigid laparoscopic probe would require significant design changes. As these instruments must have a side viewing field of view, electronic collimation is more challenging. The field of view must be limited both peripherally, along the axis of the

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probe, and circumferentially, around the long axis of the probe. Since the detectors must be co-axial with the long axis of the probe, a new geometrical relationship to impose electronic collimation is required.

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6.3 Electronic Collimation

Overall, the data provides evidence that electronic collimation can be applied using two detectors if constraints are placed on the upper and lower limit of the count rate ratio. Table

29 summarizes the limitations imposed on the count rate rations for purposes of electronic collimation. Note that these are specific to the current design.

It is also important to understand that electronic collimation can be affected by secondary sources outside of the field of view, as well as high target-to-background ratios.

Secondary sources in close proximity to the electronically collimated field of view can increase or decrease the count rate ratio, causing the included volume of the field of view to change. High target-to-background ratios can reduce the sensitivity of the electronically collimated probe to changes in the count rate ratio due to a small source, or source of low activity. It is not possible to take the many combinations of multiple sources and background activity into account for purposes of designing an electronically collimated probe. The phantom studies performed represent a limited number of target and background combinations likely to be encountered intraoperatively. The true utility of the electronically collimated probe must be evaluated and validated in a clinical setting.

Many combinations of detectors are possible to provide a variety of field of view geometries. It is not necessary to limit the field of view to the two-detector axis. For instance, a laparoscopic probe design would require a field of view at 90 degrees from the probe axis, and an additional limitation to the FOV angle around the axis of the probe.

Multiple detectors can be used to impose this field of view, but the FOV volume is no

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longer in the axis of the detectors. An array of detectors can also be used to implement a real-time measurement of background radiation, eluded to in previous sections. The specific advantages and limitations of the use of electronic collimation are best discussed in the context of subsequent sections.

6.4 Depth Detection

The study shows that the inverse squared law assumed to govern the behavior of the count rate ratio, and therefore depth detection, is applicable in a limited detection range extending from 1.5 to 4 centimeters. The variability in these results alone, presumed to be due to differences in target-to-background ratio, is still too great to accurately measure depth using the current method.

The tradeoff between the usefulness of the probe and limited circumstances under which it can be used should be re-evaluated using a mathematical model that takes both the shielding effect of the front detector and the inverse squared law into account. The presence of redundant values in the relationship eliminates the possibility of expanding the usable range using the current detector geometry.

An alternative approach to the calculations can take into account unpredictable factors in the surgical field. In place of relaying on trigonometry to calculate the depth, the control unit can be programmed to gradually increase the depth of the field of view by slowly reducing the threshold for probe positivity, using the derived relationship for the 3-sigma criterion as it applies to the count rate ratios. At some point, the majority of counts,

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associated with the radio-labeled target, will be included in the field of view, increasing the count rate abruptly. This is an indication that the more active target has moved into the field of view. Reducing the field depth until the counts rate drops out, verifies the depth of the target source. This technique would likely not work by reducing the field of view from depths greater than 4 centimeters since the count rate ratios may be redundant with more superficial extents of the field of view.

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6.5 Background Rejection

It is clear that the target-to-background ratio changes with depth to the target source, as the data from the limit of detection study demonstrates. While cut-down and resection clearly change the distance to the source, it is also possible that the local background activity is changing as well. The target-to-background ratio cannot be exploited for information about depth since the background count is not consistent from site to site or across surgical cases. The volume sensitivity study demonstrated that high background activity increases the count rate ratio. It is critical that the background count is accurate since this value establishes the threshold for probe positivity when the3-sigma criterion is applied. In light of this evidence, a real-time evaluation of the local background activity would improve spatial resolution and depth estimation of the probe. Future probe development should include an automated estimation of background activity.

6.6 A Multiple Channel Pre-amplifier

In order to reduce the diameter of the probe designs to 12 millimeters, the preamplifier dimensions must be reduced. A multi-channel pre-amplifier can be fabricated as an application specific integrated circuit (ASIC). Since ASICs are primarily CMOS devices, the JFET input stage usually used for CZT will need to be replaced by an equivalent CMOS circuit. Increasing the capacitance of the CZT detector by changing the dimensions, discussed previously, can provide a greater signal at the first stage. A reduction in the

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feedback capacitance in the charge integrating stage also increases the gain factor at the input. By incorporating this capacitance in the ASIC, the parameters can be tightly controlled, and the capacitance should generate less noise than a discrete component.

6.7 Gamma Detection System Console

This study has provided a collection of parameters that can be incorporated into the control system to provide an effective solution to both electronic collimation and depth detection. These findings are summarized in Table 29.

Table 29: Imposed limitations necessary to meet requirements for probe performance.

Combining the limitations on count rate ratio defines the acceptable range as 1.36 to

1.58. These values correspond to depths of 1.5 to 4.0 centimeters. This matches the findings for the viable operating region of the probe based on MCNP simulation results.

One further constraint on target-to-background ratio is required to guarantee a reasonable accuracy in the depth calculations (1.07 to 2.08). this range is an excellent match to target- to-background ratios encountered intraoperatively.

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Other parameters incorporated in the probe design that were used to obtain the previous results should be carried over into future designs if the preceding limitations are applied.

These include a detector spacing of 1 centimeter, and a crystal bias voltage of 120 Volts.

The Design Plan and Verification should be incorporated into the Design History File in the event that the technology developed here is transferred into the medical device industry (See Appendix B: Design Plan).

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Conclusions

While electronic collimation is not unique to this study [38], [82], this is the first study that applies the technique to solve a number of impediments in intraoperative detection of high energy ratio-isotopes. By eliminating the side shielding surrounding gamma detectors that have been used to limit the field of view, probes of reduced diameter and weight can be implemented. This allows high energy gamma radiation detection in probes suitable for laparoscopic and robotic introduction into a closed surgical field. This is also the first study that takes advantage of the variation in field of view depth associated with electronic collimation. Although further work is needed for a viable solution, adding depth detection to intraoperative gamma detection probes may enable the surgeon to localize and resect disease that would previously go undetected. Although the application presented here addresses high energy gamma emissions, electronic collimation provides effective elimination of gamma counts from off axis energy sources at all energies in the included energy range of the gamma detection system.

By expanding the energy range of the system, the sensitivity of small detectors is increased nearly two orders of magnitude (This is supported by data from the spatial resolution test performed as part of NEMA NU3, and reported in Tables 11 and 12.).

Without this increase in sensitivity at the count rate level, the detectors required for high 187

energy gamma measurements would be too large to incorporate in small diameter probes.

While this technique has a negative impact on spatial resolution, electronic collimation can recover the loss by limiting the field of view. Correct application of the statistical (3- sigma) criterion for probe positivity can also be used to localize a radiation source within an area with greater precision than relying on the spatial resolution of the probe alone.

Count rate ratios appear to be more sensitive to spatial variations in radioactivity compared to single detector count rates. To take advantage of this finding, a new criterion for probe positivity must be defined for the count rate ratio metric. This will be addressed in a future study.

At this time, no control unit exists to fully implement the techniques developed in this study. Results presented here are based on mathematical calculations and experimental measurements. While the data and analysis indicates that the science, including all three proposed hypotheses, is correct, a full implementation of the gamma detection system is required for validation and confirmation of the intended use.

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Appendix A: Characteristics of Cadmium Zinc Telluride

Table 30: Characteristics of CZT and other semi-conductors

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Appendix B: Design Plan

The Design Process

While it is not practical to meet the requirements of medical device manufacturing standards within an academic setting, considering these processes as part of any development work can greatly reduce the time to market of such a device following a transfer of the technology to a manufacturer capable of producing the product.

Regulatory Processes

Technology transfer within the medical device industry is conducted under the international standard EN or ISO-13485 [68]. This quality system, first introduced in 1996, defines the design process requirements for medical devices. Although not required here, close adherence to the standard can reduce the burden if technology transfer when the device is moved from a University setting into industry, since the Food and Drug

Administration has required design control as part of the Code of Regulations Title 21 (21

CFR 830.20) since 1990 [69]. There is a similar requirement in the European Union, MDR

(Medical Device Regulation) 2017/745 /EEC [70]. The 21 CFR 830 Regulations are cross referenced to both ISO 9001:1994[71] and ISO 13485 Section 4.4.

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The design steps required by 21 CFR 830.20 are:

1. Design and Development Planning

2. Design Input

3. Design Output

4. Design Reviews

5. Design Verification

6. Design Validation

7. Design Transfer

8. Design Changes

9. Design History File

Design and Development Planning

This part of the regulatory process defines the activities and responsibilities for each aspect of design planning. As this is specific to the quality system of each medical device manufacturer, it is not addressed here.

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Design Input

This section defines the intended use of the medical device and the requirements as

defined by the end user, in this case the surgeon.

Design Output

Design Output consist of details of the design with references back to each point in the

Design Input that a particular aspect of the design is intended to meet.

Design Verification

Design Verification consists of performing the required tests to document that the

Design Output meets the Design Input. There should be a one to one correspondence of

each Design Input item to the Design Verification testing.

Requirements expressed by a team of surgical oncologists and engineers are

incorporated in the following table. Each input requirement has a specific design output

that defines how the input criterion is met. The corresponding Design Verification lists of

describes the test used to document that the Design Output meets the Design Input criterion.

If the criterion is met, it is noted in the Design Verification section. A measurement

documenting the verification is included where appropriate.

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The Design Input, Design Output, and Verification Test Plan are compiled into tabular.

Test results compiled in the table will constitute part of the Design History File once the technology is transferred to a medical device manufacturer.

Table 31: Design Plan with one to one correspondence between Design Input, Design Output and Design Verification (continued). 201

Table 31, continued

continued

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Table 31, continued

203

Design Reviews

A Design Plan usually incorporates milestones at which the design is evaluated to ensure that it conforms to the goals set by the Design Input. Regular committee meetings are performed as part of this development process. A list of meeting dates and discussions of aspects of the design is are included in the following table.

Table 32: Design Reviews held as part of the PhD dissertation committee meetings.

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Design Validation

Design Validation is often confused with verification. Validation must be performed in the environment of the intended use of the device by the end user. For the current design, this would be performed in the operating room by a surgeon under the authority of an

Investigational Review Board (IRB). This process is often preceded by a risk analysis if appropriate.

Design Transfer

During the Design Transfer, all documents necessary to manufacture a medical device are collected in the Device Master Record (DMR). These usually contain a list of third party vendors required for acquisition of materials and standard operating procedures

(SOPs) for step by step production of the device, training material, and documentation of any test equipment or systems required to ensure that the product conforms to the approved

Design Plan.

Design Changes

During the development process and after the transfer of the technology, any design change is documented, verified, and validated. Records of reviews and approvals must accompany any design change.

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Design History File

A Design History File (DHF) contains all documentation documenting that the device was designed according to the stated Design Plan.

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Safety Testing

Prior to marketing, a medical device will undergo testing for electrical safety. These are performed by test laboratories such as Underwriters Labs, or TÜV Rhineland. At the time of writing, the international standard for the safety and effectiveness of medical electrical equipment is IEC 60601-1 [72]. This standard incorporates many safety tests including required levels of current leakage, emissions of electromagnetic radiation, immunity from electromagnetic interference, and immunity from electrical faults in power sources. It is prudent to consider how these requirements will be met at the onset of the design. An isolation diagram is constructed to identify required elements of circuit construction necessary to comply with the IEC 60601-1 safety standard.

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Device Class and Type

Many of the requirements of the safety standard are contingent upon the class and type of medical equipment. The 21 CFR Regulations, Section 860, defines the class of medical device, and defines these parameters based on the intended use of the device. I general, there are three classes, Class I, II, and III. Class I medical devices are “general control” and reserved for patient contact devices that are not diagnostic or therapeutic in nature. If a device is used to diagnose or treat a medical condition it is considered ”special control”.

If FDA approval has been granted for a similar medical device (predicate device), special control devices are assigned as a Class II device. The Class III device category is reserved for devices that represent a new application with no predicate device, or devices which provide a life-support function. A full pre-market approval is required by the FDA for

Class III medical devices.

In addition to the FDA classification, the IEC 60601-1 safety standard [72] classifies the “applied part”, the portion of a medical instrument that comes in direct contact with the patient, into three different types: Type B, BF, and CF. Type CF medical devices require the greatest amount if isolation, as they are permitted to come in direct contact with the tissues of the heart. Type BF devices consist of a conductive applied part that comes in contact with the patient, but are excluded from use in the cardiothoracic cavity. Type B applied parts are constructed of non-conductive material and are not attached to the patient in any way.

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Electrical Isolation

Since the probe is the applied part of the gamma detection system, the control unit that will eventually be used with the electronically collimated probe must provide the power and biasing voltage at an exceptionally low leakage current (<10 microamperes, Normal

Condition), to be classified as a Type CF instrument. The latter classification is essential since the instrument may be introduced into the chest cavity laparoscopically. It is assumed that this electrical isolation barrier will be implemented in the control unit, and developed at a later time. Since this investigation did not include patient contact, the method of isolating the probe electronically is beyond the scope of the study.

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Figure 74: Isolation Diagram for a gamma detection system.

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Appendix C: Derivation of the Hecht Equation

The Hecht equation which describes the total signal charge on the anode, including trapping is given by:

푄 푄 = − 0 [ (1 − 푒−((퐿−푥0)⁄푒)) +  (1 − 푒−(푥0⁄ℎ))] (1) 푠𝑖푔푛푎푙 퐿 푒 ℎ where:

푒 = 휇푒휏푒퐸

ℎ = 휇ℎ휏ℎ퐸 and

푄0 is the initial electron charge

퐸 is the magnitude of the uniform electric field (V/ cm)

퐿 is the thickness of the detector (cm)

휇푒 is the charge mobility of electrons for the material ( cm/(V*s) )

휏푒 is the electron trapping time (s)

휇ℎ is the charge mobility of holes for the material( cm/(V*s) )

휏ℎis the hole trapping time ( s)

x0 is the distance of the initial gamma event from the cathode

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A derivation of the Hecht equation (taken from reference [60]) is based on static charge analysis and modeling of point charge as a capacitive element. Consider the following geometry:

Figure 75: Charge migration for Hecht calculation

The interaction of the gamma photon results in photoelectric absorption at depth x0 in a CZT volume of thickness L, with a uniform, constant applied field of E volts/cm. The free charges that are created at x0 are –Q0, electrons, and +Q0, holes. The charges drift toward the anode and cathode respectively with a velocity of 휇푒퐸 and 휇ℎ퐸 . If the respective charge lifetimes are 휏푒 and 휏ℎ , then the trapping distances are:

푒 = 휇푒휏푒퐸

ℎ = 휇ℎ휏ℎ퐸

If de-trapping is ignored, the free electron and hole charges at depth x are given by:

−(푥−푥0)⁄푒 푄푒(푥) = −푄0 ∗ 푒 푓표푟 푥 ≥ 푥0 (2)

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and

(푥0−푥)⁄ℎ 푄ℎ(푥) = 푄0 ∗ 푒 푓표푟 푥 ≤ 푥0 (3)

Note that 푄푒(푥 = 퐿) is the total free charge collected at the anode and 푄ℎ(푥 = 0) is the total free charge collected at the cathode. For the anode, the collected charge is:

−(퐿−푥0)⁄푒 푄푒(퐿) = −푄0푒 (4)

Now assume a free point charge for each charge distribution. The total charge trapped between a path from x0 to the anode (for –e) or cathode (for +h) is distributed along x in vanishingly small increments given by:

푄 0 −(푥−푥0)⁄푒 푑푄푒푡(푥) = −|푑푄푒(푥)| = − ∗ 푒 푑푥 푓표푟 푥 ≥ 푥0(5) 푒 and

푄 0 (푥−푥0)⁄ℎ 푑푄ℎ푡(푥) = −|푑푄ℎ(푥)| = ∗ 푒 푑푥 푓표푟 푥 ≤ 푥0(6) ℎ

If each infinitesimal charge is modeled as an equivalent charged electrode, then a capacitance 퐶푎(푥) exists at each point along the path. If 퐶푇(푥) is the total capacitance due to trapped charge, then the charge induced on the anode and from each infinitesimal increment can be expressed as:

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퐶푎(푥) 푑푞푎푒푡 = 푑푞푒푡(푥)for electrons (7) 퐶푇(푥) and

퐶푎(푥) 푑푞푎ℎ푡 = 푑푞ℎ푡(푥) for holes (8) 퐶푇(푥)

At the anode, the differential induced charge from trapping is then:

퐶푎(푥) 푑푄푎푒푡 = 푑푄푒푡(푥) (9) 퐶푇(푥)

퐶푎(푥) 푑푄푎ℎ푡 = 푑푄ℎ푡(푥) (10) 퐶푇(푥)

Since capacitance can be expressed as:

퐴 퐶 = 휀 휀 (11) 푟 0 푑 where d is the inter-electrode distance, A is the overlap in area between electrodes, 휀푟 is the dielectric constant and 휀0is the electric constant. Then by proportionality of constants:

퐶푎(푥) 푥 = (12) 퐶푇(푥) 퐿

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The total charge induced at the anode is then given by substitution of equations and integration:

푥0 퐿 푄푎푡 = 푄푎ℎ푡 + 푄푎푒푡 = ∫ 푑푄푎ℎ푡 푑푥 + ∫ 푑푄푎푒푡 푑푥 = 0 푥0

푥 푥 ∫ 0 푑푄 (푥)푑푥 + 0 퐿 ℎ푡

퐿 푥 ∫ 푑푄푒푡(푥)푑푥 (13) 푥0 퐿

Substituting from equations (5) and (6):

푄 푥 푥 푄 퐿 0 0 0 (푥−푥0)⁄ℎ 0 −(푥−푥0)⁄푒 푄푎푡 = ∫ ∫ 푥푒 푑푥 − ∫ 푥푒 푑푥(14) 퐿ℎ 0 0 퐿푒 푥0

Form any standard integral tables it can be found that

푄 푄 = − 0 [ (1 − 푒−((퐿−푥0)⁄푒)) +  (1 − 푒−(푥0⁄ℎ))] + 푎푡 퐿 푒 ℎ

−(퐿−푥0)⁄푒 푄0푒 (15)

This is the total induced charge in the anode due to trapping.

The signal charge includes both induced and collected charge.

푄푠𝑖푔푛푎푙 = 푄푎푡 + 푄푒(퐿)

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From equation (4)

−(퐿−푥0)⁄푒 푄푒(퐿) = −푄0푒

Therefore, the collected charge cancels the last term of equation (15) and the total signal charge at the anode is equal to:

푄0 푄 = − [ (1 − 푒−((퐿−푥0)⁄푒)) +  (1 − 푒−(푥0⁄ℎ))] 푠𝑖푔푛푎푙 퐿 푒 ℎ

This is the Hecht Equation given in Chapter 3. - Q.E.D.

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Appendix D: Phantom Data

Phantom 1, Front Detector

Phantom 1, Rear Detector

Phantom 1,Count Rate Ratio

217

Phantom 2, Front Detector

Phantom 2, Rear Detector

Phantom 2, Count Rate Ratio

218

219

Phantom 3, Front Detector

Phantom 3, Rear Detector

Phantom 3, Count Rate Ratio

220

Phantom 4, Front Detector

Phantom 4, Rear Detector

Phantom 4, Count Rate Ratio

221

Phantom 5, Front Detector

Phantom 5, Rear Detector

Phantom 5, Count Rate Ratio

222