Master of Science Thesis

Experimental Radionuclide Therapy Quantitative Pinhole planar and SPECT imaging, aiming for dosimetry based on biokinetic modeling and small animal S-values.

Fredrik Henricsson

Supervisor: Sven-Erik Strand,Lund
Department of Medical Radiation Physics Lund University, 2005

ABSTRACT

New radionuclide therapies in humans should be preceded by experimental animal therapies, in order to evaluate the efficacy of the new therapy regime. These experimental studies have to be performed with a reliable and accurate quantification system, with properties that have been evaluated and where possible flaws have been corrected for. The aim of this work was to evaluate the SPECT pinhole collimator high resolution imaging system to investigate the possibilities of using that imaging system as an in vivo activity quantification system in vivo in a small animal model. The pinhole collimated SPECT system used in this study was a Vision SMV DST-XL two head scintillation detector system and a lead pinhole collimator with exchangeable inserts of 3 and 1 mm pinhole diameter. The imaging system was evaluated for sensitivity, contrast, spatial resolution and countrate performance using three different phantoms, a tube phantom, a line phantom and a volume phantom. The different radionuclides used were chosen according to the different calibration measurements and according to the subsequent small animal study. The radionuclides used were 99mTc, 111In and 177Lu. Each of the different calibration measurements were set up with its corresponding phantom mounted on a stand in the center of the rotational axis in the camera geometry. Data acquisition was then performed during 360 detector rotation in discrete steps to obtain a complete data set for tomographic reconstruction. The acquired information was then processed with an iterative reconstruction algorithm in a computer to generate tomographic SPECT images. The reconstruction method used was a cone beam OSEM algorithm. The pinhole SPECT investigation was then followed by an in vivo experiment utilising the knowledge from the earlier pinhole SPECT evaluation. The in vivo studies were based on a tumor model consisting of normal rats inoculated with tumor cells. The rats were injected with about 80 MBq 111In / kg and about 1 GBq 177Lu / kg. The results from the pinhole SPECT studies with the line phantom showed good spatial resolution in imaging with 3 mm pinhole collimator insert with a distance between pinhole aperture and object of 28 mm. The resulting line profile through the image was analyzed, and the resolution was measured to 3.15 mm (FWHM) and the peaks from line sources separated by 4.5 mm were easily distinguished. The measured sensitivity was 3.5 cps/MBq with the 3 mm pinhole insert for 99mTc and 3.1 cps/MBq for 177Lu on the central pinhole axis at a distance of mm from the pinhole aperture. The results from the measurements of the countrate capability of the detector system showed a non-linearity in time which was surprising. Several measurements and analyses suggested this was due to a normalization procedure included in the reconstruction algorithm. This discovery led to the development of a renormalization method to allow the use of the pinhole SPECT technique as a quantification method in future measurements. The activity quantifications in the in vivo measurements showed very good correlation with the activity measurements of the dissected tumors measured in an activity well counter. In conclusion this study has demonstrated the feasibility of using pinhole-SPECT for quantitative in vivo imaging in small animals.

TABLE OF CONTENTS

Abstract. 2 Introduction.. 4 Material and Methods. 6 Results. 12
Pinhole imaging studies. 12 The in vivo study. 20
Discussion 26 Future work. 27 Acknowledgements. 28 References. 29 Appendix.. 31
Scintillation camera properties 31 Theory of pinhole SPECT imaging. 32

INTRODUCTION

To examine the therapeutic effect of a new radionuclide therapy procedure for patients, one should first evaluate corresponding results in a similar experimental animal therapy setup. The results must then be analyzed, calculated and used in a dosimetry model to examine and evaluate the therapeutic effect. To get quantitative results for biokinetics and radiopharmaceutical distributions, high resolution in vivo scintillation images supplemented with activity measurements of dissected organs should be performed. High resolution in vivo SPECT (single photon emission computed tomography) images can be acquired using scintillation camera system with a pinhole collimator for quantitative studies. The results can then be processed in dose calculations where small animal S-values must be used to include the effect of cross dose from long range beta particles. Pinhole SPECT is a method of imaging an object in cross-sectional images (tomography) over a small field of view with high resolution. For more details on the imaging system see appendix 1. Evaluation of imaging systems based on a scintillation camera equipped with a pinhole collimator to be used in small animal studies or other examinations where a small field of view is required has been performed by several groups where the results showed good applicable use of the pinhole SPECT small structure imaging technique (S-E. Strand et al 1994, S-E. Strand et al 1993, J. Palmer et al 1989, B.T.A. McKee et al 1997, N. Schramm et al 2000, T. Zeniya et al 2004, F. Garibaldi et al 2004). The purpose of this work was to examine the possibilities and the disadvantages of a scintillation camera system coupled to a pinhole collimator to be used in small animal biokinetic studies. The aim of the pinhole SPECT calibration procedure was to investigate the important SPECT imaging factors i.e. the camera spatial resolution, sensitivity, efficacy and its properties in countrate performance. It has also been shown (D. Bequ et al 2004) the importance of the imaging geometry, the source camera positions in the SPECT system, to be able to minimize the errors and artifacts in the reconstructed images, which had to be taken in consideration during the calibration measurements. To generate the tomographic images from the sampled irradiated projections, a reconstruction program is needed. In pinhole SPECT, a FBP (filtered back projection) or an OSEM (ordered subset expectation maximization) algorithm is often used. It is important to gather a complete set of SPECT data to generate high quality tomographic images without any image artifacts, which has been shown by T. Zeniya et al 2004. A 360 rotation of the detector head round the object is often used to be able to sample the projections at many different angels and has been considered to generate a complete set of data for tomographic reconstruction. A rotation sequence of less then 360 can though be used successfully, but with a lower degree of image quality due to less sampled irradiated projections (angels). This will increase the grade of noise in the image if the number of projections is reduced. To examine the radionuclide distributions in vivo, the possibility of using high resolution pinhole SPECT and pinhole planar imaging to quantitatively evaluate the activity uptake in different regions of interest was investigated. The goal in the in vivo study was to evaluate a procedure for small animal dosimetry based on high resolution pinhole imaging. The biokinetic modulation in pretargeting experiment combined with ECAT (Extracorporeal Adsorption Treatment) was studied in brown Norwegian rats. To investigate biokinetics and the distribution of the radiopharmaceutical, the study was initiated with a series of experiments where blood analysis and dissection where performed and analyzed, to generate the biokinetics in the rat. After analysis of the experiment results, a new set of experimental set ups where constructed where evaluation of immunoradiotherapy combined with the former 4 4

studies where done, with the purpose to investigate effects on tumor growth or reduction. As a complementing quantification tool in activity determination in different organs in the rat instead of dissecting and measuring in an activity counter, pinhole SPECT was thought to be an exceptional technique to use. This imaging technique would not only be of use in determine the activity content, but also a possible way of determine the geometrical activity distribution within the target area. This would be possible regarding pinhole SPECTs properties of generating a high resolution image magnified from a small field of view. N. Schramm et al. 2000, describes a system of ultra high resolution detector system with pinhole collimator that can be used in small animal SPECT, which has an exceptional resolution and good sensitivity, and would be a promising tool to use in determination of activity distribution in small animal studies. Other groups has also shown that pinhole collimated SPECT generates excellent high resolution images over a small field of view, thus the imaging technique is well suited for small animal studies (K. Ogawa et al 1998, J.B. Habraken et al 2001).

MATERIAL & METHODS

PINHOLE IMAGING STUDIES The camera characteristics investigated for pinhole imaging was spatial resolution, noise, sensitivity and count rate capability. The scintillation camera used was a Vision SMV DSTXL dual head scintillation camera system. The collimator used in the calibrations and the study measurements was a lead pinhole collimator with two pinhole insertions of diameters 1 and 3 mm. The radionuclides used in the different studies where 99mTc, 177Lu and 111In (only animal study). Energy window was set to the following parameters.

99m 177

Tc Lu 111 In (animal study)
: 140 keV 20 % window : 115 keV 20 % window, 209 keV 15 % window : 172 keV 20 % window, 247 keV 20 % window
The matrix size was 128128 pixels and the pixel size was measured, according to the camera zoom, to 2.84 mm/pixel. Calibration of the scintillation camera was performed with three different types of phantoms. One designated tube-phantom was used for sensitivity and noise measurements, one line-phantom was constructed to measure the system resolution of the system and one volume-phantom was constructed to analyze the ability within the camera to keep linearity between activity and count rate over time. The different notations in the columns of Table 1 represent the volume phantom (V), the tube phantom (T) and the line phantom (L). These phantoms are described more in detail later in this chapter.

Table 1. The measurements and its corresponding activity and phantom, in the calibration studies. L is the line phantom, T is the tube phantom and V is the volume phantom.
Measurement Spatial Resolution Noise Sensitivity Countrate Performance

Radionuclide

99m 99m

Phantom

Tc / 177Lu

L T V V

Tube phantom (T) The tube phantom was constructed using fifteen 3 ml plastic tubes. The tube diameter was about 1.5 cm. The black marked tubes in Figure 1 were filled with 40 MBq/ml 99mTc solution and the grey tubes were filled with 20 MBq/ml 99mTc solution. The rest of the tubes were empty and were used to separate the activity sources by equal distance of 1.5 cm. The 15 plastic tubes were combined according to Figure 1 to constitute the phantom.
Figure 1. Tube phantom consisting of fifteen plastic tube filled with different amount of 99mTc.
Line phantom (L) The line phantom was constructed from a plexiglass rod. The plexiglass rod was made to have about the same dimensions as a rat, with 35 mm diameter and an axial length of 80 mm. The rod was drilled axial with 7 equally spaced parallel holes. Each hole was 2.5 mm in diameter and was drilled with 2 mm space between them. The phantom can be seen in Figure 2. In these holes a capillary of 700 mm of total length and a diameter of 2 mm was inserted which was filled with a total activity of about 100 MBq 99mTc solution. Thus there was an activity concentration of 81 MBq/ml and 1.2 MBq/cm.
Figure 2. Line phantom with parallel channels to be filled with activity solution
Volume phantom (V) The volume phantom was constructed from six identical plastic boxes, attached together into a large box as in Figure 3a and 3b. Each box measures 142424 mm3. These plastic boxes are hollow and able to be filled with approximately 4 ml of activity solution. In the countrate performance study, the volumes were filled with different amounts of 99mTc activity in each 4 ml boxes, as given in table 2.

Activity (MBq) 100 50

Box 5 6
Figure 3a. Volume phantom with boxes attached according to figure 3b.
Table 2. Activity of 99mTc In the different phantom boxes
Figure 3b. Box position in the volume phantom
The different phantoms were constructed in such small dimensions to fit the rat fixation tube. This plexiglass tube was to be mounted on an experimental stand constructed to fit the SPECT imaging setup with the rotating two head scintillation camera system. The experimental setup with the rat fixation plexiglass tube is shown in Figure 4.
Figure 4. Experimental rat fixation tube with a rat positioned for pinhole SPECT imaging
The scintillation camera was set up with the following parameters during the tests to define the experimental setup geometry for the reconstruction program. The pinhole crystal distance (a, see figure 1 in appendix) was 302 mm, distance between crystal surface on the camera heads, measured to 638 mm, and indicated radius after parking of the gantry (starting position) was 280 mm. When calibrating for SPECT, 2 different pinhole diameters were tested, 1 mm and 3 mm. The projection angles where set to (360/128) per angle, and the sampling times varied between 10 to 30 s per angle. The reconstruction program used in the pinhole SPECT studies was a cone beam OSEM reconstruction algorithm. This is an algorithm used for cone beam computer tomography in pinhole SPECT. No scatter or attenuation corrections were made in this study.

COUNTRATE CHARACTERISTICS To investigate the countrate characteristics of the pinhole SPECT system the volume phantom was filled with 99mTc in the different boxes with activity content according to Table 2 and Figure 3b. The boxes were filled with different, known amounts of activity to state the countrate abilities and possible camera countrate abnormalities in both high activity regions as in low activity regions. The volume phantom was mounted on a stand positioned in origo of the SPECT rotation geometry, CORi, in the camera. The 3 mm diameter pinhole insert was used with a radial distance between pinhole and object (b, see figure 1, appendix 1) of 28 mm. The sampling procedure used was a step-and-shoot procedure where the number of projection angles was 128 in 360 total sampling rotation. Sampling time per angle was set to 10 sec. The sampled projections were then processed in the OSEM reconstruction algorithm to generate tomographic images. When investigating the countrate characteristics of the camera, the results showed an abnormal behavior in the reconstruction algorithm which had to be taken in consideration. The reconstruction problem in renormalization of the tomographic images had to be solved, and a normalization method in re-calculating the images was developed. The normalization factor was calculated by dividing the sum of the total counts in all projections with the sum of the total counts in all tomographic images, according to Equation 1.
In Equation 1, denotes count rate density in the tomographic ROI, denotes count rate density in the projection ROI and is the normalization factor. Both ROIs are set to confine the whole phantom in the study.
IN VIVO TUMOR BIOKINETIC PINHOLE SPECT MEASUREMENTS One study for diagnostic purposes was performed. The radionuclide used was 111In, a radionuclide with a physical halflife of 2.8 days. In this study a rat was SPECT imaged 6 hours post injection of Streptavidin-111In to analyze the activity uptake, the possibility of determination of tumor size and the geometrical activity distribution in the tumor. The results from this measurement were then to be compared with measurements of the dissected tumor. The second study was a radioimmunotherapy study where 177Lu-Streptavidin was injected in rat after pretargeting with the antibody BR96-1033. 177Lu is a radionuclide with a physical half-life of 6.7 days and a maximum energy of 498.3 keV (I (%) = 78.6). A set of measurement series of pinhole SPECT imaging was setup to investigate the possibility of generating quantitative information of the activity distribution in regions of interest. The results of these measurements were then to be compared to biokinetic information obtained

COR - Center of rotation

from activity measurements of dissected organs and tissues. To sample information to generate the biokinetics, blood sampling and planar scintillation imaging was performed at 3, 6, 9, 12 and 24 hours post injection of Streptavidin-177Lu. To be able to verify the absolute activity content of different tissues, the animals were dissected at times illustrated in Figure 5. These results from activity quantification from dissections were later to be compared with measurements with the pinhole SPECT imaging. The rats were imaged with pinhole SPECT 5 times through 7 days. First imaging procedure was 6 hours 57 min post injection, second 19 hours 37 min p.i., third 27 hours 2 min. p.i., fourth 68 hours 30 min p.i. and fifth 164 hours 45 min. p.i. This procedure is illustrated in Figure 5. Every projection time was set to 15 seconds and every rotation angle was set to 360/128 degrees. The in vivo model being used was BN rats inoculated with BN7005 rat colon carcinoma cells. Pretargeting with antibody BR96 coupled to the molecule 1033 was performed. The rats were intravenously injected with DOTA-Streptavidin labeled with 111In and 177Lu. Extra corporeal adsorption treatment (ECAT) was performed using a pump with a set of capillaries surgically operated into the rat artery and vein and attached to a filter column, to be able to filtrate the blood plasma from circulating not targeted antibody. To perform the biokinetic study with pinhole SPECT imaging, Vision SNV DST-XL dual head scintillation camera system with pinhole collimator was used with adjustments according to prior calibration measurements. The time points of the experimental therapy set up were performed according to Figure 5.
Figure 5. Illustrated timescale of the experimental radionuclide treatment therapy study

RESULTS

PINHOLE IMAGING STUDIES Measurement of SPECT noise The noise was measured with the tube phantom. The reconstructed tomographic images from the pinhole SPECT measurements with the tube phantom are shown in Figure 6. A line profile of the signal (countrate) variation over two different tubes (Hi/Low activity content) has been applied. This was made according to Figure 6.

Figure 6. Illustration of the line profiles drawn through hi- and low- activity tubes in the tomographic images. Left imaged with the 3 mm pinhole insertion and right imaged with 1 mm pinhole insertion.
It is shown in Figures 7 - 10 that there is a less degree of count variation in the phantom imaged with 3 mm pinhole diameter. Figures 7 and 8 are line profiles of the tube phantom, applied according to Figure 6, imaged with the 3 mm pinhole insertion. The line profiles in Figures 7 and 8 shows a smooth profile shape with a less degree of count/pixel variation (noise), relative the images imaged with the 1 mm pinhole diameter. The line profiles in Figures 9 and 10 shows a more irregular shape of the profile and a higher variation of the count/pixel values within the tubes. This is due to a higher degree of noise in the tomographic images generated from imaging with 1 mm pinhole diameter.
Hi activity tube - 3 mm pinhole ins.
Low activity tube - 3 mm pinhole ins.
Figure 7. Line profile of the count/pixel variation through the reconstructed image according to Figure 7. Line profile of the high activity tube imaged with 3 mm pinhole insertion
Figure 8. Line profile of the count/pixel variation through the reconstructed image according to Figure 7. Line profile of the low activity tube imaged with 3 mm pinhole insertion.
Hi activity tube - 1 mm pinhole ins.
Low activity tube - 1 mm pinhole ins.
Figure 9. Line profile of the count/pixel variation through the reconstructed image according to Figure 7. Line profile of the high activity tube imaged with 1 mm pinhole insertion
Figure 10. Line profile of the count/pixel variation through the reconstructed image according to Figure 7. Line profile of the low activity tube imaged with 1 mm pinhole insertion.
The 3 mm. pinhole collimator insertion was chosen for further studies because of the lower noise. From the results of measured line profile and as seen in figure 6, the image quality (according to noise reduction) was sufficient better as the 3 mm pinhole insertion was used.
Measurement of camera sensitivity The pinhole SPECT camera sensitivity was measured with the volume phantom. The box cavities were filled with a known amount of activity and was imaged in origo of camera SPECT geometry, COR (center of rotation). The object was imaged with a fix indicated radial detector head distance of 340 mm and a pinhole diameter of 3 mm. The phantom was imaged accordingly, and with knowledge of activity content in phantom and the corresponding countrate from the images, the sensitivity was calculated. Pinhole SPECT Camera sensitivity measured with 99mTc and 177Lu: 3.5 cps/MBq (99mTc) 3.1 cps/MBq (177Lu) Measurement of spatial resolution The study of the spatial resolution was performed using an activity concentration of 81 MBq/ml 99mTc in the line phantom. The scintillation camera was able to resolve small structures as 1 mm, as seen in figure 11, which was very easily visualized as separate capillaries in the reconstructed tomographic images. With knowledge of former measurements on the countrate variation through a SPECT image of the phantom, it was decided, according to the noise, to only use 3 mm aperture in further measurements. These measurements were made with pinhole diameter of 3 mm and with an indicated radial detector head distance of 340 mm. The results from these measurements are shown in figure 11 and 12.

Figure 11. Reconstruction of the line phantom. The center of the capillaries are spaced equally in intervals of 5 mm, with inner and outer diameters of 1 mm and 2 mm.
Figure 12. The line profile according to the line drawn in figure 8, showing the count/pixel variation through the reconstructed image. The FWHM is 3.2 mm.
The results from the analysis of the count per pixel line profile can easily be separated as individual peaks. The full width at half maximum (FWHM) is measured to be approximately 3.2 mm. Analyzing Figures 7-10, it can be discovered that 1 mm aperture was generating higher resolution images, but with further study, it was decided to use the 3 mm aperture regarding the high noise and the irregular shape of the image profiles generated by the 1 mm aperture. The 3 mm pinhole diameter was discovered to generate high resolution, low noise and good contrasts of the tomographic images, and the used radial detector head distance was enough to generate images of useful FOV to get the enlargement of the capillaries. Measurement of camera count rate statistics The reconstructed images from the volume phantom (Figure 13) showed very good visual image quality.
Figure 13. Planar pinhole projection image (left), and the tomographic image reconstructed approximately from information from the transversal slice indicated by the white line
As they were imaged with constant time intervals, it was expected that the count rate density within the picture matrices would follow an exponential decay. With identical ROI measurements during the image series, it was discovered that the countrate density, which is directly related to the activity, in the reconstructed images did not follow that relationship. The relation between measured countrate density in ROIs and corresponding activity is shown in Figure 14, where the blue line is the measured countrate density and the red line is the expected normal behavior of the countrate density. This phenomenon was then further investigated in different measurements where the measured countrate as function of time was studied. The results showed that the reconstructed images were never correlated to an exponential decay relationship.
9000 Measured Countrate / cps 350 Activity / MBq Countrate Expected countrate

Figure 14. Measured ROI countrate density in series of tomographic images as function of corresponding activity and the expected behavior of the graph.
In Figure 15, the result of the effect of the renormalization in the reconstruction algorithm can be seen. The reconstruction program has generated different normalization factors at different time points to scale the images with. (for more details see discussion). In Figure 15, the normalization effect results in that the count rate relation has a high positive gradient at the first hours, which then tend to decrease to negative values at later time. These results are not expected as the count rate-activity relation should be linear. After identification of the reconstruction problem, the information of projections and reconstructed tomographic images were gathered, to compare the differences. The calculation procedure had to be done for all the measurements, if a quantification of the signal content in the tomographic images was to be studied. The calculations were made according to Equation 1. If the normalization factors are used for all the reconstructed images, the true countrate for every tomographic slice can be created as it would appear if the reconstruction algorithm was correct from the beginning. The results of a corrected countrate in a tomographic image (with activity content) are shown in Figure 17. In Figure 15 the activity content in the tomographic image # 50ii corresponds to about 750 MBq at time t = 0 and the activity content in the tomographic image # 80iii corresponds to 200 MBq at time t = 0. After correcting the measured count rates, the results in Figure 18 were obtained and a linear relationship between measured countrate and activity was found.

ii iii

Notation of a tomographic slice with high activity content, see Figures 15, 17 and 18 Notation of a tomographic slice with low activity content, see Figures 15, 17 and 18
18000 Measured Count rate / cps 16000 Count rate / cps 400 Activity / MBq Tomografic image #50 Tomografic image #600 700

30 Time / h 60

Figure 15.Uncorrected measured countrate as a function Figure 16. The sum of counts in total number of projections of activity in two reconstructed slices as a function of time. Also show the theoretical exponential decay relaxation

2,1,0,120

Upptake (% I.D./g) in tumor (ROI) in tomographic SPECT image Uptake (% I.D./g) in dissected tumor

Tumor Uptake % I.D./g

Time P.I. (h)
Figure 26. Correlation between measured and calculated uptake in tumor ROI in tomographic PSPECT images and measured activity content in dissected tumorsiv.
A mean value of three different animals was used on the data points.

DISCUSSION

Pinhole SPECT imaging in small animal studies has been evaluated and verified to be of great value by many research groups (S-E. Strand et al 1994, K. Ishizu et al 1995, J.B. Habraken et al 2001). This technology has potential of generating very high resolution tomographic images over a small field-of-view, which is very desirable in small animal studies. This work has shown that a proper evaluation of the pinhole SPECT camera system must be performed if the imaging system is going to be used in i.e. biokinetic and dosimetry models, where organ uptake and activity quantification is of great importance for the study. In this work, a use of the pinhole SPECT imaging system as an activity quantification system without proper investigation of the SPECT camera imaging system properties, could have been misleading in the following in vivo studies. Because of the abnormal behaviour in the reconstruction algorithm, a analyze of the generated tomographic images would give wrong activity content, relative the actual activity content, in the target organ, which would complicate future dosimetry calculations. By investigating the pinhole SPECT camera it is possible to develop a correction method when the problem has been identified. When the correction calculations has been applied in the imaging process, the pinhole SPECT camera is a reliable and very useful imaging tool to use in further in vivo studies. In this work, the camera countrate problem had to be considered and investigated. THE COUNTRATE PROBLEM At first, the scintillation camera properties of imaging at high countrate were thought of being the main problem after investigation of the dysfunctional countrate behavior in the reconstructed SPECT images. About 1 GBq of total 99mTc activity was used in the volume phantom, which could be a problem with deadtime and pileup effects within the camera system. After consulting documents on the Vision SNV DST-XL scintillation camera, it was believed that the scintillation camera should not have any difficulties of imaging at the present countrate. When the gathered projections alone were examined, they showed as expected, an exponential decay relation. Further investigation suggested possible problems with the reconstruction algorithm. These problems were suggested with the knowledge of expected results from the projections and the strange behavior in pixel values of the reconstructed tomographic images. Studies of the signal variation in the image matrices led to believe that the reconstruction algorithm had a build in function to renormalize every pixel values in all image matrices of the reconstruction. A probable theory of the renormalization problem in the reconstruction program was discovered. The iterative processes which are governed by the reconstruction algorithm are generating a reconstruction volume in three dimensions, V(x,y,z), in which the results from the calculation processes are stored. These iterative calculations, in this case OSEM, are products of a three dimensional pixelcount function and a multi dimensional probability function, which depends on the constructed volume geometry and the collected projection characteristics. How the functions are exactly implemented and operating in OSEM is not known. The computer workstation program is set to work with 16 bit max information per pixel. However, the true usage of every pixel is only 15 bit, hence the maximum pixel value is 32677 (0-32677). It seems that the reconstruction program in every way normalizes the iterative functions as it should in different measurement situations and different geometries, but it chooses to scale the generated results (voxels) with a value to get as good numerical dynamic proportion within the image matrix as possible. This process function in the reconstruction algorithm is hard to fully understand, because of the lack of generated information from the program after a reconstruction process.

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APPENDIX

SCINTILLATION CAMERA PROPERTIES
The scintillationcamera consists of a 3/8 inch NaI (Tl) crystal coupled to a light guide and photomultiplicator (PM) tubes. The PM-tubes are then connected to electronics and ADconverters. Every event in the crystal representing interaction with incident radiation will generate scintillation light which will generate pulses of different amplitude from all adjacent PM tubes. The PM tube closest to the event will have the highest pulse amplitude and the other surrounding tubes will have degraded pulse amplitude, which magnitude will be proportional to the distance (squared) to the interaction event. The center of light emmitance amplitude is then interpolated from the nearest PM tubes, through a couple of calculation processes to generate the resulting analog signal, which is then digitalized by a fast AD converter and in the end accumulated as a pixel value in a two- dimensional matrix. The total spatial resolution properties of the scintillationcamera are divided into three parts according to equation 1. The intrinsic resolution, Ri, is governed by the electronics and the detector quantum efficiency, which describes the scintillation light exchange of the multiple interactions in the crystal. The geometrical collimator resolution, Rc, is the dominating part of scintillation camera resolution. The collimator resolution is only dependent on the geometrical properties and the construction of the collimator. The last part, Rs, is due to scattering within the patient or object geometry.

2 Rtot = Ri2 + Rc2 + Rs2

To measure the spatial resolution of a scintillation camera, it is custom to analyze the measured point spread function or the modulated transfer function (MTF). This function is the absolute value of the Fourier transform of the point spread function and describes the camera ability to generate an image from modulated information received by the detector from the object. If an infinitesimal narrow beam of photons is exposed to the camera, the scintillation camera would modulate the information and generate a Gaussian profile over the source in the resulting image. This phenomenon is governed by the statistics in the camera electronics and physical interaction properties. The modulation transfer function is a more accurate way to describe the camera resolution.
THEORY OF PINHOLE SPECT IMAGING
COLLIMATOR CHARACTERISTICS To explain different characteristics of the pinhole collimator, it is convenient to know certain parameters to describe the geometry. The different parameters within the pinhole collimator geometry are illustrated in figure 1.
Figure 1. Geometry of the pinhole collimator
To understand the characteristics of the pinhole imaging system, the following parameters in text has to be considered. The distance from crystal surface and pinhole aperture - a, distance pinhole aperture to object b and the radial distance from the center line perpendicular to the surface through the pinhole aperture - , according to figure 1. Further on, the smallest distance between two small point sources that the collimator can resolve as two points in the image, denotes Rg. This parameter is commonly measured with a line profile through the image, where full with at half maximum (FWHM) is studied. If we reduce the distance b (see figure 1), the camera axial radius is also reduced and it will result in a better spatial resolution in the image. The resolution and sensitivity for different pinhole-object distances (b) have been evaluated by DP McElroy et al (2002). The effect of an increased spatial resolution is thus on cost of a smaller FOV. When distance between the object and the pinhole is reduced, a reduced area of the object is projected against the crystal. This effect is due to the cone formed construction of the collimator. This phenomenon can be described according to equation 2.

FOV b a

To describe the resolution properties of pinhole collimated scintillation camera systems, a couple of geometric parameters need to be defined. As shown in figure 1, , and defines the three spherical space coordinates, where defines the azimuthally angle and represents the angle relatively the central axis of the pinhole collimator.

(a + b) d e

b R0 = R + Ri + Rs2 = a
(a + b )2 d e2 + b 2 Ri2 + a 2 Rs2

de = d +

d d e

0 d /2

L ( , , )
Equation 3 expresses how the spatial resolution is dependent on the efficient pinhole diameter (de), the detector crystal surface to pinhole length (a) and the pinhole to object length (b). The variables de and b can be modified to alter the geometrical collimator resolution. The intrinsic spatial resolution, the geometrical collimator resolution and the factor due to scatter in the object are then combined to express the total resolution properties of the scintillation camera system in equation 4. As seen in equation 5 and 6, the effective diameter (de) of the pinhole insertion is influenced by the geometrical properties and has a significant part in the geometrical efficiency of the collimator. The pinhole resolution is then to be described through equation 5 (effective diameter) and its geometrical efficiency from equation 6. Planar imaging with scintillation detector system combined with a pinhole collimator is an excellent instrument to use if small structures within an object are to be imaged. The geometry of the collimator provides a magnification effect of the object. One disadvantage of the pinhole collimator is the reduction of field of view (FOV), which is an effect of the cone formed shape of the collimator. The view that the crystal in the detector head will see is small, compared to other types of detector configurations, that is, other types of collimators i.e. parallel hole collimators. The pinhole collimator has one small hole, which effective diameter (de)v which sets the crystals view of the object. In exchange of the reduced FOV, the object in the image is magnified. The camera sensitivity is strongly angle dependent and decreases in radial direction from the collimator central axis as seen when imaging a plane flood source. This angle dependence originates from the geometry of the pinhole collimator. Another effect is the phenomenon of depth of interaction (DOI) occurring at locations (according to the probability distribution)