On the usage of a photon counting CT detector for SPECT

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On the usage of a photon counting CT detector for

SPECT

Måns Andersson

mansande@kth.se

SA104X Degree Project in Engineering Physics, First Level

Supervisor: Martin Sjölin

Department of Physics

School of Engineering Sciences

Royal Institute of Technology (KTH)

Stockholm, Sweden

TRITA-FYS-XXXX

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Abstract

This work explores the possibility of using a photon counting silicon detector devel-oped for Computer Tomography (CT) in Single Photon Emission Computed Tomogra-phy (SPECT) applications. This would allow for a more versatile and a much cheaper system. The main focus is on determining the efficiency and resolution of such a system. This is done initially via an geometric model evaluating the solid angle of the collima-tor, showing promising results versus a standard Low Energy High Resolution (LEHR) collimator. Secondly a Monte-Carlo simulation is used for a more in depth analysis of the detector response by using two different radionuclides. The performance is measured with reference to efficiency and scatter to primary ratio (s/p). The energy thresholds for binning is evaluated with a Signal-Difference-to-Noise Ratio (SDNR). A Point Spread Function (PSF) is simulated with and without the impact from a human-like phantom. The work concludes that an implementation would not likely to be able to compete with specialised myocardium SPECT due too the high noise from the detector response when a high efficiency threshold is set. Further investigations in general SPECT applications is recommended.

Sammanfattning

Detta arbete undersöker möjligheten att använda en fotonräknande kiseldetektor des-ignad för datortomografi (CT) med Single Photon Emission Computed Tomography (SPECT)-tillämpningar. Detta skulle tillåta ett mer flexibelt och ett mycket billigare system. Fokus är att bestämma effektivitet och upplösning från ett sådant system. Detta görs inledningsvis genom en geometrisk modell som undersöker rymdvinkeln för detek-torkollimatorer. Den geometriska modellen ger lovande resultat för kollimatorerna jäm-fört med Low Energy High Resolution-kollimatorer (LHER) vilka är standard för SPECT. Efter detta görs en mer grundlig analys av detektorns respons för två olika radionuklider. Detektorprestandan undersöker effektivitet och scatter to primary ratio (s/p). Energi-gränser (thresholds) för klassificering av detektioner görs med avseende på en Signal-Difference-to-Noise Ratio (SDNR). En Point Spread Function (PSF) Arbetet visar att en implementation antagligen inte skulle kunna konkurrera med specaliserade myocardium-SPECT på grund av högt brus från detektoresponsen när en hög effektivitetströskel är vald. Fortsatta undersökningar i generella SPECT-tillämpningar rekommenderas.

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Chapter 1 Introduction

1.1 Medical imaging

Medical imaging enables assessment of both anatomical and functional information. Ex-amples of anatomical imaging is Computed Tomography (CT) and Magnet Resonance Imaging (MRI). Functional imaging is methods for visualisation of physiological processes in vivo (in the body), the most common methods are Single Photon Emission Tomogra-phy (SPECT) and Positron Emission TomograTomogra-phy (PET), which are collectively called Nuclear Medicine [13]. The basic theory of CT is simple, a x-ray source produces a flux of photons, the flux will attenuate depending on the object. Several projections with the mean attenuation of the cross section of the object, is produced at different angles. This is stored in an sinogram which can be transformed with the inverse Radon transform into a 2D image [6]. In Nuclear medicine on the other hand there is no external photon source, instead the patient is injected with a tracer radionuclide which emits a low flux of photons at a given energy, collimators are used to get information about the spatial origin of the x-rays. In myocardial perfusion imaging (blood uptake in the heart muscle) the tracers lipophilicity (dissolves in fat) allows it to be distributed proportionally to the myocardial blood flow, this distribution is then possible to image by collimating the γ-rays. Depending on the examination various traces can be used with different photon energies, most myocardium related examinations use 99m_{Tc which decays with 140.5 keV}

photons [13].

1.2 Background

At KTH, the Physics of Medical Imaging group has spent years developing a photon-counting spectral silicon detector for CT. This detector is, in contrast to other CT detec-tors able to count individual photons which is necessary for applications such as nuclear medicine. Traditionally SPECT uses detectors with materials with high fraction of inter-actions being photoelectric [12]. There is often a ±10% energy window around 140 keV that is accepted to be unscattered, the probability of photoeffect in traditional NaI(TI) detectors is around 83% and the detectection rate is said to be 70.65% for a 5 cm thick

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detector [4]. The semiconductor cadmium telluride (CdTe) and cadmium-zink-telluride (CZT) are more recent candidates for SPECT detectors. Silicon have a higher fraction of Compton interaction, so looking for photoelectric peak is probably not a good solution. One would instead hope that every true photon would interact several times and that the energies would add up to a around the emitted energy. This method demands that the interactions occurs in relative closeness since it is impossible to know in which order the interactions happen, and thus where the first interaction was and how the data should be counted. Another possibility is that the distribution of detected energies from scattered photons are significantly different to those of unscattered.

The collimators are designed to decide the inclination of photons onto the detector. They are made out of a high Z material, in this case tungsten, because of the high probability of photoelectric interactions in such materials. There are different designs of collimators which creates different data to reconstruct with. On this particular detector there is a fan beam collimation, allowing images larger than the object to be obtained on the detector.

In this work, a »true photon« is defined as a photon which has not scattered in the object and the first interaction is a Compton interaction or photoelectric effect in the silicon of the detector. This is considered a photon which is supposed to produce the image. A »false photon« on the other hand is a photon that has interacted in the collimators or in the object before interacting with the silicon, the information is thereby assumed to be lost. When a photon is detected and classified it is an event.

The earlier mentioned 99m_{Tc is the most commonly used tracer for perfusion imaging}

whith 140.5 keV γ-rays. Tl-thallous chloride 201Tl was the most used tracer of early nuclear imaging and decays with 68-80 keV x-rays and higher energy γ-rays [13, 11]. The decay distribution will be approximated to 70 keV for proof of concept. Both tracers have medicinal strengths and weaknesses compared to each other; however, only the photon energy differences will be analysed [11]. The results from the 201_{Tl-tracer is found in the}

appendix.

1.3 Possibilities

A combined CT and SPECT is an attractive solution for enhanced versatility and a lower cost. This has successfully been done clinically with a traditional integrating CT, these solutions are combinations of two different systems, a CT-system connected with a SPECT-system into one apparatus [10, 8]. Some work using dual purpose detectors have also been done, but only in early prototyping stages. A High Purity Germanium (HPG) system [9], and a CdTe system [1] have been proposed. A more recent CZT system has working clinical dual purpose system; however, the CT is not of diagnostic quality, it is only designed for attenuation correction [15]. A CT image can be used for spatial local-isation, usually the images are superimposed for easier diagnostics [14]. A CT/SPECT with the ability to produce CT images with diagnostic quality, attenuation correction and spatial localisation with only one detector is therefore very interesting.

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1.4 Limitations

The loss in effective detector area used when closing the iso-to-detector distance is not discussed in this thesis; however, it is a major point of concern for any type of similar systems.

1.5 Objective

This project aims to evaluate the feasibility of using a photon counting CT-detector in SPECT applications, evaluate detector characteristics and if feasible propose further subjects of investigation.

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Chapter 2 Methodology

Initially the physics of interactions and the detector is explained. An analytic model is introduced to evaluate the geometric Point Spread Function (PSF), its Full Width Half Maximum (FWHM) and the geometric efficiency. To analyse the detector re-sponse a Monte-Carlo simulation is developed in MATLAB. The rere-sponse is evaluated with a Signal-Difference-to-Noise Ratio (SDNR), together with a system efficiency and a PSF.

2.1 Photon interactions (Scattering)

Compton scattering is an incoherent type of scattering where a photon interacts with an electron from an outer layer of an atom. The electron is assumed to be in rest which is generally not the case for electrons in room temperature, giving an error in the simulation called »Doppler broadening«. The scatter angle is energy dependent and follows the Klein-Nishina distribution [7]:

dσ dΩ = re 2 1 (1 + k(1 − cos ω))2 1

1 + cos ω + 1 + k(1 − cos ω) − sin

2_ω

(2.1) Where k = _mecE2, E is the photon energy and me the electron mass. Notice that it is

defined with respect to the solid angle dΩ = 2π sin ωdω. For Rayleigh scattering, a coherent type of scattering, the scatter angle follows the distribution:

dσ dΩ = re 2 1 + cos 2_ω (2.2) The azimuthal angle is assumed to be evenly distributed in both Compton scattering and Rayleigh scattering.

The probability of scattering is material and energy dependent. NIST-data is used to find µm(E), the linear attenuation coefficient [2]. The probability of a photon of energy

E to be transmitted without any type of interaction through a material with the total linear attenuation coefficient µm and distance x:

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The probability of an interaction i is calculated by: Pi =

µi

µphoto+ µCompton+ µRayleigh

(2.4) This is still energy and material dependent. In photoelectric interactions the entire photon energy is deposited. Energy deposition from Compton scattering is found to be: Edep(ω, E) = E 1 − 1 1 + k(1 − cos ω) (2.5)

2.2 Detector and gantry geometry

The model gantry is based on a commercial scanner (GE Lightspeed VCT). The source-to-iso-center is 541 mm and the source-to-detector distance is 949 mm. However to be able to use the built-in collimators for SPECT, the iso-to-detector distance has to be lowered in order to get a high enough resolution [3]. This project assumes a perfect patient table that follows the detector keeping the detector-to-iso distance at 200-250 mm. The collimator septa are 0.1 mm thick. The length of the collimator from the detector is 32 mm. The bulk of silicon is 39 mm thick and it is separated in the rotational direction by equally thick collimators. There is no collimation in the axial direction inside the detector. The distance between collimators are 1.2 mm in width (rotational) and 2.5 mm in height (axial), this area is considered to be one pixel.

2.3 The Geometric model

An analytic model for a quick evaluation of detector parameters is presented here, the aim is to produce a PSF and a measurement of the efficiency of a detector. This is done by calculating the solid angle of all pixels. This is done purely geometrical, it is assumed that the collimators are 100% efficient and that the detector is ideal.

Ω = Z Ω dΩ = Z θn 0 sin θ0dθ0 Z φm 0 dφ0 (2.6)

This model does not use the depth of the detector or the fact that the collimators pen-etrates different depths of the detector. The pixels solid angle is divided with the solid angle of a sphere (4π) to get a measurement of the possibility of a photon hitting the pixel in question. The model uses spherical coordinates:

The detector can be represented with two matrices C (collimator tip) och D (detector surface). The source is denoted as S (this can be assumed to be the isocenter). It is assumed that m, n are pixels in a M × N - sized detector. Symmetry is used to simplify the geometry, assume the coordinates and geometry given the figure below.

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Figure 2.1: The method for evaluating the solid angle of the collimator.

φm = arccos (

(C(m)− S) · (D(m+1)− S)

||C(m)− S|| ||D(m+1)− S||

), (2.7)

The same principle is used in the axial direction, θn = arccos (

(C(n)− S) · (D(n+1)− S)

||C(n)− S|| ||D(n+1)− S||

). (2.8)

Each time the angle starts to increase the vectors must have passed each other and the solid angle is zero. This creates an intensity matrix with each position being a pixel, this is the same as the geometrical PSF.

P SFm,n =

φmsin(θn)

4π . (2.9)

The total probability of a photon hitting any pixel in the detector array is defined as the System Geometric Efficiency (SGE):

SGE =

M,N

X

m,n

P SFm,n (2.10)

2.4 The Monte Carlo-model

To evaluate the more fine aspects of the system behaviour a Monte-Carlo simulation is performed. The spatial accuracy of the simulated photon paths is one tenth of the collimator thickness (10 micrometers). The photon and the interaction energies are ap-proximated with increments of 0.5 keV. The program follows one photon at the time,

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from the γ-decay source in the object to the detector. The object is modelled as an el-liptic cylinder (15 cm x 20 cm x 10 cm) using soft tissue with attenuation characteristics from NIST [2]. For each interaction, the type of interaction is determined by a random process based on the probabilities described in Section 2.1. A binary search is used to determine photon positions in the detector geometries.

The time resolution is assumed to be 10 ns and that the source of 99mTc and 201Tl have activities of 185-1110 MBq and 74-148 MBq respectivly [13, 11], which creates an extremely low flux for this detector, making it possible to handle each photon separately. Even though more than one photon is emitted during the time resolution, it can be assumed that they do not hit close or even at all.

2.4.1 Detector response

A point source in the middle of iso center gives us a detector response. A distribution of the energy depositions for true and false photons is decided. Given the low flux and that a photon interacts more than one time, the interactions can be seen as one event, thereby summing the energy depositions could potentially separate the unscattered photons with high energies and the scattered photons with lower energies. When there is more than one interaction it is impossible to know which interaction is the first. Therefore the po-sition of the event is estimated by the centroid of the individual interactions popo-sitions. This simplification creates an error, the distance from the mean position to the first in-teractions position. How many inin-teractions each photon has in the detector is interesting for several reasons. More interactions generally mean a larger deposition of energy to the detector; however, more interactions also means that the photon move freely inside the detector and this might make the position error large and ultimately have an effect on the resolution. Finally the number of interactions is important for connecting interactions in Maximum-Likelihood algorithms, that could be used to find the first interaction.

2.4.2 Resolution, Point Spread Function

A Point Spread Function (PSF) describes the response of an imaging system to a point source, much like a impulse response for a general system. The PSF is strongly connected to the resolution. A metric of resolution is the Full Width Half Maximum (FWHM) of the PSF. The FWHM is used as a measurement of how close two PSF’s can be and still be separated.

2.4.3 Efficiency and noise

The intensity is defined as I = Ntrue+ Nfalse, where Ntrue is the number of photons which

have not interacted in the object. Ntrue hits is when the first interaction is in the detector

silicon and Nfalse hits have interacted before its interactions in the detector silicon. We

define the efficiency (or system efficiency) and the scattered-primary ratio s/p as:

= Ntrue hits

I , s/p =

Nfalse hits

Ntrue hits

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A common metric of image quality is the Signal-Difference-to-Noise ratio (SDNR) or the contrast to noise ratio (CNR). It is defined with respect to a specific object. It is therefore a difficult metric to compare. It is defined as:

SDN R = E[I

Obj_{] − E[I}Bg_]

pV [IBg_] (2.12)

Where IObj _{is a signal, and I}Bg _{is the background noise. If we assume that the object}

tissue absorb K times the radionuclide compared to the rest of the body, and the distance of travel in the body is constant for every point.

SDN R = (KI + s/pI) − (I + s/pI)

pI + s/pI = (K − 1) s

I

1 + s/p (2.13) The SDNR and the efficiency is good parameter to optimise the threshold energies from.

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Chapter 3 Results

3.1 Geometric results

The results from the analytic method resulted in the following information, remember GSE is the Geometric System Efficiency.

ISO-detector distance 200 mm 250 mm 408 mm GSE 2.5 · 10−4 2.817 · 10−4 3.508 · 10−4 F W HMaxial 17.749 mm 23.07 mm 49.954 mm

F W HMrotational 7.225 mm 9.025 mm 14.713 mm

Table 3.1: The FWHM are viewed in the detector plane, thus the rotational FWHM is not compensated for the magnifying effect of the fan beam collimination.

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3.2 PSF comparison

Figure 3.1: The PSF at the distance of 250 mm. Left: The analytical PSF. Middle: The Simulated 99mTc-PSF with no object. Right: The simulated 99mTc-PSF with 7.5cm soft tissue in between. Each of the simulated PSF is done with a threshold, decided by the maximal SDNR.

3.3 Energy distribution in the detector

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Figure 3.2: The the deposited energies of all interactions. A true photon is an unscattered photon that interacts in the detector. The first interaction of true photons is counted as a true interaction, later interactions is classified as false.

Figure 3.3: The detector response of the summed photons from a 99mTc-source without an object. This is done by summing energy depositions as if it was one event.

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3.4 Position error

Figure 3.4: The error distance between the first interaction and the mean position of interaction for summed photons.

When summing the energy depositions, the position of the interactions can be estimated by the centroid. The distribution of the errors in the position estimation is shown in Figure 3.4. The mean error is 1.7 mm and 61.16% of the interactions have an error that is lower than half the diagonal of a pixel.

3.5 Number of interactions

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Of true photons 51.23% interacts only one time. 80.96% interacts twice or less. Only 19.04 % interacts three or more times in the silicon.

3.6 Efficiency and SDNR

0 20 40 60 80 100 120 140 Thershold energy [keV]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Scatter to primaryd ration

0 0.5 1 1.5 System Efficiency 10-4 (a) 0 20 40 60 80 100 120 140 Thershold energy [keV]

0 5 10 15 20 25 30 35 SDNR (b)

Figure 3.6: a) The scatter to primary ratio (blue) and the system efficiency (red) as a function of threshold energy. b) SDNR as a function of threshold energy.

3.7 Phantom

Figure 3.7: The detector response of the summed photons from a99m_{Tc-source with the}

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0 20 40 60 80 100 120 140 Thershold energy [keV]

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Scatter to primaryd ration

0 0.2 0.4 0.6 0.8 1 1.2 1.4 System Efficiency 10-5 (a) 0 20 40 60 80 100 120 140 Thershold energy [keV]

0 1 2 3 4 5 6 7 8 SDNR (b)

Figure 3.8: a) The scatter to primary ratio and the detector efficiency. Notice that in the system efficiency the thickness of the object is included and that due to low counts, the s/p is removed at energies over 43 keV and replaced with a dotted line. b) SDNR as a function of threshold energy.

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Chapter 4 Discussion

4.1 Resolution

The FWHM of the PSF is larger than most other SPECT’s PSF:s in the axial direction, in the rotational direction is average or smaller [5, 10]. The simulated PSF converges towards a stretched version of the analytic PSF. The positioning error is low for both tracers and seems to be limited to the axial directions. This is probably due to that internal scattering is allowed in the axial direction inside the detector, and was expected when creating the analytic model. Both radionuclides act similar and there is no edge for either one (results for 201_{Tl in appendix). The conclusion is that with a lowered}

iso-to-detector distance it is possible to use collimators for a CT in a SPECT, some modification might be needed for optimal performance to the specific application.

4.2 Detector response

The difference between the energy response with and without summation is substan-tial, see figures 3.2 and 3.3. The energies of true events are significantly higher with summation, thereby more separated from the false. In the response given in figure 3.3 it is possible to separate true and false photons with a threshold energy; however, the distributions are similar and very close to each other.

Scatter from an object closes the difference between them and portions of the accepted signal have to be noise. With the object described earlier it is also possible to separate the two distributions with a threshold energy so that the signal is stronger than the noise, while the detector efficiency is high see figure 3.7.

With the 201_{Tl-tracer there is a peak around the emitted energy, which consist of both}

summed photons and first interaction of photoelectric effect. This is a low peak and the majority of true photons only deposit low energies so a high threshold would be too inefficient, instead it is possible to have several windows of acceptance.

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4.3 Number of interactions

The low number of interactions is a telling factor of why the summed energies are so small. One hypothesis would be that the anti scatter collimators inside the detector decreases the number of interactions, absorbing energy thus lowering the total energy sum for a photon. If removed, photons would be free to scatter all around the detector, this could increase the number of interactions and the amount of the deposited energy. This could result in an increased error in positioning of the photon thereby heavily affect the performance of the system as a CT where scatter is not as appreciated. There is a number of ways this could be evolved, removing all internal collimators is mentioned above. Maybe removing some would be enough. When 80% of photons interact twice or less, several assumptions must be done in a Maximum-Likelihood algorithm. There would be a much higher demand on the spatial resolution, energy resolution and computation with a limited gain.

4.4 Efficiency

The results of the SGE (System Geometric Efficency) is adequate compared to many SPECT systems; however, most of the solid angle comes from the rectangular shape, and if demands for a square pixel are high this might need to change, the dimensions are in the right order of magnitude and could probably be adapted. The SGE is also somewhat skewed due to the negligence of the collimators inside the detector in the analytic model which assumed an ideal detector. This will effectively narrow the SGE for photons that interact later in the detector.

From the simulation the system efficiency was found. To investigate how well the detector performed, the ratio between the efficiency and the SGE shows how many of photons that the detector detects of all photons that are geometrically allowed to hit the silicon. This is not purely the stopping power of silicon because of the geometrical contribution of the inner collimators that are present. It should not be directly compared with the detection rate mentioned in section 1.2; however, if they are simliar in magnitude it is good. When calculated, the detector efficiency is 52% at the threshold 0 keV. With the same threshold as the SDNR maxima the detector efficiency is 50%. With regard to 201_{Tl the detector}

efficiency is 57% at 0 keV which also is the SDNR maximum.

For the 99mTc-source the scatter to primary ratio is 0.27. With the object the s/p is 0.9 that means that even with the relative thick object the signal is stronger than the noise. Here it is obvious that a lot of scattered photons is accepted; however, given enough dose the image would be as good as the one without an object. With the 201Tl source on the other hand the s/p is over 1 for all thresholds with a high efficiency. If however two acceptance windows are set up e.g 10-30 keV and above 68 keV the s/p is 0.718 and some of the efficiency is saved. This means that a larger object may be imaged with201Tl too.

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4.5 Limitations

Ideal spatial resolution is assumed and there is an uncertainty in the simulation of 10 µm for each time a photon transit between mediums due to the algorithm, this error is not present when localising the photon. This will accumulate in a spatial error and could be solved by using analytic methods for positioning, or an existing framework for ray-tracing.

The amount of data for the detector response with the object is too small to exactly determine the distributions for high energies. More sophisticated simulations would be needed. There is also possible to recognise that the profile of the unscattered distributions are constant and that the scattered distribution is connected to the object thickness. Since201Tl decays in a distribution there would have to be a window of accepted energies. This creates some noise since the lower energies detected could be higher energies that interacted in the object or in collimators i.e. a more refined energy response is needed. This is an inherent problem with the tracer not exclusive to this detector. Different physiological effects on the tracers effecting its uptake or redistribution must be taken into account for a optimal system.

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Chapter 5 Summary and Conclusions

5.1 Conclusion

The collimators are or can be modified to produced an adequate resolution for SPECT applications. The silicon CT-detector have an energy response that makes it hard to detect numbers of true photons without at the same time accepting a lot of false pho-tons. This is in part due to the low numbers of interactions, and the low deposition of energy. However, there are still more true photons than false photons for some threshold energies even with a fairly thick object, so an image can be produced given enough dose. With the threshold set to maximal SDNR, the detector efficiency is around 50% for99m_Tc

and if enough detector area is pointed towards the volume in focus, a similar detector might be usable with a safe dose. The 201Tl-source have different characteristics but is also viable especially with thinner objects and with two windows of accepted energies. Further investigation in optimisation of in-detector collimation and energy thresholds is needed.

ACKNOWLEDGMENTS

Many thanks my supervisor Martin Sjölin for inspiration and encouragement. And to the whole Physics of Medical Imaging group at KTH.

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Chapter 6 Appendix

6.1 Results for

201

Tl

(a) (b)

Figure 6.1: The detector response from a201_{Tl-source without (a) and with the phantom}

(b). The first row shows the frequency of summed detected energies. The middle row is the error between mean interaction position and the first interaction’s position. The last row is the frequency of number of interactions

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(a) (b)

Figure 6.2: Left: The scatter to primary ratio and the system efficiency. Right: The SDNR as a function of threshold energy. (a) From a point source with no object. (b) From a point source with an object.

Figure 6.3: Left: Analytical point spread. Middle: Simulated 201_{Tl-PSF with no object.}

On the usage of a photon counting CT detector for SPECT