Compton-camera-based SPECT for thyroid cancer imaging

Abstract

Thyroid cancer is the most common type of endocrine-related cancer and the most common cancer in young women. Currently, single photon emission computed tomography (SPECT) and computed tomography (CT) are used with radioiodine scintigraphy to evaluate patients with thyroid cancer. The gamma camera for SPECT contains a mechanical collimator that greatly compromises dose efficiency and limits diagnostic sensitivity. Fortunately, the Compton camera is emerging as an ideal approach for mapping the distribution of radiopharmaceuticals inside the thyroid. In this preliminary study, based on the state-of-the-art readout chip Timepix3, we investigate the feasibility of using Compton camera for radiotracer SPECT imaging in thyroid cancer. A thyroid phantom is designed to mimic human neck, the mechanism of Compton camera-based event detection is simulated to generate realistic list-mode data, and a weighted back-projection method is developed to reconstruct the original distribution of the emission source. Study results show that the Compton camera can improve the detection efficiency for two or higher orders of magnitude comparing with the conventional gamma cameras. The thyroid gland regions can be reconstructed from the Compton camera measurements in terms of radiotracer distribution. This makes the Compton-camera-based SPECT imaging a promising modality for future clinical applications with significant benefits for dose reduction, scattering artifact reduction, temporal resolution enhancement, scan throughput increment, and others.

Keywords

Compton scattering compton camera SPECT imaging thyroid cancer

1 Introduction

The thyroid cancer is the most common type of endocrine-related cancer, the most common cancer in women 15 to 30 years old [1], and the second most common cancer after breast cancer in women under 50 [2]. It is estimated that there will be 52,890 new cases in 2020, representing 2.9% of all the new cancer cases in the United States [1]. Differentiated thyroid cancer (DTC), including papillary and follicular cancer, comprises the vast majority (>90%) of all thyroid cancers. Although patients with DTC have a good prognosis, lifelong follow-up is required, since potentially curable local recurrences and distant metastases may occur even decades later [3]. Radioiodine planar imaging with radioactive iodine-123 (I-123) or radioiodine-131 (I-131) plays a major role, and remains the gold standard in follow-up exams after initial surgery. It is highly desirable and challenging to characterize malignant radioiodine uptakes in cancer nodes with high image quality at a minimized dosage.

Currently, radioiodine scintigraphy with the single photon emission computed tomography (SPECT) integrated computed tomography (CT) is widely used to evaluate patients with thyroid cancer [4, 5]. The gamma camera for SPECT consists of a metallic collimator and a gamma ray sensitive detector. However, this structure has many disadvantages: large and heavy, restricted field of view, low detection efficiency, etc. It results in a greatly compromised dose efficiency and a severely limited diagnostic sensitivity. Fortunately, the Compton camera is emerging as an ideal approach to map the distribution of radiopharmaceuticals inside the thyroid. Because the Compton camera does not require any collimator, it can offer a superior detection sensitivity over a broad field of view. Especially in the context of SPECT imaging, this imaging mode improves the image quality and helps reduce the radiation exposure of the patient.

Compton camera is a group of imaging devices that are built based on the so called Compton scattering effect [6]. The scattering effect is the scattering of an x-ray or gamma photon by an electron into a material. The result is a decrease in the energy of the incident photon, and transfer of a part of the photon energy to the recoiling electron. Since the concept of Compton imaging was first reported in 1974 [7], different types of Compton cameras have been constructed for different applications in fields of astrophysics, nuclear medicine, molecular imaging, security inspection, and so on [8 –10]. Although many efforts have been reported to develop Compton cameras for nuclear imaging, to the best of our knowledge, there is still no one that is commercially available, and the Compton camera has not been applied for clinical applications in the nuclear medicine field. The state-of-the-art Compton camera that has a great potential for thyroid imaging is based on an event based readout chip Timepix3 [11]. The Timepix 3 chip is a general-purpose integrated circuit suitable for readout of both semiconductor detectors and gas-filled detectors [12]. It can send every hit pixel immediately to a readout and record the time-of-arrival (ToA) and energy of an incident gamma simultaneously in the pixel. The chip offers high energy resolution (1 keV at 60 keV, 7 keV at 356 keV), as well as time resolution (1.6 ns) [12]. The current pixel size is 55μmx55μm. The Timepix3 readout chip can be combined with different sensor materials. It is a perfect device for creation of a compact Compton camera. In 2018, Turecek et al. presented a very compact detector system AdvaPIX for imaging with gamma-rays using the Compton camera principle [13]. The system consists of two layers of hybrid pixel detectors Timepix3 with the sensors being optimized for gamma-ray tracking. The front detector layer (scattering) is made of silicon of 1 mm thickness, while the last layer (absorbing) is equipped with thick CdTe or CZT sensors up to 2 mm in thickness. In early 2020, this team reported a miniaturized single layer Compton camera MiniPIX consisting of a single Timepix3 detector with a thick 2 mm CdTe sensor. Thanks to Timepix3 high resolution ToA measurement, it is possible to measure the drift time of charge transport within the sensor and thus determine the vertical position (depth) of both interactions. By knowing both energy and position of the events in the sensor, the image of the gamma source can be reconstructed. Those latest advances motivate us to employ the AdvaPIX/MiniPIX to design Compton-camera-based SPECT imaging system to meet the clinical challenges, with the thyroid cancer detection and diagnosis as an example.

In this paper, we will numerically investigate the feasibility of thyroid cancer imaging using Timepix3 based Compton camera and report our preliminary results. In the next section, we present the imaging theory and method. In section III, we report our experimental design and results. In the last section, we discuss related issues and draw conclusions.

2 Theory and method

In this section, we will present our methodology. It includes the design of thyroid phantom to mimic human neck, the mechanism of Compton camera based event detection, the numerical simulation to generate realistic list-mode data, and the weighted backprojection method to reconstruction the original distribution of the emission.

2.1 Thyroid phantom

The thyroid is a butterfly-shaped gland that sits in front of the windpipe (called the trachea) and just below the larynx or Adam’s apple in the neck (see left image in Fig. 1). The thyroid has two lobes, connected by a bridge in the middle [14]. The gland makes thyroid hormone that travels in the blood to all parts of human body. The thyroid hormone controls human body’s metabolism in many ways, including how fast is the calories burned and how fast is the heart beat. Because the iodine is a building block of the thyroid hormones, thyroid tissue has the capacity to concentrate this element. Therefore, radioiodine is widely employed for thyroid functional imaging. According to the statistical information in [15], the averaged width, thickness and length of thyroid right lobe are respectively 1.57 cm, 2.09 cm and 6.18 cm, and the counterparts of thyroid left lobe are respectively 1.52 cm, 1.89 cm and 5.85 cm. To simulate a digital thyroid phantom, we assume a medium-size neck and model it as a cylinder with a 13.0 cm diameter and 13.0 cm height. We also assume that the center of the cylinder sits at the origin of the global coordinate. Two ellipsoid are employed to mimic the lobes (see right image in Fig. 1). The parameters of the lobes are listed in Table 1, where the “center” means the center of each ellipsoid in the global coordinate system, and the “half-axis lengths” are those of the ellipsoid along different directions. Those objects are used to define the thyroid gland regions that can have radioiodine uptakes. SPECT images reveal the radioiodine uptake distributions. Because cancer is rarely found in hot nodules, hot and cold nodules can be judged as benign and malignant respectively by radiologists. That is, we can use different uptake distributions to characterize heterogeneous thyroid nodules, and different uptake distributions in these regions can mimic various pathological states of the thyroid. The radioiodine-131 is assumed inside the thyroid, and gamma rays with 364keV are emitted.

Fig. 1

Rendering of the thyroid in the human (left) [14] and the designed digital phantom (right).

Table 1

Parameters of the thyroid phantom size

Object	Center (cm)	Ellipsoid half-axis lengths (cm)
Right Lobe	(0.85, 0, – 1.0)	(0.785, 1.045, 3.090)
Left Lobe	(– 0.85, 0, – 1.0)	(0.760, 0.945, 2.925)

Since the purpose of this study is to investigate the feasibility of thyroid imaging, we assume that both lobes are health, and the radioiodine-131 is uniformly distributed inside thyroid tissues. Otherwise, the lesion region will has less radioiodine-131 distribution. This assumption does not affect the evaluation for the follow-up image reconstruction algorithms. In the field of SPECT imaging, the probability for an emitted photon to arrive at a detector depends on the integral of the linear attenuation coefficient along the gamma ray path between the emission and detection sites, which reflects an average of many individual attenuation coefficients of pixels/voxels. Therefore, for most SPECT imaging tasks the attenuation map can be often approximated as a uniform distribution. In this study, we also assume they are homogenous, and a uniform attenuation coefficient of water is assigned to all the phantom pixels. Like the conventional SPECT imaging, the effect of this kind of simplification is endurable for the final results.

2.2 Compton camera based event detection

Compton scattering is the scattering of an x-ray or gamma photon by an electron into a material [6]. As Illustrated in Fig. 2, assuming the energy of the incident photon is E₀ and the electron is in the rest status, the direction of the photon will be changed after it hits the electron. The recoiled electron will have an energy E₁, the scattered photon will have an energy E₂, and the photon direction will have a change of scattering angle θ. The angle depends on the original energy E₀ and the transferred energy E₁ of the photon, and it can be described by the Compton equation $\cos (θ) = 1 - m_{ɛ} c^{2} \frac{E_{1}}{E_{0} (E_{0} - E_{1})}$ (1)

Fig. 2

Illustration of Compton scattering.

where m_ɛ = 9.109 × 10^-31kg is the electron mass, c = 2.998 × 10⁸m/s is the light speed, m_ɛc² = 8.187 × 10^-14J ≅ 511keV and 1keV = 1.602 × 10^-16J. Because of the energy conservation, we have E₀ = E₁ + E₂. Equation (1) can also be written in terms of E₁ and E₂, or E₀ and E₂.

A typical Compton camera usually consists of two layers. The front layer can record the recoiled electron energy E₁ and incident position, and the bottom layer can record the scattered photon energy E₂ and the corresponding position. The two positions in layers can uniquely determine the scattering direction. In the three-dimensional space, for a fixed direction of the scattered photon with energy E₂ and the scattering angle θ, the potential direction of incident photon with energy E₀ can form a cone whose apex angle is 2θ. To image the thyroid phantom designed in the previous subsection 2.1, we assume a cylindrical detector with a diameter of 26.0cm and height of 13.0cm, and both the detector and phantom share the same origin (see Fig. 3).

Fig. 3

Horizontal and vertical sketch views of the detector and phantom.

2.3 List-mode data generation

The thyroid gland does not distinguish between radioactive and nonradioactive iodine. In clinical applications, a very small dose of radioactive iodine (I-123 or I-131) is administered orally, and images are taken at specified intervals after the initial dose is administered. The radionuclide emits gamma photons, which allows external measurement. Once a gamma photon is emitted from the inside of human body, it will interact with the human tissue (e.g. scattering and absorption) and the procedure can be simulated using the well-established Monte-Carlo method [16]. Because the Compton camera can identify the incoming photon energy, here we use the Beer’s law to mimic the absorption and scattering effects inside the human body. This is because we can use the post-processing steps to discard the photons that arrive at the detector with an energy smaller than the original emission energy. In other words, if a photon was scattered by the soft tissues or other organs inside the human body, its energy will be decreased along with the change of its direction, and this energy decrease can be identified by the Compton detector and discarded by post-processing steps. This is similar to the parallel-hole collimator based photon detection mechanism for the conventional CT and SPECT. Figure 4 illustrate the main geometrical parameters to generate the list-mode data, and the procedure is summarized as the following five steps:

Fig. 4

Illustration of list-mode data generation.

To simulate the interaction of a photon with energy E₀, an emission position $\vec{P_{e}}$ is generated, obeying a uniform distribution inside the thyroid gland regions. The emission direction $\vec{d_{e}}$ is generated, obeying a uniform distribution on the unit three-dimensional sphere.

The line integral $a (\vec{P_{e}}, \vec{d_{e}})$ of the tissue attenuation coefficient along the direction $\vec{d_{e}}$ is computed inside the human neck, and the probability $P_{1} = e^{- a (\vec{P_{e}}, \vec{d_{e}})}$ is employed to characterize if the photon can penetrate the neck without scattering or absorption.

If the photon can arrive at the Compton camera, the position $\vec{P_{d}}$ is recorded to characterize the front layer position of the scattering and the free electron. A Compton scattering angle is randomly generated based on the probability P₂ (θ) that is proportional to D₂ (θ) defined by the Klein-Nishina formula [17, 18]: $D_{2} (θ) = \frac{r_{e}^{2}}{2 {(1 + aG (θ))}^{2}} (1 + {cos}^{2} θ + \frac{a^{2} G^{2} (θ)}{1 + aG (θ)})$ (2) where r_e = 2.818 × 10^-15m is the classical radius of the electron, $α = \frac{E_{0}}{m_{e} c^{2}}$ , and G (θ) = 1 - cos(θ). The recoiled electron energy E₁ and the scattered photon energy E₂ can be computed according to Equation (1).

In the three-dimensional space, for a fixed position $\vec{P_{d}}$ and the scattering angle θ, the potential direction of the scattered photon with energy E₂ can form a cone. Its apex angle is 2θ and axis is along the direction $\vec{d_{e}}$ . A direction $\vec{d_{s}}$ is randomly generated on the cone surface whose distribution is uniform. This direction can be computed directly from the Compton camera measurements in practice.

If both the recoiled electron with energy E₁ and the scattered photon with energy E₂ can be detected simultaneously, a qualified event is obtained for image reconstruction. This event can be expressed by a trilet $(\vec{P_{d}}, θ, \vec{d_{s}})$ .

2.4 Backprojection image reconstruction

Once we have sufficient number of detected events in terms of the trilet $(\vec{P_{d}}, θ, \vec{d_{s}})$ , the original distribution of the emission source can be reconstructed. Image reconstruction from events recorded by a Compton camera is a computationally challenging task. To date, there is no theoretically exact analytical solutions applicable to a practical imaging device [19]. Figure 5 shows the 3D backprojection process. For a given trilet $(\vec{P_{d}}, θ, \vec{d_{s}})$ , the potential emission direction $\vec{d_{e}}$ can form another cone. Its apex angle is 2θ and axis is along the direction $- \vec{d_{s}}$ . The backprojection cone is drawn from the scattering location at the position $\vec{P_{d}}$ in the Compton camera.

Fig. 5

Weighted backprojection in 3D to invert Compton scattering data.

Different from the state-of-the-art backprojection algorithm [20], for a given point vector $\vec{x}$ (the voxel center) originally from the scattering position $\vec{P_{d}}$ in the Compton camera, we define the voxel value as $W (\vec{x}) = ω_{1} (\vec{x}) ω_{2} (\vec{x}) ω_{3} (\vec{x})$ , where $ω_{1} (\vec{x}) = e^{- a (\vec{x})}$ is used to represent the probability of the gamma ray arriving at the detector, where $a (\vec{x})$ is the line integral of linear attenuation coefficients along the path from $\vec{x}$ to $\vec{P_{d}}$ in the object. This basically is identical to the probability P₁ that is defined in the previous subsection. With an increased distance, the cone-shaped shadow has a wider spread, and $ω_{2} (\vec{x}) = 1 / | \vec{L} |$ is used to normalize the spread of uncertainty, where $\vec{L}$ is the projection of vector $\vec{x}$ on the cone. Finally, $ω_{3} (\vec{x}) = h (\frac{d}{δ})$ interpolates the results on the cone surface, where h is an interpolation kernel, d is the distance from $\vec{x}$ to the cone, and $δ = | \vec{L} | tan (Δ θ)$ with Δθ being the angular resolution. The angular resolution can be determined by the Compton camera unit size and the associated geometrical configuration. In this work, a triangle interpolation kernel is employed, and it is defined as $h (t) = {\begin{matrix} 1 - | t |, & | t | ⩽ 1 \\ 0, & | t | > 1 \end{matrix}$ (3)

3 Experimental design and results

In this study, we employ a continuous model for the phantom and a discrete model for the Compton Camera based detector. That is, the coordinates of each emission position ${\vec{P}}_{e}$ are real numbers, and Compton camera is divided into finite sufficient small elements. All the photons detected by a detector element are associated with the element indexes, and the center of detector element is viewed as the position ${\vec{P}}_{d}$ for all the photons. For the cylindrical detector designed in subsection 2.2, we assume that there are 130 rings each of which has a height of 1.0 mm. The column number is 720, and each element corresponds to an angle $\frac{π}{360}$ with an arc length of 1.13 mm. This yields an angular resolution $Δ θ ≅ \frac{π}{270}$ which is about 0.67°.

3.1 Numerical verification for data generation

To verify the correctness of the list-mode data generation, we assume a total photon number of 2×10⁶ photons, and the photons are uniformly distributed in and emitted from the thyroid gland regions. The experiment is repeated for 10 times, the averaged photon numbers are used to analyze accuracy, and the statistical results are summarized as in Table 2.

Table 2
Accuracy analysis of the data generation

Items Photon number and percentile (%) Expected Percentile (%)

Emission direction covered by the Compton camera 883,050 (44.15%) 44.72%

Photons arriving at the Compton camera 405,001 (20.25%) 19.11%

Effective photons for image reconstruction 272,061 (13.60%) 13.21%

Items	Photon number and percentile (%)	Expected Percentile (%)
Emission direction covered by the Compton camera	883,050 (44.15%)	44.72%
Photons arriving at the Compton camera	405,001 (20.25%)	19.11%
Effective photons for image reconstruction	272,061 (13.60%)	13.21%

Among all the photons emitted from the thyroid gland regions, 883,050 (44.15%) emission directions can be covered by the Compton camera. That is, if the attenuation coefficient equals to zero inside the phantom everywhere, 44.15% photons can arrive at the Compton camera. To compute the expected photon number for comparison, we assume that all the photons are emitted from the origin for simplification, and the corresponding theoretical value of the probability can be calculated as $\sqrt{5} / 5 = 44.72 %$ . The small difference is due to the simplification of the theoretical computation. Among all the photons with an emission direction covered by the Compton camera, 405,001 can arrive at the camera with full energy due to the scattering and absorption. This is equivalent to 20.25% of the total photon from the emission source. For the phantom setting in subsection 2.1, we assume a homogenous attenuation coefficient 0.0117/mm which is the attenuation coefficient of water for the given emission energy E₀ = 364 keV. When a photon emits from the origin and arrives at the Compton detector, the expected probability is 42.74% considering different directions. This implies 19.11% of the total photons can arrive at the Compton camera with full energy. Comparing with the measurement 20.25%, the theoretical value is a little bit small. This is because the two thyroid glands are off the origin that will decrease the attenuation and increase the probability of arriving at the Compton camera. Finally, 13.76% photons are captured by the Compton camera that are effective for image reconstruction. To figure out a theoretical value for the purpose of validation, we compute the probability that the scattering angle is smaller than 90 degree and obtain a value of 0.7043. This implies that 13.46% of the total photons can be effectively detected by the Compton camera for image reconstruction. Comparing all the numerical measurements and the corresponding theoretically computations, we can see that the statistical results of the generated list mode data are consistent with the theoretical predictions. Our implementation for data generation is reliable and the data can be used for reconstruction and further analysis.

3.2 Compton camera detection efficiency analysis

To analyze the detection efficiency, a conventional Anger gamma camera for SPECT is also simulated. For fair comparison, we use the same parameter configuration as the Compton camera validation experiment in the above subsection. The only difference is the additional collimator. In our simulation, we assume that the collimators are ideal, that is, the thickness of the collimators are zeros. The collimators are arranged in parallel-fan-beam geometry. In the horizontal plane the collimators forms fan-beam geometry, and in the vertical plane the collimators forms parallel-beam geometry. Again, 2×10⁶ photons are uniformly distributed and emitted from the thyroid gland regions, and the experiment is repeated 10 times. From Fig. 3, one can see that the maximum available depth for the collimator is 6.5 cm in our setting. We acknowledge that the best collimator depth (∼6.0 cm) has been optimized for iodine imaging for SPECT [21, 22], but with a relative greater distance from the source to the detector in this study. To demonstrate the relationship between the collimator depth and detection efficiency as a general conclusion for more general applications, the experiments are repeated for different depths of the collimator, the average of detected photons for different depths are summarized as in Table 3. From Table 3, we can see that the deeper the collimator is for the gamma camera, the less the photons are detected by the gamma camera, and the higher the efficiency ratio is for the Compton camera with respect to the gamma camera. Here, the efficiency ratio is defined as the ratio between the photon numbers detected by the Compton camera and the gamma camera. For a moderate collimator depth (e.g. 3.0 cm), the Compton camera can improve the detection efficiency for two orders of magnitude comparing with the gamma camera. For the optimal collimator depth 6.0cm for iodine imaging, there are only 273 photons being received in total in the Anger system, which is impossible to reconstruct a volumetric image in the current dose level. However, the Compton camera can provide sufficient information to reconstruct the radiotracer distributions (see the results in next subsection). The high detection efficiency has huge benefits for dose reduction, scattering artifact reduction, temporal resolution enhancement, scan throughput increment, and so on. Because of the much-improved detection efficiency, for a given time internal we can receive the same amounts of photons for much less radioiodine uptakes, which implies dose reduction. For the same amount of radioiodine uptakes, we can receive the same amount of photons in a much shorter time interval, which implies a much higher temporal resolution for dynamic imaging. Because the Compton camera does not need the collimator, there is no photon scatter issue of the conventional SPECT camera. Currently, it takes 20 – 30 minutes to do a conventional SPECT scan. If we keep the radioiodine uptakes unchanged (that is, the radiation dose unchanged), it is our expectation that the SPECT scan will be reduced to < 1 minute and hence improve the scan throughput. Meanwhile, the high detection efficiency implies high performance point of care imaging for patients in hospitals and clinics, including but not limited to thyroid cancer. In our simulations, it should be pointed out that the physical size of the Compton camera pixel is 1.0×1.13 mm². It is way greater than the current state-of-the-art pixel size of MiniPIX Compton camera (55×55μm²). If a smaller Compton camera pixel size is used for numerical simulation, the corresponding efficiency ratio in Table 3 will be increased to higher orders of magnitude.

Table 3
Detection efficiency analysis results

Collimator Depth (cm) Gamma camera Compton camera Efficiency ratio

1.0 17285.7 272060.7 15.74

2.0 4148.7 272060.7 65.58

3.0 1638.9 272060.7 166.0

4.0 519.3 272060.7 332.1

5.0 458.0 272060.7 594.0

6.0 273.0 272060.7 996.6

Collimator Depth (cm)	Gamma camera	Compton camera	Efficiency ratio
1.0	17285.7	272060.7	15.74
2.0	4148.7	272060.7	65.58
3.0	1638.9	272060.7	166.0
4.0	519.3	272060.7	332.1
5.0	458.0	272060.7	594.0
6.0	273.0	272060.7	996.6

3.3 Reconstruction of photon source distributions

To reconstruct the original distribution of the gamma emission sources for Compton camera based SPECT imaging, the backprojection algorithm was developed. Previously, the backprojection method was reported for Compton camera based 2D imaging [20, 23]. Here, our focus is 3D imaging, and the backprojection algorithm in the subsection 2.4 is implemented in C++. For the thyroid phantom, the reconstructed volumetric image size is 150×150×150, and each voxel size covers a cubic region of 0.87×0.87×0.87 mm³. For different total photon numbers, the reconstructed volumetric images are shown in Fig. 6, and the thyroid gland regions are magnified in Fig. 7. Those 3D rendering images are generated using MatLab (Version R2020a, MathWorks, Natick, MA) Volume View App via maximum intensity projection. One can see that the greater the total photon number is, the smaller the reconstructed noise level is. This is consistent with the general knowledge that a greater photon number implies higher radiation dose and better reconstructed image quality.

Fig. 6

Maximum intensity projection rendering of 3D backprojected volumetric images from the simulations with different total photon numbers (a) 8×10⁴, (b) 2×10⁵, (c) 8×10⁵, and (d) 2×10⁶, respectively. Squares indicate the regions to be magnified in Fig. 7.

Fig. 7

Magnified thyroid gland regions in Fig. 6. (a)∼(d) are corresponding to the counterparts in Fig.(6).

Although the backprojected image quality can be improved by increasing the number of emission photons, those images still suffer from blurring effects and noise that are the inherent shortcomings of the backprojection algorithm. In the CT field, it is well known that filtering plays an important role to deblur the backprojected images. When the projections in terms of Radon transform are backprojected into the image space, a ramp filtering can be used to deblur the backprojected images to recover the original ones. Inspired by this knowledge, we introduce a ramp filter on the backprojected images for the Compton camera. Particularly, denote the 3D Fourier transform of the backprojected image as $\hat{F_{BP}} (v_{1}, v_{2}, v_{3}), | v_{k} | < M_{v}, k = 1, 2, 3$ , where M_v is the maximum frequency. In the Fourier domain, we construct the ramp filter as $\hat{R_{ft}} (v_{1}, v_{2}, v_{3}) = \sqrt{v_{1}^{2} + v_{2}^{2} + v_{3}^{2}} W_{t} (v_{1}, v_{2}, v_{3})$ where W_t(v₁,v₂,v₃) is a truncation window function. Here, a Hann window is employed and defined as $W_{t} (v_{1}, v_{2}, v_{3}) = {\begin{matrix} \frac{1}{2} (1 + cos (\frac{π R_{v}}{ρ M_{v}})), & R_{v} < ρ M_{v} \\ 0 & R_{v} ⩾ ρ M_{v} \end{matrix}$ (4)

where $R_{v} = \sqrt{v_{1}^{2} + v_{2}^{2} + v_{3}^{2}}, and 0 < ρ ⩽ 1$ is a parameter to control the window width. The purpose of this truncation window is to suppress the high-frequency components to avoid magnifying noise. For different truncation window widths with respect to different choices of ρ, Figs. 8 and 9 show the sagittal and transaxial views of the deblurred images of Fig. 6(d), and Fig. 10 presents the corresponding 3D rendering of the whole volumetric images using MatLab (Version R2020a, MathWorks, Natick, MA) Volume View App via maximum intensity projection. Comparing the images in Figs. 6 and 7 and 10, one can see that the ramp filter can effectively overcome the burring effects. The shorter the truncation window length is, the smoother the deblurred image is, and the smaller the noise level is. Therefore, we need to appropriately choose the parameter ρ to prevent over-smooth and suppress the high-frequency noise. To optimize the parameter ρ quantitative evaluation is further performed, and the structural similarity (SSIM) is employed as the quantitative image quality assessment index (the closer to 1, the higher structural similarity) [24], which is proved to be consistent with visual perception. With the phantom image as the reference, all the reconstructed image slices in Fig. 9 are evaluated in terms of SSIM and the results are shown in the same image slice. Based on our experiences,0.4< ρ<0.8 might be a better compromise.

Fig. 8

Sagittal view of the deblurred results of Fig. 6 (d) using different window length for ramp filtering. (a) is the ground truth; and (b)-(f) are the results of ρ = 0.2, 0.4, 0.6, 0.8 and 1.0, respectively.

Fig. 9

Same as Fig. 8 but for transaxial view.

Fig. 10

Same as Fig. 8 but the 3D rendings of the whole volumetric images using the maximum intensity projection.

4 Discussions & conclusions

As a general rule, for the tomographic imaging system development, the first step is to numerically investigate the feasibility of the system design. It is not cost-effective to directly build such a system and a real phantom. Hence, in this paper, we numerically investigate the feasibility of thyroid cancer imaging using Timepix3 based Compton camera and report our preliminary results. At the moment, we cannot build a real system and perform physical experiment due to lack of funding but the simulation results are solid, based on established imaging physics and reconstruction theory. These results provide us evidence and confidence to pursue along this direction. We would like to underline that the numerical simulation approach is well accepted in the tomographic imaging field, and the numerical results are typically inspiring, instead of being misleading.

While the Compton camera can be used for many cancer types, we focus on thyroid cancer for two reasons. First, the current Timepix3-based Compton camera detector is the state-of-the-art but relatively small. It is naturally suitable for imaging a small organ, and the human neck has a perfect size as well. Second, Thyroid cancer is the most common cancer in women 15 to 30 years old, and the second most common cancer after breast cancer in women under 50. The Thyroid tissue is the only organ in the human body to have iodine effectively accumulated. Therefore, as an initial application of the Timepix3-based Compton camera, Thyroid cancer is the best match.

Although the high efficiency of Compton camera for SPECT has been compared with the benchmark Anger system [22], to the best of our knowledge, for the first time 3D volumetric image is reconstructed to target clinical applications with thyroid cancer as an example. The state-of-the-art Timpix3 based Compton camera is simulated and a novel yet fast 3D backprojeciton strategy is developed. Those points are our key contributions.

In our current phantom setting, the thyroid gland regions are modeled as ellipsoids and the neck is assumed homogenous with a uniform photon attenuation coefficient. In the near future, this phantom can be re-designed to reflect 3D neck image volume for higher accuracy. The National Library of Medicine (NLM) Visible Human Project (VHP) created public and detailed 3D representations of the human male and female anatomies [25]. The neck CT volumes can be extracted from both the male and female CT scans, the thyroids can be segmented and labeled, and the Hounsfield unit can be converted to linear attenuation coefficients. Because the effective photon energy for CT images is different from that of SPECT images, the linear attenuation coefficients in the CT images can be mapped to the equivalent values for gamma rays in reference to the databases from the National Institute of Standards and Technology [26]. Meanwhile, the cancer defects can be simulated by changing the radiotracer distributions.

In the current list-mode data generation, the Beer’s law is used to mimic the interactions inside the human body. Previously, we developed a tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIM-OS) [16]. In the TIM-OS algorithm, the photon propagation is guided by a tetrahedral mesh of an object. In the future, we plan to employ this TIM-OS simulator [27] to generate gamma ray Compton scattering signals. The realistic digital phantom can be modeled as a tetrahedron-based inhomogeneous finite-element mesh. The linear attenuation coefficients will be mapped to the tetrahedrons in the phantom. An important new component is to include the Compton camera. After a gamma ray arrives at the Compton camera, a simulation procedure will be triggered to capture Compton scattering. We will incorporate the implementation of the components in subsection 2.3 into this procedure. Besides, in the absorption layer of the Compton camera, we will also consider the second or higher order scattering.

Currently, a 3D novel backprojection and ramp filter are used to reconstruct the original radiotracer distributions. It has been proved that the iterative reconstruction formula for maximum-likelihood expectation-maximization (ML-EM) hold in the list-mode case [28, 29], in which each detected event can be considered to be a unique detector unit. In the near future, we can follow the framework in [19] to implement the ML-EM algorithm for better image quality with more computational cost. The results from backprojection method can be used to initialize the ML-EM image for fast convergence. Besides, we can also introduce the sparsity of the radiotracer distributions to constraint the solutions (e.g. total variation minimization, advanced dictionary based sparse representation [30]).

Deep learning based tomographic imaging is an important application of artificial intelligence and a new frontier of machine learning. In 2016, we published the first perspective on this direction [31]. Until recently, most reconstruction approaches could be classified as analytic reconstruction and iterative reconstruction. Iterative reconstruction has been most widely used in SPECT. Recently, a third type of reconstruction was conceived: data-driven, learning-based or deep tomographic reconstruction. This new approach has become the mainstream in the imaging field. Rather than totally relying on an accurate mathematical or physics model, it is empowered by big data with which a deep network can be trained for superior tomographic reconstruction. In the near future, another direction is to employ deep learning based techniques for Compton scattering based SPECT reconstruction of radiotracer distribution in the thyroid.

In summary, comparing with the conventional gamma camera for SPECT imaging, the Compton camera does not have the heavy collimator which implies a higher photon detection efficiency. In this preliminary study, we investigate the feasibility of Compton camera for radiotracer SPECT imaging in thyroid cancer. Our numerical simulation results shows that Compton camera can improve the photon detection efficiency for at least two orders of magnitude with respect to the gamma camera, and the thyroid gland regions can be reconstructed from the Compton camera measurements in terms of radiotracer distribution. This makes the Compton-camera-based SPECT imaging a promising direction for clinical applications with huge benefits for dose reduction, scattering artifact reduction, temporal resolution enhancement, scan throughput increment, and so on.

Footnotes

Acknowledgments

The authors are grateful to Dr. Wenxiang Cong in Rensselaer Polytechnic Institute for constructive discussions.

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Compton-camera-based SPECT for thyroid cancer imaging

Abstract

Keywords

1 Introduction

2 Theory and method

2.1 Thyroid phantom

3.1 Numerical verification for data generation

Table 3 Detection efficiency analysis results Collimator Depth (cm) Gamma camera Compton camera Efficiency ratio 1.0 17285.7 272060.7 15.74 2.0 4148.7 272060.7 65.58 3.0 1638.9 272060.7 166.0 4.0 519.3 272060.7 332.1 5.0 458.0 272060.7 594.0 6.0 273.0 272060.7 996.6

Footnotes

Acknowledgments

References

Table 3
Detection efficiency analysis results

Collimator Depth (cm) Gamma camera Compton camera Efficiency ratio

1.0 17285.7 272060.7 15.74

2.0 4148.7 272060.7 65.58

3.0 1638.9 272060.7 166.0

4.0 519.3 272060.7 332.1

5.0 458.0 272060.7 594.0

6.0 273.0 272060.7 996.6