Optimal working view with dual-axis rotational angiography

Fan-beam computed tomography

In X-ray CT scans, fan beam imagery is a quite common approach to the projection geometry implementation (Zeng et al., 2010). The x-ray focal point is displayed as the “X-ray source” in Figure 1.9, angling out to create a fan shape before hitting the sensors at the detector array of the opposite side. The patient is imaged slice-by-slice, usually in the axial plane, and interpretation of the images is achieved by stacking the slices to obtain multiple 2D representations. Data is gathered using the narrow fan beam, slightly changing the angle of the x-ray source to collect data from many slices. After data is collected, the image slices are then compiled to create two dimensional representations of parts of the object. The linear array of detector elements used in conventional helical fan-beam CT scanners is actually a multi-detector array. This configuration allows multi-detector CT scanners to acquire up to 64 slices simultaneously, considerably reducing the scanning time compared with single-slice systems and allowing generation of 3D images at substantially lower doses of radiation than single detector fan-beam CT arrays.

Cone-beam computed tomography Cone-beam CT scanners, on the other hand, are based on volumetric tomography, using a 2D extended digital array providing an area detector. The cone-beam geometry immediately captures a 2D image through a 3D x-ray beam, which scans in the shape of a cone. The conebeam technique involves a single 360° scan in which the x-ray source and a reciprocating area detector synchronously move around the object of interest, as displayed in Figure 1.10. This three dimensional beam proves efficient as at most one rotation around the object provides enough information to reconstruct a three dimensional image (Sedentexct, 2016). At certain degree intervals, single projection images, known as “basis” images, are acquired. These are similar to lateral cephalometric radiographic images, each slightly offset from one another. This series of basis projection images is referred to as the projection data. Software program incorporating sophisticated algorithms including back-filtered projection are applied to these image data to generate a 3D volumetric data set, which can be used to provide primary reconstruction images in 3 orthogonal planes (axial, sagittal and coronal).

Optimal working view with dual-axis rotational angiography The conventional coronary angiography technique is limited by its two-dimensional (2D) representation of three-dimensional structures. Vessel foreshortening in angiographic images may cause errors in the assessment of lesions or the selection and placement of stents. To address this problem, the dual-axis rotational coronary angiography technique has been introduced, in which the C-arm rotates in two axes during scanning has allowed visualization of the coronary tree by using a single contrast injection. In this technique, rotation angles are used to determine the imaging orientation of the C-arm; these angles are generally defined as the left/right anterior oblique (LAO/RAO) and the caudal/cranial (CAUD/CRAN). In imaging, a physician adjusts these rotation angles to achieve different perspective projections of the coronary arteries. If these angles are incorrect, segments with stenosis are very difficult to be visualized in a 2D angiogram because of foreshortening and overlapping effects. Hence, the first objective is proposed in this section to help physical to choose the optimal working view with the dual-axis rotational angiography technique.

Projection matrix

Proper tomographic reconstruction depends on accurate calculation of the true location of the projection of each image voxel onto the detector plane. One approach to ensure this accuracy is to use a mechanically rigid system, such as in conventional CT. For systems which display some degree of mechanical deformation or instability during rotation, to achieve maximal image quality the true system geometry should be measured throughout the acquisition and incorporated into the reconstruction algorithm. With this assumption, the system geometry can be determined once and used to correct subsequent acquisitions. Let a voxel of the 3D tomographic data is P = (X,Y,Z,1). The projection of the voxel P onto the pixel p = (λx, λy, λ)T of the projection plane is simulated by a pinhole perspective model, as shown in equation (2.4). According to (Wen P.L. et al., 2015), the pinhole perspective projection model is closest to the radiographic projection of the C-Arm acquisition systems. And hence, the projection is supposed to be perfect in which the distortions of the image mainly due to the influence of the terrestrial magnetic field on the trajectory of the photons X are supposed to be corrected (Lv et al., 2009).

Fourier transform

The Fourier transform is a crucial component of most 3D CT image reconstruction algorithms. The Fourier transform provides a visualization of any waveform in the real world into a sum of sinusoids, providing another way to interpret waveforms. The function transforms a function of time into the frequency domain. The Fourier transform is useful because at times there are computations which are easier to calculate in the frequency domain rather than the time domain. In this research, the Fourier transform will transform functions in the time domain to the frequency domain for use in back projection and filtering within 3D CT image reconstruction algorithms. Let f(x, y) denote the object need to be captured by a CT system. The sources and detectors are oriented at an angle ߠsuch that the latter records the contributions of f(x, y) along the line ݔcosݕ + ߠsin = ߠr for different values of r. Mathematically, the captured signal f(r, θ) can be expressed as the Radon transform of the object that is to be reconstructed. The Radon transform is defined as the equation (2.9).

Filtering In electrical engineering and signal/image processing, filters are used to transform signals from one form to another, specifically to eliminate various frequencies in a signal. Filtering is usually needed to compensate for noise in data. A common approach for extracting the desired signals from the raw data is to convolve the filter with the Radon transform of the input data. In practice, functions representing the filters are usually defined in the frequency domain (Fourier). Thus, the filtering is performed as a multiplication in the frequency domain instead of convolution in the spatial domain. The most used filter for reconstructing projections is Ramp filter. It is a high-pass filter, increasing frequencies above the cut off and decreasing low frequencies. It is used to create a clearer image without changing projection data before the back projection step. This filter assists in reducing blur and other visual artifacts found in the projection images. The Ramp filter, defined by the inverse Fourier transform targets image noise and imperfections and smooths them out through filtering techniques. The Ramp filer is demonstrated as Figure 2.7, with Ramp filter in frequency domain (left) and corresponding spatial domain filter (right).

ECG-gated in FDK algorithm Gating techniques are used to improve temporal resolution and minimize imaging artifacts caused by cardiac motion. Two approaches to cardiac gating are typically used: prospective ECG triggering and retrospective ECG gating. The simplest technology for acquiring gated cardiac images is referred to as prospective gating or sometimes prospective ECG triggering. In this mode, the scanner monitors the patient’s ECG. It is set to scan at a particular point in the cardiac cycle, which is typically in diastole since the heart is moving the least then. The scanner interprets the ECG and determines a delay after the QRS complex to begin scanning. At that point, the ECG triggers the scanner to start scanning. The scanner must complete a 180 degree rotation in order to obtain a full image. It then waits for the next diastolic phase to scan the next part of the heart. For this reason, some people refer to this technique as “step and shoot” since the scanner moves the table in between successive diastolic phases. Each scan has a certain z-axis coverage, which is determined by the width of the CT detector and pitch. To complete the cardiac CT, we need to cover the entire heart, which is typically around 12-15 cm. Thus, with wider detectors (more rows), the heart is captured in fewer beats. The problem with needing multiple beats is that the patient may move in between the beats; if the scan is really slow, the patient may even breathe which will change the position of the heart in the chest and make the scan uninterpretable.

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Table des matières

INTRODUCTION
CHAPTER 1 LITERATURE REVIEW
1.1 Anatomy of the heart
1.1.1 Cardiac cycle
1.1.2 Coronary arteries structure
1.1.3 Electrocardiography (ECG)
1.2 Angiography technique in medical imging
1.3 Coronary artery disease (CAD)
1.3.1 Single axis rotational coronary angiography
1.3.2 Dual-axis rotational coronary angiography
1.4 Fan-beam computed tomography
1.5 Cone-beam computed tomography
1.6 Summary of reviews
1.7 Hypotheses and Objectives
CHAPTER 2 METHODOLOGY
2.1 Optimal working view with dual-axis rotational angiography
2.1.1 Rate of foreshortening
2.1.2 Rate of overlapping
2.1.3 Determination of the optimal working view
2.2 Tomographic geometry
2.2.1 Cone beam acquisition geometry
2.2.2 Projection matrix
2.3 3D CT reconstruction
2.3.1 Fourier transform
2.3.2 Filtered Back-projection
2.3.2.1 Filtering
2.3.2.2 Back-projection
2.3.3 Cone beam reconstruction process
2.3.4 FDK algorithm
2.3.5 ECG-gated in FDK algorithm
CHAPTER 3 EXPERIMENTS AND RESULTS
3.1 Experiment setup
3.2 Evaluation and result
CONCLUSION
BIBLIOGRAPHY

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