NOTES ON INTRODUCTION TO BIOMEDICAL IMAGING BY ANDREW WEBB SANDRO NUNES TÉCNICAS DE IMAGIOLOGIA Prof. Patrícia Figueiredo 1. X-Ray Imaging and Computed Tomography 1.1. General Principles of Imaging with

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NOTES ON INTRODUCTION TO BIOMEDICAL IMAGING BY ANDREW WEBB SANDRO NUNES TÉCNICAS DE IMAGIOLOGIA Prof. Patrícia Figueiredo 1. X-Ray Imaging and Computed Tomography 1.1. General Principles of Imaging with X-Rays X-Ray Imaging transmission-based technique in which X-rays from a source pass through the patient and are detected either by film or an ionization chamber on the opposite side of the body. Contrast in the image between different tissues arises from differential attenuation of X- rays in the body. Computed Tomography the source and detectors rotate together around the patient, producing a series of one-dimensional projections at a number of different angles. This data is reconstructed to give a two-dimensional image. The x-ray source is collimated to interrogate a thin slice through the patient. It has a very high spatial resolution (~1mm). 1 1.2. X-ray Production The x-ray source is the most important component in determining the image quality: X-ray Source The main structure of the X-ray source (also called tube) is shown below: Production of X-rays involves accelerating a beam of electrons to strike the surface of a metal target. The X-ray tube has 2 electrodes: a negatively charged cathode (electron source) filament of coiled tungsten wire - and a positively charged anode (metal target). An electric current passes through the cathode, heating it (~2200ºC) and causing electrons to move away from the metallic surface (thermionic emission). The tube potential causes the free electrons to accelerate towards the anode. Since the spatial resolution is determined by the effective focal spot size, the cathode is designed to produce a tight, uniform beam of electrons. To do this, a negatively charged focusing cup is placed around the cathode: Moreover, the anode is beveled in order to produce a small effective focal spot size: f = Fsin(θ) 2 The electrons striking the anode lose their kinetic energy, which is converted into X-rays. The anode must be made of a metal with high melting point and good thermal conductivity (usually tungsten) X-ray tube current, tube output and beam intensity Tube potential: kV (rectified alternating voltage, characterized by the maximum value, kilovolts peak or accelerating voltage - kv p). Tube current: mA (depends on kv p) Tube output: tube current tube potential. We need a high tube output in order to decrease the exposure time. It depends on: - kvp - Vacuum in the tube (reduces interactions between electrons and molecules and increase electrons velocity) Tube power rating: maximum power dissipated in an exposure of 0.1s. Limited by anode heating, which can be reduced by causing it to rotate at roughly 3000 rpm. Intensity of the X-ray beam: power incident per unit area (J/m 2 ). It depends on the number (α current) and energy of the X-rays (α kv p2 ) The X-Ray Energy Spectrum The output of the source is shown below: Electrons striking the anode generate X-rays by 2 processes: 3 -Bremsstrahlung: generated when an electron is deflected by the tungsten nucleus, losing kinetic energy which is emitted as an X-ray. The Bremsstrahlung radiation has a wide range of energies, with a maximum corresponding to the case where all the electron s kinetic energy is converted into a single X-ray (with energy kvp). It is characterized by a linear decrease in X-ray intensity with increasing X-ray energy, however many low energy X-rays are absorbed within the tube (additional external filters are used because low energy X-rays would be incapable of passing through the patient, adding to the dose unnecessarily).the efficiency, η, of the Bremsstrahlug is given by: k constant related to the target material Z atomic number of the target material η = k(kvp)z -Characteristic Radiation: shown as sharp peaks. It is emitted when an accelerated electron hits an electron in the inner shell of the tungsten atom, causing it to be ejected. An electron from the outer shell fills the hole, which causes a loss in potential, emitted as an X-ray. Only happens for incoming electrons with energy 70 kev Interactions of X-rays with tissue The X-ray can be classified according to the type of interaction: - Primary interaction: passes through the body with no interaction. - Secondary interaction: scattered radiation, whose trajectory between source and detector was altered. Caused by coherent and Compton scattering. - Absorbed radiation: absorbed radiation that does not reach the detector. Caused by photoelectric interactions Coherent Scattering Also called Rayleigh scattering. The radiation is absorbed by the tissue s atoms and then emitted in a random direction. Reduces the quantity of X-rays reaching the detectors and alters their trajectory Compton Scattering Refers to the interaction between an incident X-ray and a loosely bound electron in an outer shell of an atom in tissue. A fraction of the X-ray energy is transferred to the electron, the electron is ejected and the X-ray is deflected from its original path. The difference in energy is very small, which means that this radiation is detected with approximately the same efficiency as primary radiation. Also, it does not depend on atomic number, thus it is absorbed the same way in different tissues Photoelectric Effect The energy of the incident X-ray is absorbed by an atom, with a tightly bound electron being emitted from the K or L shells. A second electron with a higher energy level then fills the hole, emitting a characteristic X-ray with very low range that does not reach the detector. For an incident energy just higher than K-shell, the probability of photoelectric interactions is very high and is given by: 4 1.4. Linear and mass attenuation coefficients of X-rays in tissue Attenuation of the X-ray beam through tissue is given by: μ linear attenuation coefficient The value of μ is given by: Contributions of photoelectric interactions dominate at lower energies, whereas Compton scattering is more important at higher energies. X-ray attenuation is often characterized by mass attenuation coefficient which is equal to the linear attenuation coefficient divided by the density of the tissue. We can see from the graph below (right) that, at higher energies, little differentiation is possible because the number of photoelectric interactions decreases. 5 HVL (half value layer) thickness of tissue that attenuates half of the X-ray intensity parameter commonly used to characterize X-ray attenuation Instrumentation for planar X-ray Imaging The remaining components of an X-ray imaging system are: Collimators Restricts the dimensions of the beam in order to match the desired field of view (FOV). The collimator consists of sheets of lead, which can be slid over one another to restrict the beam in either one or two dimensions. Beam dimensions higher than the FOV increase patient dose unnecessarily and the number of Compton-scattered X-rays Antiscatter grids Even using a collimator, secondary radiation can represent between 50% and 90% of the x-rays reaching the detector. Therefore, it is placed an antiscatter grid between the patient and the X-ray detector. This grid consists of strips of lead foil interspersed with aluminum as a support, with the strips oriented parallel to the direction of the primary radiation. Two important properties are the grid ratio and the strip line density: 6 There is a tradeoff between reduction of the scattered radiation and the patient dose that must be delivered to give the same amount of detected X-rays. It can be characterized by the Bucky factor F: Intensifying screens These screens convert the X-rays into light, to which the film is much more sensitive. This is done by placing a phosphor layer before the film. The greater the thickness, the higher the SNR and lower the patient dose. However, it also worsens the spatial resolution as it increases the uncertainty in the position of the original X-ray. 7 X-ray film The presence of lighter regions is due to a chemical reaction of silver particles in the film to metallic silver. This reaction is reduced in the areas where light hits the film, so the degree of blackening depends on the intensity and time of the light hitting a specific area. This blackening is measured by the optical density (OD): I i intensity of the light incident on. I t intensity of the light transmitted through the X-ray film X-Ray image characteristics Signal to Noise Ratio SNR is proportional to the statistical variance in the number of X-rays per unit area (quantum mottle). Since this variance is characterized by a Poisson distribution, SNR is proportional to the square root of the number of detected X-rays per unit area (N). It is affected by: - X-ray tube voltage: the higher the kvp, the higher high-energy X-rays produced and thus, the number of X-rays reaching the film ( 1 ) - X-ray tube current ( ) - X-ray exposure time ( ) - Intensifying screen thickness ( ) - X-ray filtration ( ) - Object thickness ( ) - Antiscatter grid ratio ( ) Spatial Resolution The main factors affecting it are: - Effective focal spotsize ( 2 ) - Magnification factor ( ) - Film speed ( ) - Intensifying screen thickness ( ) The resultant spatial resolution is given by: 1 The arrows represent what happens to SNR if we increase the value of each given factor. 2 means higher R, the minimum distance which can be resolved, this is, worse resolution. 8 Contrast to Noise Ratio Refers to the difference in signal intensity from various regions of the body (for example the difference between the SNR of bone and soft tissue). It is affected by all the factors that affect SNR and R, in addition to: - Energy of the X-ray: if high energies are used, Compton scattering dominates ( ) - FOV: for values between 10cm and 30cm, the proportion of Compton scattering reaching the detector increases linearly. After that, it is constant. - Geometry of the antiscatter grid 1.7. X-ray contrast agents X-ray contrast agents are chemicals that are introduced in the body to increase image contrast. Some examples are the barium sulfate and the iodine-based X-ray contrast agents. These chemicals have a particular K-edge energy that can be used to distinguish the tissues on which they accumulate from the surroundings X-Ray Imaging methods The main imaging techniques that use X-rays are: X-ray angiography Angiography techniques produce images that show selectively the blood vessels in the body. Iodine-based contrast agents are injected into the bloodstream to improve contrast. A related imaging technique called digital subtraction angiography consists on taking an image before the agent is administered and one after, and then compute the difference (yielding very high contrast) X-ray fluoroscopy X-ray fluoroscopy is a continuous imaging technique using X-rays with very low energies (used, for example, for placement of stents and catheters). Since very low energies cause low SNR because of the quantum mottle, a fluoroscopic image intensifier (CsI:Na) is used to improve the SNR. A fluorescent screen is used to continuously monitor the area of interest Dual-Energy Imaging Technique that produces two separate images corresponding to soft tissue and bone (used for imaging the chest region). There are 2 ways of performing dual-energy imaging: - Two X-ray exposures, one applied immediately after the other, with different values of kvp; - Single exposure and 2 detectors. The detector placed directly beneath the patient absorbs low energy X-rays and hardens the beam detected by the second detector. Therefore, the image from the first detector corresponds to a low energy x-ray, high 9 contrast image, and that from the second, to a high energy x-ray, low contrast image. If more beam hardening is required, a copper filter can be put in front of the second detector Clinical applications of X-ray imaging Apart from the ones described above, there are additional applications of X-ray imaging: Mammography X-ray mammography is used to detect small lesions in the breasts. It requires very high spatial resolution and CNR to detect the microcalcifications ( 1mm). - A low dosage is also important to avoid tissue damage (a molybdenum filter is used to remove high energies, which also improves CNR); - Fast intensifying screen/film combinations are necessary to allow the use of low Kvp to optimize SNR; - Large source to detector distance and small focal spot size to increase resolution Computed Tomography CT enables the acquisition of 2D thin slices, which can be obtained in order to reconstruct a 3D volume. These 2D slices are reconstructed from a series of 1 dimensional projections of the object acquired at different angles. The detectors, which are situated opposite to the x-ray source, detect the total number of x-rays transmitted through the patient, producing a one dimensional projection. The signal intensities in this projection are dictated by the two dimensional distribution of the tissue attenuation coefficients within the slice. The X-ray source and the detectors are then rotated by a certain angle and the measurements are repeated. The image is reconstructed by a process termed backprojection Scanner instrumentation The basic operation of a 1 st generation scanner is shown below: 10 The image acquired this way has M X N points. The spatial resolution could be increased by using finer translational steps or the angular increments, up to a value limited by the effective x-ray focal spot size. The 2 nd generation replaced the single beam by a fan beam and used multiple detectors, which reduced the scanning time. It required the development of fan-beam backprojection. The 3 rd generation uses a much wider x-ray fan beam (45º) and an increased number of detectors (between 512 and 768). Two collimators are used to restrict the fan beam and the slice thickness (1-5mm). The rotation covers 360º. In the 4 th generation detectors, a complete ring of detectors surrounds the patient. No decrease in scanning time Detectors for Computed Tomography The most common detectors in CT are xenon-filled ionization chambers (xenon has a high atomic number of 66, thus there is a high probability of photoelectric interactions). Xenon is kept at high pressure to increase the number of interactions. X-rays transmitted through the body ionize the gas in the detector, producing electron-ion pairs, which are attracted to the electrodes by the applied voltage. This creates a current proportional to the number of incident x-rays Imaging processing for computed tomography The image reconstruction process is shown in the figure below, where only 2 projections are acquired: 11 The measured intensities can be expressed by: Simple matrix inversion is not sufficient to determine the attenuation coefficients because its computational burden is very high for large data and because the presence of noise in the projections cause instability in the inversion techniques Processing data corrections - Beam hardening: there is the need to use algorithms that account for this factor because it causes the effective linear attenuation coefficients to decrease with distance from the source; - Imbalances in detector s sensitivity: if not corrected, a ring or halo artifact can appear. It can be solved by calibrating the detectors: an object with a spatially uniform attenuation coefficient is measured before the actual patient The Radon Transform and the Backprojection Techniques The mathematical basis for reconstruction of an image from a series of projections is the Radon transform. For an arbitrary function f(x,y), its Radon transform is defined as the integral of f(x,y) along a line L: 12 Each X-ray projection, p(r, θ), can therefore be expressed as a function of the Radon transform of the object: To obtain the reconstructed image we need to compute the inverse Radon transform by using filtered backprojection. The image is displayed as a map of the tissue CT number, defined by: μ 0 - linear attenuation coefficient of the tissue Fan-beam reconstructions The 2 nd, 3 rd and 4 th generation scanners use fan-beams, which are not parallel to one another, thus the backfiltered algorithms need some modifications. The simplest way is to resort the acquired data in order to form sets of parallel X-ray paths, such as S 1D 1 and S 2D 3 in the following picture: 13 This way, the standard backprojection algorithms can be used Spiral/helical computed tomography To avoid the time delay and the spatial misregistrations between slices due to the patient movement, a technique called spiral or helical CT was developed. This technique acquires data as the table moves continuously through the scanner. This allows 10 times faster scan times and the acquisition of very fast 3D vascular imaging datasets just after injection of an iodinated contrast agent, resulting in significant increase in SNR of the angiograms. In terms of instrumentation, the main difficulty is that X-rays must be produced continuously, without the cooling period. Therefore, the X-ray source must be designed to have a high heat capacity and a very efficient cooling. Moreover, detectors must be very efficient in order to reduce the tube current and alleviate the anode heating (for example, scintillation crystals, made of BGO, are used since they have a high efficiency 75-85% in converting X-rays to light). The most important acquisition parameter in helical CT is the spiral pitch: Where d is the table feed per rotation and S is the slice thickness. p typically lies between 1 and 2, thus the radiation dose is lower than in single-slice CT. For values of p less than 1, the x-ray beams of adjacent spirals overlap, resulting in high tissue radiation dose. For values of p greater than 2, gaps appear in the data sampled along the longitudinal axis and image blurring happens due to the patient movement. Due to the helical trajectory, modifications of the backprojection reconstruction must be made. The modified algorithms use linear interpolation of data 180º apart on the spiral trajectory to estimate the data that would be obtained with a stationary table Multislice spiral computed tomography Multislice spiral CT incorporates an array of detectors in the z direction (direction of table motion). It improves efficiency by allowing higher values of the table feed to be used and, thus, lower scan times. The spiral pitch p ms is defined slightly different: Where S single is the single-slice collimated beam width In a multislice system, the focal-spot-to-isocenter and the focal-spot-to-detector distances are shortened compared to the single-slice scanner and the number of detectors in the longitudinal direction is increased from one long element to a number of shorter elements. There are 2 types of detector arrangements: - Fixed consists of 16 elements with a total length of 2 cm. Signals from sets of 4 individual elements are typically combined. Only fixed values of pitch can be chosen. 14 - Adaptive consists of 8 detectors with different lengths with also a total length of 2 cm. Any pitch value can be chosen from 1 to 8. Advantages: - Shorter acquisition time - Thinner slices: better spatial resolution - Can get isotropic volumes Disadvantages: - Larger beam width - Higher dose for the same quality - Cone beam artifacts 15 2. Nuclear Medicine 2.1. General principles of nuclear medicine Nuclear medicine images the spatial distribution of radiopharmaceuticals introduced in the body. It can detect biochemical changes in tissue, serving as a diagnostic to pathological conditions such as formation of edema, tumor enlargement or metastasis, and changes in the tissue morphology. These radiopharmaceuticals, termed radiotracers, are compounds linked to a radioactive element, whose structure determines its distribution in the body. Radiation, usually in the form of γ-rays, is detected using a gamma camera. The following picture shows the basic principles and instrumentation involved: Decay of the radioa
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