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Computed Tomography

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Tomography (CAT, PET, MRI): What it is, what it does?

Tomography is the technique of using ultrasound, gamma rays, or X-rays to obtaining a series of detailed pictures of areas inside the body (imaging); the pictures are created by a computer linked to the imaging machine. The basic problem in computerized tomography is the reconstruction of a function from its line or plane integrals. Applications come from diagnostic radiology, astronomy, electron microscopy, seismology, radar, plasma physics, nuclear medicine and many other fields. More recent kinds of tomography replace the straight line model by an inverse problem for a partial differential equation. Following is a description of some of the common types:

CT Scanner -- It is also know as CAT (Computed Axial Tomography) scan is a desired device to create images of internal structure of unrecognized object. It is a diagnostic technique in which the combined use of a computer and X rays passed through the body at different angles produces clear cross-sectional images (slices) of the tissue being examined. The accuracy of CT image in representing a physical distribution of a cross-sectional 2-D structure is essential. Therefore, standard and reference for judging a CT performance is substantial.
The basic principle of focusing scanner is described in Figure 1. The center of curved array of detectors is at the locus of radiation source that emits fan-beams with a fan angle of g. The center of rotation, O, is at the middle of the line from radiation source to the central detector in the array (s = 0). The radius of image circle is defined as R = S sin(g/2), where S is distance from source to center of rotation. The focusing scanning produces parallel projections f from fan projections q. The focusing principle requires a strict relation of f = q + s, where s indicates orientation of a detector element from the source. The focusing scanning also requires step sampling of fan-projection Dq = (S/R)Ds. This strict requirement ensures the sinogram forms a square pattern in (f, xs) space, where xs = Ss, in which a fan-projection, a set of ray-sum at certain object rotation, q, is along an inclined line (Figure 2). The fan-beam projection lies on the inclined line. The parallel projection consists of parallel ray-paths at angle of projection f. Each detector element associates with beam-width of w = S Ds.
Basic principle...Click to enlarge Sinogram mapping...Click to enlarge CT Scan...Click to enlarge ABDOMEN_CT Image ... Click to enlarge
Figure 1. The basic principle of Focusing CT scanner set-up Figure 2. Sinogram mapping for Focusing CT scanner Figure 3. CT Scan Figure 4. CT Image
This method provides clearer and more detailed information than X rays used by themselves. CT scan also has the advantage of minimizing the amount of radiation exposure. Figure 3 is a schematic of the equipments with a rotating X rays source and detector. The machine looks much like a big donut. The child is positioned in the "donut hole" and an x-ray tube will rotate around his body to generate hundreds of images, known as "slices." These images are processed by a computer to allow the doctor to see soft tissue structures in great detail. Before the scan is carried out, a contrast medium may be injected to make blood vessels, organs, or abnormalities show up more clearly; a drink of contrast medium may be given to highlight loops of intestine. The amount of X rays absorbed by different tissues is recorded by the detector and transformed by a computer into an image. Figure 4 shows a CT cross-section of the chest. The first CT scanner, which came into operation in 1972, was developed to study the brain. Since the, CT brain scanning has revolutionized the diagnosis and treatments of tumors, abscesses, and hemorrhages in the brain, as well as strokes and head injuries. It is also invaluable in investigating disease of any part of the trunk. It is particularly useful for locating and imaging tumors, and for facilitating needle biopsy (removal of a sample of tissue via a needle).

PET (Positron Emission Tomography) -- It is a diagnostic technique based on the detection of coincidence events from electron-positron annihilation, which converts the masses to two 511 Kev X-rays moving in opposite directions (see Figure 5). Before performing the scan, substances that take part in biochemical processes in the body are labeled with radioisotopes ( such as carbon 11, nitrogen 13, or oxygen 15).
PET Scan...Click to Enlarge BRAIN_PET Image...Click to Enlarge
These substances are injected into the blood-stream and are taken up in greater concentrations by areas of tissue that are more metabolically active. In the tissue, the substances emit positrons, which, in turn, release X-rays. It is the detection of these X-rays that actually forms the basis of PET scanning. By surrounding the patient with an array of detectors linked to a computer, the origin of the X-rays can be computed and a picture built of the distribution of the radio- active isotopes. Figure 6 is a sample of the PET brain scan. PET scanning is particularly valuable for investigating the brain.
Figure 5. PET Scan Figure 6. PET Image
It is used for detecting tumors, for locating the origin of epileptic activity within the brain, and for examining brain function in various mental illnesses. PET images are different from those obtained from more routine imaging equipment, such as X-Ray, CT, Ultrasound, or MRI as these scans show what the tissues look like whereas P.E.T. studies contain information about tissue function and metabolism. This technique has a serious drawback in that it requires an injection of radioactive marker. The dose is tiny but, for safety, no one person is generally allowed to have more than one scanning session a year. The most commonly used radiopharmaceutical, Fluorine deoxyglucose (FDG) demonstrates where metabolism of glucose is occurring in the body, including malignant cells. There are other radiopharmaceuticals that demonstrate other aspects of metabolism, but they are less commonly used at the present time. P.E.T. produces images of the body that represent the functional rather than anatomical characteristics of disease, resulting in the early detection of many abnormalities that are undetected using conventional X-Rays, CT, or MRI scans.

MRI (Magnetic Resonance Imaging) -- It is sometimes called NMR (Nuclear Magnetic Imaging). MRI is a diagnostic technique that provides high-quality cross-sectional or three dimensional images of organs and structures within the body without using X rays or other radiation. During the imaging, the patient lies inside a massive hollow cylindrical magnet (see Figure 7). The nuclei (protons) of the body's hydrogen atoms normally point in random directions. In a magnetic field, however, these atoms line up parallel to each other. If the hydrogen nuclei are then knocked out of alignment by a strong pulse of radio waves, they produce a detectable radio signal as they fall back into alignment.
MRI Scan...Click to Enlarge BRAIN_MRI Image...Click to Enlarge
Magnetic field gradient is required to translates the signals into separate spatial locations. Magnetic coils in the machine detect these signals and a computer changes them into a cross-sectional or three dimensional image based on the strength of signal produced by different types of tissue. Tissues that contain a lot of hydrogen (such as fat) produce a bright image; those that contain little or no hydrogen (such as bone) appear dark. Figure 8 is a MRI image of the head. MRI provides clear images of tumors of the brain and spinal cord.
Figure 7. MRI Scan Figure 8. MRI Image
Also shown clearly by MRI is the internal structure of the eye and ear. MRI can produces detailed images of the heart and major blood vessels, provides images of blood flow, and is useful for examining joints and soft tissues. Functional Magnetic Resonance Imaging (fMRI) is a technique for determining which parts of the brain are activated by different types of physical sensation or activity, such as sight, sound or the movement of a subject's fingers. This "brain mapping" is achieved by setting up an advanced MRI scanner in a special way so that the increased blood flow to the activated areas of the brain shows up on Functional MRI scans. fMRI is proving to be the most rewarding of scanning techniques, but it is phenomenally expensive. For this reason a lot of experimental work is still done by the older technique of PET. Neurosurgeons use a MRI scan not only in defining brain anatomy but also in evaluating the integrity of the spinal cord after trauma. It is also used when considering problems associated with the vertebrae or intervertebral discs of the spine. A MRI scan can evaluate the structure of the heart and aorta, where it can detect aneurysms or tears. It provides valuable information on glands and organs within the abdomen, and accurate information about the structure of the joints, soft tissues, and bones of the body. Often, surgery can be deferred or more accurately directed after knowing the results of a MRI scan.

See more information about tomography's mathematics on this Web Site


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