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Tomography is imaging by sections or sectioning. A device used in tomography is called a tomograph, while the image produced is a tomogram. The method is used in medicine, archaeology, biology, and other sciences. In most cases it is based on the mathematical procedure called tomographic reconstruction. The word was derived from the Greek word tomos which means "a section", "a slice" or "a cutting". A tomography of several sections of the body is known as a polytomography.


In conventional medical X-ray tomography, clinical staff make a sectional image through a body by moving an X-ray source and the film in opposite directions during the exposure. Consequently, structures in the focal plane appear sharper, while structures in other planes appear blurred. By modifying the direction and extent of the movement, operators can select different focal planes which contain the structures of interest. Before the advent of more modern computer-assisted techniques, this technique, ideated in the 1930s by the radiologist Alessandro Vallebona, proved useful in reducing the problem of superimposition of structures in projectional (shadow) radiography.

Origins of tomographyEdit

In the early 1900s, the Italian radiologist Alessandro Vallebona proposed a method to represent a single slice of the body on the radiographic film. This method was known as tomography. The idea is based on simple principles of projective geometry: moving synchronously and in opposite directions the X-ray tube and the film, which are connected together by a rod whose pivot point is the focus; the image created by the points on the focal plane appears sharper, while the images of the other points annihilate as noise. This is only marginally effective, as blurring occurs in only the "x" plane. There are also more complex devices that can move in more than one plane and perform more effective blurring.

Modern tomographyEdit

More modern variations of tomography involve gathering projection data from multiple directions and feeding the data into a tomographic reconstruction software algorithm processed by a computer. Different types of signal acquisition can be used in similar calculation algorithms in order to create a tomographic image. With current 2005 technology, tomograms are derived using several different physical phenomena listed in the following table.

Physical phenomenon Type of tomograph
X-rays CT
gamma rays SPECT
electron-positron annihilation PET
electrons Electron tomography or 3D TEM
ions atom probe

Some recent advances rely on using simultaneously integrated physical phenomena, e.g. X-rays for both CT and angiography, combined CT/MRI and combined CT/PET.

The term volume imaging might subsume these technologies more accurately than the term tomography. However, in the majority of cases in clinical routine, staff request output from these procedures as 2-D slice images. As more and more clinical decisions come to depend on more advanced volume visualization techniques, the terms tomography/tomogram may go out of fashion.

Many different reconstruction algorithms exist. Most algorithms fall into one of two categories: filtered back projection (FBP) and iterative reconstruction (IR). These procedures give inexact results: they represent a compromise between accuracy and computation time required. FBP demands fewer computational resources, while IR generally produces fewer artifacts (errors in the reconstruction) at a higher computing cost.

Although MRI and ultrasound make cross sectional images they don't acquire data from different directions. In MRI spatial information is obtained by using magnetic fields. In ultrasound, spatial information is obtained simply by focusing and aiming a pulsed ultrasound beam.

Synchrotron X-ray tomographic microscopyEdit

Recently a new technique called synchrotron X-ray tomographic microscopy (SRXTM) allows for detailed three dimensional scanning of fossils.

Types of tomographyEdit

Mathematical theoryEdit

The mathematical theory behind the Tomographic reconstruction dates back to 1917 where the invention of Radon Transform[1][2] by an Austrian mathematician Johann Radon. He showed mathematically that a function could be reconstructed from an infinite set of its projections.[3] In 1937, a Polish mathematician, named Stefan Kaczmarz, developed a method to find an approximate solution to a large system of linear algebraic equations.[4][5] This led the foundation to another powerful reconstruction method called "Algebraic Reconstruction Technique (ART)" which was later adapted by Sir Godfrey Hounsfield as the image reconstruction mechanism in his famous invention, the first commercial CT scanner. In 1956, Ronald N. Bracewell used a method similar to Radon Transform to reconstruct a map of solar radiation from a set of solar radiation measurements.[6] In 1959, William Oldendorf, a UCLA neurologist and senior medical investigator at the West Los Angeles Veterans Administration hospital, conceived an idea for "scanning a head through a transmitted beam of X-rays, and being able to reconstruct the radiodensity patterns of a plane through the head" after watching an automated apparatus built to reject frostbitten fruit by detecting dehydrated portions. In 1961, he built a prototype in which an X-ray source and a mechanically coupled detector rotated around the object to be imaged. By reconstructing the image, this instrument could get an X-ray picture of a nail surrounded by a circle of other nails, which made it impossible to X-ray from any single angle.[7] In his landmark paper, published in 1961, he described the basic concept later used by Allan McLeod Cormack to develop the mathematics behind computerized tomography. In October, 1963 Oldendorf received a U.S. patent for a "radiant energy apparatus for investigating selected areas of interior objects obscured by dense material," Oldendorf shared the 1975 Lasker award with Hounsfield for that discovery.[8] The field of the mathematical methods of computerized tomography has seen a very active development since then, as is evident from overview literature[9][10][11] by Frank Natterer and Gabor T. Herman, two of the pioneers in the this field.[12]

Tomography has been one of the pillars of radiologic diagnostics until the late 1970s, when the availability of minicomputers and of the transverse axial scanning method – this last due to the work of Godfrey Hounsfield and South African-born Allan McLeod Cormack – gradually supplanted it as the modality of CT. In terms of mathematics, the method is based upon the use of the Radon Transform. But as Cormack remembered later,[13] he had to find the solution himself since it was only in 1972 that he learned of the work of Radon, by chance.

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