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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 tomography
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.
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|
|electrons||Electron tomography or 3D TEM|
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 microscopy
Recently a new technique called synchrotron X-ray tomographic microscopy (SRXTM) allows for detailed three dimensional scanning of fossils.
Types of tomography
- Atom probe tomography (APT)
- Computed tomography (CT)
- Confocal laser scanning microscopy (LSCM)
- Cryo-electron tomography (Cryo-ET)
- Discrete tomography (DT)
- Electrical capacitance tomography (ECT)
- Electrical resistivity tomography (ERT)
- Electrical impedance tomography (EIT)
- Functional magnetic resonance imaging (fMRI)
- Heidelberg Retinal Tomography (HRT-II),
- Magnetic induction tomography (MIT)
- Magnetic resonance imaging (MRI), formerly known as magnetic resonance tomography (MRT) or nuclear magnetic resonance tomography
- Neutron tomography
- Optical coherence tomography (OCT)
- Optical projection tomography (OPT)
- Process tomography (PT)
- Positron emission tomography (PET)
- Positron emission tomography - computed tomography (PET-CT)
- Quantum tomography
- Single photon emission computed tomography (SPECT)
- Seismic tomography
- Ultrasound assisted optical tomography (UAOT)
- Ultrasound transmission tomography
- X-ray tomography (CT, CATScan)
- Photoacoustic tomography (PAT), also known as Optoacoustic Tomography (OAT) or Thermoacoustic Tomography (TAT)
- Zeeman-Doppler imaging, used to reconstruct the magnetic geometry of rotating stars.
The mathematical theory behind the Tomographic reconstruction dates back to 1917 where the invention of Radon Transform by an Austrian mathematician Johann Radon. He showed mathematically that a function could be reconstructed from an infinite set of its projections. In 1937, a Polish mathematician, named Stefan Kaczmarz, developed a method to find an approximate solution to a large system of linear algebraic equations. 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. 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. 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. The field of the mathematical methods of computerized tomography has seen a very active development since then, as is evident from overview literature by Frank Natterer and Gabor T. Herman, two of the pioneers in the this field.
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, he had to find the solution himself since it was only in 1972 that he learned of the work of Radon, by chance.
- Computer assisted diagnosis
- Medical imaging
- MRI compared with CT
- Network tomography
- Nonogram, a type of puzzle based on a discrete model of tomography
- Radon transform
- Tomographic reconstruction
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- Radon J., Uber die Bestimmung von Funktionen durch ihre Integralwerte Langs Gewisser Mannigfaltigkeiten (English translation: On the determination of functions from their integrals along certain manifolds). Ber. Saechsische Akad. Wiss. 1917;29: 262.
- Radon J., Translated by Parks PC., On the determination of functions from their integrals along certain manifolds. IEEE Trans. Med. Imaging. 1993;MI-5: 170-6.
- Hornich H., Translated by Parks PC. A Tribute to Johann Radon. IEEE Trans. Med. Imaging. 1986;5(4):169-9.
- Kaczmarz, S., Angenäherte Auflösung von Systemen linearer Gleichungen. Bulletin International de l'Académie Polonaise des Sciences et des Lettres. Classe des Sciences Mathématiques et Naturelles. Série A, Sciences Mathématiques. 1937;35: 355–7.
- Kaczmarz S., Approximate solution of system of linear equations. Int. J. Control. 1993; 57-9.
- Bracewell RN., [Strip Integration in Radio Astronomyhttp://articles.adsabs.harvard.edu//full/1956AuJPh...9..198B/0000198.000.html]. Aust. J. Phys. 1956;9: 198-217.
- Oldendorf WH. Isolated flying spot detection of radiodensity discontinuities--displaying the internal structural pattern of a complex object. Ire Trans Biomed Electron. 1961 Jan;BME-8:68-72.
- Oldendorf WH. The quest for an image of brain: a brief historical and technical review of brain imaging techniques. Neurology. 1978 Jun;28(6):517-33.
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- F. Natterer, "The Mathematics of Computerized Tomography (Classics in Applied Mathematics)",Society for Industrial Mathematics, isbn= 0898714931
- F. Natterer and F. Wübbeling "Mathematical Methods in Image Reconstruction (Monographs on Mathematical Modeling and Computation)", Society for Industrial (2001), isbn= 0898714729
- More Mathematics into Medicine!. Zuse Institute Berlin.
- Allen M.Cormack: My Connection with the Radon Transform, in: 75 Years of Radon Transform, S. Gindikin and P. Michor, eds., International Press Incorporated (1994), pp. 32 - 35, ISBN 1-57146-008-X