SPECIAL FEATURE: MEDICAL PHYSICS

www.iop.org/Journals/PhysEd

X-ray computed tomographyGreg Michael

The Centre for Medical, Health and Environmental Physics, Queensland University ofTechnology, GPO Box 2434, Brisbane 4074, Australia

AbstractX-ray computed tomography (CT) is a medical imaging technique thatproduces images of transaxial planes through the human body. Whencompared with a conventional radiograph, which is an image of many planessuperimposed on each other, a CT image exhibits significantly improvedcontrast although this is at the expense of reduced spatial resolution.

A CT image is reconstructed mathematically from a large number ofone-dimensional projections of the chosen plane. These projections areacquired electronically using a linear array of solid-state detectors and anx-ray source that rotates around the patient.

X-ray computed tomography is used routinely in radiologicalexaminations. It has also been found to be useful in special applicationssuch as radiotherapy treatment planning and three-dimensional imaging forsurgical planning.

IntroductionIn an x-ray radiograph, e.g. a chest x-ray as shownin figure 1, the three-dimensional (3D) structureof the body is represented by a two-dimensional(2D) image. During the imaging process one of thedimensions is lost. All of the planes in the patientthat are parallel to the x-ray film are superimposedon top of each other. In figure 1 one can see ribs,soft tissues and lung all overlying each other. Theimage is a projection of a 3D volume onto a 2Dsurface.

Because of the superimposition of structures,radiographs do not exhibit high contrast. Boneand air cavities are easily seen but very littlecontrast is obtained in soft tissue regions, e.g. ablood vessel surrounded by muscle will not beseen. In some situations this lack of contrast canbe overcome by using contrast media containingelements such as iodine and barium which highlyattenuate the x-rays. For example, a liquid contrastmedium injected into the bloodstream is used inangiography to make the blood vessels visible.

X-ray computed tomography (CT) is animaging technique which overcomes the problem

of poor contrast and the inability of radiographsto provide depth information. It does this byproducing a 2D image of a 2D plane (slice) throughthe patient as shown in figure 2. Because there isno longer superposition of structures on top of eachother, contrast in the image is greatly improved.Tomography refers to any technique that producesan image of a single plane in the body. Adescription of positron emission tomography canbe found elsewhere in this issue (Badawi 2001).

The production and detection of x-raysIn an x-ray tube, electrons, emitted by thermionicemission from a cathode consisting of a heatedfilament and a focusing cup, are accelerated bya high voltage and focused into a beam so thatthey impinge on a target which forms part of ananode (figure 3). These electrons are referred toas projectile electrons. X-rays are produced bythe sudden deceleration of the projectile electronsby the nuclei of the target material or by collisionof projectile electrons with electrons in the targetatoms. These are referred to as bremsstrahlungx-rays and characteristic x-rays respectively.

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Figure 1. A chest x-ray.

Bremsstrahlung x-rays are emitted when anelectron slows down by coulombic interaction withthe electrostatic field of a target nucleus. When theelectron slows down it loses kinetic energy, whichis converted to electromagnetic radiation, i.e. anaccelerated (or decelerated) charge will radiateelectromagnetic radiation.

The amount of energy radiated depends on the

Figure 2. X-ray computed tomography.

closeness of approach of the projectile electronto the target nucleus. Therefore bremsstrahlungx-rays can have a range of energies from 0up to a maximum equal to the energy of theprojectile electrons. Thus the maximum possiblex-ray energy (in eV) is numerically equal to theaccelerating electric potential, e.g. if the x-ray tubeis operated at 50 kV the maximum x-ray energyis 50 keV. Bremsstrahlung radiation is also calledwhite radiation because of the broad continuousspectrum of x-ray energies produced.

Characteristic x-rays arise from vacancies thatare created in the electron shells when the targetatoms are ionized by the projectile electrons.Electrons from outer shells drop down to fillthe vacancy and release their excess energy inthe form of x-rays. Characteristic x-rays aremonoenergetic. Their energies depend on thebinding energies of the electrons in the electronshells, which in turn depend on the type of theatoms in the anode.

Both bremsstrahlung and characteristic x-rays are produced simultaneously. An examplespectrum for a tungsten target is shown in figure 4.The x-ray tubes used in CT are typically operatedat potentials in the range 100 kV to 150 kV.

Usually a projectile electron does not loseall its energy in one interaction. It undergoesmultiple collisions with the target atoms. Mostof these collisions occur with outer electrons ofthe target atoms and produce mainly heat. Only

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Figure 3. Schematic diagram of a stationary anode x-ray tube. X-rays are emitted in all directions and must becollimated by lead shielding (not shown) to produce a useful beam.

Figure 4. A typical x-ray spectrum for a CT x-ray tubeoperated at 120 kV.

a small proportion of projectile electrons undergointeractions that produce x-rays.

The efficiency of x-ray production is given by(Krestel 1990)

η = aUZ

where U is the accelerating potential (V), Z is theatomic number of the target material, and a is aconstant equal to 1.1 × 10−9 (V−1).

For a tungsten target (Z = 74) and anaccelerating potential of 100 kV the efficiency is0.0081, i.e. < 0.1%. Most of the electron energyis converted to heat. Therefore many of the designfeatures of x-ray tubes are for the dissipation oflarge quantities of heat. These design featuresinclude a line focus and rotating anode to distribute

Figure 5. A typical rotating anode x-ray tube.

the heat over a large target area. A typical rotatinganode medical x-ray tube is shown in figure 5.X-ray tubes used in CT scanners must withstandheavy loads and incorporate additional featuressuch as large diameter compound anodes, metalenvelopes and circulated cooling fluid.

The most common detectors used in CTscanners are scintillator–photodiode solid statedetectors. Some of the materials used asscintillators are caesium iodide (CsI), cadmiumtungstate (CdWO4) or ceramic materials based onyttrium–gadolinium oxides. The x-rays interactwith the scintillator and produce visible light. Thislight is then converted to an electric current by thephotodiode. Some features of these detectors arehigh detection efficiency, good stability, small sizeand high packing density. Examples are shown infigure 6.

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(a) (b)

Figure 6. (a) Two solid state CT detectors. The one on the left is a CdWO4 detector from a fourth generationCT scanner. The other is a CsI detector from a third generation scanner. The scale units on the ruler are mm.(b) A board from a fourth generation CT scanner containing 60 of the larger detectors from (a). Here they areshown, on the left-hand side of the board, with a protective aluminium covering. This particular scanner has 20such boards containing a total of 1200 detectors in a full circle.

Figure 7. (a) The pencil-beam of x-rays is scanned across the patient to acquire a projection that is made up of alarge number of raysums. (b) A large number of projections are acquired, each at a different angle.

The measurement processUnlike the x-ray detector used in radiography(film) the x-ray detectors in a CT scanner donot directly produce an image. They makemeasurements of the transmission of a narrow (1 to10 mm) fan-beam of x-rays through the chosenslice (figure 2) from many different directions andan image is reconstructed mathematically fromthese measurements. The depth information alongthe direction of the x-ray beam that is lost inradiography is recovered by viewing the slice frommany different directions. This is analogous tousing triangulation to determine the distance toa faraway object: the angle between a baseline

and the object must be measured from the twoends of the baseline, i.e. views from two differentdirections are required.

The measurements made by a CT scanner aremost easily explained using a pencil-beam of x-rays (a fan-beam can be considered to be madeup of many adjacent pencil-beams). The beamof x-rays is translated across and rotated aboutthe patient. Figure 7 shows the acquisition beingmade up of a large number of projections (views)taken at different angles around the patient. Eachprojection is made up of a large number of pencil-beam attenuation measurements. Each pencil-beam measurement is referred to as a raysum.

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Figure 8. Each pixel in the image represents a voxel oftissue in the patient.

Mathematically, a measurement made by aCT detector is proportional to the sum of theattenuation coefficients that lie along the raydefined by the pencil-beam of x-rays, hence theterm raysum.

The CT scanner, being an inherentlyelectronic imaging device, produces a digitalimage that consists of a square matrix of pictureelements, i.e. pixels. Each of the pixels in theimage represents a voxel (volume element) oftissue in the patient. This is depicted in figure 8.

Assuming that the x-rays are monoenergeticthen the intensity I1 of an x-ray beam ofincident intensity I0 transmitted beam through asmall volume of tissue having thickness x andattenuation coefficient µ1 is

I1 = I0 exp(−µ1x) (1)

This is depicted in figure 9(a).In traversing from one side of the patient to

the other, the x-ray beam will be attenuated byall of the voxels through which it passes (refer tofigure 9(b)). The emerging x-ray beam will havean intensity I given by

I = I0 exp

(−x

n∑i=1

µi

). (2)

This can be rearranged to give

lnI0

I= x

n∑i=1

µi. (3)

Thus, the natural logarithm of the ratio of incidentto transmitted x-ray intensities is proportional tothe sum of the attenuation coefficients of the voxels

Figure 9. (a) The transmission of an x-ray beamthrough a single voxel. (b) A raysum is the sum ofattenuation coefficients along the path of a single raythrough the patient.

Figure 10. A single projection shown as (a) anintensity profile and (b) an attenuation profile.

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Figure 11. The methods of simple back-projection and filtered back-projection. In simple back-projection themeasured attenuation profiles (a) are simply spread out, or projected, across the image plane (b). In filteredback-projection the attenuation profiles are convolved with a filter function (c) before being back-projected (d).

in the path of the beam. The measured x-rayintensities and the corresponding logarithms ofthe intensity ratios are shown for one projectionin figure 10. The graph of the logarithms of theintensity ratios is often referred to as an attenuationprofile.

Since the x-rays produced by an x-raytube are polyenergetic, equation (3) is only anapproximation. As the beam passes through thepatient the lower energy x-rays are preferentiallyabsorbed and the average energy of the beamincreases. This effect is referred to as beamhardening and it leads to underestimation of thepixel values in the image. A number of algorithms(for example, McDavid et al 1977) have beendeveloped to correct for beam hardening. Theyachieve this by modifying the raysums prior toimage reconstruction.

Image reconstructionConsider a CT image that consists of 512 rowseach containing 512 pixels, i.e. a square matrix

with a total of 262 144 pixels. This is a commonimage format for current scanners. The imagereconstruction process must calculate a value ofthe attenuation coefficient, µi , for each of the262 144 voxels corresponding to these pixels.

One possible method is to measure 262 144raysums (i.e. 512 projections each containing512 raysums) so that we have 262 144 equationsin the form of equation (3). These 262 144simultaneous equations can then be solved for the262 144 unknown values of µi . Solving this manysimultaneous equations is not an easy task andis complicated by the fact that the x-rays rarelyfollow paths that correspond to rows or columnsof pixels as depicted in figure 9(b). Fortunatelythere is a better way to reconstruct the image.

The method used on all current CT scannersis the method of filtered back-projection. Themathematics of filtered back-projection dates backto 1917 with the work of the mathematician,J Radon. Webb (1990) gives an excellentaccount of the history of radiological tomography.

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Filtered back-projection is best explained by firstdescribing the process of simple back-projection.

Simple back-projection is depicted in figures11(a) and 11(b). A single attenuation profile(projection) lacks any depth information and so thevalue of each raysum is shared out equally amongall of the voxels through which the ray passed,i.e. the raysums are back-projected. As shown infigure 11(b), as each attenuation profile is back-projected an image, albeit a poor one, is formed.Each point in the image is surrounded by a star-burst pattern which degrades contrast and blurs theedges of objects.

The degrading star-burst patterns of simpleback-projection can be removed by convolving theattenuation profile with a filter function prior toback-projection (see figure 11(c)). Thus the termfiltered back-projection. The action of the filterfunction is such that the negative values created inthe filtered projection will, when back-projected,exactly cancel out the star-burst patterns andproduce an image that is an accurate representationof the original object (figure 11(d).)

An additional advantage of filtered back-projection is that image reconstruction does notneed to wait until all of the projections have beenacquired. As soon as the first set of measurementsare made by the x-ray detectors they can bepre-processed (i.e. calculate the logarithm of theintensity ratios), filtered and then back-projected.Image reconstruction can proceed simultaneouslywith scanning.

The mathematics of filtered back-projectionand other methods of image reconstruction aredescribed in a review article by Brooks and DiChiro (1976) and in detail by Kak and Slaney(1988). The book by Kak and Slaney is availablefree of charge (for personal use only) in electronicform on the internet at www.slaney.org/pct/.

Scanning geometriesThe x-ray tube and detector geometry depicted infigure 7 is referred to as first generation. Onlythe very first CT scanners (early 1970s) were ofthis configuration. Because of the single detectorand the combination of both translate and rotatemotions, scan times were very long: of the orderof a few minutes.

Second generation CT scanners (figure 12)were developed to decrease scan times. Theyhad a narrow fan-beam of x-rays and a small

Figure 12. Second generation CT scanner.

number of detectors. Multiple projections wereacquired simultaneously (one per detector) duringeach translation and therefore the number oftranslations required was reduced accordingly.

Nearly all current CT scanners use eitherthe third or fourth generation geometries. Thirdgeneration is that shown in figure 2, i.e. the fan-beam of x-rays is wide enough to cover the fullwidth of the patient and therefore no translationmotion is required. The x-ray tube and detectorarc rotate only. The arc of detectors may containup to 1000 individual detectors.

In fourth generation scanners the detectorsform a complete ring around the patient and onlythe x-ray tube has to rotate. These scannersmay use up to nearly 5000 individual detectors.A fourth generation CT scanner is depicted infigure 13.

The fifth generation of CT scanners haseliminated all mechanical motion by using an x-ray tube with an anode that forms a circular arcof about 210◦ around the patient. The scanningmotion is achieved by using magnetic fields tosweep the electron beam along the anode. Thisscanner can acquire a complete set of projectiondata in as little as 50 ms and is designed specificallyfor cardiac imaging.

For the reader who wishes to investigate thesegeometries and methods of image reconstructionfurther, an excellent software simulation of a CT

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Figure 13. The fourth generation geometry.

scanner has been written by Kevin M Rosenbergand can be downloaded free of charge from theinternet at www.ctsim.org.

Helical CTThe conventional way in which CT is used is tokeep the patient stationary during the scanningprocess. Scanning is then halted while the patientis positioned, using a motorized table-top, for thenext scan. During chest and abdominal scans itis necessary for the patient to hold his/her breathduring scanning. Therefore, although one imagemay be acquired in as little as 0.5 s, a procedurerequiring 20 to 30 images may take many minutesto complete.

In helical CT (also referred to as spiral CT andvolume scanning) the x-ray tube and detectors useslip-rings, rather than cables, for their electricalconnections so that they may rotate continuouslywithout stopping. In acquiring multiple images,the x-ray tube and detectors rotate continuouslywhile the patient is translated perpendicular tothe plane of rotation (figure 14). The relativemotion of the x-ray tube and the patient is thatof a helix. Helical CT scanners can scan a largevolume of the patient during a single breath-hold. All the acquired projection data are storedon the computer’s hard disk and the images arereconstructed retrospectively.

The most recent advancements in CTscanning are multi-slice helical scanners. These

Figure 14. Helical computed tomography.

scanners have up to four parallel banks of detectorsso that they acquire multiple slices simultaneously.With a complete set of projection data beingacquired in 180◦ rotation, two complete rotationsper second and four banks of detectors, the latestmulti-slice helical CT scanners can acquire up to16 images per second.

Further information on current CT scannertechnology can be obtained from manufacturers’internet sites, e.g. www.gemedicalsystems.com,www.Picker.com, www.SiemensMedical.com andwww.Toshiba.com. The GE Medical Systems sitealso has a good collection of CT images.

Image displayBefore the image is displayed, the CT scannerconverts the measured attenuation coefficients ofthe voxels to CT numbers. For a voxel, i, the CTnumber, Ni , of the corresponding pixel is relatedto the attenuation coefficient, µi , of the tissue inthe voxel by

Ni = 1000 × µi − µw

µw(4)

where µw is the attenuation coefficient of water.Expressing the attenuation coefficient relative tothat of water dates back to the first clinicalCT scanner, the EMI Mark 1 head scanner of1972. The detectors of this scanner had a lowdynamic range. Therefore the patient’s head wassurrounded by a water bag to reduce the veryhigh x-ray intensity of the unattenuated x-raybeam that would otherwise reach the detectors.The scaling factor of 1000 in equation (4) is

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Figure 15. Range of CT numbers for some tissuetypes.

Figure 16. CT scan of the abdomen with a displaywindow optimized for the liver.

used so that the CT numbers can be expressedas integers. This reduces computer memory andstorage requirements.

From equation (4) it can be seen that the CTnumber of water will be zero, the CT number ofair (µ ≈ 0 cm−1) will be −1000, and a voxelwith tissue having an attenuation coefficient twicethat of water (e.g. bone) will have a CT numberof +1000. Most soft tissues of the human body liein the range ±100. Figure 15 shows the typicalrange of CT numbers for a number of tissues.

CT images are usually viewed as greyscaleimages on a computer monitor. The contrast in the

image can be further enhanced by displaying only awindow of CT numbers. Rather than allocating thefull range of CT numbers to the range of availablegrey levels (from black to white) only a limitedrange of CT numbers is displayed. For example,for the brain, only the range of CT numbers from0 to 70 might be displayed, whereas for the lung,a window from −1000 to −200 might be used.Figure 16 shows an image of the abdomen whichuses a narrow window centred on the range of CTnumbers appropriate for the liver. Pixels with CTnumbers outside this range, such as bone or fat,appear as either pure white or pure black.

ApplicationsComputed tomography is used routinely inradiological examinations because it providescross-sectional images and improved contrastcompared with other x-ray imaging techniques.Its main limitation compared with x-ray film ispoor spatial resolution. The minimum object sizevisible with CT is about 0.5 mm compared withabout 0.05 mm for x-ray film.

Special applications of CT include bonemineral content measurement, cerebral bloodflow using diffusion of inhaled xenon, theuse of stereotactic frames to assist in accuratelocation for needle biopsies, and 3D imaging.Pseudo-3D displays are created from a stackof 2D images of a large number of parallelplanes. An example is shown in figure 17.Clinical applications of 3D imaging includesurgical planning, prosthesis design, craniofacialreconstructions, stereotactic biopsy planning andradiotherapy treatment planning.

CT is useful for radiotherapy treatment plan-ning for a number of reasons, i.e. high soft tissuecontrast provides good visualization of tumours,the images provide accurate spatial informationfor treatment planning, and the pixel values pro-vide radiological properties of the tissues that canbe used for inhomogeneity corrections in dose cal-culations. More information on the application ofCT in radiotherapy is provided by Oldham (2001).

ConclusionDespite the rapid growth of magnetic resonanceimaging (MRI) in the past decade, MRI hasnot superseded CT. CT is still used routinelyin radiological examinations and is, itself,

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Figure 17. A pseudo-3D image of a skull, computergenerated from a stack of 2D images of a large numberof parallel slices.

undergoing rapid growth and development inthe form of multi-slice helical x-ray computedtomography.

Received 6 September 2001PII: S0031-9120(01)28564-5

ReferencesBadawi R 2001 Nuclear medicine Phys. Educ. 36 452Brooks R A and Di Chiro G 1976 Principles of

computer assisted tomography (CAT) inradiographic and radioisotope imaging Phys.Med. Biol. 21 689–732

Kak A C and Slaney M 1988 Principles ofComputerized Tomographic Imaging (New York:IEEE)

Krestel E 1990 Imaging Systems for MedicalDiagnostics (Munich: SiemensAktiengesellschaft)

McDavid W D, Waggener R G, Payne W H andDennis M J 1977 Correction for spectral artefactsin cross-sectional reconstructions from x-raysMed. Phys. 4 54–7

Oldham M 2001 Radiation physics and applications intherapeutic medicine Phys. Educ. 36 460

Webb S 1990 From the Watching of Shadows (Bristol:Adam Hilger)

Greg Michael holds a PhD in medicalphysics from the University ofQueensland. He spent 11 years from1978 at the Queensland Radium Instituteand Royal Brisbane Hospital, then taughtphysics at Central Queensland Universityfor three years before moving toQueensland University of Technology(QUT), where he is currently a lecturerin the School of Physical and ChemicalSciences. His research involves medicalimaging and Monte Carlo modelling.

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