Medical Physics. Medical Physics. Medical Imaging. Medical Imaging X-rays. Medical Imaging Nuclear Medicine

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1 Medical Physics Prof. Clive Baldock Institute of Medical Physics School of Physics University of Sydney 1 2! "#$%&'(&'%&) Medical Physics! *+,'-$.&/0$1'21! 3$,'4%#+5$67! 8+$.%#&9#7('-( Medical Imaging! :'$124('(&4;&,'(+$(+! :'$124(%'-&3$,'4.417! <=5$7( '0$1'21&+1 -#+(%&A=5$7 > B406C%+5&D40415$6#7&EBDF! GC-.+$5&*+,'-'2+! H.%5$(4C2,! *$12+%'-&3+(42$2-+&/0$1'21&E*3/F 3 4 Medical Imaging X-rays Medical Imaging Nuclear Medicine 5 6 1

2 Medical Imaging MRI Medical Imaging Ultrasound 7 8 Radiotherapy Health Physics! 3$,'$%'42&954%+-%' Resources

3 Web Resources! /2%+52$%'42$.&I51$2'($%'42 4;&*+,'-$.&9#7('-( > /I*9J&KKKL'406L451! M0+5'-$2&M((4-'$%'42&4;&9#7('-'(%(&'2&*+,'-'2+ > MM9*J&KKKL$$60L451! MC(%5$.$('$2&B4..+1+&4;&9#7('-$.&N-'+2%'(%(&$2,& O21'2++5(&'2&*+,'-'2+ > MB9NO*J&KKKL$-6(+0L451L$C! /2(%'%C%+&4;&9#7('-(&$2,&O21'2++5'21&'2&*+,'-'2+ > /9O*J&KKKL'6+0L451LCP CANCER TREATMENT TUMOR CELLS CARCINOMA EXTRAVASATION INTERVASATIE HYPERPLASIE METASTASIS TRANSPORT DYSPLASIE ADHESION INVASIE IN SITU SURGERY CHEMOTHERAPY RADIOTHERAPY BASAL LAYER STROMA HEALTHY CELLS TUMOR- CELLS ORGAN 2 HORMONE THERAPY BLOOD VESSEL IMMUNOTHERAPY ORGAN CAPILARY THE PROBLEM IN RADIOTHERAPY THE PROBLEM IN RADIOTHERAPY : Depth-dose curve Cross section patient Irradiation dose Irradiation target (tumour) depth depth

4 CONFORMAL RADIOTHERAPY TUMOR VERSUS HEALTHY TISSUE CHANGE OF CURE / COMPLICATIONS TUMOR CONTROL 100 % COMPLICATIONS Irradiation 50 % target (tumor) COLLIMATOR LINEAR ACCELERATOR Healthy (critical) organ DIFFERENT BEAM INCIDENCES 0% ABSORBED DOSE MULTI-LEAF COLLIMATOR THE NORMAL PROCEDURE IN CONFORMAL RADIOTHERAPY INTENSITY MODULATED RADIOTHERAPY MR-scan 1st beam 2nd beam 10 Gy 3th beam Image set 20 Gy Patient Computerplanning CT-scan 30 Gy 21 simulator Treatment 22 GEL DOSIMETRY: THE IDEA THE NEED OF EXPERIMENTAL DOSE VERIFICATION RADIATION-DOSIMETRY IN THREE DIMENSIONS Discrepancies with computer calculations Deviations of machine and beams Radiation sensitive agent Transfer errors, set-up errors (iso center) Radiation sensitive agent dissolved in gel

5 Gel Dosimetry Method a) b) c) Polymer Gel Dosimeters Based on polymerisation and cross-linking of monomers. d) e) f) Polymer Gel Dosimeters Polymer Gel Dosimeters Typical composition 89% Water 5% Gelatin 3% Acrylamide 3% N,N -methylene-bis-acrylamide 27 PAG or BANG-type - note BANG is now a commercial product 28 CH 2 = CH! C=O! NH 2 Acrylamide CH 2 = CH! C=O! NH! CH 2! NH! C=O! CH 2 = CH CH 2 -- CH--! C=O! NH 2 CH 2 -- CH--! C=O! NH n! CH 2! NH! C=O! CH 2 -- CH-- CH 2 -- CH--! C=O! NH 2 n Polyacrylamide CH 2 -- CH-- CH 2 -- CH--!! C=O C=O!! N,N -methylenebis-acrylamide NH 2 NH 2 n n

6 Co-polymerisation Reactions Water + " # Radicals + Ions Electron microscopic images of PAG Radicals + Monomers # RM (Initiation step) RM + M # RM RM + M 1 (ACR) # RM (Propagation) RM + M 2 (BIS) # RM RM + RM # Dead polymer (Termination) 0 Gy 25 Gy H NMR spectra FT-Raman Spectra 3% AA, 3% BIS, 5% gelatin, 89% D 2 O 3% AA, 3% BIS, 5% gelatin, 89% H 2 O 1 H NMR INTENSITY (arb. units) BIS NH AA NH 2 BIS and AA H 2 C=C 0 Gy 10 Gy H 2 O BIS CH 2 gelatin CH, CH 2 x 20 x 5 x 1 x 50 FT-RAMAN INTENSITY (arb. units) 0 Gy 10 Gy 50 Gy 50 Gy CHEMICAL SHIFT (ppm) WAVENUMBERS (cm -1 ) 34 3% AA, 3% BIS, 5% gelatin, 89% H 2 O 100 Decay of vinyl CH 2 asymmetric and symmetric stretches Growth of alkyl CH 2 asymmetric and sysmmetric stretches INTENSITY (arb. units) cm -1 CH 2 a.s. stretch BIS+AA 7.28 ± 1.62 Gy 3039 cm -1 CH 2 s. stretch BIS+AA 6.63 ± 0.53 Gy 2940 cm -1 CH 2 a.s. stretch polyacrylamide 6.20 ± 1.81 Gy 2884 cm -1 CH 2 s. stretch polyacrylamide 5.37 ± 2.15 Gy DOSE (Gy)

7 Magnetic Resonance Imaging (MRI) (1.5 Tesla, 64 MHz). DOSE MEASUREMENT OF A SINGLE BEAM GEL 37 DIAMOND- DETECTOR 38 Depth Dose Curve FROM TUMOUR TO GEL DOSIMETRY TUMOR Dose [Gy] REGION under investigation! Depth [mm] Polymer Gel Diamond detector COMPARISON WITH FILM DOSIMETRY IRRADIATION OF A TORSO PHANTOM Gantry: 190 º Collimator: 180 º Table: 0º Gantry: 170º Collimator: 180º Table: 0º Radiographic film Polystyrene plates Wedge out out out in I 6 MV 0.5 % 0.0 % 1.1 % 15.4 % 25 MV 0.0 % 3.0 % 0.8 % 10.9 % in out Wedge 15.5 % 1.7 % 11.7 % 3.1 % II 6 MV 25 MV Gantry: 310º Collimator: 228 Table: 300 º º Gantry: 50 Collimator: 132 Table: 60 º º º Wedge out out in III 6 MV 0.6 % 0.0 % 9.2 % 25 MV 0.0 % 1.6 % 9.4 % III Cranial IV in out out out out Wedge 10.2 % 9.4 % 1.1 % 2.2 % 0.9 % 10.6 % 3.9 % 3.1 % 2.4 % 7.0 % IV 6 MV 25 MV º Gantry: 300 Collimator: 206 Table: 315 º º Gantry: 60º Collimator: 154 Table: 45 º º Wedge out out out out in V 6 MV 2.2 % 1.3 % 2.2 % 2.4 % 25 MV 2.4 % 0.8 % 1.6 % 5.5 % 8.6 % 8.6 % V I II VI in out 9.8 % 4.5 % 9.4 % 5.4 % Wedge VI 6 MV 25 MV Patient Right 0 º 90º Patient Left Gantry angle FILM DOSIMETRY GEL DOSIMETRY

8 TRANSVERSE DOSE IMAGES COMPARISON OF DOSE IMAGES GEL GEL FILM - GEL FILM FILM PLANNING - GEL PLANNING PLANNING PLANNING - FILM -93 mm -42 mm 5 mm 63 mm 9443 mm Position: Position: Position: Position: (from iso) +63 (from iso) +5 (from iso) +63 (from iso) QUANTITATIVE COMPARISON OF DOSE IMAGES QUANTITATIVE COMPARISON OF DOSE IMAGES GEL Pixel value averaged in region i = diffi 6 MV 25 MV Film - Gel Planning - Gel Planning - Film Film - Gel Planning - Gel Planning - Film FILM GRID RMSDSTRUCT 2.3 % 3.6 % 4.1 % 2.8 % 4.8 % 4.2 % DIFFERENCE IMAGE RMSD % n 1.& ( diff n i% 1 diff ) struct $ 2 i RMSD stoch % n 1 1.& n N i% 1 reg N reg.& ( diff j% 1 2 j, i $ diff i ) RMSDSTOCH 0.98 % 1.0 % 0.59 % 0.65 % 0.68 % 0.44 % Sys. Dev % 2.5 % 3.1 % -0.7 % 3.2 % 3.9 % RMSD tot % ( RMSD struct ) ' ( RMSD stoch ) 46 3D Reconstruction

9 MRI Optical 8cm

10 Physics Education Volume 36, Number 6, November 2001 C O M M E N T Medical Physics strides forward The majority of physics applications in medicine may be said to stem from two discoveries at the end of the 19th century. In 1895 Roentgen discovered x-rays and in 1896 Becquerel discovered radioactivity. Subsequently, both of these discoveries resulted in fundamental changes in the way medicine was practised. X-rays have since been used to produce images of the inside of the human body and in the treatment of cancer, with radionuclides also being used for both of these purposes. The discovery of the electron by Thomson in 1897 was also to have a major impact on medicine with the subsequent development of electro-medical instrumentation. The use of x-rays to investigate the body resulted in the development of the field of diagnostic radiology. The use of x-rays along with the radiation emitted by radioactive decay for the treatment of malignant tumours resulted in the development of the field of radiotherapy or radiation oncology. Early estimates of the amount of radiation delivered to tumours were made by observing the skin redness that occurred after exposure. However, it was realized that more quantitative and precise methods were required to determine radiation doses. This led to the appointment of physicists to hospitals to develop techniques of radiation dosimetry. As the effects of radiation on the body became better understood it was necessary to limit the indiscriminate exposure of individuals to ionizing radiation. This resulted in the field of radiation protection. After the second world war numerous artificially produced radionuclides became available. As well as being used for the treatment of cancer, radionuclides were used to localize specific organs and diseases in the body. This resulted in the development of the field of nuclear medicine. With the development of digital computers it was subsequently possible to reconstruct crosssectional images of the body, resulting in the 1970s in computerized tomography. As a further result of developments that took place during the second world war, Clive Baldock A century ago the profession of medical physics did not exist. Today, however, thousands of individuals work in this speciality throughout the world ultrasound scanners were developed which enabled the foetus to be viewed during pregnancy using non-ionizing radiation. Another important development utilizing non-ionizing radiation was nuclear magnetic resonance, with the potential for magnetic resonance imaging being realized in the 1980s and subsequently becoming a major diagnostic tool. There are a number of exciting developments in medical physics which may in the future contribute to a greater understanding of how the body functions. These include the use of SQUID (superconducting quantum interference devices) magnetometers and terahertz imaging. However, it remains to be seen what impact they will have in the medical field. A century ago the medical physics profession did not exist. Today, however, thousands of individuals work in this speciality throughout the world. Over the last 50 years there has been a growth of international organizations concerned with the application of physics in medicine. See the Web Watch on page 507. There is lots of interest in medical physics, and there are always students who want to know more. If a student wants a career in medical physics they would be advised to follow a BSc in Physics or Biomedical Engineering with a specific medical physics postgraduate degree. Further details regarding career opportunities may be obtained from the Web Watch links or from the author. Physics Education would like to thank guest-editor Alan Piercy for assembling this series of useful, interesting and informative articles covering a wide range of applications of physics in medicine. These articles bring us right up to date and point the way of developments in the 21st century. Clive Baldock P HYSI C S E D U C AT I O N 441

11 SPECIAL FEATURE: MEDICAL PHYSICS X-ray computed tomography Greg Michael The Centre for Medical, Health and Environmental Physics, Queensland University of Technology, GPO Box 2434, Brisbane 4074, Australia Abstract X-ray computed tomography (CT) is a medical imaging technique that produces images of transaxial planes through the human body. When compared with a conventional radiograph, which is an image of many planes superimposed on each other, a CT image exhibits significantly improved contrast although this is at the expense of reduced spatial resolution. A CT image is reconstructed mathematically from a large number of one-dimensional projections of the chosen plane. These projections are acquired electronically using a linear array of solid-state detectors and an x-ray source that rotates around the patient. X-ray computed tomography is used routinely in radiological examinations. It has also been found to be useful in special applications such as radiotherapy treatment planning and three-dimensional imaging for surgical planning. Introduction In an x-ray radiograph, e.g. a chest x-ray as shown in figure 1, the three-dimensional (3D) structure of the body is represented by a two-dimensional (2D) image. During the imaging process one of the dimensions is lost. All of the planes in the patient that are parallel to the x-ray film are superimposed on top of each other. In figure 1 one can see ribs, soft tissues and lung all overlying each other. The image is a projection of a 3D volume onto a 2D surface. Because of the superimposition of structures, radiographs do not exhibit high contrast. Bone and air cavities are easily seen but very little contrast is obtained in soft tissue regions, e.g. a blood vessel surrounded by muscle will not be seen. In some situations this lack of contrast can be overcome by using contrast media containing elements such as iodine and barium which highly attenuate the x-rays. For example, a liquid contrast medium injected into the bloodstream is used in angiography to make the blood vessels visible. X-ray computed tomography (CT) is an imaging technique which overcomes the problem of poor contrast and the inability of radiographs to provide depth information. It does this by producing a 2D image of a 2D plane (slice) through the patient as shown in figure 2. Because there is no longer superposition of structures on top of each other, contrast in the image is greatly improved. Tomography refers to any technique that produces an image of a single plane in the body. A description of positron emission tomography can be found elsewhere in this issue (Badawi 2001). The production and detection of x-rays In an x-ray tube, electrons, emitted by thermionic emission from a cathode consisting of a heated filament and a focusing cup, are accelerated by a high voltage and focused into a beam so that they impinge on a target which forms part of an anode (figure 3). These electrons are referred to as projectile electrons. X-rays are produced by the sudden deceleration of the projectile electrons by the nuclei of the target material or by collision of projectile electrons with electrons in the target atoms. These are referred to as bremsstrahlung x-rays and characteristic x-rays respectively. 442 P H Y S I C S E D U C A T I O N /01/ $ IOP Publishing Ltd

12 X-ray computed tomography Figure 1. A chest x-ray. Bremsstrahlung x-rays are emitted when an electron slows down by coulombic interaction with the electrostatic field of a target nucleus. When the electron slows down it loses kinetic energy, which is converted to electromagnetic radiation, i.e. an accelerated (or decelerated) charge will radiate electromagnetic radiation. The amount of energy radiated depends on the closeness of approach of the projectile electron to the target nucleus. Therefore bremsstrahlung x-rays can have a range of energies from 0 up to a maximum equal to the energy of the projectile electrons. Thus the maximum possible x-ray energy (in ev) is numerically equal to the accelerating electric potential, e.g. if the x-ray tube is operated at 50 kv the maximum x-ray energy is 50 kev. Bremsstrahlung radiation is also called white radiation because of the broad continuous spectrum of x-ray energies produced. Characteristic x-rays arise from vacancies that are created in the electron shells when the target atoms are ionized by the projectile electrons. Electrons from outer shells drop down to fill the vacancy and release their excess energy in the form of x-rays. Characteristic x-rays are monoenergetic. Their energies depend on the binding energies of the electrons in the electron shells, which in turn depend on the type of the atoms in the anode. Both bremsstrahlung and characteristic x- rays are produced simultaneously. An example spectrum for a tungsten target is shown in figure 4. The x-ray tubes used in CT are typically operated at potentials in the range 100 kv to 150 kv. Usually a projectile electron does not lose all its energy in one interaction. It undergoes multiple collisions with the target atoms. Most of these collisions occur with outer electrons of the target atoms and produce mainly heat. Only Figure 2. X-ray computed tomography. PHYSICS EDUCATION 443

13 G Michael Figure 3. Schematic diagram of a stationary anode x-ray tube. X-rays are emitted in all directions and must be collimated by lead shielding (not shown) to produce a useful beam. Figure 5. A typical rotating anode x-ray tube. Figure 4. A typical x-ray spectrum for a CT x-ray tube operated at 120 kv. a small proportion of projectile electrons undergo interactions 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 the atomic number of the target material, and a is a constant equal to (V 1 ). For a tungsten target (Z = 74) and an accelerating potential of 100 kv the efficiency is , i.e. < 0.1%. Most of the electron energy is converted to heat. Therefore many of the design features of x-ray tubes are for the dissipation of large quantities of heat. These design features include a line focus and rotating anode to distribute the heat over a large target area. A typical rotating anode medical x-ray tube is shown in figure 5. X-ray tubes used in CT scanners must withstand heavy loads and incorporate additional features such as large diameter compound anodes, metal envelopes and circulated cooling fluid. The most common detectors used in CT scanners are scintillator photodiode solid state detectors. Some of the materials used as scintillators are caesium iodide (CsI), cadmium tungstate (CdWO 4 ) or ceramic materials based on yttrium gadolinium oxides. The x-rays interact with the scintillator and produce visible light. This light is then converted to an electric current by the photodiode. Some features of these detectors are high detection efficiency, good stability, small size and high packing density. Examples are shown in figure PHYSICS EDUCATION

14 X-ray computed tomography (a) Figure 6. (a) Two solid state CT detectors. The one on the left is a CdWO 4 detector from a fourth generation CT 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 are shown, on the left-hand side of the board, with a protective aluminium covering. This particular scanner has 20 such boards containing a total of 1200 detectors in a full circle. (b) Figure 7. (a) The pencil-beam of x-rays is scanned across the patient to acquire a projection that is made up of a large number of raysums. (b) A large number of projections are acquired, each at a different angle. The measurement process Unlike the x-ray detector used in radiography (film) the x-ray detectors in a CT scanner do not directly produce an image. They make measurements of the transmission of a narrow (1 to 10 mm) fan-beam of x-rays through the chosen slice (figure 2) from many different directions and an image is reconstructed mathematically from these measurements. The depth information along the direction of the x-ray beam that is lost in radiography is recovered by viewing the slice from many different directions. This is analogous to using triangulation to determine the distance to a faraway object: the angle between a baseline and the object must be measured from the two ends of the baseline, i.e. views from two different directions are required. The measurements made by a CT scanner are most easily explained using a pencil-beam of x- rays (a fan-beam can be considered to be made up of many adjacent pencil-beams). The beam of x-rays is translated across and rotated about the patient. Figure 7 shows the acquisition being made up of a large number of projections (views) taken at different angles around the patient. Each projection is made up of a large number of pencilbeam attenuation measurements. Each pencilbeam measurement is referred to as a raysum. PHYSICS EDUCATION 445

15 G Michael Figure 8. Each pixel in the image represents a voxel of tissue in the patient. Mathematically, a measurement made by a CT detector is proportional to the sum of the attenuation coefficients that lie along the ray defined by the pencil-beam of x-rays, hence the term raysum. The CT scanner, being an inherently electronic imaging device, produces a digital image that consists of a square matrix of picture elements, i.e. pixels. Each of the pixels in the image represents a voxel (volume element) of tissue in the patient. This is depicted in figure 8. Assuming that the x-rays are monoenergetic then the intensity I 1 of an x-ray beam of incident intensity I 0 transmitted beam through a small volume of tissue having thickness x and attenuation coefficient µ 1 is Figure 9. (a) The transmission of an x-ray beam through a single voxel. (b) A raysum is the sum of attenuation coefficients along the path of a single ray through the patient. I 1 = I 0 exp( µ 1 x) (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 by all of the voxels through which it passes (refer to figure 9(b)). The emerging x-ray beam will have an intensity I given by ( ) n I = I 0 exp x µ i. (2) This can be rearranged to give i=1 ln I n 0 I = x µ i. (3) i=1 Thus, the natural logarithm of the ratio of incident to transmitted x-ray intensities is proportional to the sum of the attenuation coefficients of the voxels Figure 10. A single projection shown as (a) an intensity profile and (b) an attenuation profile. 446 PHYSICS EDUCATION

16 X-ray computed tomography Figure 11. The methods of simple back-projection and filtered back-projection. In simple back-projection the measured attenuation profiles (a) are simply spread out, or projected, across the image plane (b). In filtered back-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-ray intensities and the corresponding logarithms of the intensity ratios are shown for one projection in figure 10. The graph of the logarithms of the intensity ratios is often referred to as an attenuation profile. Since the x-rays produced by an x-ray tube are polyenergetic, equation (3) is only an approximation. As the beam passes through the patient the lower energy x-rays are preferentially absorbed and the average energy of the beam increases. This effect is referred to as beam hardening and it leads to underestimation of the pixel values in the image. A number of algorithms (for example, McDavid et al 1977) have been developed to correct for beam hardening. They achieve this by modifying the raysums prior to image reconstruction. Image reconstruction Consider a CT image that consists of 512 rows each containing 512 pixels, i.e. a square matrix with a total of pixels. This is a common image format for current scanners. The image reconstruction process must calculate a value of the attenuation coefficient, µ i, for each of the voxels corresponding to these pixels. One possible method is to measure raysums (i.e. 512 projections each containing 512 raysums) so that we have equations in the form of equation (3). These simultaneous equations can then be solved for the unknown values of µ i. Solving this many simultaneous equations is not an easy task and is complicated by the fact that the x-rays rarely follow paths that correspond to rows or columns of pixels as depicted in figure 9(b). Fortunately there is a better way to reconstruct the image. The method used on all current CT scanners is the method of filtered back-projection. The mathematics of filtered back-projection dates back to 1917 with the work of the mathematician, J Radon. Webb (1990) gives an excellent account of the history of radiological tomography. PHYSICS EDUCATION 447

17 G Michael Filtered back-projection is best explained by first describing the process of simple back-projection. Simple back-projection is depicted in figures 11(a) and 11(b). A single attenuation profile (projection) lacks any depth information and so the value of each raysum is shared out equally among all of the voxels through which the ray passed, i.e. the raysums are back-projected. As shown in figure 11(b), as each attenuation profile is backprojected an image, albeit a poor one, is formed. Each point in the image is surrounded by a starburst pattern which degrades contrast and blurs the edges of objects. The degrading star-burst patterns of simple back-projection can be removed by convolving the attenuation profile with a filter function prior to back-projection (see figure 11(c)). Thus the term filtered back-projection. The action of the filter function is such that the negative values created in the filtered projection will, when back-projected, exactly cancel out the star-burst patterns and produce an image that is an accurate representation of the original object (figure 11(d).) An additional advantage of filtered backprojection is that image reconstruction does not need to wait until all of the projections have been acquired. As soon as the first set of measurements are made by the x-ray detectors they can be pre-processed (i.e. calculate the logarithm of the intensity ratios), filtered and then back-projected. Image reconstruction can proceed simultaneously with scanning. The mathematics of filtered back-projection and other methods of image reconstruction are described in a review article by Brooks and Di Chiro (1976) and in detail by Kak and Slaney (1988). The book by Kak and Slaney is available free of charge (for personal use only) in electronic form on the internet at Scanning geometries The x-ray tube and detector geometry depicted in figure 7 is referred to as first generation. Only the very first CT scanners (early 1970s) were of this configuration. Because of the single detector and the combination of both translate and rotate motions, scan times were very long: of the order of a few minutes. Second generation CT scanners (figure 12) were developed to decrease scan times. They had a narrow fan-beam of x-rays and a small Figure 12. Second generation CT scanner. number of detectors. Multiple projections were acquired simultaneously (one per detector) during each translation and therefore the number of translations required was reduced accordingly. Nearly all current CT scanners use either the third or fourth generation geometries. Third generation is that shown in figure 2, i.e. the fanbeam of x-rays is wide enough to cover the full width of the patient and therefore no translation motion is required. The x-ray tube and detector arc rotate only. The arc of detectors may contain up to 1000 individual detectors. In fourth generation scanners the detectors form a complete ring around the patient and only the x-ray tube has to rotate. These scanners may use up to nearly 5000 individual detectors. A fourth generation CT scanner is depicted in figure 13. The fifth generation of CT scanners has eliminated all mechanical motion by using an x- ray tube with an anode that forms a circular arc of about 210 around the patient. The scanning motion is achieved by using magnetic fields to sweep the electron beam along the anode. This scanner can acquire a complete set of projection data in as little as 50 ms and is designed specifically for cardiac imaging. For the reader who wishes to investigate these geometries and methods of image reconstruction further, an excellent software simulation of a CT 448 PHYSICS EDUCATION

18 X-ray computed tomography Figure 14. Helical computed tomography. Figure 13. The fourth generation geometry. scanner has been written by Kevin M Rosenberg and can be downloaded free of charge from the internet at Helical CT The conventional way in which CT is used is to keep the patient stationary during the scanning process. Scanning is then halted while the patient is positioned, using a motorized table-top, for the next scan. During chest and abdominal scans it is necessary for the patient to hold his/her breath during scanning. Therefore, although one image may be acquired in as little as 0.5 s, a procedure requiring 20 to 30 images may take many minutes to complete. In helical CT (also referred to as spiral CT and volume scanning) the x-ray tube and detectors use slip-rings, rather than cables, for their electrical connections so that they may rotate continuously without stopping. In acquiring multiple images, the x-ray tube and detectors rotate continuously while the patient is translated perpendicular to the plane of rotation (figure 14). The relative motion of the x-ray tube and the patient is that of a helix. Helical CT scanners can scan a large volume of the patient during a single breathhold. All the acquired projection data are stored on the computer s hard disk and the images are reconstructed retrospectively. The most recent advancements in CT scanning are multi-slice helical scanners. These scanners have up to four parallel banks of detectors so that they acquire multiple slices simultaneously. With a complete set of projection data being acquired in 180 rotation, two complete rotations per second and four banks of detectors, the latest multi-slice helical CT scanners can acquire up to 16 images per second. Further information on current CT scanner technology can be obtained from manufacturers internet sites, e.g and The GE Medical Systems site also has a good collection of CT images. Image display Before the image is displayed, the CT scanner converts the measured attenuation coefficients of the voxels to CT numbers. For a voxel, i, the CT number, N i, of the corresponding pixel is related to the attenuation coefficient, µ i, of the tissue in the voxel by N i = 1000 µ i µ w µ w (4) where µ w is the attenuation coefficient of water. Expressing the attenuation coefficient relative to that of water dates back to the first clinical CT scanner, the EMI Mark 1 head scanner of The detectors of this scanner had a low dynamic range. Therefore the patient s head was surrounded by a water bag to reduce the very high x-ray intensity of the unattenuated x-ray beam that would otherwise reach the detectors. The scaling factor of 1000 in equation (4) is PHYSICS EDUCATION 449

19 G Michael image can be further enhanced by displaying only a window of CT numbers. Rather than allocating the full range of CT numbers to the range of available grey levels (from black to white) only a limited range of CT numbers is displayed. For example, for the brain, only the range of CT numbers from 0 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 which uses a narrow window centred on the range of CT numbers appropriate for the liver. Pixels with CT numbers outside this range, such as bone or fat, appear as either pure white or pure black. Figure 15. Range of CT numbers for some tissue types. Figure 16. CT scan of the abdomen with a display window optimized for the liver. used so that the CT numbers can be expressed as integers. This reduces computer memory and storage requirements. From equation (4) it can be seen that the CT number of water will be zero, the CT number of air (µ 0 cm 1 ) will be 1000, and a voxel with tissue having an attenuation coefficient twice that of water (e.g. bone) will have a CT number of Most soft tissues of the human body lie in the range ±100. Figure 15 shows the typical range of CT numbers for a number of tissues. CT images are usually viewed as greyscale images on a computer monitor. The contrast in the Applications Computed tomography is used routinely in radiological examinations because it provides cross-sectional images and improved contrast compared with other x-ray imaging techniques. Its main limitation compared with x-ray film is poor spatial resolution. The minimum object size visible with CT is about 0.5 mm compared with about 0.05 mm for x-ray film. Special applications of CT include bone mineral content measurement, cerebral blood flow using diffusion of inhaled xenon, the use of stereotactic frames to assist in accurate location for needle biopsies, and 3D imaging. Pseudo-3D displays are created from a stack of 2D images of a large number of parallel planes. An example is shown in figure 17. Clinical applications of 3D imaging include surgical planning, prosthesis design, craniofacial reconstructions, stereotactic biopsy planning and radiotherapy treatment planning. CT is useful for radiotherapy treatment planning for a number of reasons, i.e. high soft tissue contrast provides good visualization of tumours, the images provide accurate spatial information for treatment planning, and the pixel values provide radiological properties of the tissues that can be used for inhomogeneity corrections in dose calculations. More information on the application of CT in radiotherapy is provided by Oldham (2001). Conclusion Despite the rapid growth of magnetic resonance imaging (MRI) in the past decade, MRI has not superseded CT. CT is still used routinely in radiological examinations and is, itself, 450 PHYSICS EDUCATION

20 Figure 17. A pseudo-3d image of a skull, computer generated from a stack of 2D images of a large number of parallel slices. undergoing rapid growth and development in the form of multi-slice helical x-ray computed tomography. Received 6 September 2001 PII: S (01) X-ray computed tomography References Badawi R 2001 Nuclear medicine Phys. Educ Brooks R A and Di Chiro G 1976 Principles of computer assisted tomography (CAT) in radiographic and radioisotope imaging Phys. Med. Biol Kak A C and Slaney M 1988 Principles of Computerized Tomographic Imaging (New York: IEEE) Krestel E 1990 Imaging Systems for Medical Diagnostics (Munich: Siemens Aktiengesellschaft) McDavid W D, Waggener R G, Payne W H and Dennis M J 1977 Correction for spectral artefacts in cross-sectional reconstructions from x-rays Med. Phys Oldham M 2001 Radiation physics and applications in therapeutic medicine Phys. Educ Webb S 1990 From the Watching of Shadows (Bristol: Adam Hilger) Greg Michael holds a PhD in medical physics from the University of Queensland. He spent 11 years from 1978 at the Queensland Radium Institute and Royal Brisbane Hospital, then taught physics at Central Queensland University for three years before moving to Queensland University of Technology (QUT), where he is currently a lecturer in the School of Physical and Chemical Sciences. His research involves medical imaging and Monte Carlo modelling. PHYSICS EDUCATION 451

21 SPECIAL FEATURE: MEDICAL PHYSICS Nuclear medicine Ramsey D Badawi Dana-Farber Cancer Institute, 44 Binney Street, Boston, MA 02115, USA ramsey badawi@dfci.harvard.edu Abstract This article describes the use of nuclear medicine techniques in diagnosis and therapy. The process of generating radiopharmaceuticals is introduced and relevant interactions of radiation with matter are discussed. Instrumentation in diagnostic nuclear medicine is described and future trends in nuclear medicine imaging technology are predicted. What is nuclear medicine? Nuclear medicine is a branch of medicine in which patients are given radioactive substances (to be taken internally) either to diagnose or to treat a disease. This differs from traditional radiology and radiotherapy techniques, where radiation is normally applied from an external source. Nuclear medicine has become quite widespread since its inception in the 1950s, and nuclear medicine departments can be found in most medium and large hospitals. Therapy A common use of nuclear medicine therapy is in the treatment of thyroid cancer. We know that iodine collects in the thyroid gland, and it turns out that most thyroid cancer cells also accumulate iodine. Therefore, if we give a dose of radioactive iodine (e.g. 131 I) to a patient with thyroid cancer, the radioactivity will accumulate within the thyroid cancer cells. If sufficient radioactive iodine is given, the cancer cells will be killed by the radiation, thus (hopefully) curing the patient. Care must be taken to avoid damage to healthy parts of the body when nuclear medicine therapy is given. Luckily, in this case, iodine does not accumulate to any significant extent in other parts of the body, so the radiation dose outside of the tumour is low. Most of the radiation dose in nuclear medicine therapy arises from absorption of beta particles, which have a very short range in human tissue (a few millimetres or less). The process of calculating the radiation doses to various parts of the body during a nuclear medicine procedure is known as dosimetry, and is an important sub-topic within nuclear medicine physics. Diagnosis Nuclear medicine is more frequently used in the diagnosis of disease. In this case, a radioactive substance is given to the patient and then its distribution in the body imaged with some form of detector. The distribution might be imaged over time to see how it changes (dynamic imaging), or it might be imaged just once (static imaging). The essential idea is that the radioactive substance should act as a tracer for a particular physiological process. To understand the tracer principle, consider a simple tracer used in engineering the smoke in a wind tunnel. In a wind tunnel, a small amount of smoke is injected into the air stream, where it is carried past the object we are interested in, for example a car or an aircraft wing. When we watch where the smoke goes, we learn something about the airflow around the object of interest does the air flow smoothly or is there turbulence? In order for the smoke to be a good tracer for the airflow, it should behave in the same way as the air (at least with respect to the phenomena we are examining), and it should not disrupt the airflow. So the smoke particles should be sufficiently small 452 P H Y S I C S E D U C A T I O N /01/ $ IOP Publishing Ltd

22 Nuclear medicine that the effects of gravity are negligible compared with the effects of the viscosity of the air, and the volume of smoke injected per second should be small compared with the volume of air flowing in the wind tunnel per second. This illustrates a general point about tracers they should be present in sufficiently small concentrations that they do not disrupt the system they are intended to monitor. In nuclear medicine, we can perform procedures similar to wind tunnel tests to measure lung function. If we ask a patient to inhale a radioactive aerosol, and subsequently obtain an image of the radioactivity distribution, we can see if there are any regions in the lung which are poorly ventilated (as they might be if the lung has collapsed or there is fluid in it). We can also inject radioactive pharmaceuticals into the blood stream to examine other disease processes. The trick is to identify a compound (not necessarily naturally occurring) which is absorbed by tissue in proportion to some physiological process. We then modify the compound by adding an atom of a radioisotope (a process known as radiolabelling ), but hopefully in such a way that its physiological properties are not significantly changed. For example, we can track bone formation by using methylene diphosphonate labelled with radioactive technetium-99 ( 99m Tc). The diphosphonate behaves in a similar way to natural phosphates in the body and it is incorporated into bone, bringing the 99m Tc with it. Abnormalities in bone deposition rate can then be identified (see figure 1). Designing nuclear medicine tracers is a highly multidisciplinary process radiochemists are required to manufacture the tracer, physiologists are needed to understand its behaviour in the body, and physicists are required to work out dosimetry and imaging issues. Generation of radiotracers A list of the more common radionuclides used in diagnostic imaging is given in table 1. The half-lives of these radionuclides are quite short, which helps to reduce the radioactive exposure to the patients. However, it is also clear that these substances cannot be stored, but must be produced on demand, either by a nuclear reactor, a cyclotron or a generator. A generator is a device containing a quantity of relatively long-lived Figure 1. A planar whole-body bone scan showing disease in the left shoulder, spine and right pelvis. The bladder activity is normal. Left: front view. Right: rear view. Note the differences between the two views this is due to the attenuating effects of human tissue. Table 1. Some radionuclides commonly used in diagnostic nuclear medicine. Radionuclide Photon energies (kev) Half-life 99m Tc hours 111m In 172 and days 67 Ga 93, 185 and days 201 Tl 135 and 167, with 3.04 days characteristic x-rays at 80 kev 123 I 159 and hours parent radionuclide, which decays into a shorterlived daughter radionuclide that is to be used for imaging purposes. The generator is configured so that daughter radionuclides can be periodically milked off by chemical means, before being incorporated into the desired radiotracer. The most commonly used generator in nuclear medicine is that used for production of 99m Tc. The parent radionuclide is molybdenum ( 99 Mo), which decays to radioactive 99m Tc (87%) and stable 99 Tc (13%) with a half-life of 66 hours. The molybdenum, in the form of molybdate ions PHYSICS EDUCATION 453

23 R D Badawi Figure 2. A scintillation detector. The incoming gamma ray interacts with the scintillator to produce a scintillation flash. Photons from the scintillation flash dislodge photoelectrons from the photocathode in the photomultiplier tube. These are accelerated to the nearest dynode, where they dislodge further electrons. This process continues down the tube, resulting in a cascade of electrons. There are usually about ten dynodes, and a multiplication factor of about 6 at each dynode. The efficiency of the photocathode is such that about 3 5 photoelectrons are released for every ten incident scintillation photons. The intensity rise time and decay time of the scintillation flash are determined by the scintillator the total charge collected from the back of the photomultiplier tube is a measure of the energy deposited by the gamma ray. (MoO 2 4 ), is adsorbed onto an alumina column, which resides in a shielded container. As the 99 Mo decays, the concentration of 99m Tc in the column increases, and it reaches a maximum after about 24 hours. The column is then flushed with aqueous sodium chloride, yielding a solution containing sodium pertechnetate, NaTcO 4, which can then be used to produce the required radiotracer. After flushing, the concentration of 99m Tc starts to increase again, and a single generator can be used daily for about a week. Relevant interactions of radiation with matter Only photon emissions are useful for diagnostic imaging because for the most part alpha and beta radiation has too short a path in human tissue and is absorbed before it can be detected. The energy of the photons used lies in the range of roughly 100 to 400 kev and, at these energies, the photons have two principal interactions with matter Compton scattering and photoelectric absorption. In a Compton scattering event, the photon interacts with an electron, giving it some of its energy. The electron recoils, and in order to conserve momentum, the scattered photon (now with less energy) progresses in a different direction. Compton interactions within the body can cause problems in nuclear medicine imaging, because when we detect the scattered photons they appear to come from somewhere other than the point from which they were originally emitted. This causes erroneous signals in the images. In a photoelectric event, the photon transfers all of its energy to the electron and completely disappears. The relative probability of a Compton interaction or a photoelectric interaction depends on the energy of the photon and on the electron density of the scattering material (and thus on the density and the effective atomic number). In human tissue, Compton interactions dominate for photons in the kev range. In materials such as lead, photoelectric interactions dominate. 454 PHYSICS EDUCATION

24 Nuclear medicine Figure 3. A dual-headed gamma camera (top) and a gamma camera detector (bottom). Each head on the gamma camera consists of a detector with supporting electronics and a collimator (not shown). The detector consists of a crystal of thallium-doped sodium iodide of area approximately cm and about 1 2 cm thick. This crystal is viewed by about 50 PMTs. Since sodium iodide is hygroscopic, the crystal must be enclosed in an airtight seal. Photographs courtesy of Siemens Medical Systems. Detector systems for nuclear medicine The photons encountered in nuclear medicine most often have substantially higher energies than those used in x-ray imaging. Film-based imaging systems such as those found in dentistry clinics don t work at these high energies, because the high-energy photons just pass straight through the film. The detector of choice for nuclear medicine is the scintillation detector. This consists of a crystal attached to a photomultiplier tube (see figure 2). The crystal is a scintillator: when a gamma ray interacts with it, a flash of visible light is produced. Optically coupled to the scintillator is a photomultiplier tube (PMT), which turns incoming light into an electrical pulse. Ideally, the gamma ray should undergo a photoelectric interaction with the crystal, because then all of its energy is turned into scintillation light. A scintillation detector on its own is not an imaging device. We can use it to detect the presence of a high-energy photon. We can use it to measure its energy as well, within certain limits. However, to obtain an image, we need the position of the interaction of the photon with the detector, and we need the direction of the photon s flight. These last two pieces of information can be obtained using a gamma camera (also known as an Anger Camera, after its inventor, Hal Anger). A gamma camera consists of a large scintillating crystal (usually made of thallium-doped sodium iodide) with about 50 photomultiplier tubes on the back (figure 3). In front of the detector is a lead collimator. The collimator ensures that only those photons with paths parallel to the collimator holes strike the detector (figure 4). In this way we can be sure of the direction of the photons we detect. Positional information is obtained by examining the flash of scintillation light generated by the incoming photon when it interacts with the crystal. This light propagates through the crystal and is picked up by the PMTs. The most intense signal is obtained from the PMT nearest the event, and progressively weaker signals are found as the distance increases. By examining the relative strength of the signals from all of the PMTs, the location of the interaction point can be determined to within a few millimetres. Planar imaging The simplest way to use an Anger camera is analogous to a plain x-ray film. The camera is placed adjacent to the patient and both patient and camera are kept still while the signal accumulates. This results in a single planar view of the patient. The advantage of this method is that it is fast and computationally simple, but the disadvantage is that structures that overlay each other along the line of sight to the camera are difficult to distinguish. In addition, gamma rays arising from tracer concentrations on the far side of the patient tend to be scattered and absorbed ( attenuated ) by the patient s body, rendering them difficult to see. It may therefore be necessary to acquire more than one view of the patient (from different angles) to obtain the necessary information (see figure 1). PHYSICS EDUCATION 455

25 R D Badawi Figure 4. A gamma camera collimator. The collimator prevents photons which are not approximately perpendicular to the collimator holes from interacting with the detector. The field of view for the detector element behind each collimator hole is divergent, so that in a gamma camera spatial resolution degrades as the distance to the object is increased. The collimators are usually made of lead. For medium energy photon imaging, the holes are typically about 3 mm across, with the sides (the septa ) being about 1 mm thick and the collimator depth about mm. Not all collimators use parallel holes there are converging or diverging slant-hole collimators, and pin-hole collimators which can be used for very high resolution imaging. Single-photon emission computed tomography (SPECT) If many views are taken from different angles around the patient, it is possible to mathematically reconstruct slices through the patient from the views. This process uses very similar methods to those used to obtain the slices in x-ray computed tomography (so-called CAT or CT scanning) or magnetic resonance imaging (MRI) and is known as single-photon emission computed tomography (SPECT). The advantage of the SPECT technique is that the full three-dimensional nature of the tracer distribution in the patient can be appreciated, but the disadvantage is that it takes longer and requires more signal to reduce noise in the crosssectional images. In practice, both SPECT and planar imaging methods are frequently used in concert. Attenuation of signal is still a problem in SPECT, but since views are taken from all around the patient, it is the centre of the tracer distribution that is affected most. Attenuation correction schemes for SPECT are becoming more widely available, and very substantial efforts have been made in recent years to optimize the treatment of the noisy data during the image reconstruction process. Positron emission tomography (PET) An exciting and developing area of nuclear medicine is the field of positron emission tomography or PET. In PET, the radionuclide used for labelling is a positron emitter rather than a gamma emitter. The positrons are emitted with an energy of the order of 1 MeV, and being beta particles, they have a very short range in human tissue ( 1 2 mm). When an emitted positron has given up most of its kinetic energy through collisions with ambient particles (i.e., it has reached thermal energy) it combines with an electron to form a short-lived entity called positronium (see figure 5). This rapidly undergoes an annihilation reaction, in which the all the energy of the electron and positron pair is converted into radiation. The most likely course of this reaction is the production of two photons, each of energy very close to 511 kev (equivalent to the rest mass of the electron). In order to conserve momentum, the two photons are emitted in exactly opposite directions in the frame of the positronium. Since the positronium has some momentum in the observer s frame, the observer detects a small uncertainty in the direction of travel of the photons, amounting to about 0.5 about a mean of 180. It is possible to image positron-emitting 456 PHYSICS EDUCATION

26 Nuclear medicine Figure 5. Positron emission and annihilation. Figure 6. A dedicated PET system (photograph courtesy of CTI, Inc.). tracers by detecting the annihilation radiation using a conventional Anger camera as described above, but problems arise because of the high energy of the photons. They tend to penetrate the collimators, leading to loss of image contrast, and are not easily stopped by the thin scintillation crystals, resulting in a loss of sensitivity. PET imaging is best performed using a dedicated system with specialized high-energy detectors and operating on the principle of coincidence detection. Coincidence detection takes advantage of the fact that each annihilation event gives rise to two photons travelling in opposite directions to obtain information about the direction of flight of the photons without the use of a collimator. This avoids the problems of collimator penetration and at the same time leads to a substantial increase in sensitivity. Dedicated PET systems usually consist of a series of rings of detector units sharing common electronics (see figure 6). In coincidence detection, the time of arrival of each detected photon interaction is checked to see if it is contemporaneous with a photon seen at any other detector. If so, the two photons are deemed to be in coincidence, and are assumed to have come from the same annihilation event. This event can then be assigned to a line of response joining the two detectors (figure 7). During a PET scan, the lines of response are populated with data according to the number of coincidence events recorded. The data in the lines of response can then be reordered into views and reconstructed into three-dimensional images in the same way as SPECT data. A factor that has significantly contributed to the recent growth in the clinical use of PET is the nature of the tracers that can be created using positron emitters. The more commonly PHYSICS EDUCATION 457

27 R D Badawi Figure 7. The concept of coincidence detection. If pulses from separate detector elements overlap in time, it is assumed that the detectors registered photons arising from the same annihilation event. In practice, events are assigned digital time stamps, which are compared to find coincidences. Table 2. Some positron-emitting radionuclides using in PET imaging. Radionuclide Half-life Maximum positron energy (min) (MeV) 11 C N O F Rb used positron-emitting radionuclides are listed in table 2, and it can be seen that many of them are either directly biogenic or can be easily incorporated into naturally occurring biological substances. To date, the most widely used PET tracer has been 18 F-fluoro-deoxyglucose (FDG). This substance is taken up into cells using the same mechanism as normal glucose, but once in the cell, it cannot be further metabolized and remains trapped there. Consequently, it preferentially accumulates in cells with a high glucose metabolic rate. Since most tumours have an elevated glucose metabolic rate, it acts as an excellent tumour marker (figure 8), and it has also been very successfully used in cardiology and neurology. A disadvantage of PET (at least in the clinical sphere) is the short half-life of the positron emitters. They must be created on the day of use and indeed, for all radionuclides except 18 F, actually at the site of use. Only 82 Rb can be produced in a generator (from 82 Sr) the others are all produced in cyclotrons. Since most Figure 8. A whole-body 18 F-FDG image. hospitals cannot afford the expense of an onsite cyclotron and radiopharmaceutical production facility, this is a serious limitation. Luckily the two-hour half-life of 18 F is sufficiently long that tracers can be labelled with it and shipped to several hospitals from a central location, and 18 F is likely to remain the workhorse clinical PET radionuclide for the near future. The future: multi-modal imaging Diagnostic nuclear medicine is essentially a functional imaging process we are trying to obtain information on physiological processes. 458 PHYSICS EDUCATION

28 Nuclear medicine This contrasts with conventional radiology, where the aim is predominantly to obtain anatomical images reflecting form and structure. To illustrate this difference, consider a CT scan of the brain of a man who has just died of a heart attack. The brain may well appear perfectly normal. However, an FDG PET scan will be completely blank there will be no glucose metabolism at all. Functional and anatomical images are highly complementary for example, a nuclear medicine image using a good tumour marker will show tumours but will not show very much normal tissue. As a result, determining the position of the tumours can be difficult. If a CT or MRI scan is obtained simultaneously, the tumours revealed by the nuclear medicine scan can be correlated with the anatomy shown by the CT or MRI, and the location of the tumours can be established much more precisely. New scanning devices combining CT with PET, and CT with SPECT, are already on the market. Combining MRI with PET or SPECT is much harder, but small-scale systems for animals have been built and we may see humansized systems within the decade. Received 6 September 2001 PII: S (01) Further reading Saha G B 1997 Fundamentals of Nuclear Pharmacy (Berlin: Springer) Sorenson J A and Phelps M E 1987 Physics in Nuclear Medicine (New York: W B Saunders) Ramsey D Badawi entered the field of nuclear medicine in 1992, and obtained a PhD in biophysics from the University of London in He is currently responsible for positron emission tomography physics at the Dana-Farber Cancer Institute in Boston, Massachusetts, and is an Assistant Professor at Harvard Medical School. PHYSICS EDUCATION 459

29 SPECIAL FEATURE: MEDICAL PHYSICS Radiation physics and applications in therapeutic medicine Mark Oldham William Beaumont Hospital, Royal Oak, Michigan, USA Abstract Radiation therapy is an example of the successful application of advanced physics to the treatment of human disease leading to improved quality of life and even cure for many patients. The German physicist William Roentgen ( ), who discovered x-rays in 1895 and pioneered early x-ray applications, would likely be astonished if he could see the breadth and depth of their application in the modern hospital setting. This article gives an overview of some modern applications of high energy radiation beams in therapeutic medicine and the underlying physics which forms the basis of their curative effects. Radiation biology what does radiation do to cancer cells? Cancer cells are characterized by uninhibited and prolific replication which can interfere with the function of normal cells and organs, thereby endangering the life of the patient. The aim of radiation treatment is to deliver a sufficient radiation dose to sterilize cancer cells while limiting accidental damage to adjacent healthy tissue. But what is dose, and what does it mean to sterilize a cell? Radiation dose is the energy absorbed by cells from an incident radiation beam, per unit mass of tissue, and is a measure of molecular damage inflicted on the cells. Many different types of radiation have been investigated for cancer-cell killing efficacy with varying results: these include beams of photons, electrons, neutrons, protons, pions and even heavy atoms like carbon-12. The majority of modern clinics use photon and/or electron beams to treat cancer, and these beams disrupt normal cellular function principally by breaking chemical bonds through ionizing interactions. These ionizations can corrupt key molecules required for cellular replication and metabolism. A cell is sterilized when sufficient molecular damage has been inflicted that the cell can no longer replicate. Note that while cancer cell-death may be preferable, cell sterilization is often sufficient to preserve the life of the patient. Radiation damage to DNA molecules in the cell nucleus is the primary mechanism for cell sterilization. DNA contains coded instructions for the entire functionality of the cell, and when a cell replicates the DNA divides and an identical copy is made for the offspring cell. Radiation damage to DNA can prevent cell replication and the viability of the offspring cell. Radiation biologists have developed the linear quadratic (LQ) mathematical model to describe radiation sterilization of cancer cells. The model assumes that a cell is sterilized when both strands of a DNA double helix molecule are broken. This can occur either by a single particle that breaks both strands at the same time, or by two particles that each break one of the strands with a short time interval between breakages. The significant difference between this single or double DNA hit is that normal cellular 460 P H Y S I C S E D U C A T I O N /01/ $ IOP Publishing Ltd

30 Radiation physics and applications in therapeutic medicine repair mechanisms can repair some or all of the double hit damage (the first broken strand may be repaired before the second strand is broken) but these mechanisms are unable to repair the substantial damage when both strands are broken at the same time. According to the LQ model, the surviving fraction of cells S fx after a dose of radiation D is given by S fx = exp( αd βd 2 ) (1) where α is the coefficient of non-repairable damage and β is the coefficient of repairable damage. A plot of log(s fx ) against dose is called a cell-survival curve and an example is shown in figure 1. Empirical tests determine that DNA repair mechanisms of tumour cells are significantly less effective than those of normal healthy cells (i.e. tumour cells exhibit low values of β). This effect is exploited by fractionating the radiation treatment into a succession of small doses, typically one dose-fraction a day for 6 7 weeks. After each fraction the normal healthy cells are able to repair some of the radiation damage whereas the tumour cells are unable to repair the damage, leading to compounded decimation with each new fraction. The fractionation is optimized when maximum cancer cell sterilization is achieved with minimal damage to normal tissues. Determining the optimal trade-offs between dose per fraction, time interval between fractions and total treatment dose is the subject of a great deal of current research. How do we generate radiation in a hospital setting? Photon beams are used for both the localization and treatment of human tumours. Localization is the process of defining the physical extent and location of the tumour and is performed using low energy diagnostic x-rays, typically 0.03 MeV mean energy, which yield relatively high soft-tissue/bone contrast. Low energy diagnostic beams are ineffective for therapy of most cancers, however, as they have poor penetration (especially through bone) and a significant fraction of radiation scatters out of the treatment region. Radiation therapy therefore utilizes high energy photon and electron beams, typically with a mean energy of 2 10 MeV. The problem of generating radiation therefore Figure 1. Cell survival curve illustrating the surviving fraction of cells after a single dose of radiation. The repairable and non-repairable components are also shown. falls into two divisions: the production of low and high energy x-rays. Interestingly, although the two divisions differ dramatically in technical implementation, they both employ the same physical mechanism of radiation generation the bremsstrahlung interaction. Bremsstrahlung, or braking radiation, is the phenomenon whereby a fast moving electron is suddenly decelerated by coulombic interaction with a heavy, positively charged target nucleus. During deceleration the electron radiates away some of its energy in the form of a photon. In general, faster moving electrons radiate a greater fraction of their energy as bremsstrahlung photons and deposit less heat to the heavy target atoms. In a low-energy x-ray generator (figure 2) electrons emitted from a heated filament via thermionic emission are accelerated across an evacuated tube to strike a high-z tungsten target where the bremsstrahlung interaction occurs. Notice how the radiation emerges almost at right angles to the direction of the incident electrons. The Linear Accelerator: at the heart of radiation treatment! The low energy x-ray tube of figure 2 is only required to accelerate electrons to a few tenths of an MeV, which can be achieved with this simple design. Therapy machines are required to accelerate electrons up to 25 MeV, and this requires very high electromagnetic (EM) fields and a substantial number of high technology components. The Linear Accelerator is a PHYSICS EDUCATION 461

31 M Oldham Figure 2. Low-energy diagnostic and superficial therapy x-ray tube. Bending magnet Target Electron gun Collimators Electron accelerating waveguide (a) Photon beam Figure 3. The linear accelerator. (a) Treatment-room view of the Elekta travelling wave accelerator; (b) Schematic diagram of a standing wave accelerator. (b) technological wonder at the heart of the radiation therapy department, and generates both the highenergy photon and electron beams used in cancer therapy. It is usually located in a thick concrete underground bunker to minimize exposure to hospital staff and the general public. A treatmentroom view and a schematic design are shown in figure 3. Echoes of the basic x-ray circuit are seen in the electron gun, corresponding to the filament, the main accelerator waveguide, where electrons are accelerated (necessarily longer than in an x-ray tube) and the high-z tungsten target. Intense EM fields generated by a complex resonant microwave cavity combination called a klystron accelerate electrons almost to the speed of light along the main waveguide of the accelerator. A variety of beam modifiers are placed in the beam to adapt it for clinical use. The most important modifiers are the flattening filter, which achieves a flat uniform beam, and the multi-leaf collimator, which shapes the cross section of the beam to match the projection of the tumour. 462 PHYSICS EDUCATION

32 Radiation physics and applications in therapeutic medicine Figure 4. The klystron. The klystron A cross-sectional drawing of an elementary twocavity klystron is shown in figure 4. The klystron is able to massively amplify low-power input microwaves using two coupled resonant microwave cavities. Thermionic emission from a heated cathode introduces electrons into the first cavity, where they are bunched together by the low-power input microwaves. The first cavity also exerts velocity modulation on the electron bunches, which become progressively more distinct as they travel along the drift tube. The second resonant catcher microwave cavity has intense electric fields induced on it by the electron bunches, which are consequently decelerated. Energy is thus transferred from the kinetic energy of the electron bunches to EM microwave power, which then exits the klystron and is transported to the main accelerator waveguide. Treatment with photon beams Photons are regarded as indirectly ionizing radiation. That is to say that photon interactions in tissue generate fast moving electrons that propagate through tissue directly damaging cells via multiple ionizations along the electron s track. Electron interactions are predominantly with orbital electrons of atoms and molecules in the tissue. Photons have greater penetrability into tissue than electrons (see figure 6) and therefore create significant electron fluence at depth, without giving excessive dose to the intervening healthy tissue. Although photons penetrate tissue quite well, they still deposit significant dose superficially. To maintain the surface dose below acceptable levels several photon beams are generally used in crossfire techniques. All the beams in the treatment plan contribute dose to the tumour, at the point of crossfire, but surface tissue generally only receives dose from one or two beams. Physical interactions There are three main physical interaction mechanisms by which a therapeutic energy photon can interact with human tissue: the photoelectric effect, Compton scattering and pair production. The relative probabilities of each interaction are simple functions of the energy of the incident photon and the atomic mass number of the target atom. More complicated relations relate interaction probability to parameters like the scattering angle and energy distribution amongst particles. Over the therapeutic range of energies considered here, Compton scattering is generally the dominant mechanism, although photoelectric absorption becomes important at lower energies (< 100 kev) and pair production becomes important at high energies (> 5 MeV). A schematic diagram of the Compton scattering interaction is shown in figure 5. An incident photon scatters off an outer orbital electron with reduced energy. The electron leaves the atom carrying off the energy difference between the incident and scattered photons. In the photoelectric effect, the incident photon interacts with an inner bound orbital electron. The incident photon is completely absorbed in the interaction (i.e. no scattered photon) and the electron leaves the atom carrying off the difference energy accounting for the binding energy of the electron PHYSICS EDUCATION 463

33 M Oldham Figure 5. Schematic diagram of inelastic Compton scattering. An outer orbital Compton electron is ejected from the atom by a high-energy incident photon, which loses energy in the interaction and is scattered. Figure 6. Photon and electron depth dose curves. to the atom. In pair production, the incoming photon is once again completely absorbed, this time in an interaction with the field of the nucleus, resulting in the production of an electron positron pair. The incident photon therefore has to have energy greater than the rest masses of the electron positron pair. The positron causes ionization similar to an electron until it is brought to rest, when it annihilates with an electron producing a characteristic back-to-back 511 kev photon pair. A typical depth dose curve for a clinical photon beam is illustrated in figure 6. A depth dose curve for a typical electron beam is also shown to illustrate the increased penetration of the photon beam. Clinical examples of photon beam treatment Breast cancer. Breast cancer is the most common malignant disease of women in the western world. The lifetime probability of a woman developing breast cancer is estimated to be about 11%. Breast cancer is a particularly dangerous disease because of its tendency to break through basement membranes of small tissue-ducts, leading to metastatic spread through the lymphatic system. Typical treatment will involve lumpectomy of the gross tumour followed by post-operative irradiation of the entire breast tissue. The entire breast is treated because of the microscopic invasive potential of breast cancer to the surrounding tissue to uniform dose. A typical photon beam treatment arrangement and dose distribution are illustrated in figure 7. Two opposed tangential 6 MV radiation beams deliver a near-uniform dose to the breast and lumpectomy cavity. Dose uniformity is enhanced by placing metal wedge filters in the beam, which reduce the intensity of radiation progressively towards the thick end of the wedge. The wedge compensates for the missing tissue towards the apex of the breast. Although both beams are wedged, only one is shown in figure 7. A typical radiation treatment course is a dose of 180 cgy per day, five days a week, to a total dose of 45 Gy. A boost dose to microscopic tumour residue around the surgical scar is sometimes given with an electron beam. Recent advances in breast radiotherapy (Kestin et al 2000) use intensitymodulated radiation therapy (IMRT), which leads to improved dose homogeneity and better cosmetic outcome. Prostate cancer. Prostate cancer is the most common malignant disease of men in the US and Europe, with a lifetime probability of development of about 12%. Radiation therapy has been found to be as effective as radical prostatectomy for tumours limited to the prostate, and has considerably less toxicity. The prostate is located close to the rectum and bladder, and sophisticated treatment planning techniques are employed to shape the dose distribution to the shape of the prostate and to avoid excessive damage to these critical organs. An example of a four-field prostate treatment is shown in figure 8. The treatment plan consists of two pairs of beams: an anterior posterior pair and a right left lateral pair. The 464 PHYSICS EDUCATION

34 Radiation physics and applications in therapeutic medicine Tumor cavity Tumour cavity wedge lung heart ribs Shaped radiation field Spinal chord (a) Figure 7. (a) Transaxial view through a CT scan illustrating a typical radiation treatment for breast cancer. Two opposed wedged tangential 6 MV radiation beams (only one shown) deliver a near-uniform dose to the entire breast. Isodoses illustrate dose uniformity across the breast. (b) The radiation fields are shaped to minimize dose to lung and heart tissue. (b) beams crossfire on the prostate to give a uniform therapeutic dose. Often higher energy photon beams ( 18 MeV) are used to take advantage of their greater penetrability to the prostate, which can lie at depths of 18 cm or more. In a typical fractionated course of radiation therapy the patient will receive a daily dose of 180 cgy, five days a week, for eight weeks. Areas of current research interest include incorporating organ motion into treatment planning (Yan and Lockman 2001, Yan et al 2000), and online imageguided therapy, where anatomical information is obtained at the time of treatment (Jaffray and Siewerdsen 2000). Treatment with electron beams Electron beams are obtained from the linear accelerator by simply moving the tungsten target out of the path of the accelerated electrons travelling along the waveguide of the accelerator. The electrons exit the head of the treatment machine and are incident on the patient after passing through a scattering foil which widens the beam and increases uniformity. Electron beams are useful for treating superficial lesions within 6 cm of the skin surface. The depth dose curve illustrated in figure 6 shows that, unlike photons, the dose decreases rapidly with depth after a maximum value. Both the depth of the maximum and the gradient of dose falloff vary with the incident energy of the electrons. Electrons lose energy in tissue through coulombic interactions with atomic electrons and atomic nuclei (bremsstrahlung). In low-z materials (e.g. tissue) energy loss is predominantly by inelastic ionizing events with atomic electrons. The mean rate of energy loss of electrons in tissue is 2 MeV cm 1. This means that a 10 MeV beam will have a maximum range of 5 cm. The dose distribution from electron beams can be difficult to predict, especially for small fields, due to electron scattering and build-up effects. Electrons backscatter at an interface to a high-z material (e.g. metal dental implant or hip prosthesis), causing significant increase in dose upstream from the interface. In low-density regions like the lung, electrons can travel three times further than in normal tissue. In such cases it may be necessary to modify the angle of incidence of the treatment beam or the treatment dose to minimize the dose to healthy tissue. A clinical example of the application of an electron beam would be to boost the dose to the surgical scar after lumpectomy of the breast. The surgical scar may be contaminated with sub-clinical tumour deposits during the surgical procedure. Electrons are also often used to boost the dose to superficial lymph nodes after a predetermined photon dose has been delivered. PHYSICS EDUCATION 465

35 M Oldham prostate Femoral head Rectal wall Figure 8. Typical four-field radiation treatment for cancer of the prostate. Isodose lines show a uniform dose delivered to the whole prostate organ. The dose-limiting healthy structures are the rectum, bladder and femoral heads. This mixed-beam approach achieves dose at depth with the photon component with a boosted superficial dose from the electron component. What s it like to have radiation treatment? We have seen that a tremendous amount of activity occurs at the atomic and subatomic level when a patient is irradiated with a photon or an electron beam. The patient, however, does not feel anything at all at the time of treatment. All the millions of interactions that take place in tissue are completely undetectable to the human nervous system at the time of treatment. Patients only feel the effects of their radiation treatment when significant numbers of targeted cells have been sterilized and removed by the immune system. This time interval depends on many issues like cell-cycle time and the structure and sensitivity of the irradiated tissue. Patients undergoing palliative treatment, when the aim is to improve quality of life rather than to cure the patient, often receive pain relief within a few days. Negative symptoms from radiation treatment normally occur after 2 3 weeks if at all. Side effects that may occur are red and tender patches of skin, mild nausea and vomiting for abdominal treatments, diarrhoea and rectal discomfort for pelvic irradiation. The medical physicist and the radiation oncology treatment team The patient interacts with a highly trained team of specialists who form the radiation oncology team. The primary roles in the team are the physician who determines the nature of the treatment, the physicist who advises on technical aspects, the dosimetrist who formulates the computer treatment plan, the therapist who delivers the treatment to the patient and the nurse who is the primary care-giver. The medical physicist makes critically important contributions at many stages of the treatment process. The physicist is responsible for correct functioning of all aspects of radiation equipment, and for the purchasing and clinical acceptance and commissioning of 466 PHYSICS EDUCATION

36 Radiation physics and applications in therapeutic medicine all new equipment. Research physicists are responsible for analysing treatment efficacy and for developing and implementing improvements whether from technological advances or new possibilities in treatment technique. An example is gel-dosimetry, a new technique for obtaining high resolution 3D images of complex dose distributions either by MR imaging or by laserbased optical-ct scanning (Oldham et al 2001). This is often a very interesting and challenging task given the rapid development of computing and technical hardware and software. The physicist also plays a critical role as the department troubleshooter, available at immediate notice to solve problems as they arise at treatment time and during the treatment planning process. Such a role often demands quick thinking in a stressful situation. The role of the medical physicist is a challenging one and demands high professional standards. At the same time it can be an exciting and rewarding profession, which makes a real difference to the quality of life of patients treated in the Radiation Therapy department. Received 6 September 2001 PII: S (01) References Jaffray D A and Siewerdsen J H 2000 Cone-beam computed tomography with a flat-panel imager: initial performance characterization Med. Phys Kestin L L, Sharpe M B, Frazier R C, Vicini F A, Yan D, Matter R C, Martinez A A and Wong J W 2000 Intensity modulation to improve dose uniformity with tangential breast radiotherapy: initial clinical experience Int. J. Radiat. Oncol. Biol. Phys Oldham M, Siewerdsen J H, Shetty A and Jaffray D A 2001 High resolution gel-dosimetry by optical-ct or MR scanning Med. Phys Yan D and Lockman D 2001 Organ/patient geometric variation in external beam radiotherapy and its effects Med. Phys Yan D, Lockman D, Brabbins D, Tyburski L and Martinez A 2000 An off-line strategy for constructing a patient-specific planning target volume in adaptive treatment process for prostate cancer Int. J. Radiat. Oncol. Biol. Phys PHYSICS EDUCATION 467

37 SPECIAL FEATURE: MEDICAL PHYSICS Medical ultrasound imaging Stephen Hughes Queensland University of Technology, Australia Abstract Ultrasound is used extensively in the field of medical imaging. In this paper, the basic principles of ultrasound are explained using everyday physics. Topics include the generation of ultrasound, basic interactions with material and the measurement of blood flow using the Doppler effect. Introduction Ultrasonic imaging is the second most popular imaging modality in medicine (the first being x-rays). It is estimated that over 25% of all medical imaging procedures involve ultrasound. Ultrasonic imaging complements the other major imaging modalities, i.e. x-rays and magnetic resonance (MR) imaging etc. Ultrasonic imaging is used extensively in obstetrics (figure 1(a)). For example, the size and weight of a baby can be estimated by measuring the diameter of the head, abdominal circumference and femur length on an ultrasound image. If the time since conception is known, then the projected weight of the baby at birth can be estimated. Two-dimensional (2D) ultrasound images such as the type shown in figure 1(a) can be combined together to produce three-dimensional (3D) images of a fetal face (figure 1(b)). Studies have shown that congenital abnormalities are easier to detect using 3D images than 2D images. Ultrasound is also used extensively to image the heart and to measure blood flow in arteries and veins (to detect blockages, for example). Ultrasound, as the name implies, is sound that is so high pitched that it is beyond the range of human hearing. Sound is considered to be ultrasonic if the frequency is above 20 khz. (NB: Sound of a frequency below the lower frequency threshold of human hearing, 20 Hz, is known as infrasound.) Some animals, e.g. bats and dolphins, use ultrasound to locate objects. Bats emit sound at a frequency of about 25 khz, and dolphins around 125 khz. If you lived near some bats when you were a child, you could probably hear them. Adults cannot hear bats as the frequency range of human hearing gradually reduces with age from a peak in childhood of about 25 khz. Ultrasound as a medical imaging modality was developed in the 1950s and is really an application of SONAR (Sound Navigation and Ranging) to imaging the human body. If we think for a moment how SONAR works, we will understand the basic principles of the production of ultrasound images. In SONAR, a pulse of sound (a high pitched ping) is sent out into the ocean. If the sound hits a solid object, e.g. the hull of a submarine, the sound is reflected back and is picked up by an underwater microphone called a hydrophone. As the name SONAR implies, an object is located by knowing the direction and distance of the echoes. A blob of light is plotted on a display unit, indicating the presence of an object at a certain direction and range. The range of a structure causing the echo is calculated from the product of the time delay between the emitted and return pulses and the velocity of sound in sea water ( 1510 m s 1 ). The result needs to be divided by a factor of 2 since the sound has travelled out to the reflecting structure and back again. For example, if an echo returns after 2 s the range of the reflecting object is 1.5 km. Medical ultrasonic imaging is basically a scaled down version of SONAR in the ocean, although, of course, there are important differences. One difference is that SONAR is in 468 P H Y S I C S E D U C A T I O N /01/ $ IOP Publishing Ltd

38 Medical ultrasound imaging (a) Figure 1. (a) Ultrasound image of a fetal face. (b) 3D rendering of a fetal face. (Both images courtesy of Acuson.) (b) Figure 2. Principles of ultrasound production. the audible range of frequencies in fact, if you happen to be swimming underwater within a few km of a ship using SONAR it is possible to hear the pings. Ultrasound emitted from a medical transducer is of much higher frequency typically in the range 3 7 MHz. The reason for using a much higher frequency than audible sound is to obtain high-resolution images. How is ultrasound generated? There are a number of ways of generating ultrasound. As can be imagined, bats and dolphins do it differently from an ultrasound machine! In this article we will just deal with medical ultrasound machines. A piece of piezoelectric material is used to generate an ultrasound pulse and receive echoes (figure 2). A commonly used medical transducer material is a ceramic, lead zirconate titanate (PZT). Polyvinylidine difluroide (PVDF), a polymer, is another piezoelectric material commonly used in the construction of hydrophones. Piezoelectric material contains dipoles, which are all oriented in the same direction. A thin metal film is deposited on two opposing parallel PHYSICS EDUCATION 469

39 S Hughes faces. Compression of the material changes the orientation of the dipoles, making one side of the material more positive than the other. Expansion of the piezoelectric ceramic results in an electric field of reverse polarity. Therefore the material will act as a receiver and produce an alternating voltage when subjected to an acoustic pressure wave. Conversely, application of an electric field across the material results in either compression or expansion, depending on the field polarity. There are two basic ways of inducing piezoelectric material to vibrate. One way is to apply a sinusoidal electric field across the material. Another way is to apply a sharp electrical spike across the material. This causes the material to vibrate at the resonant frequency of the slab. This is analogous to hitting a bell with a hammer the bell will ring at a certain frequency the smaller the bell the higher the frequency and vice versa. In the case of a piezoelectric slab the resonant frequency is determined by the thickness of the slab being equal to one half of the wavelength of the sound within the piezoelectric material. For example, suppose that we want to build a transducer that emits ultrasound at 5 MHz. How thick should the PZT be? The speed of sound in PZT is about 4000 m s 1, therefore the wavelength of 5 MHz ultrasound will be λ = c f = = = 0.8 mm. Therefore we need a sliver of PZT 0.4 mm thick. Returning echoes cause the PZT to vibrate, which induces a varying voltage across the PZT. Due to multiple reflections and continuous attenuation, the amplitude of the deepest echoes is very small compared with the initial pulse. How is an image formed? The simplest way to produce an ultrasound image is to rock a one-dimensional A-scan transducer (as shown in figure 2) back and forth. This is what we might call the lighthouse analogy to ultrasonic image formation. By knowing the direction and distance of each returning echo we can build up an image. Most scanners today have a transducer composed of a linear or curvilinear array of piezoelectric elements. The piezoelectric elements are excited in a certain sequence in Figure 3. The phased array principle. order to obtain reflections from within an image plane. Many transducers work on the phased array principle. A phased array transducer has a much smaller transmission footprint, enabling images to be obtained through a restricted window, for example between the ribs in order to image the heart. The principle is shown in figure 3. Imagine that we had a device for dropping stones into a pond. Suppose that we could adjust the precise time that each stone dropped into the water. If we were to drop a single stone into the water the ripples would spread out in a circular fashion. If all the stones were dropped at once in a line, the ripples from each stone would spread out in a circular pattern, but all the wave fronts would combine together to produce a straight wave front. This is known as Huygens principle. As we move further away from the stones, the combined wave front becomes straighter. Now suppose that we arrange for one of the end stones to drop first, followed by the stone next to it, and so on up to the opposite end. What would happen then? The ripples would combine to form a wave front angled away from the normal direction. If the two end stones were dropped together, followed by the next stones in, and so on, the wave front would focus inwards, as shown in figure 3. Suppose that we arrange for the waves to arrive at a rock in the pond at the same time. The waves will reflect off the rock and arrive back at the edge of the pond with the same relative time delay. In an ultrasound scanner, the piezoelectric elements are excited in a certain pattern so that the wave fronts arrive simultaneously at a specific point. The same phase delay is applied to the return signal to obtain the total reflection from a single point. The phase delay pattern is varied to obtain echoes back from points at regular positions within the image plane. 470 PHYSICS EDUCATION

40 Medical ultrasound imaging Figure 4. Schematic diagram depicting the relation between frequency and axial spatial resolution. Resolution As with all imaging modalities, image resolution is directly proportional to the frequency of the radiation used. The higher the frequency, the shorter the wavelength and therefore the higher the resolution. Suppose that we have an ultrasound probe capable of producing pulses of two different frequencies, high and low as shown in figure 4. The pulse contains four periods with a wavelength λ; for the moment we need not worry about the actual value of λ. At the first interface some of the energy is reflected and some is transmitted. The transmitted ultrasound travels through medium 2 to the second interface where again some sound is reflected and some transmitted. The pulse reflected off interface 2 travels back through interface 1 and back to the probe. (The return pulse is also reflected back off interface 1, but we need not worry about that for the purposes of this discussion.) If we know the time that it has taken each pulse to return to the probe, we can easily calculate the distance travelled by each pulse and draw a dot on a display representing the distance from the probe. As we can readily see from the diagram, pulse B has travelled further than pulse A, so on our display dot B will be further from the probe than dot A. If the dots are too close together they will appear as one dot. In other words, we would be unable to tell that the sound had reflected off two interfaces. The question is, for any given ultrasound frequency what is the smallest separation of two interfaces that we can resolve? We can work this out by inspecting figure 4. In this figure two pulses of differing frequency reflect off a structure of a certain width. If the tail of pulse A has not left interface 1 before the head of pulse B has started passing through interface 1, the two pulses will overlap. On the display, the two dots will overlap and we will not be able to tell for sure whether there is one dot or two. On the other hand, if the tail of pulse A has left interface 1 as the head of pulse B comes through, the two pulses will not overlap and on our display we will have two dots with a bit of space between them. We can see intuitively that, to avoid pulse overlap, the distance between interface 1 and interface 2 ( x) must be at least half the pulse length. The distance between the centres of the two dots on the display will represent the distance between interface 1 and interface 2. Notice that in the bottom part of figure 4 the frequency of the signal is higher, therefore the pulse length is shorter for the same number of periods. We can now combine what we know into an equation: x = nλ 2 = nc 2f where x is the separation of interfaces 1 and 2, n is the number of periods in the ultrasound pulse, c is the velocity of sound in the medium and f is the frequency of ultrasound. We can see that we can improve resolution either by reducing the number of periods in a pulse or by increasing the frequency. Let us consider an example. Suppose that we have a probe that emits ultrasound at a frequency of 5 MHz and has four periods per pulse. The minimum separation that PHYSICS EDUCATION 471

41 S Hughes Table 1. Density, velocity and acoustic impedance of a selection of materials. (The unit of acoustic impedance is the Rayl: 1 Rayl = 1 kg m 2 s 1.) Material Density Velocity Z Attenuation coefficient (10 3 kg m 3 ) (m s 1 ) (MRayl) (db cm 1 ) at 1 MHz Air Water Soft tissue Liver Fat Bone Aluminium we can resolve is x = nc 2f = = m = 0.6 mm Reflection We are all familiar with echoes. If we are a few tens of metres away from a concrete wall and we shout or clap, the echo comes back. If we are between two walls, or in a cave, some interesting effects can be produced! In this case, echoes work because the bulk acoustic properties of air and concrete or rock are very different. Conversely, a room full of soft furnishings (carpets and curtains etc) tends to absorb sound. In other words, some sound has been transmitted into the curtains rather than being reflected back. It is the bulk properties of a material that are important for example, a sheet of plastic is more reflective than a wad of steel wool. Exactly the same physics describes the propagation of ultrasound through the body. The amount of sound energy transmitted and reflected at each interface is dependent on the difference in the acoustic impedance of the media on either side of the interface. The acoustic impedance (Z) is defined as the product of the density of the medium (ρ) and the velocity of sound (c) in a medium, i.e. Z = ρc. The velocity of sound in a medium is given by the expression c = B/ρ where B, the bulk modulus, is defined as B = P V /V where P = pressure and V = volume. We see from this equation that high-b materials undergo a smaller change in volume for a given change in pressure than low-b materials. In other words, high-b materials are stiffer than low-b materials. If we substitute the expression for c in terms of B and ρ into Z = ρc, we obtain Z = ρb. We can see from this equation that denser, stiffer materials have higher acoustic impedance than materials of lower density and stiffness. For example, steel has a much higher acoustic impedance than air. The term acoustic impedance is a bit unfortunate in that sound actually travels more efficiently in materials of higher acoustic impedance and vice versa an extreme example being outer space, where the acoustic impedance is virtually zero and yet no sound can propagate! When sound travels through a material with acoustic impedance Z 1 and then encounters a material of much higher Z, most of the sound is reflected back rather than being transmitted. This is also true if Z 1 is much lower than Z 2. The amount of sound transmitted and reflected depends on the degree of mismatch between the acoustic impedances of the two media on either side of the interface. Typical values of density, velocity, acoustic impedance and attenuation for various materials are shown in table 1. As an example, suppose we want to transmit sound through the side of the skull. This was actually done in the early days of ultrasound to look for brain tumours. Brain tumours have a tendency to push the central structure of the brain, the corpus collosum, over to one side. This can be detected as an asymmetry in the pattern of reflected ultrasound pulses. Initially, the sound has to pass through the skin and then into the bone. We can calculate the 472 PHYSICS EDUCATION

42 Medical ultrasound imaging intensity of the sound reflected at an interface using the reflection coefficient, R, as follows: ( ) Z1 Z 2 ( ) R = = = Z 1 + Z This means that 41% of the sound energy is reflected and 59% transmitted. Sine Z air is so small, we can see, without bothering to do the calculation, that sound is more or less completely reflected from any interface between the materials in table 1 and air. Attenuation As with most types of radiation, the intensity of ultrasound is attenuated exponentially as it passes through a medium, i.e. a constant fraction of the energy is removed per unit length of travel. This is true of light passing through a window, or x-rays passing through a sheet of lead. As ultrasound passes through a medium it is exponentially attenuated according to the equation A = A 0 e αx where A is the amplitude of the sound wave, i.e. pressure, A 0 is the the initial amplitude of the sound wave, α is the amplitude attenuation coefficient and x is the distance travelled by the sound wave. As the sound moves through the medium, some of the energy is scattered and some is absorbed. The absorbed energy raises the temperature of the medium. This is the principle behind the ultrasound machines used by physiotherapists to improve the healing of muscle injuries. The heat improves the circulation in the affected region. Ultrasonic heating is also used in cancer therapy. A tumour heated to 43 C, or above, can be treated effectively with a much lower dose of x-rays than an unheated tumour. The amplitude attenuation coefficient is normally expressed in db cm 1 and is defined as follows: α ( db cm 1) ( ) ( ) 1 = 20 log x 10 AA0 = α ( cm 1). The intensity attenuation coefficient, µ, is similarly defined as µ ( db cm 1) ( ) ( ) 1 = 10 log x 10 II0 = µ ( cm 1). Figure 5. Ultrasound propagating through a layer of fat and liver. Note that µ ( db cm 1) = α ( db cm 1). The attenuation coefficient varies approximately with f 2 for water and f 1.2 for soft tissue. A general rule of thumb is that the attenuation coefficient increases by 1 db cm 1 MHz 1. So for example, over a distance of 10 cm, a 5 MHz signal would be attenuated by 50 db. Now that we have dealt with reflection and attenuation, we are in a position to be able to calculate the intensity of an ultrasound pulse returning from deep inside the body. Figure 5 shows a simplified model (in reality an ultrasound pulse passes through multiple tissue layers). The intensity of a returning ultrasound pulse depends on the reflection coefficient at each boundary and also the attenuation coefficient of the material between the boundaries. In figure 5 an ultrasound pulse passes through the skin, through a 5 cm fat layer and then through a 5 cm layer of liver. (To simplify matters, we have assumed perfect matching between the transducer and skin.) The sound reflects off the far liver fat interface and travels back to the transducer. We can calculate the intensity of the return pulse from the following equation: I = I 0 e µ 1x 1 T 1 e µ 2x 2 R 2 e µ 2x 2 T 1 e µ 1x 1 = T 2 1 R 2e (µ 12x 1 +µ 2 2x 2 ). In words, what we have to do is to square all the transmission coefficients (T = 1 R) and take the product. We then multiply this result by the reflection coefficient of the boundary that we are interested in. Finally we multiply this result by a combined attenuation factor. If we use the values in table 1, I/I 0 = db. PHYSICS EDUCATION 473

43 S Hughes Measuring blood flow using the Doppler effect The Doppler principle is used by the police to catch speeding drivers and also results in a change in pitch when an emergency services vehicle, for example, passes by with the siren blaring. The Doppler principle can be used to measure the velocity of blood flow in vessels in the body. Let us imagine for the moment that we are sitting on a stationary red blood cell (RBC) and that we have some experimental tools on board a pressure gauge, a speedometer and a clock. A piezoelectric transducer in the blood vessel is sending sound towards us. As the waves come towards us we measure peaks of pressure followed by troughs. By measuring the time between successive peaks or troughs and knowing the velocity of ultrasound in blood (1570 m s 1 ) we can calculate the wavelength. Suppose now that we are sitting on a moving RBC. We continue to measure the time between successive pressure peaks. However, we now notice that the time between peaks has increased. It is now T + T. The reason is that since we are moving away from the source of sound, each pressure peak has to catch up to the RBC for us to record it. We can in fact measure the catchup distance. Since we know the time between successive peaks and we know our velocity, v, we can calculate the apparent extra distance the peaks travel in other words, the apparent increase in wavelength λ: λ = v(t + T ). T is the time it takes a peak to travel the distance that a RBC travels in time T. Since the velocity of sound in blood (1570 m s 1 ) is very much faster than the velocity of a RBC (< 0.5 m s 1 ) we know that T T. Therefore we can simplify the above equation and write Using the fact that we can write c = f λ λ = vt. λ + λ = or λ = c/f c f + f. We now need to manipulate this equation to obtain the change in frequency in terms of the velocity of the RBC and the velocity of sound in tissue. If we multiply out the wavelength and frequency terms we obtain λf + λ f + λ f + λ f = c. By replacing λ by v/f in the above expression and rearranging we obtain f f = v c + v. Since we know that the velocity of blood is very much less than the velocity of sound in blood (i.e. v c), we can simplify the above equation to f f = v c or f = f v c. The negative sign indicates that the frequency of sound decreases when the RBC is moving away from the source and vice versa. The RBC is in effect a moving receiver. However, the ultrasound reflects off the RBC and so the RBC in effect becomes a source of ultrasound. However, since the RBC is a moving source, the wavelength of the emitted sound arriving at the detector will also appear to be stretched. It will be stretched by exactly the same amount as the sound absorbed by the RBC. So the change in frequency of the sound that has reflected off a RBC will be f = 2f v c. We re not quite over yet! There is one more factor that we need to apply to this equation. The above equation assumes that the direction of sound propagation is parallel to the direction of motion of the RBC. In practice, for a medical ultrasound scanner with an external probe placed on the skin, this will not normally be the case. If the ultrasound beam were to reflect off an RBC moving at right angles to the direction of propagation of the ultrasound, there would be no forward or backward motion relative to the ultrasound and therefore no Doppler shift. To describe all situations we just need a cosine term. So, if θ is the angle between the direction of motion of the RBC and ultrasound beam as shown in figure 6, then our final Doppler equation is f = 2f v cos θ. c 474 PHYSICS EDUCATION

44 Medical ultrasound imaging Figure 6. Schematic diagram of the measurement of blood flow using the Doppler effect. As an example, suppose that a 5 MHz transducer is being used with the direction of sound propagation at 60 to the central axis of the blood vessel. If blood at the centre of the vessel is flowing at 0.5 m s 1 this will result in a Doppler shift frequency of f = cos = 1.6 khz. By measuring the change in frequency in the reflected wave from the transmitted wave, f, we can calculate the velocity of the blood. The future of ultrasound Ultrasound has a bright future. Many developments are underway, many of them proceeding hand in hand with advances in computing technology. For example, tissue harmonic imaging (THI) enables improved image resolution, producing images of the beating heart of unprecedented clarity. THI images of the heart are so clear that it is possible to see the slender fibres that anchor the heart valves! Advances in 3D imaging have enabled more accurate diagnosis of congenital fetal defects, enabling doctors to decide on the best treatment before a baby is born. What about the more distant future? Where is it possible for ultrasound to go? Let us let our imagination run riot and try and glimpse what is possible in the future. We might imagine a kind of mat or carpet that is draped across the patient that generates 3D images in real time. Compared with the ultrasound technology of today such a device would appear to operate by magic! So let us call this device a magic carpet (MC). We pick up the MC it is a few cm thick and is fairly heavy this is hardly surprising since the MC is a combined ultrasound machine, supercomputer and high resolution 3D display. The MC that is draped across the part of the patient to be investigated contains thousands of piezoelectric elements. The side of the MC that is placed against the patient is made from a kind of sticky rubber that excludes air pockets between the MC and the skin so that messy ultrasound gel is not required. Moreover the MC is active and is able to conform itself to the contours of the patient. The MC contains numerous position sensors that enable the precise location of each piezoelectric element to be known. This is required if the generated image is to be spatially accurate. The circuitry to transmit and receive the ultrasound pulses is also embedded within the MC. The MC contains a computer, maybe an optical computer or even a quantum computer, which uses highly sophisticated algorithms that enable the ultrasound echoes to form the basis of an accurate 3D model of the internal structure of the patient. The upper surface of the MC is a highresolution colour display. Technology, not yet developed, enables the operator to see the inside of the patient in 3D without the aid of special glasses. The operator is able to zoom into the image so that it s as if they are climbing inside the body to have a look around. Labels appear suspended in space indicating the blood flow at strategic points in the vessel. All of this may seem like pure science fiction, but the MC is in fact a reasonable extrapolation from today s technology. How far into the future will this be? Maybe sooner than we think. Received 6 September 2001 PII: S (01) Further reading Fish P J 1990 Physics and Instrumentation of Diagnostic Medical Ultrasound (Chichester: Wiley) Hill C R (ed) 1986 Physical Principles of Medical Ultrasonics (Chichester: Ellis Horwood) Stephen W Hughes holds a PhD from King s College, London, and is currently a lecturer in physics at Queensland University of Technology (QUT). He has previously held appointments in bioengineering and medical physics at King s College Hospital and Guy s and St Thomas Hospital, London. Research interests: 3D medical imaging. PHYSICS EDUCATION 475

45 SPECIAL FEATURE: MEDICAL PHYSICS Magnetic resonance imaging in medicine Stephen F Keevil Magnetic Resonance Physics Group, Department of Radiological Sciences, Guy s, King s and St Thomas School of Medicine, King s College London, Guy s Campus, London SE1 9RT, UK stephen.keevil@kcl.ac.uk Abstract Over the past twenty years, magnetic resonance imaging (MRI) has become one of the most important imaging modalities available to clinical medicine. It offers great technical flexibility, and is free of the hazards associated with ionizing radiation. In addition to its role as a routine imaging technique with a growing range of clinical applications, the pace of development in MRI methodology remains high, and new ideas with significant potential emerge on a regular basis. MRI is a prime example of the spin-off benefits of basic science, and is an area of medicine in which physical science continues to play a major role, both in supporting clinical applications and in developing new techniques. This article presents a brief history of MRI and an overview of the underlying physics, followed by a short survey of current and emerging clinical applications. Historical introduction In the 1940s, in a laboratory somewhere in the depths of Stanford University, a physics researcher did something that would now be regarded as highly irresponsible and ill-advised. Felix Bloch put his finger into the apparatus that he had built to study a newly discovered phenomenon known as nuclear magnetic resonance (NMR). Because of its high water content, Bloch s finger produced a strong NMR signal. This observation is now regarded as the first step on the path towards biomedical magnetic resonance imaging (MRI): a technique based on fundamental nuclear physics that has spawned a multibillion pound industry and made tremendous contributions to the health and quality of life of millions of people. NMR was anticipated on theoretical grounds, and was searched for unsuccessfully by the Dutch physicist Cornelius Gorter in Isidor Rabi observed the phenomenon in molecular beams in 1937, but it was 1946 before it was observed in liquids and solids, resulting in the award of the Nobel Prize for Physics to Bloch and Edward Purcell of Harvard in Since then, NMR has become a routine tool for physicists and chemists to probe molecular structures. These applications, fascinating though they may be, are beyond the scope of this article. However, the samples studied soon came to include biological materials. These were not imaging studies: their aim was to characterize tissue samples according to water content and nuclear relaxation times (see below). In 1960 a report from the US National Heart Institute noted that NMR experiments might lead to a scanning technique [that] will give coarse pictures... of muscle, arteries and other structures. This was the first suggestion that NMR might be the basis of a new medical imaging modality, although the idea was not pursued at the time. In 1971, writing in the journal Science, 476 P H Y S I C S E D U C A T I O N /01/ $ IOP Publishing Ltd

46 Magnetic resonance imaging in medicine Raymond Damadian reported differences in NMR signals obtained from cancerous and normal tissues. These findings played a key role in stimulating interest in NMR as a potential diagnostic technique. Damadian developed the first whole-body NMR imaging system in 1977 (using himself as the first guinea pig) and the first commercial scanner in His work was regarded by most of his contemporaries as at best a curiosity, but he had patented his ideas and in 1997 received $128 million from the General Electric Corporation for patent infringements. Meanwhile, Paul Lauterbur developed the idea of using magnetic field gradients (see below) to map out signals from within the body. Using this approach, he published the first NMR image in Nature in Many key developments over the next few years took place in the UK. In 1974, Peter Mansfield (now Sir Peter) of the University of Nottingham produced the first NMR images of the human finger, and in 1978 Ian Young at EMI produced the first head images. In 1980 John Mallard s group at the University of Aberdeen, building on work by Richard Ernst in Zurich, developed the spin-warp imaging technique that forms the basis of almost all modern MRI. By the early 1980s, major medical imaging equipment manufacturers were beginning to recognize the potential of NMR, and the first prototype systems were installed in hospitals. Because the word nuclear had unfortunate connotations for the public, the technique was marketed as magnetic resonance imaging to avoid misconceptions. By 1988, 1300 MRI systems had been sold; today, there are perhaps systems in hospitals worldwide, with around 2500 more scanners (worth around 1.5 billion) being installed each year. The capabilities and applications of these systems have grown to an astonishing extent, and there is no sign of decline in the rate of innovation. The physics of NMR A rigorous description of NMR requires the use of sophisticated quantum mechanics. Fortunately, for our purposes, a classical or semiclassical approximation is adequate, although it is important to keep in mind the fact that the analogies used here are not exact! Nuclear spin is the key concept in NMR. As its name implies, spin is related to the angular Figure 1. Origin of nonzero spin in the carbon-13 nucleus. The six protons provide no net spin, but the unpaired neutron endows the nucleus as a whole with a spin quantum number I = 1 2. momentum of the atomic nucleus, which in turn originates from that of the constituent nucleons. Protons and neutrons each have spin quantum number I = 1. When a nucleus contains an even 2 number of protons and neutrons, the individual spins of these particles pair off and cancel out and the nucleus is left with zero spin. However, in a nucleus containing an odd number of protons or neutrons, pairing is incomplete and the nucleus has a net spin of 1 (see figure 1). All such 2 nuclei undergo NMR, but in medical MRI the hydrogen nucleus, consisting of a single proton, is used because of its high NMR sensitivity and natural abundance, and because of the very high concentrations of water found in the body. In a simple model, a nucleus with spin is pictured as a charged sphere rotating on its axis. According to classical electromagnetism, a spinning sphere of charge generates a magnetic dipole moment, µ. The fundamental requirement for NMR to occur is application of a magnetic field to the tiny nuclear magnetic moments. This is generated using a powerful magnet: for clinical MRI the field strength is usually times that of the Earth. Quantum mechanics stipulates that the magnetic moment of a nucleus with I = 1 will adopt one of only two possible 2 orientations relative to the direction of the field conventionally defined as the z-axis. These orientations are shown in figure 2, which also defines the coordinate axes to be used. Each magnetic moment also experiences a torque due to the field, resulting in precession about the z-axis so that the moment describes a cone in the xy plane as illustrated in figure 2. The angular frequency of precession, known as the Larmor frequency, is given by ω 0 = γ B 0 PHYSICS EDUCATION 477

47 S F Keevil Figure 2. Possible orientations of a nucleus with I = 1 in a static magnetic field. The size of the magnetic 2 moment is well defined, and only two values of the z-component are possible corresponding to alignment with or against the applied magnetic field. Nuclei precess about the z-axis, and the x and y components of the moment of a given nucleus at a given time are random. Figure 3. Origin of the bulk magnetization vector in a macroscopic sample. Excess magnetic moments aligned in the positive z-direction sum to give M, while the random x and y components cancel. The excess of a few nuclei per million has been greatly exaggerated in this diagram. where B 0 is the flux density of the applied magnetic field and the gyromagnetic ratio, γ, is characteristic of the nucleus (for hydrogen, γ = MHz T 1, so in a magnetic field of strength 1 T hydrogen nuclei precess at a rate of million revolutions per second). Thus the z-component of the magnetic moment is well-defined and may adopt one of only two values while, in the classical model, the x and y components vary rapidly (ω 0 lies in the range from megahertz to hundreds of megahertz) and the position (or phase) of the magnetic moment on the precessional cone at a given time is random. This can also be understood in quantum mechanical terms as a manifestation of Heisenberg s uncertainty principle. Spins in the two orientations have different energies, the difference being E = hω 0, where h = h/2π (h is Planck s constant). Because of this, the populations of the two states differ slightly, with a few more nuclei per million aligned with B 0 than against. This is sufficient to endow the sample as a whole with a small bulk magnetization, M, lying along the positive z-axis (see figure 3). There is no net magnetization in the xy plane because of the random phases of the moments. The next step in the NMR experiment is to irradiate the sample with radiofrequency (RF) electromagnetic waves. The effect of this irradiation can be described in either quantum mechanical or classical terms. In the quantum model, if the energy of the RF photons is equal to the difference between the two energy levels, nuclei in the lower level may gain energy by absorbing photons and those in the higher level may be induced to emit photons and so lose energy. These processes cause nuclei to flip between the two orientations, modifying the population distribution and hence the magnitude and direction of M. However, considering the colossal number of nuclei present in a macroscopic sample, it is convenient to adopt an entirely classical model. In this approach, NMR is described in terms of interactions between the bulk magnetization and the magnetic field component of the RF wave, B 1. If the RF frequency, and hence the frequency at which B 1 rotates in the xy plane, matches the precessional frequency of the magnetic moments, ω 0, a resonant condition is achieved in which M tips, or nutates, from the z-axis towards the xy plane. Nutation continues until B 1 is removed, so the amplitude and duration of B 1 can be tailored to nutate M through specific angles. An important special case is that in which M is nutated entirely into the transverse plane, leaving no magnetization along the z-axis. An RF wave of sufficient duration 478 PHYSICS EDUCATION

48 Magnetic resonance imaging in medicine Figure 4. Special cases of an RF pulse: (a) 90 pulse, (b) 180 inversion pulse, (c) 180 refocusing pulse. Rotation of B 1 and precession of M about B 0 have been omitted for clarity. Table 1. Relaxation times of water protons in brain tissues measured in a healthy volunteer at 1.5 T (courtesy of Dr Marcus Newbold, GKT School of Medicine, King s College London). Tissue T 1 (mean ± SD) (ms) T 2 (mean ± SD) (ms) Grey matter ± ± 12.3 White matter ± ± 5.0 Cerebrospinal fluid (CSF) ± ± and amplitude to achieve this is known, for obvious reasons, as a 90 pulse. Similarly, a 180 pulse inverts M or, if applied after a 90 pulse, rotates M through 180 in the transverse plane (figure 4). These pulses are the basic building blocks of NMR, and by stringing them together in different combinations an essentially limitless range of experiments can be performed. Whichever model is adopted, the RF frequency required to induce NMR is equal to the nuclear Larmor frequency, ω 0 = γ B 0. A 90 pulse generates net transverse magnetization, which precesses about the direction of B 0. This precessing magnetization can be detected by means of electromagnetic induction, by placing a tuned antenna close to the sample. In the context of biomedical NMR, such an antenna is usually known as an RF coil, and similar coils are used to transmit RF and to detect the emitted NMR signal. Following excitation, nuclei return to their initial population distribution via a variety of relaxation processes, categorized according to whether they cause loss of energy from the spin system or simply exchange of energy between spins. These two phenomena are known as spin lattice and spin spin relaxation, and are characterized by the relaxation times T 1 and T 2, respectively. T 1 relaxation results in exponential recovery of z-magnetization, M z, while T 2 processes cause exponential decay of the precessing transverse magnetization, M xy : M z = M(1 e t/t 1 ) M xy = Me t/t 2. Thus the NMR signal detected by the RF coil rapidly decays due to T 2 relaxation. Relaxation behaviour is strongly dependent on the physicochemical environment of the nucleus, and hence on the tissue type in which the nuclei are located, and this is an important source of image contrast in biomedical MRI. Table 1 shows typical in vivo relaxation time values for brain tissues. From NMR to MRI The NMR experiment described thus far results in acquisition of an undifferentiated signal, with no means of incorporating spatial information so as to produce an image. Study of a specific tissue can only be achieved by excising the tissue from the body, or if the tissue is superficial by placing a small RF coil, known as a surface coil, against the body. The method of spatial encoding used universally in MRI is due to Lauterbur. As with many of the great ideas of science, it is at once simple and extremely powerful. Temporary imposition of an additional static magnetic field, which lies parallel to B 0 but varies linearly in strength with position along the x, y or z-axis PHYSICS EDUCATION 479

49 S F Keevil Figure 5. Effect of a magnetic field gradient along the x-axis. (a) Without the gradient, B is independent of x. (b) In the presence of the gradient, B varies linearly with x. Note that the direction of the B vector is the same in both cases; only the amplitude varies in case (b). (or indeed some direction oblique to these axes) (figure 5) results in a linear variation in the Larmor frequency as a function of position: ω(x) = γ B = γ (B 0 + G x x) where the strength of the gradient (in mt m 1 ) is G x (in this case applied along the x-axis). This frequency variation can be used in three ways to achieve spatial localization. 1. Slice selection. If the gradient is applied at the same time as the initial RF pulse, and the pulse is modified to contain a narrow band of frequencies rather than a single frequency, a thin slice of spins can be selectively excited. Using this approach, MRI becomes a twodimensional tomographic imaging technique (figure 6). 2. Frequency encoding. If the gradient is applied during signal acquisition, the resonance frequency of spins contributing to the signal becomes a linear function of their position along the gradient direction. The signal can be decomposed using Fourier methods to determine the amount of signal at each frequency and hence at each position, resulting in a projection through the sample (figure 7). At this point, it is perhaps worth eliminating a common misconception. Many people who are learning about MRI imagine that images are formed by scanning line by line through the object, obtaining signal from each point in space sequentially. We can see from the preceding description that this is not the case. The signal acquired originates from the entire object under study, and spatial information is obtained only by breaking that signal down into its different frequency components. Figure 6. Use of a magnetic field gradient for selective excitation of a transaxial slice. If a gradient is applied along the z-direction together with an RF pulse of bandwidth δω magnetization will be excited within a slice of thickness δz = δω/γ G z. If performance is ideal, magnetization outside this slice will be left along the z-axis and will produce no signal. Figure 7. Frequency encoding. If a gradient is applied during signal acquisition, the resulting NMR signal will contain components with a range of frequencies. Fourier transformation of this signal yields a projection through the object. A greatly simplified object is shown in this diagram. 3. Phase encoding. By applying a gradient for a short time between excitation and signal acquisition, and repeating the experiment a number of times with different gradient amplitudes, it is possible to generate a set of data that may be Fourier transformed to yield spatial information along the direction perpendicular to the frequency encoding axis. Phase encoding is one of the most difficult concepts in MRI, and a full explanation is beyond the scope of this article. Suffice it to say that the process is mathematically equivalent to frequency encoding, and is really a trick to get around the fact that frequency encoding cannot be performed along two axes simultaneously. In conventional MRI, all three methods are applied to generate multiple two-dimensional slices through the object or patient under study. To allow time for this process, acquisition of the NMR signal is delayed for up to a few hundred milliseconds after excitation. This is achieved by 480 PHYSICS EDUCATION

50 Magnetic resonance imaging in medicine (a) Figure 8. Flexibility of imaging plane and image weighting in MRI. (a) Transaxial T 1 -weighted image of the head at the level of the orbits. There is good soft tissue contrast, and fluid-filled structures, such as the eyes and the ventricles in the brain, appear dark. (b) Heavily T 2 -weighted parasagittal image of the head. Note the intense signal from CSF around the surface of the brain and from the contents of the eye, except for the dark lens (pictures courtesy of Guy s and St Thomas NHS Trust). (b) using magnetic field gradients and RF pulses to produce what is known as an echo at the desired time. Unlike x-ray CT, MRI can image slices in any desired plane by appropriate use of gradients. Alternatively, the technique can be modified to produce three-dimensional volumes of data that can be viewed using special software or postprocessed to generate arbitrary slices. The images generated in MRI are made up of voxels (three-dimensional pixels), and the brightness of each voxel is dependent on the intensity of signal from the corresponding location in the object. A typical image consists of or, increasingly, voxels. This means that the in-plane resolution is typically mm. The voxel is usually considerably larger in the third dimension, as the slice thickness is typically 1 5 mm. For specialist (usually non-medical) applications, NMR microscopes are available that can achieve a resolution of a few micrometres. As described so far, an MR image of the body is essentially a map of water distribution. Such an image would be of limited clinical value, since water density varies relatively little between tissues. One of the major strengths of MRI is the ability to manipulate image contrast. The two simplest ways of doing this follow readily from the discussion above, and involve weighting the image according to tissue relaxation times. During the interval between excitation and acquisition of an echo, magnetization in different parts of the sample will be undergoing T 2 decay at different rates depending on its environment (i.e. the tissue in which it is located). Thus by varying this interval, known as the echo time, T E, it is possible to vary the degree of T 2 weighting i.e. the extent to which differences in T 2 affect the appearance of the image. In addition, as noted above it is necessary to repeat acquisition a number of times to allow phase encoding. During the interval between repetitions, known as the repetition time, T R, magnetization undergoes differential T 1 recovery. By varying this interval, the user can alter the extent of T 1 weighting. T 1 and T 2 weighting result in very different image appearances. T 1 -weighted images provide excellent soft tissue contrast, and material with long T 1, such as cerebrospinal fluid (CSF) in the ventricles of the brain, appears dark. This type of imaging is often used to depict anatomical structures. On T 2 -weighted images, tissues with increased water content appear bright. This includes CSF, but also pathological processes such as neoplasm, inflammation, ischaemia and degenerative changes. Thus T 2 -weighted images are often used to highlight areas of disease. Typical T 1 - and T 2 -weighted images are shown in figure 8. Many other types of image contrast may be introduced by appropriate adaptation of the PHYSICS EDUCATION 481

51 S F Keevil sequence of magnetic field gradients and RF pulses. For example, images may be produced that highlight flowing blood, diffusion of water molecules, blood perfusion, temperature or tissue magnetic susceptibility. All of these types of image have or are finding a role in clinical medicine. When contrast manipulation is inadequate, artificial contrast agents may be used to highlight particular structures of interest. These are usually based on metal ions with large magnetic moments and have a dramatic effect on the relaxation properties of water protons and hence on signal characteristics. The active component of the most commonly used agents is the gadolinium ion, Gd 2+. These agents are usually given by intravenous injection and distribute in the body according to blood flow. Thus they are of most use for highlighting highly vascular tissues, such as tumours, or for imaging blood vessels themselves. Orally administered agents are also available, often consisting of macroscopic magnetic particles, and targeted agents have the potential to enhance signal from specific tissues or even from regions in which specific genes are being expressed. Figure 9. Superconducting MR system. This particular design is available in 0.5, 1.0, 1.5 and 3.0 T versions (picture courtesy of Philips Medical Systems). MRI instrumentation The appearance of a clinical MR scanner is dominated by the magnet. Until recent years these were almost invariably large and forbidding, with a bore that totally enclosed the patient and frequently disappeared into the wall of the examination room. Now, developments in magnet technology have led to designs that increase both patient acceptance and the range of potential applications. Also, whereas most MR magnets once operated at a field strength of T, the market has now polarized between low ( T) and high (1 3 T) field strength systems (with a few research systems at 4 8 T). The lower field systems are cheaper and, being more open and more patient-friendly, are arguably more suitable for paediatric and interventional work. Higher field systems produce better quality images and are appropriate for more specialized work in areas such as neurology and cardiology. High fields are achieved using superconducting electromagnets: once the magnet is on field, current flows without loss and no power supply Figure 10. Low-field (0.2 T) open MR system using a permanent magnet (picture courtesy of Siemens Medical Solutions). is needed. Newer high-temperature superconductors have had a limited impact on MRI thus far, and superconductivity is maintained by immersing the turns of the magnet in a bath of liquid helium (at 4.2 K). Modern superconducting MR systems are far more compact and patient-friendly than older designs (figure 9). Lower field systems are usually based around resistive electromagnets or permanent magnets. These are typically more open than superconducting systems, allowing more interaction with the patient (figure 10). As well as the magnet, the performance of an MR scanner depends on the design of the gradient and RF systems, and increasingly on the performance of the computer system used to control data acquisition and image processing. 482 PHYSICS EDUCATION

52 Magnetic resonance imaging in medicine Figure 11. Sagittal MR image of the knee. The plane has been selected to show the cruciate ligaments (the black X -shaped structure behind the knee joint). Damage to these ligaments due to sporting injuries is a major indication for MRI of the knee (picture courtesy of Guy s and St Thomas Hospital NHS Trust). Innovations in all these areas are increasing the speed of MRI data acquisition and opening up new possibilities in real-time imaging. Clinical applications Because of its excellent depiction of soft tissues, MRI has long been the modality of choice for examination of the central nervous system (brain and spine), with indications including suspected tumours, slipped disks, multiple sclerosis and degenerative diseases (see figure 8). It now also has a major role in orthopaedics and musculoskeletal imaging (figure 11). Cardiac MRI is an area of increasing importance, including investigation of both congenital abnormalities and acquired conditions such as coronary heart disease. The high resolution and contrast between tissues possible using MRI allow image processing techniques to be applied to extract features of interest (figure 12). Improvements in the speed of MRI in recent years have made abdominal imaging possible. Figure 13 shows an MR angiogram of the kidneys, acquired using an injection of contrast agent to highlight flowing blood. Images such as this can be used to investigate narrowing of the arteries due to fatty plaques. Figure 12. Rendered view of the heart and major vessels obtained by computerized post-processing of MR images in a patient with patent ductus arteriosus, a form of congenital heart disease (picture courtesy of Dr Marc Miquel, GKT School of Medicine, King s College London). Figure 13. MR angiogram showing the abdominal aorta and its various branches, including the renal arteries that feed the kidneys with blood. The aorta forks into the right and left common iliac arteries, each of which in turn divides into external and internal branches supplying the legs and pelvis (picture courtesy of Guy s and St Thomas Hospital NHS Trust). PHYSICS EDUCATION 483

53 S F Keevil Figure 14. Brain activation due to a simple right-handed motor task investigated using fmri. The images show activation in the part of the left hemisphere responsible for controlling the right hand (picture courtesy of Dr Andrew Simmons, Institute of Psychiatry, King s College London). Functional MRI (fmri) allows parts of the brain involved in processing sensory data (e.g. from the eyes and ears) or involved in motor tasks (such as moving the fingers) to be identified and studied. The technique uses the fact that activation of part of the brain results in increased delivery of oxygenated blood to that area, and the magnetic properties of this blood allow the area to be identified using MRI (figure 14). The fmri technique is helping to improve our understanding of the basic functioning of the brain, and in individual patients it can be used to map the function of important parts of the brain prior to surgery. Proton magnetic resonance spectroscopy (MRS) uses minute differences in the resonance frequencies of protons in different chemical environments to perform noninvasive chemical analysis. NMR spectroscopy considerably predates MRI and has wide applications outside medicine. However, MRS is now starting to have a role in the diagnosis and understanding of conditions such as epilepsy and Alzheimer s disease, in which the relative levels of the compound visible in the spectrum are found to change (figure 15). Carrying out surgical procedures in or close to an MR scanner might seem a dangerous or at best an unpromising idea. The high magnetic field turns conventional surgical instruments into deadly missiles, while the restricted bore of conventional MR systems offers little access to the patient. However, the development of special tools and more open magnet geometries has led to the development of interventional MRI, in which minimally invasive procedures or even open surgery can be performed inside the MR scanner. Figure 16 shows an artist s impression of an interventional MR room, similar to a suite soon to be installed at the author s institution. Developments like this have led some commentators to speculate that MR scanners may have a prominent place in the operating theatre of the future. 484 PHYSICS EDUCATION

54 Magnetic resonance imaging in medicine Figure 15. Proton magnetic resonance spectrum of the temporal lobe of the brain in a healthy volunteer. The three large peaks shown (left to right) are due to (1) compounds containing choline, (2) creatine and phosphocreatine, and (3) N-acetyl aspartate (picture courtesy of Dr Marcus Newbold, GKT School of Medicine, King s College London). The horizontal axis represents the resonance frequency of protons in each of the compounds in units of parts per million relative to an agreed standard frequency. The height of each peak on the vertical axis is proportional to the amount of the corresponding compound present in the tissue under study. Conclusion This brief overview has described the basic physics of MRI and some of its current clinical applications. In the space available it has not been possible to give more than a cursory survey of the field, but hopefully this is sufficient to give an indication of the power and flexibility of MRI. New advances in techniques, instrumentation and applications are announced on a weekly basis, and we can be sure that MRI is still a long way from fulfilling its full potential in medical diagnosis and treatment. Received 6 September 2001 PII: S (01) Figure 16. Artist s impression of an interventional MR facility based around a 1.5 T superconducting MR system (picture courtesy of Philips Medical Systems). Suggestions for further reading The physics of MRI is usually taught to physicists at postgraduate level. Many of the newer developments referred to in this article are as yet described only in research papers and highly specialized textbooks. Here is a small selection of more accessible books aimed primarily at radiography graduates. Elster A D and Burdette J 2001 Questions and Answers in MRI (St Loius: Mosby) Hashemi R and Bradley W G 1997 MRI: the Basics (Philadelphia: Lippincott Williams and Wilkins) Westbrook C 1998 MRI in Practice (Oxford: Blackwell Science) The following website may also be of interest: Hornack J P The Basics of MRI Stephen Keevil holds a PhD in NMR spectroscopy from the University of London, and is currently senior lecturer in radiological sciences and joint director of the Research Centre for Magnetic Resonance Imaging and Intervention at King s College London. His research includes various aspects of MRI and he has taught magnetic resonance physics at all levels from A-level to PhD. PHYSICS EDUCATION 485