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An Introduction See index terms on page 383. to the Physics of Resonance Magnetic Stephen Baiter, Imaging Ph.D. Editors Note: Meetings of the RSNA for many years has been the Symposium on by a committee of the American Assoclaflon of Physicists In with the Program Committee of the RSNA RadioGraph/cs Is pleased to published the symposium presented on November 29, 1986 in conjunction with the 72nd ScientifIc Assembly and Annual Meeting of the Society. The symposium, Introduction to the Physics of Magnetic Resonance Imaging, will appear serially throughout Volume 7 (1987) of the journal. The first portion by Dr. BaIter, who chairs the AAPM Symposium Planning committee, Is presented here. Radiologists who wish to use this material for group teaching or who, for other reasons, desire It In an audiovisual format are reminded that this and most previous symposia are available as “slide-tape” sets that may be ordered by writing to RSNA Educational Audio-Visual Materials, P.O. Box 10168 Chicago, IL 60610, or by calling (312) 943-0450. A valued feature of the Annual Basic Physics prepared Medicine in cooperation and presented In the 1980s, the technology magnetic resonance emerged of nuclear from the labora- tory and became a major medical imaging technique. The optimum clinical application this new entity can only be achieved when of the physician understands enough of the basic principles to apply the technique to the requirements of imaging an lndMdual patient. This essay, and those which will follow in succeeding Issues of RadioGraph/cs, will provide a review of those physical and technological principles needed for an adequate clinical understanding of magnetic resonance imaging (MRI). The technique of nuclear magnetic resonance (NMR) was initially developed in the 1940s by two independent groups: Bioch et al. at Stanford and Purcell et al. at Harvard. These groups discovered that when certain atomic nuclei are placed into a strong magnetic field their magnetic moments will precess around the field with a known frequency. A condition called resonance can be observed by irradiating the sampie with radio waves and measuring the interaction at the precessional frequency. (The terms used in the preceding sentences will be defined and amplified below.) Thus, the name nuclear magnetic resonance is a short but precise doscription of the process. NMP is a useful technique for analyzing molecular structure because the exact resonant frequency of any atom in a molecule is influenced by the magnetic fields of neighboring atoms. In addition, the time sequence in which atomic nuclei Interact with the external magnetic field and with the perfurbing radio frequency (RF) field Is influenced by the size and shape of the molecules as well as by their surroundings. In the early 1970s, Damadian introduced the concept of deliberately modulating the external magnetic field so that only one small volume element of the sample was in resonance with the RF field. By moving either the sensI1ve point or the sample, he was able to form an Image of the NMR properties of his specimen. In the same time period, Louterbur devised a method for modulating the his specimen field so that a line in By using back projection techniques, similar to those used in CT, he also was able to reconstruct the NMR properties of his specimen. Both groups realized that deliberate inhomogeneUles in the magnetic field could yield positional Information. In oddi- Dr. Batter is Adjunct Associate Professor of Radiology, Cornell University Medical Physicist, Philips Medical Systems, Inc., Sh&ton, ci. Address reprint requests to Stephen Baiter, Ph.D., Philips Medical Systems, Inc., Volume magnetic was in resonance. 7, Number 2 college, 710 Bridgeport March, #{149} New Vorlc NV; and 1987 Avenue, Senior Shelton, RadioGraphics #{149} Medical CT 06484. 371 MRI physics Balfer tion, they were both able to scale the size of their magnets up to the point at which the “specimen” became a whole body, and NMR imaging became a reality. The last decade has seen an explosion of image acquisition and image reconstruction techniques. When the technique was introduced into clinical practice, there was public confusion beiween nuclear magnetic resonance imaging and radionuclide imaging. This confusion has been minimized, at the suggestion of the American College of Radiology, by renaming the former as magnetic resonance imaging (MRI). The basic principles of MRI are shown in Figure I. With one key exception, these are identical to the technology of NMR spectroscopy used in the laboratory. In both areas, the sample is magnetized. A strong radio frequency (RF) signal, at the resonant frequency, is used to inject the energy needed to excite atomic nuclei in the sample. These nuclei then emit an RF signal for a brief period of time. The use of controlled nonuniformities in the magnetic field distinguishes NMR from MRI. In the NMR laboratory, great care Is taken to provide an absolutely uniform magnetic field, and in many cases, the sample is rotated during the measurement to average out any residual magnetic field inhomogeneities. In MRI, deliberate spatial and temporal inhomogeneities are introduced into the magnetic field to provide the information needed to form an image. It Is appropriate that we review some elementary physics before proceeding to the details of MRI. First, is the concept of magnetic flux density (Figure 2). Magnetic lines of force are pictured as vectors emerging from the north pole of a magnet and entering the south pole of the same magnet. The strength of the magnet is described by the number of lines of force crossing a measuring area between the poles. In the SI system of measurement, the unit of magnetic flux density is the tesla (T). Figure 2 gives some indication of the relative strengths of different magnets. The next principle is that of electromagnetic induction (Figure 3). A moving charge creates a magnetic field. If the charge moves in a straight line, the lines of magnetic flux wrap around the direction of motion. If the charge moves in a circle, the lines of flux com- 372 RadioGraphlcs March, #{149} 1987 Volume #{149} bine so that they are perpendicular to the plane of motion at the center of the circuit. This motion produces a magnetic dipole or more descniptively a “bar magnet”. Conversely, if a magnet is moved, it will generate current flow in a nearby circuit if the moving lines of magnetic flux “cut” across the circuit. Magnetic 1. Piace 2. Resonance patient Perturb Imaging into uniform equilibrium Magnetic magnetization Field with RF Fieid 3. Observe RF Emissions from perturbed nuclei Figure 1 If one looks at the classical model of a hydrogen atom, there are three souces of moving electrical charge. These are the motion of the electron in its orbit, the intrinsic motion of charge within the orbital electron as it spins, and the intrinsic motion of charge within the proton (nudeus) as It spins. Each of these motions gives rise to an atomic scale magnetic dipole (Figure 4). Nature tends to organize itself so as to minimize the build up of effects such as magnetic fields; more complex atoms possess atomic magnetic moments that are of the same general strength as hydrogen, or they may possess no net magnetic moment at all. This is due to the occurrence of atomic and nuclear spins in antiparallel pairs; each member of the pair cancels the other’s field. Nuclei possessing a net magnetic dipole must have an odd number of protons or an odd number of neutrons. Nuclei of biological significance with net nuclear spins are shown in Table I. It may be important to remind patients that these are all radiochemically-stable isotopes of their respective elements. 7, Number 2 MRI physics Balfer Magnetic Flux Density Figure 2 Magnetic lines of force are pictured as vectors emerging from the north pole of a magnet and entering the south pole of the same magnet. A strong magnet is represented by many lines of force. The magnetic flux density (B) is a vector quantity; the arrow above the (B) is a reminder that direction and magnitude are both important in a vector. B Earth’s Field Household Magnets MR Magnets -c 501i.T mT 0.1 -4T Motion k1iiiIIIIIIi: #{182}IjIII:: Figure 3 The principles of electromagnetic induction: A moving charge induces a magnetic field. The direction of the field is determined by the direction of motion. Also, a moving magnetic field can induce charges to move (a current) in a circuit. Proton Electron Intrinsic Intrinsic Electron Orbital Spin Spin Motion Figure 4 Each of the motions present in an atom gives rise to a magnetic dipole. In the hydrogen atom these motions are the proton’s intrinsic spin, the electron’s intrinsic spin, and the electron’s orbital motion. In a more complex atom, the pairing of the electron and nuclear spins and electron orbital motions largely cancels these effects. TABLE I Volume 7, Number 2 March, #{149} 1987 RadioGraphics #{149} 373 MRI physics Balfer When an atom with a net magnetic moment is placed in a magnetic field, all of its magnetic moments (electron and nuclear) will try to align themselves with the field. Because the components of the atom each have mechanical angular momentum, they cannot come into complete alignment with the field. The individual components of the atom will precess around the direction of the field, each separate component of the atom will rotate at its own precessional frequency. The precessional motion of the magnetic moment around the direction of the external field looks like the motion of a spinning top as it circles the vertical line representing the gravitational field. To simplify the discussion and the drawings, we will consider only The nuclear magnetic dipole and The precession of The nucleus about The external field (Figure 5). The precessional frequency is given by the Larmor equation. It is proportional to the strength of the magnetic field. It is also proportional to the mechanical and electrical charge distribution of the nucleus. The constant of proportionalily is called the gyromagnetic ratio. The gyromagnetic ratios of useful isotopes are also shown in Table I. Thus, in any given magnetic field, each of the usable nuclei will precess at a different frequency. The Larmor equation is exactly satisfied at all times; any change in the field produces an instantaneous change in the precessional frequency. The ability to change precessional frequency by changing field strength is critical to image reconstruction. Also shown in Table I are the relative concentrations of different nuclei in a typical tissue. Perusal of this table shows that hydrogen is not only the most abundant nucleus in tissue, but it produces the strongest signal for each atom present. It comes, therefore, as no surprise that hydrogen is the most important nucleus for MRI. It may be worthwhile to remember the value for the gyromagnetic ratio of hydrogen is 42.#{243} MHz/tesla. When a patient is placed In a magnetic field, each individual hydrogen atom will try to align its magnetic moment along the direction of the external field. In a classical physics sense, this alignment is disturbed by random thermal motions of the atoms. There is a continuous activily of alignment and disturbance. An equilibrium is reached that is dependent on temperature and magnetic field strength. At body temperature (300 K), only a few hydrogen atoms per 374 RadioGraphics March, #{149} 1987 Volume #{149} Larmor Equation to = Bo y = Gyromagnetic Ratio Bo = Magnetic Density Flux for ‘H i_ 2vr =426M T rN Figure 5 Because of the mechanical spin of the proton, its dipole can not completely line up with the external field. The tip of the dipole’s vector (represented by the arrow through the proton) describes a circular motion about the vector representing the external field (Bo). This motion is called precession. The relation between the precessional frequency and the external field strength is given by the Lanmor Equation. Remember: the arrow over B0 indicates only that B0 is a vector it does not indicate the direction of the external field. quan- tity; million are effectively aligned with the field of the largest MRI magnets. (Figure #{243}). Hence, even though drawings are made showing the patient converted into a bar magent, only a minute amount of organization is imparted to tissue when a patient is put into even the strongest imaging magnet. (The reader should be aware that these devices are extremely powerful magnets in the conventional sense and can pose major safety problems owing to their intense attractive force. There have been incidents reported in which patients and personnel have been injured because of missile and torque effects in ferromagnetic materials. Safety issues will be discussed in a subsequent article in this series.) When the protons precess around the direction of the external magnetic field, their angular position or phase may be of importance. This is shown schematically in Figure 7. The relative phases of protons in different areas of the patient are often used as a portion of the reconstruction information. Proton A is aligned with its spin antiparallel to the field (a position deliberateIy induced by the pulse sequence known as 7, Number 2 MRI physics Baiter Figure 6 The number of protons aligned with the external field is an equilibrium between the alignment forces of the field and the disruptive effects of thenmal motion. In an MR imagen, the number of protons aligned is only a few pen million protons present. Jhe entire MRI process depends upon these relatively few protons. © S AB Figure 7 Representation of phase relations between precessing protons, Proton A is antiparallel to (Bo), protons B, C, D are parallel to (Bo). Protons B and C are in phase relative to each other. Proton D is precessing out of phase relative to protons B and C. Remember: quantity; the arrow above it does not indicate inversion recovery). Protons B,C,D are aligned parallel to the field. Protons B and C are precessing so that they are in phase with each other. Proton D is out of phase with B and C. When a patient is placed in a magnet, the small atomic dipoles will combine to produce a net magnetic moment (Mo). The temporal growth of the magnetic moment is exponential because of the interaction of magnetic alignment and thermal disturbance forces. The time B0 indicates only that the direction of the external field. B0 is a vector constant for this exponential function is called the spin-lattice relaxation time or TI. In pure water, TI is 2.8 seconds. The value of TI will differ for different tissues and for different pathological states, but it is typically of the order of a few hundred milliseconds. Nominal values of TI for selected tissues are shown in Table 2. (The reader might observe that the values of TI are somewhat dependent upon the strength of the external magnetic field.) TABLE II Tissue Relaxation Characteristics nominal relaxation time in milliseconds Volume 7, Number 2 March, #{149} 1987 RadioGraphics #{149} 375 MRI physics Baiter Unfortunately, it is impossible for an external observer to directly measure the growth of the net tissue magnetization (Figure 8). This is because the phases of the individual precessing hydrogen atoms are random, and there is no net flux produced that will be available to cut across the loop and, thereby, induce a signal in the observer’s probe. This is modeled by picturing the net magnetization vector to lie in the direction of the external field (longitudinal direction). If the net magnetization could be tipped (notated) so that it would lie at a 90-degree angle to the external magnetic field, and if simultaneously all of the protons could be caused to precess in phase, then the precessional motion would generate a net moving magnetic signal which could be measured by the observer (Figure 9). This, in fact, is adcomplished by irradiating the patient with a burst of radio frequency energy at exactly the Larmor precessional frequency. The phases of the individual atomic dipoles will be synchronized by the external RF signal. The amount of angular rotation of the net magnetization vector (tip) is controlled by the amount of RF energy applied to the patient (Figure 10). After a 90 degree tip, the net magnetization lies in the plane perpendicular to the external magnetic field (transverse plane). This vector rotates in the transverse plane with the Larmon frequency. It is noted that pulse powers of hundreds of watts are required to tip the spins and that the resulting precessional signal seen by the observer has a strength of a few microwatts. Since both the transmitted and received signals must be at exactly the same frequency, considerable engineering design is needed to separate one from the other. As will be seen, this is achieved by the temporal separation obtained from a spin-echo pulse sequence. Mo S 1 M /\Mo Figure 8 The net magnetization of the patient is represented by a vector (Mo). The net magnetization grows exponentially toward its equilibrium value, Mo, with a time constant, TI. As the mdividual precessing atoms align with the field, they will have random phase. No net external signal is produced. Bo N 376 RadioGraphics March, #{149} 1987 Volume #{149} 7, Number 2 MRI physics Baiter S Figure 9 The patient’s net magnetization vector (M) has been rotated (tipped) into the plane which is perpendicular to the direction of the external magnetic field. This process is done in such a manner as to align the phases of all of the precessing protons. This is represented as a precession of (M) in the transverse plane. An externally observable signal is produced. N S Bo Figure 10 The tip of (M) from the longitudinal direction into the transverse plane is accomplished by irradiating the patient with radio waves at the Lanmor frequency (as a reminder, the transmitten is given the call letters WLF). The protons initially will all be in phase relative to each other. 42.6 MHz I N Volume 7, Number 2 March, #{149} 1987 RadioGraphics #{149} 377 MRI physics Baiter Under ideal conditions (i.e., a perfect magnet), as soon as the observer detects the signal, he observes that it decays in an exponential fashion with a time constant T2 (Figure II). In most cases, T2 (the spin-spin relaxation time) is less than TI. The loss of signal is due to Iwo effects: the first is the return of individual nuclear dipoles into alignment with the main field; the second, and usually dominant process, is due to loss of phase coherence between those spins remaining in the transverse plane (Figure 12). These activities are separate processes. In a substance such as pure water placed in a perfect magnetic field, there is nothing available to disturb phase coherence. In this special case, TI = T2. In all other cases, TI is greater than T2. Nominal values for T2, for different tissues, are also given in Table 2. It can be seen that the values of TI and T2 for different tissues do not have the same ratio. It can also be seen from the table that this ratio is dependent upon magnetic field strength. The net spin state of tissue can be manipulated by controlling the time of application of RF pulses and magnetic field gradients. These combinations are called pulse sequences. It is worthwhile to examine patients using, at least, Iwo different pulse sequences; one, to produce contrast resulting from TI differences between tissues, and a second to produce contrast resulting from T2 differences beiween tissues. The reader should also note that the TI and T2 differences between different tissues are much greater than the differences in proton density between these tissues. Hence, MRI is capable of producing greaten tissue differentiation than CT. It cannot be overemphasized that observed tissue contrast is a function of both the tissue and the technique used for imaging. An inappropriate technique can cause a total loss of contrast and may even cause contrast reversals. S I 12 iL’’ I 1 Figure 11 Decay of the observable signal: Under ideal conditions the observer will note that the signal decays with an exponential time constant T2. For most substances T2 < TI. N 378 RadloGraphics March, #{149} 1987 Volume #{149} 7, Number 2 2 3 4 5 MRI physics Baiter S Figure 12 ML The loss of signal is due both to a return of mdividual dipoles to alignment with the external field and to a loss of phase coherence between the precessing dipoles remaining in the tnansverse plane. In general, these are separate processes. MT N In a real magnet, the net signal decays even more rapidly than predicted by the T2 curve (Figure 13). The actual loss of signal is known to have an exponential form. The time constant for this phenomenon is called T2*, Because there are variations in the external magnetic field in the parts per million range, all of the protons in the patient will not have exactly the same precessional frequency. Those protons located in a higher local field will precess a tiny bit faster than those in a lower local magnetic field. This will alter the relative phases of protons in different locations. As time goes by, the minutely different notation speeds will alter the relative phases of protons in different locations. This causes a loss of signal which typically occurs in a few milliseconds; a short time relative to the tens of milliseconds characteristic of T2 and a very short time compared with the hundreds of milliseconds characteristic of TI. .1\ 1/ ( I II III Figure 13 In a neal magnet, minute variations in the external field cause a rapid exponential loss of phase coherence with a time constant T2”, In general T2* << TI. At time I, all of the proton dipoles are in phase coherence and the extennal signal is at a maximum. At time II, the protons in stronger fields have precessed a bit more rapidly resulting in a spread in phase and a weaken external signal. At time III, the spread has progressed to a point at which the phases of the protons are uniformly dispensed resulting in no external signal. time , . ;j,#::II Tj Volume 7, Number 2 March, #{149} 1987 RadioGraphlcs #{149} 379 MRI physics Baiter In Figure 14, one sees the situation that occurs when the spins are losing phase coherence because of variations in the external magnetic field. I, All of the protons are precessing in the transverse plane, the observer is looking down on this plane from one of the poles of the magnet. The instantaneous direction of each of the spins lies somewhere in the “spin phase bundle” beiween F and S. (For simplicity, only the leading and trailing edges of the spin phase bundle are shown.) It is possible to flip the entire spin phase bundle like a pancake, so that instead of the faster spins (corresponding to protons in a stronger field) being ahead of the slower ones in relative phase, they are behind them. 2, This flip is produced by supplying an additional RF pulse with enough energy to flip the spins of each of the protons by 180 degrees. Eventually, the faster spins catch up in phase with the slower spins, resulting in a strong external signal. 3, This is called an echo. A little later, the fast spins have outraced the slow spins, resulting in another loss of signal, 4. The process may be repeated and multiple echoes may be observed. Because of the T2 decay of the signal, each echo is weaker than its predecessor. Eventually, the loss of phase coherence caused by T2 effects eliminates the possibility of observing further echoes. The description of the timing of radio frequency pulses and magnetic field gradients is called a pulse sequence. Clinical image contrast is determined in large part by the selection of the appropriate pulse sequence. It is, therefore, worthwhile for the clinician to become adcustomed to this notation. The RF portion of a typical pulse sequence is shown in Figure 15. This example is called a spin-echo sequence because the clinically useful data is obtained from the echo. It is the most common sequence used for clinical MR imaging. The entire pulse sequence is repeated periodically with a time interval called the repetition time, TR. A clinical study will involve repeating the pulse sequence several hundred to several thousand times. The time between the start of the initial pulse and the maximum echo strength is called the echo time, TE. The center of the 180 degree pulse is located at time TE/2. In an actual MRI scanner, the initial signal, called the free induction decay (FID), is ignored and the clinical data is based upon the echo. This Is the principal way in which the transmitted stimulation and the received signal are isolated from one another. Figure 14 CD I V WLF 2F 2 : 3 4 380 RadioGraphlcs March, #{149} 1987 Volume #{149} The formation of a spin echo: At some time (I), the spins are losing phase coherence due to variations in the external magnetic field. The vectors representing the spins of individual protons are contained in the arc between F and S. The vector representing the fastest proton is F, that representing the slowest is S. The protons are precessing in the direction of the circular arrow. At time (2), a pulse of RF energy is injected at the Larmon frequency by the same transmitter that was previously used to tip the spins. This flips each of the spins by 180 degrees in phase so that now the fasten spins are behind the slower ones. At time (3), the faster protons have overtaken the slower ones resulting in a regrowth of coherence and a reemergence of the external signal (the echo). At a further time (4), the fasten protons have passed the slower protons causing another loss of phase coherence and another loss of the external signal. 7, Number 2 Baiter MRI physics 18 iaO#{176} Figure 15 Spin-Echo Pulse Sequence: This is a representation of the RF portion of a common clinical sequence. The entire sequence is repeated periodically (several hundred to several thousand times) during the course of a study. The time interval between one repetition of the sequence and the next is called TR. It is usually measured between the 90degree RF flip pulses. The time between the 90-degree pulse and the peak of the echo is TE.The 180-degree flipping pulse occurs at time TEI2. Note that exactly twice as much RF energy is required for the 180-degree as for the 90-degree pulse. The flipping sequence is shown again in this illustration, 900 900 echo TR = TE = Repetition Echo time time 4 ‘Lt e k*:E? *E The received signal can be characterized by its frequency and phase as well as by its intensily. The frequency and phase information are used to localize the source of the signal spatially. The signal intensity itself, in turn, is a function of the number of accessible protons in the measuring volume, the flow of protons through the volume, the presence of natural or enhanced concentrations of paramagnetic nuclei, and the relaxation constants TI and T2. The contnibution of the relaxation constants of each tissue to the received signal strength is critically influenced by the pulse sequence used for scanning. To repeat: The available MR signal, and the contrast in MR signals beiween tissues is dependent both on intrinsic tissue properties and upon all of the operating parameters of the scanner. The details of these processes will be the subject of later articles in this series. The selection of the appropriate pulse sequence required for the examination of an individual patient involves the use of careful clinical judgment coupled with a firm understanding of the technology. This will also be discussed in a separate article. The distinguishing feature beiween magnetic resonance imaging and NMR spectrosdopy is the use of deliberate magnetic field gradients for spatial localization of the signal. This is adcomplished by appropriately shaping the magnetic field and by a corresponding selection of the frequency content of the RF pulse. The simplest example of the use of magnetic gradients is slice selection (Figure 16). Figure 16 Slice Selection Gradient: The magnetic field is made slightly nonuniform in the axial (7) direction. The 90-degree flipping pulse is given a limited frequency content. Only those protons that satisfy the Lanmor equation are flipped. In this case, this selection conresponds to a transverse plane through the patient. higher precessKn frequency precession frequency excitation frequency = lower precession frequency single excitation frequency Volume 7, Number 2 March, #{149} 1987 RadloGraphics #{149} 381 MRI physics Baiter In this example, the magnetic field is made slightly nonuniform along the patient’s longitudinal axis (i.e., the Z direction) b,’ supplying power to a gradient electromagnet. If the RF pulse contains only one frequency, then only one transverse plane in the patient will meet the requirements of the Lanmor equation. Only the protons in this plane will absorb the energy from The transmitter and will be flipped into the emitting position. The emitted signal can come only from protons in that plane. This still leaves the problem of deciding where on the plane any panticular portion of the signal originates. The next step is to apply a second magnetic field gradient in the active plane only during the readout of the echo. This readout gradient is applied in the X direction in Figure 17. This gradient will cause the protons to precess at a slightly higher frequency where the field is stronger and at a slightly lower frequency where the field is weaker. Remember that only those protons in the previously selected slice are emitting a signal. This signal will now contain a band of frequencies, and the RF intensity at each frequency will correspond to the protons found in one line of tissue in the preselected slice. By electrically notating the direction of the readout gradient and repeating the process many times, one obtains enough information to reconstruct the patient’s cross section using CT mathematics. Many MRI scanners use the phase information present in the emitted RF echo to obtain still further information about the distribution of signal in the patient. If a third orthogonal gradient, i.e., in the V direction, is applied during the time of the initial free induction decay, it is possible to speed up the the precession of the protons proportional to their V coordinate (Figure 18). When the V gradient is switched off, each proton returns to precessing at the original frequendy, but, because of the previous speedup, the phases of spins now differ along the V axis. A brief analogy may be appropriate to demonstrate the use of frequency and phase information for spatial localization. A small choir is shown in Figure 19. We would like to know how loud Jim is singing. If we happen to know that Jim is a tenor, then we know that he is in the column with all of the other tenors. But, how do we know which tenor is Jim? If the choir is singing a round Gz phase-encoding mae gradient / p-on G x gradnt G frequency / / frequencies fres onginal frequency hher frequencies frequency Figure 17 Frequency Encoding: By applying a gradient in the X direction during the readout process, protons in different lines in the selected plane are caused to emit their signal at different frequencies. 382 RadioGraphics March, #{149} 1987 Volume #{149} frequendes Figure 18 Phase Encoding: By applying a gradient in the V direction during the initial free induction decay, the relative precessional phases of protons are made proportional to the V coordinate in the selected plane. Different magnitudes of this gradient are required for different pulses in a complete pulse sequence. 7, Number 2 Bolter MRI physics (i.e., Three Blind Mice), each row will be singing a different portion of the round. That is to say, each row will be singing in a different phase. If we now happen to know which phase Jim is singing, then we have him uniquely identifiedhe is the only tenor singing the third phase of three blind mice. Although the mathematics of image reconstruction is more complex than our simple analogy, the principle of isolating a pixel by using its phase and frequency information are identical. In conclusion, let us review a typical pulse sequence (Figure 20). The magnetic field gradients lGx, Gy, Gz) are used to reconstruct the positions of MR emitters in the patient and the relative strengths of the signals are determined by the pulse timing parameters TR and TE. The optimum strategy for examining patients requires that the technical parameters must be related to the clinical question. In addition, due consideration must be given to safety as well as efficiency. Future articles in this series will cover all of this material in detail. S A T B Jim 2 iE;E Figure 19 Analogy of Frequency and Phase Encoding: How loud is Jim singing? Jim is a tenor, so he must be in the tenon’s column of the choir. He is also singing the third pant (phase) of Three Blind Mice so he must be in the third now. Jim is now uniquely identified among the members of the choir. Figure 20 A more complete spin-echo pulse sequence. The magnetic field gradients are shown, Gz is the slice selection gradient, Gy is the phase encoding gradient (different intensities are applied at different times during the study), and Gx is the frequency encoding gradient. Note the relationships between the various magnetic field gradients, the RF pulses, and the observed signal intensity 5(t). Note that IR is not drawn to scale. RadloGraphlcs index terms: Magnetic Resonance Imaging physics Magnetic Resonance Imaging radIation physics cumulative Magnetic physics Index terms: resonance (MRI), Volume 7, Number 2 March, #{149} 1987 RadioGraphlcs #{149} 383