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An Introduction to MRI

for Medical Physicists and Engineers

ANTHONY WOLBARST AND NATHAN YANASAK

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1

SAMPLE CHAPTER (PARTIAL)—NOT FOR DISTRIBUTION

C H A P T E R 1

Introduction to MRI1.1 A Stratospheric, Warp-Speed Sketch of NMR and MRI .....................................................................................2

The nuclear magnetic moment is proportional to the nuclear spin............................................................................ 2Some Notes on Vectors ............................................................................................................................................... 3First picture of NMR: Quasi-quantum mechanical (spin-up/spin-down along Bz and the z-axis) ............................ 4MRI of a 1D patient .................................................................................................................................................... 6Second picture of NMR: Classical (magnetization precessing in x-y plane) ............................................................. 7Proton spin relaxation ................................................................................................................................................ 7Longitudinal proton spin relaxation time, T1............................................................................................................. 8Transverse proton spin relaxation time, T2................................................................................................................ 9T1-weighted and T2-w clinical images....................................................................................................................... 9

1.2 Uniqueness of MRI ............................................................................................................................................101.3 A Real MRI Case Study .....................................................................................................................................10

Computed tomography (CT) ..................................................................................................................................... 10MRI: T1-w, T2-w, and FLAIR imaging ................................................................................................................... 10Magnetic resonance spectroscopy (MRS) ................................................................................................................ 11Functional MRI (f MRI)............................................................................................................................................ 12Diffusion tensor MR imaging (DTI) ......................................................................................................................... 13 MRI-guided fine-needle biopsy................................................................................................................................. 14Should we try positron emission tomography?......................................................................................................... 15Treatment guidance and follow-up ........................................................................................................................... 15

1.4 A Brief History of MRI: Bloch, Purcell, Damadian, Lauterbur, et. al. ..............................................................161.5 A Critical Caveat ................................................................................................................................................19

The story of Magnetic Resonance Imaging (MRI)begins with the nuclear magnetic resonance phenome-non, discovered just before and during the SecondWorld War. The technique was refined over the ensu-ing decades, and a multitude of experimental and theo-retical studies were devised to explore the factors thataffected the precise magnetic resonance frequencies atwhich nuclei resonate in a strong external field. A keyrevelation was that even slight differences in the

molecular environments of the nuclei cause detectableshifts in their behaviors. Researchers realized that suchstudies, especially when in combination with x-ray dif-fraction results, could be invaluable in unravelingmolecular structures. Also of great importance, itbecame possible to explain the associated nuclear-spinrelaxation (T1, T2) mechanisms, which would come toplay so central a clinical role in MRI.

2 An Introduction to MRI for Medical Physicists and Engineers



In the mid-1970s, scientists designed methods tocarry out NMR voxel-by-voxel within a thin slice oftissue, thereby enabling the delineation of two-dimen-sional MRI maps of T1 and of T2 throughout the body.This led to further approaches—such as MR spectros-copy (MRS), functional MRI (fMRI), diffusion tensorimaging (DTI), and MR angiography (MRA)—thatportray the spatial dependences of other physiologicaland metabolic tissue properties, too. All of this hasestablished MRI as a powerful and extraordinarily ver-satile diagnostic modality with a number of uniqueimaging capabilities. Were it not for their still signifi-cantly greater cost, MRI machines might well drive CTlargely out of business.

This chapter will say a bit about NMR and MRI ingeneral, then illustrate some of the remarkable capabil-ities of MRI with a real case study.

There follows a sketch of the rich history of thefield, and an important caveat: there are potentiallylethal but preventable hazards associated with strongand rapidly switching magnetic fields and with theintense pulses of radiofrequency (RF) energy from anMR device. Be careful for yourself, your patients, andall others.

1.1 A Stratospheric, Warp-Speed View of NMR and MRIThis brief section zip-lines through much of the phys-ics of NMR and MRI. We shall provide only cursorydescriptions now, but you can expect the explanationsand fuller descriptions to follow in the rest of the book.Many of the whys and wherefores may not be apparenthere, but they will come later.

The nuclear magnetic moment is proportional to the nuclear spinThe normal chemical properties of virtually any atomare determined solely by the arrangement of its elec-trons, hence ultimately by the number of protons in thenucleus, the atomic number, Z. Gases, liquids, solids,and living cells behave the way they do because of, andalmost only because of, the configurations of the Zelectrons of their constituent atoms.

The properties of a nucleus itself, however, dependon the number of neutrons, N, as well. The values ofboth Z and N together govern whether or not a specificisotope is radioactive, of importance in nuclear medi-cine, and in the cleanup of nuclear power reactors and

weapons facilities. The makeup of a nucleus also deter-mines its magnetic properties, which are fundamentalto MRI. It can be fruitful to think of a nucleus as beingsomewhat like a spinning ball of positive charge [Eis-berg et al. 1985]. A proton, a neutron, or a compositenucleus has a quantum mechanical (QM) attribute thatis called, by analogy with the corresponding vectorproperty of classical physics, nuclear spin angularmomentum, I, or just spin, as in Figure 1.1.

The only nucleus currently of major interest inclinical MRI is the simplest of them all, namely that ofan atom of ordinary hydrogen, i.e., a solitary proton. Anuclear physicist views a proton as a subatomic particlemade up of two up-quarks and one down-quark heldtogether by the strong nuclear force. Just as interactionsamong charged particles are brought about by the vir-tual photons of quantum electrodynamics, likewisequarks are bound by the virtual gluons of chromody-namics, within a sea of virtual quarks that are con-stantly appearing and vanishing. Mother Nature has

+++

N

+

I

Nuclear spinmagnetic moment

Nuclear spinangular momentum

Figure 1.1 A free nucleus has a quantum mechanical attributeanalogous to classical spin and is said to possess spin angularmomentum, S. As a ‘spinning’ charged body, it produces its ownweak magnetic field, like that of a compass needle or small barmagnet. The strength of this nuclear magnet is parameterizedby its nuclear spin magnetic moment, represented as the vectorquantity µn, of magnitude µn |µn|.

31. Introduction to MRI



decreed that, despite the problems theorists are havingin getting the spins of its quarks and gluons to add upright (a situation known as the ‘proton spin crisis’), alone proton is one of many nuclei considered to be a‘spin-½’ particle, therefore a fermion.

Every nucleus comprised of an odd number of pro-tons or of neutrons or both possesses non-zero spin. Inany nucleus with even numbers of both protons andneutrons, at the other extreme, each proton pairs up andaligns anti-parallel to another, for reasons that can beexplained with QM, and their two dipole magneticfields cancel—they have zero net spin. The same isalso true of the neutrons. As a result, carbon-12, oxy-gen-16 (which, together with hydrogen, make up ¾ ofthe mass of soft tissues), and calcium-40 play no activerole in imaging.

As with any other charged and moving entity, a‘spinning’ nucleus produces its own magnetic dipolefield, its nuclear magnetic moment, a vector entity thatis represented by a lower-case italic Greek mu, µ. Themagnitude or strength of the inherent nuclear momentof the nth isotope, designated µn |µn|, is a principalmeasure of its ‘magnetness,’ the strength of the field ititself produces.

The gyromagnetic ratio, n, is a slightly differentmeasure of the same thing, the strength of the intrinsicnuclear magnetic field of the nucleus. Encounteredmore commonly as (n/2), it relates the nuclear mag-netic moment to the nuclear spin angular momentumvector, In,

At times it is more convenient to use n/2 rather thanµn in discussion, or vice versa, but otherwise the twoare equivalent, apart from a constant.

The subscripts on In, µn, and n label specificnuclear isotopes by their atomic weight,

Clinical MRI deals almost exclusively with the nucleiof regular hydrogen atoms, 1H1 or H-1 in the standardnotation, so there is no further need for the subscript,and the magnitudes of the two vectors can be related as

The protons that are imaged are found almost entirelyin cellular or extra-cellular water or lipids and, again,we shall refer to them generally as tissue protons. Sohereafter, and µ will appear unadorned with an ‘n,’and they will refer only to hydrogen nuclei in tissues.

From here, traditional introductions to NMR andMRI physics take one of two pedagogic paths, thequasi-quantum ‘spin-up/spin down’ and the ‘classical.’We shall, however, be guided by the incontrovertiblewisdom of Yogi Berra, philosopher and former catcherfor the resplendent New York Yankees: “If you cometo a fork in the road, take it.” Both routes happened topass by his house, and such is the case here, too.

Before proceeding withour story, we shouldclarify the notation forvectors. A magnetic

field, B, which has both magnitude and direction, is avector entity and is represented with a bolded sym-bol. Its strength, B, a scalar, is not in bold. B(r) is avector field that has magnitude or direction that mayvary according to the value of the position vector r.We shall deal frequently with the particular one-dimensional situation of a 1D patient reposing alongthe x-axis and in an external field whose strength var-ies with x—but that always points along the z-axis!This might be written B(x), but when it is necessary toemphasize the fixed direction of the external field, itwill be presented as Bz (x).

Individual components of a vector will not be

denoted in bold: for example, x is the first spatial com-ponent of the three-space position vector r {x,y,z} = xi + yj + zk, where i, j, and k are the orthonor-mal unit vectors of ‘real-’ or ‘three-’ space. This mayalso be expressed as r {x1, x2, x3} = x1i + x2j + x3k.

In mathematics and computer science, on theother hand, some quantities with multiple, discretevalues can be treated as vectors or arrays, such aswith the vector x {x1, x2, x3, …, xn} that specifies thepositions of voxels 1, 2, …, n along the x-axis of animage. We shall not denote the individual membersof this set as vectors with bold font.

Similarly, when discussing the rather enigmaticconstruct known as k-space, k {kx, ky, kz} (which istotally, absolutely not related to the unit k-vector ofreal-space) will represent a single vector location inthat space.

Some Noteson Vectors

(1.1a)n n n I

n Z N .n n ( ) (1.1b)

(1.1c) I




Every concept introduced briefly in this chapter, bythe way, will be pursued more fully later on.

First picture of NMR: Quasi-quantum mechanical (spin-up/spin-down along Bz and the z-axis) The easier way to begin addressing proton NMR is byway of a great simplification of the full quantum

mechanical (QM) treatment.Imagine that in a magnetically shielded room, a

tray of compasses is being mechanically rattled gently.With no external magnetic field, their needles are jos-tled about and randomly point in all directions becauseof the effects of the ‘noise’ energy being inputted.When a strong external field, Bz, is present, however,then the needles will tend to align relative to it, eachwith its own north pole heading toward the magnet’s

Low-energy state

0

+ z

North

High-energystate

South

– z

B

E

EBz

z

Figure 1.2 There are two pedagogical pictures of NMR, the quasi-QM and the classical, that are commonly drawn upon in introducingMRI physics. The two are mutually incompatible and inconsistent, and they cannot be combined together, because of the quite differ-ent assumptions adopted in constructing each of them out of the fully correct, rigorous quantum theory. But both are useful in differ-ent ways. Here we discuss only the greatly simplified quasi-QM picture. (a) A single proton behaves like a tiny compass needle, but itcan align in an externally magnetic field, Bz, only along or against it and the z-axis. The energy levels for the two quasi-QM proton spinstates diverge by the amount of the Zeeman energy, which is linear in the strength of the total local magnetic field. Nearly all of this Bzcomes from the main magnet, and is constant. Much of the rest is from the intermittently activated gradient coils, and from the briefpulses from the RF (radiofrequency) transmitter. Finally, the amount of random RF ‘noise’ generated by fluctuations in molecularmotions is tiny, but it greatly influences proton spin relaxation processes. A spin-½ nucleus such as a proton is allowed to inhabiteither one of the two levels: in the lower-energy, ‘spin-up’ state, the projection of µ onto the z-axis is aligned parallel to Bz. Alterna-tively, in the ‘down,’ high-energy state, it points against Bz. Also, unlike a compass needle, a proton can remain for long periods of timein a quasi-stable, higher-energy spin-orientation state, pointing the ‘wrong’ direction. (b) The two spin states differ by the Zeemanenergy, E = 2z Bz. A photon (or phonon) of the right energy can cause a transition up or down between the two. The horizontaldashed line in the middle indicates the energy the nucleus has at Bz = 0.

(a)

(b)

spinflip+ z

– zE 0

E = hf




south pole. But by grabbing and twisting a needle youcan make it point in any direction you choose, until youlet it go.

Protons behave only somewhat like that. When abunch of them are inserted into the uniform field Bz,they will be polarized, but—as it happens, perhapssomewhat mysteriously—with only half of themaligned along it and the other half against. This is awonderful example of what is affectionately known asquantum weirdness. The spin magnetic moment of aproton is spatially quantized, and its z-component canalign only ‘up’ along the direction of the external fieldor ‘down’ against it. According to this simplified,quasi-QM picture, the nucleus can exist in either ofthese two possible spin states in the external field—and, unlike a compass needle, with no other alignments(Figure 1.2a). In other words, the z-components of aproton’s nuclear magnetic moment can assume onlythe values

If the field produced by the nucleus itself aligns alongan external field, as with a compass needle, then thenucleus is said to inhabit the lower-energy, or spin-up,state.

It simplifies many of the illustrations in this bookto align the main external field vertically, somewhatlike the energy scale. While the fields of superconduct-ing magnets are mostly horizontal, those of permanentand electromagnets are vertical, so there’s nothingreally to unlearn to assume, for now, that they pointupward.

The classical energy of alignment of a magneticdipole moment in a z-orientated external field is givenby the vector dot (or scalar) product

and this general form remains valid quantum mechani-cally. To avoid confusion with the electric field E, theE intended to represent the non-vector energy is shownin Arial typeface. From Equations (1.1) and (1.2a), theQM Zeeman splitting, EZeeman, between the twoenergy levels of a spin-½ nucleus, is proportional bothto its innate magnetness (µ or ) and to the strength ofthe local magnetic field there, Bz:

At the heart of MRI is the critical fact that a proton inits lower-energy spin state can be elevated to a high-energy state by interaction with an applied radiofre-quency photon that carries exactly the right energy.Indeed, one easy way to determine that the nuclearmagnetic resonance process is occurring in a sample ofwater, say, is to turn on an external magnetic field B,pass a beam of RF photons through it, and detect therate at which it absorbs the energy as a function of thefrequency, v. Bearing in mind the ubiquitous Planck-Einstein relationship between the energy of a photonand its frequency, E = hv, then the energy required toflip over a proton in the field Bz is

This is the central Larmor equation, which relates thefrequency at which a cohort of protons gatheredtogether in a magnetic field of local magnitude Bz willundergo the phenomenon of nuclear magnetic reso-nance. NMR is one of the two essential concepts ofMRI (the other being spin-relaxation), and here you areat only page 5! Imagine how much more you’ll pick upin the rest of the book.

The essential Larmor equation for isolated protons is

describes the condition under which RF photons from atransmitter will be absorbed by tissue protons andinduce nuclear spin transitions (both up and down).Like the Bohr atom, the notion is conceptually andmathematically uncomplicated, yet it is still solid, evenif not derived here in a quantum mechanically rigorousmanner. In any case, the up-down space quantizationconstraint is powerful enough for the approach to leadto this fundamental result.

(1.1d) z h 12 2( / )

(1.2a)E Bz ,

(1.2b)EZeeman z zB h B 2 2 z ( ) ./

EXERCISE 1.1 What are the units of µ?

hv h B

v B B

Zeeman

Larmor

,

( ) ( .

( )

)

E

/

/

2

2

z

z z

(1.2c)or

EXERCISE 1.2 What is the Larmor frequency, vLarmor , at which the NMR process takes place for a free proton?

EXERCISE 1.3 What is the conceptual difference between the two forms of Equation (1.2c)?

(1.3)vLarmor

zB free protons

[ ] ( )]

[ ] ( ),

MHz MHz / tesla

T

[ .42 58




MRI of a 1D phantomWe can advance from NMR of tissue in a single voxel,at a single point in space, to MRI throughout a regionwith this spin-up/spin-down model. Consider here a 1Dphantom consisting of a single row of voxels lyingalong the x-axis and containing different amounts ofwater (Figure 1.3a). The trick is just to establish a gra-dient magnetic field, Gx, that varies along the x-direc-tion,

The direction of the gradient magnetic field itselfalways points 100% upward everywhere, but its mag-nitude is designed to increase linearly with x-position,

where B0 is the very strong (1.5 or 3 tesla), uniformfield from the MRI instrument’s main magnet.

This elementary generalization of the Larmorequation provides the critically important prescriptionfor connecting a measured reading of vLarmor(x) to thecorresponding value of Bz(x). And once the precisemagnitude of Gx has been established and is routinelychecked, knowledge of the local Bz(x), in turn, gives upvoxel position, x. Now, with the location of each voxeland a measurement of the RF signal strength from it, it

EXERCISE 1.4 What is the Larmor frequency for protons in a 1.5 T main magnetic field? 3 T? 7 T?

Figure 1.3 This 1D phantom consists of a row of small, hollow chambers, all of width x. (a) The one at x = 0 cm contains twice asmuch water as that at 5 cm, and the others are empty. The main magnetic field points upward along the z-axis at each chamber, butthe x-gradient component causes the strength of the net local field at each voxel, Bz(x), to increase linearly with position x. Fieldstrength increases as the dashed field lines come closer together. Each of the two water samples undergoes NMR at a different, butprecisely measurable frequency. This is an encoding technique that allows determination of voxel position along the x-axis (b), whichmakes possible the creation of a MR image of proton density (PD) along the phantom. The greater the PD in a voxel, the brighter thepixel shines on the display.

–10 0 cm 5 +10

x

z

x

(a)

(b)

PD-w

Bz(x)

(1.4a)G B xx z / .

(1.4b)B x B G xz x( ) , 0

EXERCISE 1.5 Find an expression for the frequency at which the protons in the voxel at position x of a linear phantom resonate.




is but a hop, skip, and jump to determining the spatialdistribution of proton density (PD) within a one-dimen-sional patient lying along the x-axis—which amountsto creating an honest-to-goodness 1D PD MR image(Figure 1.3b). By convention, the greater the PD in avoxel, the brighter the pixel is made to be on the dis-play.

Second picture of NMR: Classical (magnetization precessing in x-y plane)The other general didactic technique for introducingthe NMR phenomenon, the so-called classical picture,can actually be derived fully and rigorously from QMtheory. It focuses on the composite nuclear magnetiza-tion, m(rj, t), the overall magnetic field produced bythe tissue protons in the j th voxel at position rj in 2D or3D real space:

m(rj, t): at position rj in 2D- or 3D-space

And despite its quantum mechanical roots, the QMexpectation value of the time-dependent magnetization,<m(rj, t)>, ends up behaving entirely classically, gov-erned by the Bloch equations, in complete agreementwith Newtonian dynamics.

When in a strong magnetic field, the component ofthe magnetization in the j th voxel that inhabits (at leasttemporarily) the x-y plane normal to Bz, namelymxy(rj , t), will precess about it, quite like a toy top or agyroscope in a gravitational field (Figure 1.4a). (Forboth proton and gyroscope, the rate of precessionincreases linearly with field strength.) This rotation ofmxy(rj, t) about Bz happens at the same Larmor fre-quency as was obtained from the spin-up/spin-downmodel (Exercise 1.2). Meanwhile, the component ofthe voxel magnetization that lies along Bz and the z-axis, mz(rj , t), does not change (unless outside factorssuch as RF pulses or spin-relaxation processes are atwork conspire to disrupt the situation). Hereafter wewill adopt the r notation or the j, but not both, unlessnecessary for book-keeping purposes.

The classical picture plays an essential role in dis-cussing the T2 relaxation process, and also the varioussequences of RF pulses and gradient magnetic fieldsthat generate signal and contrast in clinical MRI, suchas those of the saturation-recovery, spin-echo, and gra-dient-echo techniques.

The classical approach is conceptually very differ-ent from the quasi-QM, and the two are mutually

incompatible, as will be demonstrated later. If you tryto combine them, you inevitably end up in trouble. ASunfish sailboat and a Corvette convertible can eachget you from here to the other side of the lake, but youwon’t get far if you try to fuse the two. The quasi-QMpicture has the spin axes of protons pointing up ordown in it, while the classical picture has them lying inthe x-y plane and precessing about the z-axis—bothobviously cannot hold at the same time, an impossibil-ity. To maintain your sanity, don’t try to figure out howboth can be going on simultaneously, just accept themystery of it as just being so. More later.

But while seemingly inconsistent, the two modelsare complementary to one another. In fact, each can bevaluable in the right context. But avoid trying to thinkabout NMR with both pictures at the same time. Doingso leads only to weeping and wailing and gnashing ofteeth. So just don’t try it!

Proton spin relaxationAs the theory and practice of NMR evolved, physicistsundertook a second main line of inquiry into the inter-actions of a nucleus with its environs, namely the spin-relaxation mechanisms. The two most important of

mxy(0)z

Bmxy(t)

mxy(t>>0) = 0

(a)

(b)

(c)

Figure 1.4 The ‘classical’ view is clearly incompatible with the‘quasi-QM’. (a) The magnetization of a cohort of protons,mxy(t), starts out precessing like a single, narrow vector in theplane transverse to Bz. (b) Over time, the protons precess atslightly different rates because of minute differences in theirlocal environments, and they begin to lose phase coherence.The transverse magnetization spreads out and diminishes at therate 1/T2, as e–t/T2. (c) After a period several times the tissue’stransverse or spin-spin relaxation time, T2, the protons will bepointing every which way, the sum of their spin vectors will bezero, and mxy(t≫T2) will vanish.




these are nuclear longitudinal spin relaxation (parame-terized by the relaxation time T1) and nuclear trans-verse spin relaxation (T2). These, along with theproton density of the tissue contributing to the signal,play fundamental roles in creating the exquisite soft-tissue contrast associated with clinical MRI.

Perhaps the best way to get into classical resonanceis by way of a familiar analogy. After an initial push, achild’s swing resonates at its inherent normal-modefrequency (Figure 1.5), as with many other disturbedphysical systems. But any of these will dissipate itsenergy over time, because of frictional or similareffects, and the amplitude of its oscillation willundergo near-exponential relaxation (decay) with acharacteristic relaxation or damping time T.

Longitudinal proton spin relaxation time, T1Imagine a bunch of identical compass needles fidgetingabout on a gently vibrating table, each trying to alignalong the Earth’s magnetic field. In your mind’s eye,give the table a hard whack, immediately after whichthe needles will point randomly in all directions. Nowleave it alone again, and the needles will settle downand begin to re-align mostly northward again. The

average amount of time this recovery process takes forthe ensemble of compasses is the system’s relaxationtime, Tneedles. It is determined by the strength of theinteraction between the field and a needle, by its massand shape, and by the nature of the dissipative forcespresent, such as those occurring at the mechanical pivotpoints where the needle is supported.

A proton is a fully quantum mechanical entity, ofcourse, but in some ways a cluster of them in a voxel oftissue do behave rather like a bunch of tiny compassneedles. They differ, however, in that when a patientlies in the strong magnetic field of an MRI device, avery little bit more than half of them will settle into thelower energy-state. (Here, of course, we’re thinkingonly in terms of the quasi-quantum mechanical picture,in which proton spin axes can point only up or downrelative to the strong external field!) They don’t all endup in the more comfortable and ‘natural,’ lower-energyalignment along the field, like real compass needles,because magnetic noise from random molecularmotions will continuously be knocking their spins bothup and down. In a standard 1.5 tesla field, the systemachieves a dynamic thermal equilibrium with aboutfive in a million more protons in the lower-energystate, as predicted by Boltzmann statistics. (That maynot seem like much, but how many of them are there ina 1 mm3 voxel?)

You can, with RF excitation at the Larmor fre-quency, flip some of the lower-energy protons up, andtickle some of the others down, and thereby disturb theequilibrium condition. Do this effectively, and the sys-tem eventually has about the same numbers in the twoenergy levels, a situation known as spin saturation.Turn off the RF, and the spins will begin to undergo akind of spontaneous, thermally induced relaxation pro-cess over time analogous to (but in actuality quite dif-ferent from) that of the compass needles,approximately as

with the exponential decay rate of 1/T1. You mightassume that it is the photons emitted during this relax-ation process that are detected and used to create T1-type MRI images, but that is too rudimentary an expla-nation. A big issue, indeed, is how to follow all this intime as it happens, a topic to be explored on severaloccasions along the way.

EXERCISE 1.6 What are some other systems, mechanical or otherwise, that exhibit near-exponential fall-off behavior over time, distance, radiation dose, etc.?

Am

plitu

de

0.37

T

1

0

e – t / T

t

Figure 1.5 A pendulum serves as simple analogue (but not atall a direct model!) for proton resonance and T1 relaxation.The oscillatory motion is affected by friction-like forces thatcause it to fall off exponentially over time with a characteristictime ‘T.’ Analogous phenomena are responsible for the declineof a NMR signal at the rate 1/T1 or 1/T2.

(1.5a)[ ],/1 1 e t T




The time it takes for a voxel-sized cohort of pro-tons to return 63% of the way back toward their equi-librium condition is designated T1, known as theproton spin-lattice or longitudinal spin-relaxation time.At t = T1, [1 – e–t/T1] = [1 – e–1] = 0.63. But be fore-warned —T1 relaxation is only part of what’s going on.This argument, by the way, applies to a number ofother phenomena that diminish exponentially, such asradionuclides popping off over time, x-ray photonspassing deeper into tissue, cells exposed to variousamounts of high-LET (linear attenuation coefficient)radiation dose, etc.

Transverse proton spin relaxation time, T2At the heart of the classical picture of NMR is thenotion of the magnetization, m(t), of a voxel of protonsprecessing in the x-y plane. This commonly starts outwith all the protons aligned together at t = 0, so thatmxy(t) can be represented as a rotating narrow vector,the arrow back in Figure 1.4a. The individual protonsin the voxel, however, sit in magnetic fields that differslightly from place to place, so that they do not allrotate at exactly the same frequency. For this and otherreasons, the orientations of individual spin packetsbegin to spread out over time as

and they lose their initial phase coherence (Figure1.4b). The time it takes to fall 37% of the way to thissituation is called T2, the spin-spin or transverse relax-ation time. After several more periods of duration T2,the spin alignments are so dispersed that their vectorsum has dropped to near zero (Figure 1.4c) and mxy(t)vanishes.

T1 and T2 clinical imagesT1 and T2 are measures of different but overlappingphysical processes, such as the rotations of water mole-cules near a large biomolecule. These times involve theinterplay of protons with their biochemical environ-ments in and between the cells of a tissue. T1 and T2 ina voxel are exquisitely sensitive to the detailed natureof friction-like and other interactions of the water andlipid protons with one another and with nearby ions,biomolecules, and membranes. The concentrations andbiophysical characteristics of these ions and biomole-cules are affected by the type and physiologic status of

the cells they constitute—which, in turn, depend on thebiological makeup and pathological condition of thetissues. MRI may, therefore, be able to distinguish notonly between histologically different tissues, but evenbetween normal and unhealthy regions of the same tis-sue.

T1 and T2 can be assessed point by point through-out a portion of the patient, in effect, and utilized tocreate two related but separate kinds of medicalimages. Through selection of the operating parametersof the MRI device, it is a straightforward matter to dis-play spatial variations in T1, T2, and a range of otherclinically revealing tissue characteristics. Put anotherway, the numerous types of MRI contrast, arising fromand reflecting separate physical and physiological pro-cesses, are obtained with distinct operational settings ofthe device (sequences of RF and gradient-field pulses,echo time TE, repetition time TR, etc.)

With the widely employed spin-echo pulsesequences, the proton MRI signal strength, s(x,t), fromthe voxel at position x commonly decays through spin-relaxation mechanisms approximately as

PD(x) is the proton density for the voxel at x, vL(x) theLarmor frequency there, and T1(x) and T2(x) are thetwo principal spin-relaxation times.

If given the value of s(xj, t) over time for the voxelat each position xj, it would be a simple matter toextract and map PD(x), T1(x), and T2(x) throughout thepatient. Regrettably, an MR device does not detectindividual signals from all the voxels separately, butrather only their superimposed, summed value:

Much of this book will explore the physical origin,meaning, and analysis of this equation, and of the threeclinically important tissue parameters—PD, T1, andT2—and related matters. The mathematical process ofseparating S(t) into its (thousands of) constituentparts {s(xj, t)} is known as MR image reconstruction.A very simple example of this appeared in connectionwith Figure 1.3

The above has been a rapid sketch of some centralaspects of NMR and MRI. The following chapters will

(1.5b)e t / ,T 2

(1.6a)s x t PD x iv t

TR T x TE T x

L( , ) ( ) [ ]

[ ] [ ]/ ( ) / ( )

e

e e

2

1 21

(1.6b)S t s x tj j , .




explain and discuss in detail what has been noted sobriefly here, starting over at the beginning.

1.2 Uniqueness of MRIMRI can do much of what CT does, but it is much bet-ter at defining the anatomy and finding pathologies insoft tissues. Similarly, it can reveal much of what canbe found with nuclear medicine, ultrasound, and othermodalities. But there are also valuable studies that onlyMRI can carry out.

MRI reflects primarily upon the interactions ofwater and lipids with the biomolecules that happen tobe present within and between the cells of tissues. T1-and T2-imaging are powerful because they provideforms of image contrast, based on those interactions,that are altogether different from those of other modali-ties—ones that are sensitive, in particular, to differ-ences in soft tissue types and that correlate withspecific pathologies. As medical physicists, computerscientists, and others continue to provide technicalimprovements at a rapid clip, the transfer of theseevolving technologies to the clinic will open new areasof medical research and, thereafter, of widespreadapplication.

One area of significant clinical growth potential inMRI is in the prediction and monitoring of response totreatment, whether radiation therapy, chemotherapy,local heat ablation with US, gene therapy, or whatever.In cancer therapy, for example, ionizing radiation andcertain tumoricidal drugs are relatively ineffective ontumor cells that are poorly oxygenated. Indeed, themost radio-resistant cells are commonly those inhabit-ing a barely viable hypoxic rind between active tumor,on the outside, and necrotic tumor cells within thathave died from anoxia. MRI may well be able to revealwhether a pharmaceutical intended to promote angio-genesis in that rind, or to facilitate the perfusion or dif-fusion of water or oxygen into it (which may render itmore radiation-sensitive), will be successful on a spe-cific patient. Likewise, following the administration ofa drug or dose of radiation, MRI and perhaps MR spec-troscopy can assess the degree to which the opening orproliferation of blood vessels has increased the oxygenlevel in hypoxic regions and, therefore, the likelihoodof destroying the tumor. These are but two out ofcountless examples of image-guided therapy (involv-ing MRI alone or in collaboration with other modali-

ties, e.g., PET) that either already exist or areforthcoming.

1.3 A Real MRI Case StudyA female associate professor of genetics experiencederratic diffuse headaches that responded to an Advil orTylenol. The headaches were mild but still a little dis-ruptive, so after several months she turned to her gen-eral practitioner. She presented as a healthy 52-year-oldin no apparent distress apart from mild hypertensionthat was controlled by medication. She followed a gooddiet and exercised moderately several times a week.Other aspects of her physical examination were unre-markable and, in particular, a neurological examinationrevealed no deficits. She claimed to be happily marriedto her best friend and reported no major stresses or anx-ieties, apart from those arising from rearing two inde-pendent and adventurous teenage daughters.

Computed tomography (CT)Uncomfortable with the duration of the problem, herinternist ordered a CT scan of the brain at the localclinic. The results were suggestive of an irregularity inthe right posterior temporo-occipital region, partiallyreplacing some of the occipital horn of right lateralventricle. He felt that an MRI head study could providebetter information.

The next day she and her husband drove a half hourto one of her university’s teaching hospitals. In herhaste at home, she misplaced the DVD of the CT study.After her check-in at the medical center, however, allof her subsequent images, along with lab results andother medical records, were stored safely and keptavailable for immediate retrieval on the Department ofRadiology’s Picture Archiving and CommunicationsSystem (PACS).

MRI: T1-w, T2-w, and FLAIR imagingAlthough not available, the CT had already performedan invaluable service by drawing attention to the possi-ble irregularity. In any case, the MRI studies would bemore revealing of soft-tissue problems. The patientunderwent a number of standard MR studies, includingthe gathering of T1-weighted and so-called FLAIRimages (Figure 1.6).

The T1-w image supported the CT report, and alsonoted the extension of a well-circumscribed 1.7 ×1.1 cm2 lesion to the lining of the occipital horn of the




right lateral ventricle. The absence of bilateral symme-try of the brain was striking, but there was no midlineshift or hydrocephalus. The T1-w scan was thenrepeated following the injection of 20 ml of gadolinium(Gd) contrast agent, and little change occurred. Higher-grade neoplasms in the brain are more likely to disruptthe blood-brain barrier, and are thus associated withmore avid contrast enhancement. The failure of theregion to noticeably take up the agent implied that thelesion was probably not a high-grade neoplasm, ahopeful sign.

A FLAIR image (FLuid Attenuation InversionRecovery) is similar, but suppresses signals from aque-ous fluids. In the brain, for example, it eliminates muchof the appearance of cerebrospinal fluid (CSF), facili-tating a better evaluation of the surrounding edema, aswell as enhancing lesion conspicuity (Figure 1.6b). Thereading radiologist felt that the image indicated alower-grade glioma protruding into the ventricle, orpossibly (although less likely) a tumor-like demyelinat-ing lesion. (A glioma is a common type of tumor thatoccurs in glial cells, most frequently of the brain; theprimary job of these cells is to nurture and maintainneurons, but researches have recently found that theyalso play a role in neuron functionality.) He alsoreported several small point-like T2 signal abnormali-ties scattered throughout the subcortical white matterof the cerebral hemispheres, possibly representing

chronic small-vessel blockages or conceivably furtherareas of neural demyelation.

Magnetic resonance spectroscopy (MRS)The gold standard in identifying a tumor is a biopsy(physically sampling and microscopic analysis of thetissue). But MRI can provide, in addition to images,quick and non-invasive preliminary informationregarding tissue pathology by means of an advancedprocedure known as MR spectroscopy (MRS).

The Larmor frequency of a proton is determinedprecisely by the exact magnetic field it experiences.The electrons circulating throughout a biomoleculethemselves create a weak magnetic field, and this willaffect the magnetic field seen by its tissue protons atvarious locations. This results in parts-per-millionchemical shifts in the resonance frequencies of the pro-tons in different molecular surroundings. Then Equa-tion (1.3a) should be modified, if the protons are in auniform external magnetic field B0, as

where the chemical shift coefficient, , for a particularproton is strongly dependent on the details of its uniquemolecular environment. This may seem a little like theproton density imaging of Figure 1.3, but here the Lar-mor frequency is being shifted by the field from orbit-

T1-w with Gd T2-w FLAIR

Figure 1.6 Two MR images of the samethin (1 mm), transverse slice. As withCT, a transverse MRI scan looks upwardfrom the feet. (a) The T1-weighted studyreveals a right posterior temporo-occipi-tal lesion adjacent to occipital horn ofthe right lateral ventricle. Injection of agadolinium-based MRI contrast agent, asshown here, made no difference visuallyfrom an earlier scan obtained withoutthe contrast agent, suggestive that theblood-brain barrier had not (yet) beenbreached by a growing tumor. (b) TheFLAIR (FLuid Attenuation Inversion Recov-ery) study provided different but comple-mentary clinical information. Heresignals from cerebralspinal fluid (CSF) andother fluids are suppressed, yielding asomewhat different type of MRI contrast,one that better demonstrates the lesion,which is now hyperintense. [Courtesy ofCharles Smith, Peter Hardy, David Powell,University of Kentucky MR Imaging andSpectroscopy Center (MRISC)].

(a) (b)

(1.7)v BLarmor / ,2 10




ing molecular electrons, not by an externally appliedgradient field.

The proton nuclear magnetic resonance spectrumof the simple acetic acid (CH3COOH) molecule, forexample, appears as two distinct MR peaks, both veryclose in resonance frequency to that of a free proton.They are separated by a 1.56 parts per million (ppm)chemical shift in the Larmor frequency, indicating thetwo slightly different local magnetic fields that the pro-tons can feel (Figure 1.7a). One of the resonance linesis three times the other in amplitude: the three protonswithin the methyl (CH3–) group all experience thesame swirl of electrons and identical surroundings.The electron flow within the acid (–OOH) group,on the other hand, is different, and its single protonresides in a slightly lower local field.

Protons in molecules imposing a chemical shift areusually too few in number, and with too small a shift,to be seen in standard MRI images, other than lipids.But an MRS instrument combines exceptional homo-geneity of the external field with the excellent RF fre-quency-resolution of an NMR spectroscope, so thatprotons in different molecular structures can often bedistinguished. This allows in vivo examination of

small, well-localizable volumes of soft tissues, and thespectra obtained may lead to the identification of cer-tain irregularities.

MRS is capable of performing nuclear resonancespectroscopy on small, multi-voxel blocks of tissues atspecific locations within the body. For tissues awayfrom the lesion (Figure 1.7b,c) the proton spectra forN-acetylaspartate (NAA), creatine and phospho-cre-atine (Cr), and choline (Cho) appeared normal. Thelesion itself, however, reveals a statistically significantirregularity in the concentrations (areas under thepeaks) of Cr and NAA, relative to that of Cho. Thespectral signatures for numerous normal and abnormaltissues have been studied, and the pattern seen here,when combined with the imaging information, is indic-ative of a glioma, but of indeterminate stage.

Functional MRI (fMRI)Treatment of a tumor depends on its type, anatomicallocation, grade (degree of abnormality and growth rateseen under a microscope), and stage (size and degree ofspread). In the present case, the lesion’s position issuch that surgery or radiation therapy might well resultin the loss of one of the patient’s two fields of vision

NAACho Cr

CH3

COOH

acetic acid

1.56 ppm

vLarmor

Figure 1.7 An MRS spec-trum (a) reflects theuneven circulation of elec-trons within a molecule(acetic acid) that give riseto small variations in localmagnetic field, hence inparts per million (ppm)chemical shifts in protonLarmor frequency. (b) Tis-sue just outside thepatient’s lesion (yellow box)yields a normal MRS spec-trum. The spectrum fromthe lesion itself appearsnearly identical, (c) but itshigher Cr/NAA and Cho/NAA ratios are character-istic of a glioma.

(a)

(b) (c)




(to the left or right). While she could accept that, shemade it unambiguously clear that she would not agreeto any action that would seriously jeopardize her abilityto read; she would prefer to leave the disease untreatedand take her chances.

Before proceeding to a needle biopsy—which itselfcould impose some risk to reading vision—she under-went two noninvasive MRI-based studies that wouldhelp to determine the closeness of the apparent tumorto optically active regions. The first was functionalMRI (f MRI) (Figure 1.8a).

In an f MRI study, a subject is asked to undertake amental process of some sort, such as repeatedly view-ing a visual stimulus or tapping a finger. In the process,associated brain tissues become unusually active andconsume extra oxygen, transforming oxyhemoglobininto deoxyhemoglobin there more rapidly than when atrest. These two molecules differ magnetically, anddeviations in their balance may produce detectable tis-sue contrast where a region of the brain is being trig-gered. You might suspect that the relevant neurons aresimply burning more oxygen; that indeed happens but,as will be seen later, the brain is far cleverer than that,and the process is actually more subtle and interesting.

Functional MRI data complement those of PET,which lights up those parts of the brain that happen tobe burning excess radio-labeled glucose. Other modali-ties, like electroencephalography (EEG) and magneto-encephalography (MEG), are also being developed formapping brain function. Establishing correlationsamong their results and those of f MRI and PET willgreatly enhance the medical value of all of them.

The patient underwent f MRI with two separatesets of periodic stimuli, self-directed finger tapping andvisual images. Temporal variations (which is what is ofinterest here) in the MRI signal are much smaller thanthe average value of the signal voltage itself, and effec-tive noise-rejection and statistical information-process-ing programs must be invoked. The finger-tapping taskdemonstrated robust activation within the associatedregion of the motor cortex of the cerebral hemispheres.The patient’s response to an intermittent visual stimu-lus is shown here in a thin sagittal slice that passesthrough the circled lesion; it indicates that one of theoptically active regions of the brain (in green) lies adja-cent to it, and possibly within it. Damage to it couldcause catastrophic sight loss.

Diffusion tensor MR imaging (DTI)In view of the rather discouraging f MRI results, it wasfelt to be worthwhile to carry out a diffusion tensorimage study, as well. With DTI, contrast arises fromthe unidirectional diffusion of water molecules alongthe long axons of a nerve trunk, against a backgroundof other water molecules that are diffusing isotropi-cally, thereby bringing the nerve trunks into view. Fig-ure 1.8b. A sagittal, thin-slice DTI corroborated theearlier f MRI finding that the patient’s probable gliomalies directly adjacent to, and possibly infiltrating, supe-rior portions of a nerve trunk, the optic radiation (thepale horizontal ribbon).

f MRI

DTI

Figure 1.8 MRI for pre-surgical planning. (a) A thin (1 mm)slice sagittal T1-w image with a functional MRI (fMRI) overlayhighlights small regions of the brain (yellow-green), near thecircled lesion, that respond to a flashing light stimulus. (b) A dif-fusion tensor image (DTI) further indicates the close proximityof the patient’s nerve trunks, the ‘optic radiation’ (white hori-zontal strands) to the glioma (red solid). [With thanks toCharles Smith and David K. Powell, University of KentuckyMRISC].

(a)

(b)




MRI-guided fine-needle biopsyAfter viewing all the evidence, and particularly the DTIresults, a neurosurgeon felt that with MRI guidance, shecould very probably obtain a fine-needle tissue biopsysample with low chance of damaging the optic radia-tions. After consulting with her personal physician, thepatient agreed to the three-step invasive process.

First, in the operating room and under local anes-thesia, a rigid, nonmagnetic frame was screwed firmlyinto the skull¸ providing the platform for establishing afixed Cartesian coordinate system within which tolocalize the tumor, and later to reach it with a finebiopsy needle.

A separate assembly comprising a box with fourflat, transparent walls embedded with weakly magneticorthogonal positional markers and lines was attached.This provides an orthogonal frame of reference that is

visible to the MRI device. Any point within the braincould now be expressed as a set of x-, y-, and z-coordi-nates relative to the frame, to within one millimeter(Figure 1.9a). MR images were now taken, and fromthese the neurosurgeon decided where in the lesion shewould obtain the biopsy sample, and the path shewould follow in getting there.

Then, with the frame still attached rigidly to theskull, the first (MRI-imaging) assembly is removedfrom it and the second, a stereotactic biopsy needleguidance assembly, is fixed to it (Figure 1.9b). A medi-cal physicist experienced in the use of the equipmentmade the necessary calculations, based on the imagesjust obtained, and he and the neurosurgeon set therequired angles and distance limiters on the mechanicalneedle-guidance assembly. Soon thereafter, after drill-ing a small bore-hole in the skull, the surgeon advanced

Figure 1.9 A stereotactic fine-needle biopsy device consists of an immobile frame screwed firmly into the scull in the operatingroom, along with two separate attachments used in sequence. (a) The first of these consists of an array of paramagnetic fiducial mark-ers embedded in plastic planes; these can be read precisely by the MRI device during a clinical study. These make possible accuratelocalization of a target point within the lesion. (b) Then, with the frame still fastened rigidly to the skull, the first assembly is removedand a second attached. This one can guide insertion of a hollow sampling needle along any direction chosen by the neurosurgeon, suchthat its tip will end up within 1 mm of the target point. [Courtesy of Elekta]. (c) Photomicrograph from one of the biopsy slides. Thepathologist reported that the sample collected from this lesion displays scattered and atypical cellular nuclei, suggestive of an astrocy-toma, a form of glioma, but of undeterminable grade.

(a) (b)

(c)




the hollow needle exactly the right distance andobtained the sample without incident.

It was expected that the samples obtained would bedefinitive, but they were not (Figure 1.9c). The surgeonphoned the patient the evening of the biopsy with avery unoptimistic report from the pathologist: the tis-sues obtained were equivocal, but suggestive of anadvanced, fast-growing high-grade glioma. The patientreacted to the news calmly, her greatest concern beingthe impact this would have on her husband and daugh-ters, to whom she was devoted. Further examination ofthe slides a few days later by several other pathologists,remarkably, led to the far less awful prognosis that theglioma may be only of stage-1 or -2, which either canbe watched for changes or treated with drugs and radio-therapy with a reasonable chance of control.

Should we try positron emission tomography?A final diagnostic test was considered, but rejected.Tumors commonly oxidize glucose at a faster rate thando healthy tissues of the same type, and positron emis-sion tomography (PET) is a nuclear medicine modalityhighly sensitive at detecting excessive cellular uptakeand use of it, Figure 0.4b. Sugar molecules are labeledwith radioactive fluorine-18, and the injected 18-fluo-rodeoxyglucose (18FDG) concentrates preferentially infast-metabolizing tissue, such as neoplasms. The fluo-rine nucleus decays with the emission of a positivelycharged positron, which travels 1 mm or so and imme-diately collides with its anti-particle, an electron. Thetwo particles mutually annihilate, giving birth to a pairof 511 keV annihilation photons, which fly away fromthe site of the interaction in almost exactly (to within¼°) antiparallel directions. If the two are detectedsimultaneously on the opposite sides of a PET imager,within a tiny time window, they will contribute to theformation of a PET image of the region that had takenup the radiopharmaceutical. Thus, PET is anothersource of tissue image contrast, but one that exploitsthe metabolism of radioactive glucose, rather than ofnormal oxygen, like f MRI. PET findings might be helpful, such as in findingother lesions in the brain, but it would probably havelittle or no effect on the patient’s treatment, and she andher physicians decided against pursuing it.

Treatment guidance and follow-upThe patient and her physicians, hopeful that the gliomamight turn out to be slow-growing or even quiescent,

decided that the best course of action was to do noth-ing. An MRI examination every six months for threeyears has revealed that, in fact, her tumor was notgrowing appreciably, and she’s still alive and well.In an ironic twist, upon returning home she learned thatother residents of her condo were also experiencingheadaches. The epidemic ended, as did her own head-aches, when the large construction project next door,which frequently produced unpleasant fumes, termi-nated. So her glioma may well have had nothing at allto do with her symptoms, and was identified by acci-dent.

One area of significant clinical growth potential inMRI is in the prediction and monitoring of response totreatment, whether radiation therapy, chemotherapy,local heat ablation with ultrasound, gene therapy, etc.For example, MRI continued to play a role in treatmentof our patient, in part by monitoring any change in thesize, shape, or any other aspect in the appearance of thelesion. But some developments in her status might callfor additional or alternative treatments.

The purpose of nearly any curative (non-palliative)surgical or other therapy, of course, is to eliminate theproblem without causing unacceptable damage tohealthy (especially critical) tissues. A procedure simi-lar to that for the fine needle aspiration biopsy (Figure1.9) can be used to direct a narrow but intense beam ofx-rays at the lesion. Linear accelerators (linacs) havebeen modified to perform microradiosurgery on braintumors with very small fields and, guided by CT orMRI, with very high precision. Brachytherapy withsuitable and meticulously located radioactive seedsmight also be appropriate. And for some kinds of sur-gery, a growing number of institutions have MRI in theoperating room in order to aggressively, and moresafely, resect the disease. Similarly, chemotherapydrugs can be infused under guided delivery alone or inconjunction with radiation or surgery. How might thegeneral approach described here be applied in othermedical procedures [Jolesz 2008]?

In the long run, perhaps the most extraordinary(from our current perspective) clinical advances willarise from ongoing efforts to establish strong linkagesamong the various forms of physiologic imaging—especially MRI, nuclear medicine, and optical imag-ing—with genomics, proteomics, molecular biology,and nanotechnology. These fields are just beginning tooverlap and unify, yet already they have created novel

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