Author: Prof. Dr. Hans H. SchildLt. Oberarzt im Institut für KlinischeStrahlenkunde des Klinikums derJohann-Gutenberg-Universität

All rights, particularly those of translationinto foreign languages, reserved. No partof this book may be reproduced byany means without the written permissionof the publisher.Printed in Germany by NationalesDruckhaus Berlin.

© Copyright by Schering AGBerlin/Bergkamen 1990

ISBN 3-921817-41-2

PrefaceThis book is dedicated- to anyone, who tries to teach medicine insteadof just reporting medical facts (like myanatomy teacher, Prof. Dr. R. Bock, who isa master of this art).- and to anyone, whose stumbling feet find theMRI path difficult (The book was written inthe hope rather than the belief that they mayfind some help from it).

(modified from Alastair G. Smith, Surgeons Hall,Edinburgh, October 1939)

H. H. Schild

About this bookThis book was written as anintroduction to magnetic reson-ance imaging (MRI). It is dedi-cated to anyone, who would liketo know something about MRIwithout having to study physicsfor years. If this applies to you,then read this text from front toback, though not at one sitting.While the subject matter is ex-tremely complex, it is not by anymeans beyond comprehension.It does however, require someconcentration and consideration.I have therefore on occasionsuggested that you set the bookdown and take a break. Do so,it will help you to stick with thematerial, but don't forget tocome back.Subjects, that in my experienceare particularly difficult to under-stand, I have repeated once oreven more times, so the readerwill be able to understand andremember them by the end ofthe book.Some valuable introductory textshelped with writing this book;they are cited in the references,and recommended for furtherinformation, as a text of thissize cannot cover everything.Indeed, it is not the objectiveof this book to represent the'be all and end all' of MagneticResonance Imaging, butrather to serve as an appetizerfor further reading.

Let us start witha generaloverview of MRI. .

The single steps of an MRexamination can be describedquite simply:• the patient is placed ina magnet,• a radio wave is sent in,• the radio wave is turned off,• the patient emits a signal,which is received and used for• reconstruction of the picture

Let's take a lookat thesesteps in detail

What happens, when we put apatient into the magnet of anMR machine?To understand this, it isnecessary to at least know somevery basic physics - even thoughthis may seem to be boring.As we all know, atoms consistof a nucleus and a shell, whichis made up of electrons. In thenucleus - besides other things -there are protons, littleparticles, that have a positiveelectrical charge (whatever thatmay actually be). These protonsare analogous to little planets.Like earth, they are constantlyturning, or spinning around anaxis (fig. 1); or - as one says,protons possess a spin. Thepositive electrical charge, beingattached to the proton, naturallyspins around with it. And whatis a moving electrical charge?It is an electrical current.

Now, may be you rememberfrom your physics at school thatan electrical current induces,causes a magnetic force, ormagnetic field. So, where thereis an electrical current, there isalso a magnetic field.

This can be demonstrated veryeasily. Take a rusty nail andapproach an electrical outlet -closer, closer. Do you feel itbeing repelled by the magneticforce so you do not put the nailinto the outlet?

Protons possess a positive charge.Like the earth they are constantly turningaround an axis and have their ownmagnetic field.

Let's review whatwe have read

A proton has a spin, and thusthe electrical charge of theproton also moves. A movingelectrical charge is anelectrical current, and this isaccompanied by a magneticfield. Thus, the proton hasits own magnetic field and itcan be seen as a little barmagnet (fig. lc) .

Fig. 2Normally protons are aligned in a randomfashion. This, however, changes whenthey are exposed to a strong externalmagnetic field. Then they are aligned inonly two ways, either parallel or anti-parallel to the external magnetic field.

What happens tothe protons,when we put theminto an externalmagnetic field?

The protons - being littlemagnets - align themselves inthe external magnetic field likea compass needle in the magnet-ic field of the earth. However,there is an importantdifference. For the compassneedle there is only one wayto align itself with themagnetic field, for the protonshowever, there are two (fig. 2).The protons may align withtheir South and North poles

in the direction of the externalfield, parallel to it. Or they maypoint exactly in the completeopposite direction, anti-parallel.These types of alignment areon different energy levels.To explain this; a man can alignhimself parallel to the magneticfield of the earth, i.e. walk onhis feet, or he can align himselfanti-parallel, in the oppositedirection. Both states are on dif-ferent energy levels, i.e. needdifferent amounts of energy.Walking on one's feet isundoubtedly less exhausting,takes less energy than walkingon one's hands. (In the figures,this will be illustrated aspointing up or down, see fig. 2).

Naturally the preferred state ofalignment is the one that needsless energy. So more protonsare on the lower energy level,parallel to the external magneticfield (walk on their feet).The difference in number is,however, very small and dependson the strength of the appliedmagnetic field. To get a roughidea: for about 10 million pro-tons "walking on their hands",there are about 10 000 007"walking on their feet" (thedifference "007" is probablyeasy to remember).

It may be obvious at this pointalready, that for MRI themobile protons are important(which are a subset of all pro-tons that are in the body).

Fig. 3When there are two possible statesof alignment, the one that takes lessenergy, is on a lower energy level,is preferred.

Let us takea closer look atthese protons

We will see that the protonsdo not just lay there, alignedparallel or anti-parallel to themagnetic field lines. Instead,they move around in a certainway. The type of movementis called precession (fig. 4).

What type ofmovement is"precession"?

Just imagine a spinning top.When you hit it, it startsto "wobble" or tumble around.It does not, however, fall over.During this precession, the axisof the spinning top circlesforming a cone shape (fig. 4).It is hard to draw such a pre-cessing proton, as this is a veryfast movement as we will seebelow. For the sake ofsimplicity, we will just make"freeze frame" pictures, as ifwe were taking a fast flashlight photograph of the situationat a specific moment in time.

For reasons we will learn below,it is important to know howfast the protons precess. Thisspeed can be measured asprecession frequency, that is,how many times the protonsprecess per second. This pre-cession frequency is notconstant. It depends upon thestrength of the magnetic field(for magnetic field strengthsee page 96), in which theprotons are placed.The stronger the magnetic field,the faster the precession rateand the higher the precessionfrequency.

This is like a violin string:the stronger the force exertedupon the string, the higher itsfrequency.

Fig. 4A spinning top, which is hit, performsa wobbling type of motion. Protons in astrong magnetic field also show this typeof motion, which is called precession.

It is possible and necessary toprecisely calculate this fre-quency. This is done by usingan equation called Larmorequation:

is the precession frequency(in Hz or MHz),B0 is the strength of theexternal magnetic field, whichis given in Tesla (T)(see page 96), and

is the so-called gyro-magnetic ratio.The equation states that theprecession frequency becomeshigher when the magnetic fieldstrength increases. The exactrelationship is determinedby the gyro-magnetic ratioThis gyro-magnetic ratio is dif-ferent for different materials(e.g. the value for protons is42.5 MHz/T). It can becompared to an exchange rate,which is different for differentcurrencies.

Time to take abreak

however, let us briefly review,what we have read up to now:

• Protons have a positiveelectrical charge, whichis constantly moving, becausethe protons possess a spin.• This moving electrical chargeis nothing more than anelectrical current, and the latteralways induces a magnetic field.• So every proton has its littlemagnetic field, and can thus beseen as a little bar magnet.• When we put a patient in theMR magnet, the protons, beinglittle magnets, align with theexternal magnetic field. They dothis in two ways: parallel andanti-parallel. The state thatneeds less energy is preferred,and so there are a few moreprotons "walking on their feet"than "on their hands" (fig. 3).• The protons precess alongthe field lines of the magneticfield, just like a spinning topthat precesses along thefield lines of the magnetic fieldof earth.

• The precession frequency canbe calculated by the Larmorequation, and is higher in strong-er magnetic fields. Why isthis precession frequencyimportant?It has something to do with theresonance in magnetic reson-ance imaging. But to under-stand this will take a fewmore minutes.After the break you should goover the last summary again,and then continue . . .

Introducing thecoordinate system

To make communication (anddrawing of illustrations) easier,let us start using a coordinatesystem like we know fromschool (fig. 5). As you see, thez-axis runs in the direction ofthe magnetic field lines, andthus can represent them. So wecan stop drawing the externalmagnet in all other illustrations.

From here on we will alsoillustrate the protons as vectorsas little arrows. Maybe youremember: a vector representsa certain force (by its size)that acts in a certain direction(direction of the arrow).The force that is representedby vectors in our illustrations,is the magnetic force.

Fig. 5Using a coordinate system makes thedescription of proton motion in themagnetic field easier, and also we canstop drawing the external magnet.

Now, look at figure 6. Therewe have 9 protons pointing up,precessing parallel to theexternal magnetic field lines,and 5 protons pointing down,precessing anti-parallelto the external magnetic field.As we stated above, what wesee in the figure is justa picture taken at a specificpoint in time. A picture takenjust a little later would show theprotons in different positionsbecause they precess. The pre-cession actually goes very fast,the precession frequency forhydrogen protons is somewherearound 42 MHz in a magneticfield strength of 1 Tesla(see page 96); this means thatthe protons precess around the

"ice cream cone" more than42 million times per second.Now there are millions andmillions of protons in your bodyprecessing this fast. It is easyto imagine, that at a certainmoment, there may be oneproton (A in the illustration)pointing in one direction, andanother proton (A') pointingexactly in the opposite direc-tion. The result is veryimportant; the magnetic forcesin the opposing directionscancel each other out, like twopersons pulling at the oppo-site ends of a rope.Finally, for every protonpointing down, there is onepointing up, cancelling itsmagnetic effects. But as we

Fig. 6The five protons, which "point" downcancel out the magnetic effects of thesame number of protons, which "point"up (6a). So in effect it is sufficientto only look at the four unopposedprotons (6b).

have read: there-are moreprotons pointing up than down,and the magnetic forces ofthese protons are not cancelledby others. So we are left - ineffect - with some protons(4 in our example) pointing up(fig. 6).

However, not only magneticforces pointing up and down cancancel or neutralize each other.As the protons that are leftpointing up, precess, there maybe one pointing to the right,when there is another onepointing to the left; or for onepointing to the front, thereis one pointing backwards, andso on (the correspondingprotons in fig. 7 are marked Aand A', B and B' for example)This means that the opposingmagnetic forces of the re-maining protons cancel eachother out in these directions.This is true for all but onedirection, the direction of thez-axis, along the externalmagnetic field (fig. 7). In thisdirection, the single vectors,the single magnetic forces addup, like people pulling onthe same end of a rope.What we end up with in effectis a magnetic vector in thedirection of the external mag-netic field (the arrow on thez-axis in fig. 7); and this vectoris a sum vector made up byadding the magnetic vectors ofthe protons pointing upwards.Now - what does this mean?This means that by placing apatient in the magnet of the MRunit (or in any other strongmagnetic field), the patient him-self becomes a magnet, i.e. has

his own magnetic field. Why?Because the vectors of the pro-tons, that do not cancel eachother out, add up (fig. 8).As this magnetization is indirection along/longitudinalto the external magnetic field,it is also called longitudinalmagnetization.

Fig. 7The magnetic force of proton A,illustrated as an arrow, a vector, can belooked at as resulting from two compo-nents: one pointing up along the z-axis,and one in direction of the y-axis.The component along the y-axis is can-celled out by proton A', the magneticforce of which also has a componentalong the y-axis, however, in the oppo-site direction. The same holds truefor other protons, e.g. B and B', whichcancel their respective magnetic vectorsalong the x-axis. In contrast to themagnetic vectors in the x-y-plane, whichcancel each other out, the vectors alongthe z-axis point in the same direction,and thus add up to a new magnetic sumvector pointing up.

Fig. 8In a strong external magnetic field a newmagnetic vector is induced in the patient,who becomes a magnet himself. Thisnew magnetic vector is aligned with theexternal magnetic field.

As we have seen, the resultingnew magnetic vector of thepatient points in the directionof the external field, along itsfield lines. This is described aslongitudinal direction. And it isactually this new magnetic vec-tor that may be used to get asignal. It would be nice if wecould measure this magnet-ization of the patient, but thereis a problem: we cannotmeasure this magnetic force,as it is in the same direction,parallel to the externalmagnetic field (figs. 7 and 8).

To illustrate this:imagine that you are standingon a boat, floating down a river.You have a water hose in yourhand and squirt water into theriver. For somebody who iswatching you from the shore, itis impossible to tell how muchwater you pour out (this shallbe how much new magnetizationis added in the old direction).

However, when you point thewater hose to the shore, changethe direction of the newmagnetic field, then the watermay perhaps be directly pickedup and measured by an impartialobserver on the shore (fig. 9).What we should learn fromthis is: magnetization along or,better, longitudinal to the ex-ternal magnetic field cannot be

measured directly. For this weneed a magnetization which isnot longitudinal, but transversalto the external magnetic field.

Fig. 9Magnetization along an external magneticfield cannot be measured. For this amagnetization transverse to the externalmagnetic field is necessary.

Time to takea break . . .

but before you walk off, justread the short summary. Andwhen you come back, startout with the summary again.• Protons have a positivecharge and possess a spin.Due to this, they have a mag-netic field and can be seenas little bar magnets.• When we put them into astrong external magneticfield, they align with it, someparallel (pointing up), someanti-parallel (pointing down).• The protons do not just laythere, but precess around themagnetic field lines. And thestronger the magnetic field,the higher the precession fre-quency, a relationship that ismathematically described inthe Larmor equation.

• Anti-parallel and parallel pro-tons can cancel each othersforces out. But as there aremore parallel protons on thelower energy level ("pointingup"), we are left with someprotons, the magnetic forcesof which are not cancelled. Allof these protons pointing up,add up their forces in the direc-tion of the external magneticfield. And so when we put thepatient in the MR magnet,he has his own magnetic field,which is longitudinal to the ex-ternal field of the MR machine'smagnet (figs. 7 and 8). Becauseit is longitudinal however,it cannot be measured directly.

What happens afterwe put the patientinto the magnet?

We send in a radio wave. Theterm radio wave is used to de-scribe an electromagnetic wave,that is in the frequency rangeof the waves which you receivein your radio. What we actuallysend into the patient is not awave of long duration, but ashort burst of some electro-magnetic wave, which is calleda radio frequency (RF) pulse.The purpose of this RF pulse isto disturb the protons, whichare peacefully precessing in

alignment with the external mag-netic field. Not every RF pulsedisturbs the alignment of theprotons. For this, we needa special RF pulse, one thatcan exchange energy with theprotons.This is as if someone were look-ing at you. You may not noticeit, because there is no exchangeof energy, so you do not changeyour position/alignment. How-ever, if someone were to poundyou in the stomach, exchangeenergy with you, your alignmentwould be disturbed. And thismay explain why we need acertain RF pulse that can ex-change energy with the protonsto change their alignment.

Fig. 10 a + bEnergy exchange is possible whenprotons and the radiofrequency pulsehave the same frequency.

Fig. 10a

Fig. 10b

But when can an RF pulse ex-change energy with the protons?For this it must have the samefrequency; the same "speed"as the protons.Just imagine that you aredriving down a race track inyour car, and someone inthe lane next to you wants tohand you a couple of sand-wiches, i.e. exchange energywith you (as you are hungry,the sandwiches would give younew energy). This energy trans-

fer is possible when both carshave the same speed, movearound the race track with thesame frequency.With differences in speed/frequency less or no energytransfer is possible (fig. 10b).

Fig. 11The radiofrequency pulse exchangesenergy with the protons (a), and someof them are lifted to a higher levelof energy, pointing downward in theillustration (b). In effect the mag-netization along the z-axis decreases,as the protons which point down"neutralize" the same number of pro-tons pointing up.

What speed, orbetter, whatfrequency did theprotons have?

They had their precession fre-quency which can be calcu-lated by the Larmor equation(see page 10). So the Larmorequation gives us the necessaryfrequency of the RF pulseto send in. Only when the RFpulse and the protons have thesame frequency, can protonspick up some energy from theradio wave, a phenomenoncalled resonance (this is wherethe "resonance" in magneticresonance comes from).

The term resonance can beillustrated by the use of tuningforks. Imagine that you are ina room with different kinds oftuning forks, tuned e.g. toa, e, and d. Somebody entersthe room with a tuning fork with"a"-frequency, that was struckto emit sound. From all thetuning forks in the room, all ofa sudden the other "a" forks,and only those, pick up energy,start to vibrate and to emitsound, they show a phenomenoncalled resonance.

What happens withthe protons, whenthey are exposed tothis RF-pulse?

Some of them pick up energy,and go from a lower to a higherenergy level. Some, which werewalking on their feet, start walk-ing on their hands. And this hassome effect on the patientsmagnetization, as you can see infigure 11. Let us assume thatfrom the net sum of 6 protonspointing up, after the RF pulseis sent in 2 point down. Theresult is that these 2 protonscancel out the magnetic forcesof the same number of protons,

that point up. In effect, then,the magnetization in longitudinaldirection decreases from 6 to 2.But something else happens.Do you remember what draw-ings of radio waves look like?Just look at fig. 12; theyresemble a whip, and the RFpulse also has a whip-likeaction (fig. 13): it gets theprecessing protons in synchand this has another importanteffect.

When the protons randomlypoint left/right, back/forth andso on, they also cancel theirmagnetic forces in these direc-tions (as we read on page 13).Due to the RF pulse, theprotons do not point in randomdirections any more, but movein step, in synch - they are"in phase". They now point inthe same direction at the sametime, and thus their magneticvectors add up in this direction.

This results in a magneticvector pointing to the side towhich the precessing protons .point, and this is in a transversedirection (—• fig. 13).This is why it is called trans-versal magnetization.

Fig. 12The drawing of radiowaves normallyresembles a whip, and radiowaves inMRI also have a whip-like action.

Fig. 13The radiowave has two effects on theprotons: it lifts some protons to a higherlevel of energy (they point down), andit also causes the protons to precess instep, in phase. The former results indecreasing the magnetization along thez-axis, the so-called longitudinalmagnetization. The latter establishes anew magnetization in the x-y-plane(—•) , a new transversal magnetization,which moves around with the precessingprotons.

The situation can be comparedto a ship: think about thepassengers being distributedrandomly all over the deck, theship then is in a normal posi-tion. Then have all passengerswalk in equal step around therailing; what happens? The shipis leaning towards the sidewhere the people are, a newforce is established, and be-comes visible (fig. 14).

So the RF pulse causes a trans-versal magnetization. This newlyestablished magnetic vectornaturally does not stand still,but moves in line with theprecessing protons, and thuswith the precession frequency,(fig. 13).

Fig. 14Protons precessing in phase causea new transversal magnetization.

So - what were thenew things thatwe have learned?

Repeat them using fig. 15!• When we put the patientin the MR machine, the protonsline up parallel or anti-parallelto the machines magnetic field.A magnetic field in the patient,longitudinal to the externalfield results (fig. 15a).

fig. 15In a strong external magnetic field a newmagnetic vector along the external fieldis established in the patient (a). Sendingin an RF pulse causes a new transversalmagnetization while longitudinal magneti-ation decreases (b). Depending on theRF pulse, longitudinal magnetization mayeven totally disappear (c).

• Sending in an RF pulse thathas the same frequency as theprecession frequency of theprotons causes two effects:- Some protons pick up energy,start to walk on their hands,and thus decrease the amountof longitudinal magnetization.- The protons get in synch, startto precess in phase. Theirvectors now also add up in adirection transverse to the ex-ternal magnetic field, and thusa transversal magnetization isestablished.In summary: the RF pulse causeslongitudinal magnetization todecrease, and establishesa new transversal magnetization(figs. 13 and 15).

Let us have a lookat that newlyestablished trans-versal magnetizationvector

This moves in phase with theprecessing protons (fig. 16).When you watch what is happen-ing from outside, the newmagnetic vector comes towardsyou, goes away from you, comesagain towards you, and so on.And this is important: themagnetic vector, by constantlymoving, constantly changing,induces an electric current.We talked about the oppositealready: the moving electrical

charge of the proton, theelectrical current, induces theproton's magnetic field.This also is true the other wayaround: a moving magnetic fieldcauses an electrical current,e.g. in an antenna, as is thecase with TV/radio waves.(The term electromagnetic fieldshould actually remind us ofthe relationship between elec-trical current and magnetism).As we learned above we alsohave a moving/changingmagnetic vector in MRI. Thiscan also induce an electricalcurrent in an antenna, which isthe MRI signal.As the transversal magnetic vec-tor moves around with theprecessing protons, it comes to-

wards the antenna, goes awayfrom it, comes towards it againand so on, also with the pre-cession frequency. The re-sulting MR signal thereforealso has the precessionfrequency (fig. 16).

But . . . how can we make apicture out of this electricalcurrent, which actually is ourMR signal?

For this we have to know wherein the body the signal camefrom. How can we know that?The trick is really quite simple:we do not put the patient intoa magnetic field which has thesame strength all over thesection of the patient, whichwe want to examine. Instead wetake a magnetic field, whichhas a different strength at eachpoint of the patients cross sec-tion. What does this do?We heard that the precessionfrequency of a proton dependson the strength of the magneticfield (as the frequency of aviolin string depends on thestrength with which you pull it).If this strength is different frompoint to point in the patient,then protons in different places

Fig. 16The new transversal magnetizationmoves around with the precessing pro-tons (see fig. 7). Thus for an externalobserver, transversal magnetizationconstantly changes its direction, andcan induce a signal in an antenna.

precess with different fre-quencies. And as they precesswith different frequencies,the resulting MR signal fromdifferent locations also hasa different frequency. And bythe frequency we can assigna signal to a certain location.It is like with your TV: when youare in the kitchen (where youprobably do not have a TV) andhear a sound from your favouriteTV show, you know where thesound is coming from. It comesfrom that spot in your apart-ment where the TV stands.What you subconsciously do,is connect a certain sound toa certain location in space.This shall suffice for spatialinformation right now, on page89 we will go into more detailabout this.

Further detailsabout the MR signal

If our protons rotated aroundin synch, in phase, and nothingwould change, then we wouldget a signal as it is illustratedin fig. 16. This, however, is notwhat happens. As soon as theRF pulse is switched off, thewhole system, which was dis-turbed by the RF pulse, goesback to its original quiet, peace-ful state, it relaxes. The newly

established transverse magneti-zation starts to disappear(a process called transversalrelaxation), and the longitudinalmagnetization grows back toits original size (a processcalled longitudinal relaxation).Why is that?The reason why the longitudinalmagnetization grows back toits normal size is easier to ex-plain, so let us start with that(see fig. 17).No proton walks on its handslonger than it has to - sort of ahuman trait. The protons thatwere lifted to a higher energylevel by the RF pulse go backto their lower energy level,and start to walk on their feetagain.

Fig. 17After the RF pulse is switched off,protons go back from their higher to thelower state of energy, i.e. point up again.This is illustrated "one-by-one".The effect is that longitudinal magneti-zation increases and grows back to itsoriginal value. Note that for simplicitythe protons were not depicted as beingin phase; this subject is covered in moredetail in fig. 20 and 26.

Not all protons do this at thevery same time, instead it is acontinuous process, as ifone proton after the other goesback to its original state.This is illustrated in fig. 17 fora group of protons. For thesake of simplicity the protonsare shown as being out ofphase, which of course theyaren't in the beginning.Why and how they stop pre-cessing in phase will be ex-plained a little later.

What happens to the energywhich they had picked up fromthe RF pulse?This energy is just handed overto their surroundings, the so-called lattice. And this is whythis process is not only calledlongitudinal relaxation, butalso spin-lattice-relaxation.

By going back on their feet,pointing upwards again, theseprotons no longer cancel outthe magnetic vectors of thesame number of protons point-ing up, as they did before.So, the magnetization in thisdirection, the longitudinalmagnetization increases, andfinally goes back to its originalvalue (fig. 17).If you plot the time vs. longi-tudinal magnetization, you geta curve like fig. 18, it increaseswith time. This curve is alsocalled a T1-curve.

Fig. 18If one plots the longitudinal magnetizationvs. time after the RF pulse was switchedoff, one gets a so-called T1-curve.

The time that it takes for thelongitudinal magnetization to re-cover, to go back to its originalvalue, is described by thelongitudinal relaxation time,also called T1. This actually isnot the exact time it takes,but a time constant, describinghow fast this process goes.This is like taking time for oneround at a car race. The timegives you an idea of how longthe race may take, but not theexact time. Or more scientifi-cally, T1 is a time constant com-parable to the time constantsthat for example describe radio-active decay.That T1 is the longitudinalrelaxation time can easily beremembered by looking atyour typewriter: (fig. 19)

Fig. 19T1 is the longitudinal relaxation timethat has something to do with theexchange of thermal energy.

The " 1 " looks very much likethe , reminding you also thatit describes the spin-"l"atticerelaxation. But there are morehidden hints to this: the "1"also looks like a match. And thismatch should remind you ofsomething, which we also havementioned already: longitudinalrelaxation has something to dowith exchange of energy,thermal energy, which the pro-tons emit to the surroundinglattice while returning to theirlower state of energy.

Enough of thelongitudinalmagnetization -what happens withthe transversalmagnetization?

After the RF pulse is switchedoff, the protons get out of step,out of phase again, as nobodyis telling them to stay in step.For the sake of simplicity thishas been illustrated for a groupof protons which all "point up"in fig. 20.We heard earlier that protonsprecess with a frequency whichis determined by the magnetic

field strength that they are in.And all the protons shouldexperience the same magneticfield. This, however, is notthe case:• the field of the MR magnet,in which the patient is placed,is not totally uniform, nottotally homogenous, but variesa little, thus causing differentprecession frequencies• and each proton is influencedby the small magnetic fieldsfrom neighbouring nuclei, thatare also not distributed evenly,thus causing different pre-cession frequencies too. Theseinternal magnetic field vari-ations are somehow charac-teristic for a tissue.

So after the RF pulse is switch-ed off, the protons are nolonger forced to stay in step;and as they have differentprecession frequencies, theywill be soon out of phase.It is interesting to see, howfast the protons get out ofphase: just suppose that oneproton (p1) is rotating/precessing with a frequency of10 megahertz, i.e. 10 millionrevolutions per second. Due toinhomogeneities a neighbouringproton (p2) is in a magneticfield, which is 1 % stronger; thisproton has a precession fre-quency of 10.1 megahertz, 1 %more. In 5 microseconds(0.000005 sec or 5 x 10-6), p1

will have made 50.5 turns/revo-lutions, while proton p2 willhave made only 50. So in thisshort time span, the protonswill be 180° out of phase, can-celling their magnetic momentsin the respective plane.

Fig. 20After the RF pulse is switched off,protons lose phase coherence, they getout of step. When you look at these de-phasing proton ensembles from the top(which is illustrated in the lower partof the figure), it becomes obvious, howthey fan out. Fanning out, they point lessand less in the same direction, and thustransversal magnetization decreases.

Similar to what we did for thelongitudinal magnetization,we can plot transversal mag-netization versus time. What weget is a curve like in figure 21.This curve is going downhill, astransversal magnetization dis-appears with time. And as youprobably expect: there is alsoa time constant, describing howfast transversal magnetizationvanishes, goes downhill. Thistime constant is the transversalrelaxation time T2. How toremember what "T2" is?Easy:T2 = T x 2 = T T = Tt,and this means, it describesthe "T transversal", thus therelaxation of the transversalmagnetization. The resultingcurve in figure 21 thus iscalled a T2-curve. Another termfor transversal relaxation isspin-spin-relaxation, reminding

us of the underlying mechanism,a spin-spin interaction.How to remember, which one isthe T1- and which the T2-curve?Just put both curves together,and you can see something likea mountain with a ski slope.You first have to go uphill(T1-curve), before you jumpdown (T2-curve) (fig. 22).

Fig. 21If one plots transversal magnetizationvs. time after the RF pulse is switchedoff, one gets a curve as illustrated,which is called a T2-curve.

Fig. 22Coupling of a T1- and a T2-curveresembles a mountain with a slope.It takes longer to climb a mountainthan to slide or jump down, whichhelps to remember that T1 is normallylonger than T2.

So, time to reviewWe have learned that• protons are like little magnets• in an external magneticfield they align parallel or anti-parallel• the lower energy state(parallel) is preferred, soa few more protons alignthis way• the protons perform a motionthat resembles the wobblingof a spinning top, that was hit• this motion is calledprecession• the precession frequencyis dependent on the strengthof the external magnetic field(a relationship which is de-scribed by the Larmorequation).The stronger the magnetic field,the higher the precession fre-quency.• protons "pointing" in oppo-site directions cancel eachother's magnetic effects in therespective directions• as there are more protonsaligned parallel to the externalfield, there is a net magneticmoment aligned with or longi-tudinal to the external mag-netic field

• a radio frequency pulse thathas the same frequency as theprecessing protons, can causeresonance, transfer energy tothe protons. This results inmore protons being anti-paralleland thus neutralizing/cancellingmore protons in the oppositedirection. Consequence:the longitudinal magnetizationdecreases• the RF pulse also causes theprotons to precess in synch,in phase. This results in a newmagnetic vector, the transversalmagnetization

• when the RF pulse isswitched off- longitudinal magnetizationincreases again; this longi-tudinal relaxation is describedby a time constant T1, thelongitudinal relaxation time- transversal magnetizationdecreases and disappears; thistransversal relaxation is de-scribed by a time constant T2,the transversal relaxation time.Longitudinal and transversalrelaxation are different, in-dependent processes, and thatis why we discussed them indi-vidually (see figs. 17 and 20).

This is what you should knowby now.

How long is arelaxation time? \

Look at our example with theT1- and T2-curves in fig. 22.It is probably easy and logical,that it takes you more timeto get to the top of the moun-tain, than to go back down, tojump off. This means T1 is longerthan T2, and just to give youan idea: T1 is about 2-5-10 timesas long as T2. Or in absoluteterms in biological tissues:T1 is about 300 to 2000 msec,and T2 is about 30 to 150 msec.It is difficult to pinpoint the endof the longitudinal and trans-versal relaxation exactly. Thus,T1 and T2 were not defined asthe times when relaxation iscompleted. Instead T1 was de-fined as the time when about63% of the original longitudinalmagnetization is reached.T2 is the time when transversalmagnetization decreased to 37%of the original value. Thesepercentages are derived frommathematical equations (63% =1-1/e; 37% = 1/e) describingsignal intensity, but we do notwant to go into more detail here.

(However, we should mentionthat 1/T1 is also called longi-tudinal relaxation rate, and 1/T2transversal relaxation rate).

Previously it was believed thatmeasuring the relaxation times,would give tissue characteristicresults, and thus enable exacttissue typing. This, however,proved to be wrong, as thereis quite some overlap of timeranges; and also T1 is dependenton the magnetic field strengthused for the examination(see page 36).

What is a long/short relaxationtime, and which tissues havelong/short relaxation times?Look at fig. 23 - what do yousee? You see somebodyhaving a long drink, somethingliquid (representing water).When you go to your favouritebar (which naturally is crowded,as it is a popular place) andorder a long drink, you have to

wait quite a while to get yourdrink - T1 is long. When youfinally have your long drink, ittakes you also a long timeto drink it, so T2 also is long.And we want to remember:water/liquids have a long T1and a long T2.

Fig. 23Liquids have a long T1 and a long T2.

Now look at fig. 24, you seesomebody getting a hamburger.These normally contain much fat,and shall represent fat for us.The hamburger is fast food, youget it fast, thus fat has a shortT1. What about T2? It takes sometime to eat fast food, fat; how-ever, you normally spend moretime with your long drink, sofat has a shorter T2 than water.

As water has a long T1 anda long T2, it is easy to imaginethat "watery tissues", tissueswith a high water content, canalso have long relaxation times.Interestingly enough, patho-logical/diseased tissues oftenhave a higher water contentthan the surrounding normaltissues.

Fig. 24Compared to liquids/water fat hasa short T1 and a short T2.

What is T1influenced by?

Actually, T1 depends on tissuecomposition, structure and sur-roundings. As we have read,T1-relaxation has somethingto do with the exchange ofthermal energy, which is handedover from the protons tothe surroundings, the lattice.The precessing protons havea magnetic field, that constant-ly changes directions, thatconstantly fluctuates with theLarmor frequency. The latticealso has its own magnetic fields.The protons now want tohand energy over to the latticeto relax. This can be donevery effectively, when the fluc-tuations of the magnetic fieldsin the lattice occur with a fre-quency that is near the Larmorfrequency.

When the lattice consists ofpure liquid/water, it is difficultfor the protons to get rid oftheir energy, as the small watermolecules move too rapidly. Andas the protons (which are onthe higher energy level) cannothand their energy over to thelattice quickly, they will onlyslowly go back to their lowerenergy level, their longitudinalalignment. Thus it takes along time for the longitudinalmagnetization to show up again,and this means that liquids/water have long T1s.

When the lattice consists ofmedium-size molecules (mostbody tissues can be looked atas liquids containing varioussized molecules, kind of likea soup), that move and havefluctuating magnetic fields nearthe Larmor frequency of theprecessing protons, energy canbe transferred much faster,thus T1 is short.

This can again be illustrated byour sandwich and race car ex-ample: (see page 17) handingover sandwiches (i.e. energy)from one car (proton) to theother (lattice) is easy andefficient, when both move withthe same speed. With a dif-ference in speeds, the energytransfer will be less efficient.

Why does fat have a short T1?

The carbon bonds at the endsof the fatty acids havefrequencies near the Larmorfrequency, thus resulting ineffective energy transfer.

And why is T1 longer in strongermagnetic fields?

It is easy to imagine that in astronger magnetic field it takesmore energy for the protonsto align against it. Thus theseprotons have more energy tohand down to the lattice, andthis takes longer than handingdown just a small amout ofenergy. Even though it mayseem logical, this is the wrongexplanation. As we heard inthe beginning, the precessionfrequency depends on magneticfield strength, a relationshipdescribed by the Larmorequation. If we have a strongermagnetic field, then the pro-tons precess faster. And whenthey precess faster, theyhave more problems handingdown their energy to a latticewith more slowly fluctuatingmagnetic fields.

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What influences T2?T2-relaxation comes about whenprotons get out of phase, which- as we already know - hastwo causes: inhomogeneities ofthe external magnetic field,and inhomogeneities of thelocal magnetic fields within thetissues (see page 29). As watermolecules move around veryfast, their local magnetic fieldsfluctuate fast, and thus kindof average each other out, sothere are no big net differ-ences in internal magneticfields from place to place.And if there are no big differ-ences in magnetic field strengthinside of a tissue, the protonsstay in step for a long time,and so T2 is longer.

With impure liquids, e.g. thosecontaining some larger mol-ecules, there are bigger vari-ations in the local magneticfields. The larger molecules donot move around as fast, sotheir local magnetic fields donot cancel each other out asmuch. These larger differencesin local magnetic fieldsconsequently cause largerdifferences in precession fre-quencies, thus protons getout of phase faster, T2 isshorter.

This can be illustrated by thefollowing example: imagine thatyou drive down a street withmany pot holes. When you driveslow (which is equal to thesurroundings moving slow and

you standing still), you will bejumping up and down in yourcar with each pot hole. The dif-ferences in the surroundings(the magnetic field variations)influence you considerably.When you drive very fast (whichis the same as if the surround-ings move very fast), you do notfeel the single pot holes any-more. Before they have a majoreffect on you, you are alreadyback on the normal street level;thus their effect is averaged out,you are much less influenced bydifferences in the surroundings(the variations in magneticfield strength).

What does all this have to dowith what we want to know?All these processes influencehow your MR picture willfinally look!

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A brief reviewmight be advisable

• T1 is longer than T2• T1 varies with the magneticfield strength; it is longerin stronger magnetic fields• water has a long T1, fat hasa short T1• T2 of water is longer than theT2 of impure liquids containinglarger molecules.

Now let us performan experiment

Look at figure 25, where you seetwo protons, precessing aroundthe z-axis. I hope that yourecall, that the z-axis indicatesthe direction of a magnetic fieldline (see page 11). Instead ofonly these two protons, inreality there may be 12 pointingup and 10 pointing down, or102 up and 100 down - thereshall only be two more protonspointing up. As we know, theseare the ones that have a netmagnetic effect because theireffects are not cancelled out.

Now let us send in an RF pulse,which has just the correctstrength and duration, that oneof the two protons picks upenergy, to go into the higherstate of energy (points down/walks on its hands).

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What will happen? The longitudi-nal magnetization (up to nowresulting from two protons point-ing up) will decrease, in ourexample to zero (one pointingup is neutralized by one point-ing down). But: as both protonsare in phase, now there is atransversal magnetization whichhad not been there before.This can be looked at - in effect- that a longitudinal magneticvector is tilted 90° to the side(fig. 25).An RF pulse which "tilts" themagnetization 90° is called a 90°pulse. Naturally, other RF pulsesare also possible, and are namedaccordingly, e.g. 180° pulse.

Fig. 25If after the RF pulse, the number ofprotons on the higher energy levelequals the number of protons on thelower energy level, longitudinalmagnetization has disappeared, andthere is only transversal magnetizationdue to phase coherence. The magneticvector seems to have been "tilted"90° to the side. The corresponding RFpulse is thus also called a 90° pulse.

To really understand this letus look at another example.In figure 26 (a) we have 6protons pointing up; we sendin a RF pulse, which lifts up3 of them to a higher energylevel (b).The result: we no longer havea longitudinal, but a transversalmagnetization (again havingused a 90° pulse).What happens, when the RFpulse is switched off?Two things: protons go back totheir lower state of energy, andthey lose phase coherence.

It is important to note that bothprocesses occur simultaneouslyand independently. For the sakeof simplicity, let us look at whathappens step by step, and firstfocus on the longitudinalmagnetization:

• in 26 (c), one proton goesback to the lower energy state;resulting in 4 protons pointingup, and two pointing down. Innet effect: we now have a longi-tudinal magnetization of "2".

• Then the next proton goesback up; now 5 protons pointup, and one down, resulting ina net longitudinal magnetizationof "4" (fig. 26d).• After the next proton goesup, longitudinal magnetizationequals "6" (fig. 26 e).At the same time, transversalmagnetization decreases(fig. 26c-e). Why? You shouldbe able to answer this: theprecessing protons lose phasecoherence.In fig. 26b, all protons pointin the same direction, but thenget increasingly out of phase,and thus kind of fan out(fig. 26c-e).

Fig. 26In (a) is the situation before and in (b)immediately after an RF pulse is sentin. The RF pulse causes the longitudinalmagnetization to decrease, andwith a 90° pulse as illustrated, it be-comes zero (b). Protons also start toprecess in phase (b), which causesthe new transversal magnetization

. After the RF pulse is switchedoff (c-e) longitudinal magnetizationincreases, recovers, and transversalmagnetization disappears, decays. Bothprocesses are due to entirely differentmechanisms, and occur independentlyeven though at the same time.

In fig. 27, only the longitudinaland transversal magnetic vectorsare depicted at correspondingtimes as in figure 26. Thesemagnetic vectors add up to asum vector. ( —• )If you have forgotten; vectorsrepresent forces of a certainsize and a certain direction.If you add vectors pointing todifferent directions up, you willcome up with a direction thatis somewhere in between,depending on the amount offorce in the original directions.

This sum vector is very im-portant, as it represents thetotal magnetic moment ofa tissue in general, and thuscan be used instead of the twosingle vectors, representinglongitudinal and transversalmagnetization separately. Ourmagnetic sum vector duringrelaxation goes back to alongitudinal direction, in theend equaling the longitudinalmagnetization.

What we have to remember isthat this whole system actuallyis precessing, including the summagnetic vector/moment. Andthus the sum vector will actuallyperform a spiraling motion(fig. 27f).

Fig. 27In this illustration only the longitudinaland transversal magnetization vectorsfrom our experiment in figure 26 are de-picted. In (a) - before the RF pulse -there is only longitudinal magnetization.Immediately after the 90° RF pulsethere is no longitudinal but new trans-versal magnetization (b), and thistransversal magnetization vector is spin-ning around. With time this transversalmagnetization decreases, while longi-tudinal magnetization increases (c-d),until the starting point with no trans-versal but full longitudinal magnetizationis reached again (e). Transversal andlongitudinal magnetization vectors addup to a sum vector ( —• ). Thissum vector performs a spiraling motion(f) when it changes its direction frombeing in the transversal (x-y) plane(no longitudinal magnetization) to itsfinal position along the z-axis(no transversal magnetization).

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I hope that you recall, that achanging magnetic force/moment can induce an electricalcurrent, which was the signalthat we receive and use in MR.If we put up an antennasomewhere, as in figure 28, wewill get a signal as illustrated.This is easy to imagine, if youthink of the antenna as a micro-phone, and the sum magneticvector as having a bell at its tip.The further the vector goesaway from the microphone, theless loud the sound. The fre-quency of the sound, however,remains the same becausethe sum vector spins with theprecessing frequency (fig. 29).This type of signal is called aFID signal, from free inductiondecay. It is easy to imagine,that you get a very good strongsignal directly after the 90° RFpulse (as the bell comes veryclose to the microphone in ourexample).

By now it should be obviousthat the magnetic vectors direct-ly determine the MRI signal andsignal intensity by inducingelectrical currents in the an-tenna. Instead of the terms"longitudinal" or "transversalmagnetization", we can also usethe term "signal or signal in-tensity" at the axis of our T1,and T2 curves. This will hope-fully become clearer as youcontinue reading.

Fig. 28For an external observer, the sum vectorof figure 27f constantly changes itsdirection and magnitude while it per-forms its spiraling motion. The sumvector induces an electrical current inan antenna, the MR signal. This is ofgreatest magnitude immediately afterthe RF pulse is switched off and thendecreases.

Fig. 29The signal from our experiment infigures 26 to 28 disappears with time,however, has a constant frequency.This type of signal is called a FID(free induction decay) signal.

What about anotherexperiment?

Let us perform another experi-ment similar to the one above,which is illustrated in figure 30.In figure 30a, we have twotissues, A and B, which havedifferent relaxation times(tissue A has a shorter trans-versal as well as longitudinalrelaxation time). We send in a90° RF pulse, and wait a certaintime TRlong (we will explain laterwhy we use the term TR), andthen send in a second 90° pulse.What will happen?As after the time TRlong tissue Aand tissue B have regained allof their longitudinal magneti-zation (frame 5), the transver-sal magnetization after thesecond pulse will be the samefor both tissues, as it was inframe 1.

What if we do not wait so longfrom pulse to pulse?Look at figure 30b, where thesecond 90° pulse is sent in afterthe time TRshort, i.e. afterframe 4 already. At this time,tissue A has regained more ofits longitudinal magnetizationthan tissue B. When the second90° pulse now "tilts" the longi-tudinal magnetization 90 degrees,the transversal magnetic vectorof tissue A is larger than that oftissue B. And when this vectorof A is larger, it will reachcloser to our antenna; thus theimaginary bell at the tip ofvector A will cause a louder,stronger signal in our "micro-phone", the antenna, thanvector B.The difference in signal inten-sity in this experiment dependson the difference in longitudinalmagnetization, and this meanson the difference in T1 betweenthe tissues.

Using these two pulses, we cannow differentiate tissue A fromtissue B, which might have beenimpossible chosing only one 90°pulse or two 90° pulses that area long time apart (after a longtime, the differences in T1 be-tween tissue A and B no longerplay a role in our experiment,because after that time thetissue B with the longer T1 isback to its original state, too).

Fig. 30 aA and B are two tissues with differentrelaxation times. Frame 0 shows thesituation before, frame 1 immediatelyafter a 90° pulse. When we wait for along time (TRlong) the longitudinalmagnetization of both tissues will havetotally recovered (frame 5). A second90° pulse after this time results inthe same amount of transversalmagnetization (frame 6) for bothtissues, as was observed after the firstRF pulse (frame 1).

When you use more than oneRF pulse - a succession of RFpulses - you use a so-calledpulse sequence. As you can usedifferent pulses, e.g. 90° or 180°pulses, and the time intervalsbetween successive pulses canbe different, there can be manydifferent pulse sequences. Aswe saw in our experiment, thechoice of a pulse sequence willdetermine what kind of signalyou get out of a tissue. So it isnecessary to carefully chose andalso describe the pulse se-quence for a specific study.The pulse sequence that weused was made up of one typeof pulse only, the 90° pulse.This was repeated after a cer-tain time, which is calledTR = time to repeatHow did TR influence the signal

in our experiment?

With a long TR we got similarsignals from both tissues, both

would appear the same on aMR picture. Using a shorter TR,there was a difference in signalintensity between the tissues,determined by their differencein T1. The resulting picture iscalled a T1-weighted picture.This means, that the differenceof signal intensity betweentissues in that picture, thetissue contrast, is mainly dueto their difference in T1.However, there is always morethan one parameter influencingthe tissue contrast; in our ex-ample, T1 is just the most out-standing one.

What is a short or a long TR?

A TR of less than 500 msecis considered to be short, aTR greater than 1500 msec tobe long.As you may imagine or know al-ready, we can also produce T2-weighted images, and so-calledproton density (-weighted)images.

That proton density, which isalso called spin density, in-fluences tissue contrast, can beexplained quite simply; wherethere are no protons, there willbe no signal; where there aremany protons, we will have"lots" of signals. We will readmore about this later. The pointis that by using certain pulsesequences, we can make certaintissue characteristics to bemore or less important in theresulting image.

Fig. 30bWhen we do not wait as long as in figure30a, but send in the second RF pulseafter a shorter time (TRShort), longi-tudinal magnetization of tissue B, whichhas the longer T1, has not recovered asmuch as that of tissue A with the shorterT1. The transversal magnetization of thetwo tissues after the second RF pulsewill then be different (frame 5). Thus,by changing the time between successiveRF pulses, we can influence and modifymagnetization and the signal intensityof tissues.

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By choosing a pulse sequence,the doctor can be comparedto a conductor of an orchestra(figure 31): he can influencethe overall appearance of thesound (signal), by making cer-tain instruments (parameters)influence the sound more thanothers. All instruments (para-meters), however, always playsome role in the final sound(signal).

Fig. 31The MRI doctor can be compared to aconductor: by choosing certain pulsesequences, he can modify the resultingsignal, which is itself influenced bydifferent parameters.

Let us go backto our experimentonce more for ashort repetition

• With a certain type of RFpulse we can cause the longi-tudinal magnetization to dis-appear, while a transversalmagnetization appears.The "net magnetization" (thesum vector of longitudinal andtransversal magnetization) is"tilted" 90° in this case(when we started we only hadlongitudinal magnetization).The corresponding RF pulse istherefore called a 90° pulse.• The transversal componentof the net magnetization caninduce a measurable signal inan antenna• Immediately after the RFpulse relaxation begins; trans-versal magnetization starts todisappear and longitudinal re-laxation begins to reappear. Thesum magnetic vector goes backto its original longitudinal align-ment, the signal disappears.

• When we send in the second90° pulse, the net magnetizationis again tilted 90°, and we againreceive a signal.• The strength of this signaldepends (among other things)on the amount of longitudinalmagnetization we start out with.Do you remember the T1-curve(if not see page 27)? The T1-curve described the relationshipbetween time (after an RFpulse) and the amount of longi-tudinal magnetization (fig. 18).When we wait a long time untilwe send in our second RFpulse, longitudinal magnetizationwill have recovered totally.The signal after the secondRF pulse will thus be the sameas the one after the first pulse.However, when the secondpulse comes in earlier, the sig-nal will be different, as theamount of longitudinal magne-tization at that time is less.

In fig. 32 we plotted the T1-curves for brain and for cere-brospinal fluid (CSF). At thetime 0 we have no longitudinalmagnetization at all, and thiscan be the time immediatelyafter our first 90° pulse. Whenwe wait a long time before werepeat the 90° pulse (TRlong),longitudinal magnetization haspretty much recovered. Thelongitudinal magnetic vectorsthat will be "tilted" 90° differonly in a small amount, so therewill be only a small differencein signal intensity, i.e. tissuecontrast between brain and CSF.If we, however, send in thesecond pulse after the shorterTRshort, the difference in longi-tudinal magnetization is ratherlarge, so there will be a bettertissue contrast. And as we cansee from the distance betweenthe two curves, there is atime span where tissue contrastis most pronounced.

Fig. 32Brain has a shorter longitudinalrelaxation time than CSF. With a shortTR the signal intensities of brain andCSF differ more than after a long TR.

Why are the signalsafter a very longtime TR betweenpulses not identical?

We have heard the explanationalready. The signal intensitydepends on many parameters.When we wait a long time, T1does not influence the tissuecontrast any more, however,there may still be a possibledifference in the proton den-sity of the tissues in question.And when we wait a very longtime TR in our experiment fromfig. 32, the difference in signalis mainly due to different pro-ton densities, we have a so-called proton density (or spindensity) weighted image.Now we have read about T1-and proton density-weightedimages.

How do we obtaina T2-weightedimage?

This is a little more difficultto understand. Let us performanother experiment, which isa little different from the onesbefore. First, we use a 90°pulse. The longitudinal mag-netization is tilted, we get atransversal magnetization.What happens after this pulse,when we wait a short time?You should be able to answerthis question without diffi-culties - if not go back to page37 before you continue to read.After the pulse is switched off,longitudinal magnetization startsto reappear, the transversal

magnetization, however, startsto disappear. Why does thetransversal magnetization dis-appear? The protons lose phasecoherence, as we have heardabove. And this is illustratedin figure 33 for three protons,which are almost exactly inphase in (a) but increasinglyspread out, as they have dif-ferent precession frequencies(b and c). The loss of phasecoherence results in decreasingtransversal magnetization andthus loss of signal.Now we do something new:after a certain time (which wecall TE/2, half of TE, forreasons you will understand ina few minutes) we send in a180° pulse. What does this do?

The 180° pulse acts like a rubberwall; it makes the protons turnaround, so that they precess inexactly the opposite direction,which is clockwise in figure 33d.The result is that the fasterprecessing protons are now be-hind the slower ones. If we waitanother time TE/2, the fasterones will have caught up withthe slower ones (fig. 33f).At that time the protons arenearly in phase again, whichresults in a stronger trans-versal magnetization, and thusin a stronger signal again.A little later however, thefaster precessing protons willbe ahead again, with the signaldecreasing again.

Fig. 33After the RF pulse is switched off, theprotons dephase (a-c). The 180°pulse causes them to precess in theopposite direction and so they rephaseagain (d-f).

Fig. 34When a rabbit and a turtle run in onedirection for a certain time, then turnaround and run in the opposite directionwith the same speed for the same time,they will arrive at the starting pointat the same time.

To illustrate this:think about a race between arabbit and a turtle starting atthe same line (fig. 34). Aftera certain time (TE/2), the rab-bit is ahead of the turtle.When you make the competitorsrun in the opposite directionfor the same length of time,they will both be back at thestarting line at exactly thesame time (assuming, that theyrun with constant speed).

The 180° pulse in our experi-ment acts like a wall, from whichthe protons bounce back, likea mountain reflecting soundwaves as echoes. This is whythe resulting strong signalis also called an echo, orspin echo.After we have our signal, ourspin echo, the protons losephase coherence again, thefaster ones getting ahead aswe have heard. We naturallycan perform the experimentagain with another 180° pulse,and another and another . . .If we now plot time vs. signalintensity, we get a curve likein fig. 35.

Fig. 35The 180° pulse refocusses the dephasingprotons which results in a strongersignal, the spin echo after the time TE.The protons then dephase again andcan be refocussed another time by a 180°pulse and so on. Thus it is possible toobtain more than one signal, more thanone spin echo. The spin echoes, how-ever, differ in intensity due to so-calledT2-effects.A curve connecting the spin echointensities is the T2 curve. If we didnot use the 180° pulse, the signal in-tensity would decay much faster. A curvedescribing the signal intensity in thatcase is the T*2 (T2 star) curve, whichis described in a little more detail onpage 54.

From this curve we can see,that the spin echo, the result-ing signal, decreases withtime. Responsible for this isthe fact that our 180° pulseonly "neutralizes" effects thatinfluence the protons in aconstant manner, and these arethe constant inhomogeneitiesof the external magnetic field.Inconstant inhomogeneities fromlocal magnetic fields insideof the tissue cannot be "evenedout", as they may influencesome protons before the 180°pulse differently than after the180° pulse. So some of theprotons may still be behind orin front of the majority of theprotons, that will reach thestarting line at the same time.So from echo to echo the in-tensity of the signal goes downdue to the so-called T2-effects.

May be we should illustrate thisby an example: imagine twobuses full of people, e.g. aftera soccer or football game. Theyare standing at a starting line(fig. 36). With two micro-phones, you record the signal(e.g. the singing from thecrowd) that is coming fromeach bus. Then the busesleave in the same direction.Recording the signal, you mayrecognize, that one signal dis-appears faster, than the other.

This can have two differentcauses: may be one bus drivesfaster than the other (loss ofsignal would thus be due to ex-ternal influences, the externalmagnetic field inhomogenei-ties).Or the difference in signalintensities, the difference insinging, may be due to dif-ferences of inherent propertiesof the two groups (internalinhomogeneities); may be in onebus, there are only the "partyanimals", who do not becometired as fast, as the people inthe other crowd.To figure out what actually isthe reason for the signal dis-appearing, you can make thebuses turn around after a cer-tain time TE/2, and have themdrive back with the same speedalso for the time TE/2. Aftertime 2 x TE/2 = TE thebuses will be back at the start-ing line. The signal intensity,that you record with your micro-phone then depends only oninherent properties, i.e. howtired the crowds have become.

If you do not use a 180° pulseto neutralize constant externalinhomogeneities, the protonswill experience larger differ-ences in magnetic field strengthwhen the RF pulse is switchedoff. Due to this they will beout of phase faster, the trans-versal relaxation time will beshorter. To distinguish thisshorter transversal relaxationtime from the T2 after the 180°

pulse, it is called T*2 (T2 star).The corresponding effects arenamed T*2-effects. TheseT*2-effects are important withthe so-called fast imagingsequences (see page 81).In our example with the busesthis would mean that we justrecord the signals as the busesdrive away. The signals vanishdue to extrinsic (bus speed)and intrinsic (exhaustion of thepassengers) properties underthese circumstances (see fig. 36).

The type of pulse sequence,that we used in our experiment,is called a spin echo sequence,consisting of a 90° pulse and a180° pulse (causing the echo).This pulse sequence is veryimportant in MR imaging, as itis the workhorse among thepulse sequences, which can beused for many things. It is im-portant to realize that with aspin echo sequence, we cannotonly produce T2-, but also T1-and proton density - weightedpictures. We will get to that alittle later.

Fig. 36Without having the buses come back(i.e. a 180° pulse), it is impossible tosay whether a decrease in signalintensity is due to inherent tissue prop-erties (the differing shape of thebus passengers), or due to externalinfluences, i.e. different bus speeds.

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Fig. 37T2-curves for two tissues with differenttransversal relaxation times; tissue Ahas a shorter T2 than tissue B, thus losestransversal magnetization faster.With a short TE (TEshort) the differencein signal intensity is less pronouncedthan after a longer TE (TElong).

Let us first look atsuch a T2-weightedsequence

What did we do? First we sentin a 90° pulse, resulting insome transversal magnetization.Immediately after the 90° pulsewe have a maximum transversalmagnetization. However, thistransversal magnetization dis-appears, due to T2-effects. Howfast transversal magnetizationdisappears, can be seen froma T2-curve; in fig. 37 we haveplotted T2-curves for two dif-ferent tissues, tissue A havinga short T2 (e.g. brain), tissue Bhaving a long T2 (water or CSF).Both curves start at 0, which is

the time immediately after the90° pulse is switched off.When we wait for a certain timeTE/2 to send in the 180° pulse,transversal magnetization willhave become smaller. Afterwaiting another time TE/2 (thatis TE after the 90° pulse isswitched off), we will receivea signal, the spin echo.The intensity of this echo isgiven by the T2-curve at the timeTE. This time TE between the90° pulse and the spin echo iscalled

TE = time to echo.The time TE can be chosen bythe operator. And as we cansee from the T2-curves, TEinfluences the resulting signal,and thus also the image:

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the shorter the time TE, thestronger the signal that we getfrom a tissue.To get the best, strong signal,it may seem reasonable to usea short TE, because with longerTEs signal intensity decreases.With a short TE, however, therewill be a problem (fig. 37).Both T2-curves in this examplestart at the same point. If weonly wait a very short TE, thedifference in signal intensitybetween tissue A and tissue Bis very small, both tissues mayhardly be distinguished as thereis hardly any contrast (which isthe difference in signal intensityof tissues). Consequence: witha short TE, differences in T2do not influence tissue contrast

very much. As both T2-curvesdiverge, with a longer TE thedifference in T2-curves, andthus the difference in signalintensity = contrast, is morepronounced in our example.So it might be reasonable towait a very long TE; the result-ing picture should be veryheavily T2-weighted.But (and there is always a"but") if we wait longer, thetotal signal intensity becomessmaller and smaller. The signalto noise ratio becomes smaller,the picture appears grainy.An example to illustrate thissignal-to-noise problem: whenyou receive a local radio stationin.your radio, this gives youa good signal, e.g. loud music

and only little static noise.When you drive out of town, thesignal intensity of the radiostation becomes weaker, andyou will hear more static noise;and when you drive even furtheraway, you may not be ableto discern the music from thebackground noise. And thisis the same for the MR signal:there is always some noise inthe system, however, when thesignal is strong, this does notmatter much. However, thesmaller the signal, the harderit is, to differentiate it fromthe background noise.

Let us reviewsome facts

We have learned that• the spin echo sequence con-sists of a 90° and a 180° pulse• after the 90° pulse protonsare dephasing due to externaland internal magnetic fieldinhomogeneities• the 180° pulse rephases thedephasing protons (sometimesthe term spins is used inter-changeable for protons), anda stronger signal, the spinecho results• the 180° pulse serves to"neutralize" the external mag-netic field inhomogeneities• signal decrease from oneecho to the next, when usingmultiple 180° pulses is dueto internal T2-effects• by choosing different TEs(different times after the 90°pulse) the signals can be T2-weighted in varying degrees -with very short TEs, T2-effectshave not yet had time to reallyshow upnwith longer TEs, the signalintensity difference betweentissues will be depending verymuch on their T2s, their trans-versal relaxation times

• with very long TEs, thereshould be even more T2-weight-ing, however, signal intensity assuch would be so small, that atbest it can just barely be dis-tinguished from the backgroundnoise

What actually is a short/long TR or TE?

A short TR is one that isabout as short as the smallest/shortest T1 that we are inter-ested in (Remember: T1 wasa time constant, not the timethat it takes for a tissue toregain its longitudinal magneti-zation!). A long TR is about3 times as long as a short TR.A TR of less than 500 msec isconsidered to be short, a TR ofmore than 1500 msec to be long(just to give you a rough idea).A short TE is one that is asshort as possible, a long TEalso is about 3 times as long.A TE of less than 30 msec isconsidered to be short, aTE greater than 80 msec tobe long.

Cina Joseph Ali

Cina Joseph Ali

Cina Joseph Ali

Cina Joseph Ali

Let us go back toour spin echo pulsesequence

This sequence can beillustrated schematicallyas in figure 38:90° pulse - wait TE/2 - 180°pulse - wait TE/2 - record signal

For certain different reasons,such a pulse sequence is re-peated two or more times.The time to repeat a pulse se-quence was TR, time to repeat;so what we get is the follow-ing scheme:1.(90° - TE/2 -180° - TE/2 ->record signal at TE)

after TR (time from thebeginning of one 90° pulse tothe next 90° pulse) followsanother pulse cycle and signalmeasurement:

2.(90° - TE/2 -180° - TE/2 ->record signal at TE)

Fig. 38Schematic illustration of a spin echopulse sequence.

To figure out how much signalyou get from a certain tissuewith certain parameters of aspin echo sequence, you actual-ly have to do no more than com-bine its T1- and T2-curves, as isillustrated in figure 39. Therewe have the T1 and T2-curve ofa certain tissue.Which parameter determinedthe amount of longitudinalmagnetization?That was TR. To see how muchlongitudinal magnetization willbe tilted 90° to the side (andthus to figure out, with howmuch transversal magnetizationwe start out with), we just lookat the intensity of the longi-tudinal magnetization at thetime TR. The longitudinal mag-netization at this point, "tilted"in the transversal plane, is

the starting point from whichtransversal magnetizationdecays. So we just attach the T2-curve at this point. How muchsignal we get with a spin echosequence to construct theimage, also depends on TE, thetime that we wait after the90° pulse. So we now only haveto look for the signal intensityat the time TE on the T2-curve.

Fig. 39It is possible to determine signalintensity for a tissue using a spin echosequence by combining the T1-and theT2-curve for that tissue.The longitudinal magnetization after thetime TR is equal to the amount of trans-versal magnetization we start out with,as it is "tilted" 90 degrees. This trans-versal magnetization immediately startsto disappear by a rate which is deter-mined by the transversal relaxation time,and thus by the T2-curve. The signalintensity of the tissue after a time TEcan then be inferred from the T2-curveat this time TE (which starts after TR!).

What picture do we get,when we choose a long TRand a short TE?

This is illustrated in figure 40,where the T1- and T2-curvesfor two different tissues aredepicted. Maybe you rememberour experiment from page 46,when we sent in a 90° pulse,which was followed by another90° pulse after the time TR.The 90° pulse "tilts" the exist-ing longitudinal magnetizationinto a transversal plane,resulting in a transversalmagnetization. The more longi-tudinal magnetization we have,the stronger the initialtransversal magnetization im-mediately after the 90° pulse.As we read earlier, with a verylong TR, all tissues will haverecovered their longitudinal mag-netization totally; differencesin T1 of the tissues examinedwill not influence the signal,

as enough time passed by toallow even tissues with a longT1 to relax totally.In the spin echo sequence westart with a 90° pulse, whichalso tilts what is there as longi-tudinal magnetization (it doesnot matter, that there wereother pulses such as the 180°pulse in between). When wechoose a long TR, as we justsaid, then differences in T1 donot really matter. When wealso use a short TE, differencesin signal intensity due todifferences in T2 have not hadenough time to become pro-nounced yet. The signal, thatwe get, is thus neither T1- norT2- weighted, but mainly in-fluenced by differences in pro-ton or spin density. The moreprotons, the more signal, if youlook at it in a simple manner(figure 40).

Fig. 40By combining T1- and T2-curves signalintensity of certain tissues can bedetermined for a pulse sequence usingTR and TE as illustrated, and asexplained in figure 39. What happens,when we choose a long TR, asillustrated? With a long TR, differencesin T1, in longitudinal magnetizationtime are not very important any more,as all tissues have regained their fulllongitudinal magnetization. When we onlywait a very short TE then differencesin signal intensity due to differencesin T2 have not yet had time to be-come pronounced. The resulting pictureis thus neither T1- nor T2-weighted,but mostly determined by the protondensity of the tissues (for this, ideallyTE should be zero).

Cina Joseph Ali

Cina Joseph Ali

And when we use a long TRand a long TE?

With a long TR there are noprevailing differences in T1.With the long TE however, dif-ferences in T2 become pro-nounced (figure 41). Thus theresulting picture is T2-weighted.

Fig. 41When we wait a long TR and a long TE,differences in T2 have had time enoughto become pronounced, the resultingpicture is T2-weighted.

What if we use a shorter TRand a short TE?

With a short TR, tissues havenot recovered their longitudinalmagnetization, thus differencesin T1 (which determines, howfast longitudinal magnetization isregained) will show up in formof signal intensity differences(fig. 42). When TE is short,differences in T2 cannot reallymanifest themselves, so theresulting picture is still T1-weighted (there is a lower limitfor TE, because it takes sometime for the 180° pulse tobe sent in and do its effects).

What if we use a very shortTR and a very long TE?

This is only a theoreticalquestion. Why? With a very shortTR, there will be only very littlelongitudinal magnetization whichis "tilted". And with a long TEwe even allow the small amountof transversal magnetizationresulting to disappear to a largeextent. The resulting signal willbe so small, of so little inten-sity, that it cannot be used tomake a reasonable picture.

Fig. 42When we wait a shorter time TR,differences in T1 influence tissue con-trast to a larger extent, the picture isT1-weighted, especially when we alsowait a short TE (when signal differencesdue to differing T2s have not had timeto become pronounced).

If you have notbeen concentrating

for the last minutes, you willprobably be just short of givingup right now. How to remem-ber this - even if you do notunderstand all of it (whichhopefully is not the case)?Try looking at fig. 43. What doyou see? A man with shortTRousers. And considering theweather conditions, this makesonly one person in the picturehappy.This should remind you that ashort TR (ousers) gives a T1-weighted image (only l is happy).

Fig. 43What to choose for a T1-weighted image?

What do you see in figure 44?The same couple is having tea.Now having tea, which is usuallyserved hot, always takes long.And in the illustration the longTEa makes two people happy.This should remind you that along TE gives a T2-weightedimage.

Fig. 44What to choose for a T2-weighted image?

Fig. 45T1- (a), proton (spin) density- (b),and T2-weighted (c) images of the samepatient. The CSF is black on the T1-weighted image. However, it has thestrongest signal in the T2-weightedimage. On the spin-density image it isof intermediate signal intensity.

Some practicalhints to imageinterpretation

How can we tell from a picture,whether it is a T1- or a T2-weighted image, when imagingwas done with a normal pulsesequence, not one of the fastsequences (see below).As a rule of thumb: if you seewhite fluid, e.g. CSF or urine,you are dealing with a T2-weighted image. If the fluid isdarker than the solids, we havea T1- or a proton-density image.Look at fig. 45: in (a) CSF isdark, the grey substance isdarker (more grey) than thewhite substance; this is a typicalT1-weighted image.In (b) CSF still is dark, eventhough its signal intensity isslightly higher than in the T1-weighted image; contrast be-tween grey and white substanceis reversed. This is a proton/spin density-weighted image,and as grey substance has ahigher water content, i.e. con-tains more protons, its signalintensity is higher than that ofthe white substance.In (c) CSF has a higher signalintensity than grey and whitesubstance, the picture is T2-weighted.

Cina Joseph Ali

These are rules-of-thumb only.Actually, to be really sure, youwould have to look at twopictures taken with differentimaging parameters. Why?Look at figure 46. You see thatin this example the T2-curvesstart at different "heights", andcross each other (they do nothave to run parallel, it is justbetter to understand them inthe beginning, when they do andfor didactic reasons they havebeen depicted like that).The fact that the curves inter-sect is very important:• with a TE before the crossingpoint (TE1), tissue A will havea higher signal intensity• with a TE right at that point,(TEC), we cannot distinguishthe tissues at all, as they havethe same signal intensity.

Thus, you might be unlucky,and choose a pulse sequencewith just those imaging para-meters that do not allow tissuedifferentiation (which is thereason for performing twodifferent examinations with dif-ferent T1- and T2-weightings).• with a TE beyond the crossingpoint (TE2), tissue A will havea lower signal than tissue B.• before this crossing point(which you do not know, lookingat a picture normally), the rela-tive signal intensities are stillgoverned by differences in T1.The tissue with the shorter T1(or the higher proton density,if we have a long TR) still hasthe higher signal intensity. Onlywith longer TEs does the T2-weighting come up. Think aboutthat for a moment!

Fig. 46T2-curves of different tissues can inter-sect. The signal intensity of the tissuesis reversed choosing a TE beyond thecrossing point (TEC): before this cross-ing point (e.g. at TE1) tissue A hasa higher signal intensity than tissue B.This means that image contrast is stilldetermined by differences in T1: thetissue A with the shorter T1 has thestronger signal intensity. At TEC bothtissues have the same signal intensity,and thus cannot be differentiated.After the crossing point (e.g. at TE2) therelative signal intensities are reversed,and tissue B has the stronger signal.

Now we have already heardabout many parameters, thatinfluence the MR picture, soT1, T2, proton density, pulsesequences, TR and TE - butthere are more, e.g. flow, andcontrast media.

How does flowinfluencethe signal?

The fact that flow influencesthe MR signal has been knownfor a long time. The first experi-ments on this subject werecarried out about 30 years ago.Interestingly enough, this phe-nomenon was used to measureflow in the fuel pipes of satel-lite rockets, without havingto put any obstruction into theflow lines.

The subject of how flow in-fluences the MR signal is rathercomplex and difficult, but let usat least get some idea about it.In fig. 47 we have a body sec-

tion through which a vessel iscrossing. When we send in ourfirst 90° pulse, all the protonsin the cross section are in-fluenced by the radio wave.After we turn the RF pulse off,we "listen" into the section andrecord a signal. At this time,all the original blood in ourvessel may have left theexamined slice. So there is nosignal coming out of the vessel;it appears black in the picture.This phenomenon is calledflow-void phenomenon.

Fig. 47Flow effects are responsible for theblack appearance of flowing blood, thesignal void in blood vessels.

Cina Joseph Ali

This is not the only way in whichflow may influence the picture,there may be all kinds ofthings, e.g. also flow-relatedenhancement.Take a look at figure 48, whichshows a blood vessel goingthrough a slice which is beingexamined, (a) representsthe situation before the 90°pulse and (b) immediately afterthe pulse. If we wait somemope time before we send ina second 90° pulse, like in (c),protons will have undergonesome relaxation, and there issome longitudinal magnetizationagain, as shown by the arrowspointing back up. The protonsin the bloodvessel, however,have left the slice and been

replaced by protons that stillhave all of their longitudinalmagnetization. If we send ina second 90° pulse now, therewill be more signal coming fromthe vessel than from its sur-roundings, because there ismore longitudinal magnetizationat this time.

The whole subject with signalstrength and flow effects is evenmuch more complicated. Forexample, when you do multisliceimaging; i.e. take images ofmore than one slice at the sametime (see page 85), the signalalso depends on the directionof the flow. In addition, itdiffers over the cross sectionof a vessel, depending on theflow profile, and whether thereis laminar or turbulent flow.If you want to know more aboutthis, you should look it upin one of the comprehensivestandard text books.

Fig. 48Flow can have differing effects on signalintensity, and can also cause flow-related enhancement, which is explainedin detail in the text.

They will also give you moreinformation on MRI angiography.In this technique the fact thatflow influences the MRI signalis used in a beneficial man-ner by displaying the movingprotons.

Fig. 49Paramagnetic substances like Gadoliniumshorten the T1 and the T2 of theirsurroundings. The respective T1- and T2-curves are shifted towards the left.In effect, that means that for a certainTR there is more, for a certain TE thereis less signal.

Now what aboutMR contrast media?

Certain so-called paramagneticsubstances have small localmagnetic fields which cause ashortening of the relaxationtimes of the surrounding pro-tons. This effect is namedproton relaxation enhancement.The body contains paramagneticsubstances under normal cir-cumstances. Examples aredegradation products of hemo-globin, e.g. deoxyglobinand methemoglobin, which arefound in hematomas, or alsomolecular oxygen.

Gadolinium, a paramagneticsubstance, is used as an MRcontrast medium (Magnevist®).Chemically the substance is arare earth. As Gadolinium istoxic in its free state, it isbound to DTPA in a certain way(chelation), which solves theproblem of toxicity.The effect of the contrast me-dium is a change of the signalintensity by shortening T1 and T2in its surroundings (fig. 49).

Cina Joseph Ali

In fig. 50 this is illustrated fortwo tissues, A and B. The i.v.administered Gadolinium enterstissue A, the T1 of tissue A be-comes shorter and the T1-curve is shifted to the left. Theresult is that the signal fromtissue A at time TR is strongerthan it was before and thetwo tissues can be better dif-ferentiated, because there isbetter contrast.When we perform a T2-weightedexamination there is less signalcoming from tissue A aftercontrast medium application,because the contrast mediumshortens T2, and shifts the T2-curve to the left.As loss of signal often is moredifficult to appreciate than asignal enhancement, T1-weightedimages are the predominantimaging technique used aftercontrast medium injection.

Fig. 50In (a) the T1-curves for tissue A and Bare very close to each other, resultingin only a small difference in signalintensity between the tissues at TR.In (b) the T1-curve of tissue A is shiftedto the left, as contrast agent enteredtissue A but not tissue B. At the sametime TR there now is a much greaterdifference in signal intensity, i.e.tissue contrast.

As the substance is not distrib-uted evenly throughout thebody, signals from differenttissues will also be influenceddifferently. Vascularized tumortissues are enhanced for ex-ample. It is also important thatthe Gadolinium does not gothrough the intact, but ratherthe disrupted blood-brain-barrier.It has been shown that the useof contrast media increaseslesion detection and diagnosticaccuracy of MRI. It may, for ex-ample, help with differentiationbetween tumor tissue and sur-rounding edema, which mightbe otherwise indistinguishable.Gadolinium entering into thetumor tissue shortens the T1,thus making the tumor bright ina T1-weighted image, while thesurrounding edema may not beinfluenced at all.As Gadolinium shortens T1, weare able to shorten TR in ourexamination (see page 72).And because imaging time de-pends on TR, as we will seelater, imaging then may takeless time.

The pharmacological propertiesof Gadolinium-DTPA are verysimilar to the ones of contrastmedia in conventional radiology;Gadolinium-DTPA however seemsto be even better tolerated.

Ready for arepetition?

As we know by now, many para-meters, e.g. T1, T2, proton den-sity, pulse sequence, influencethe appearance of tissues inan MR picture.• With a short TR we get a T1-weighted image• With long TE the image isT2-weighted• Flow effects can be variable,and cover the spectrumfrom signal loss to signalenhancement• Paramagnetic substances, e.g.the contrast medium Gado-linium-DTPA, shorten T1 and T2of the surrounding protons. Thisresults in a signal increase inT1-weighted images and a signaldecrease in T2-weighted images

• T1-weighted imaging is thepreferred technique after con-trast medium injection.By choosing the pulse sequenceand imaging parameters, like TRand TE, we can get T1-, T2- orproton density (spin density)-weighted images, as we havealready heard. Many differentpulse sequences have been de-veloped and we should be famil-liar with their basic concepts.So let us take a look at them.

Cina Joseph Ali

Cina Joseph Ali

Cina Joseph Ali

Cina Joseph Ali

Cina Joseph Ali

Partial saturation/Saturation recoverysequence

Pulse sequences that use 90°pulses only, are the saturationrecovery pulse sequence andthe partial saturation sequence(fig. 51). We have alreadydiscussed them, but we didnot give them a name. Basically,the sequences are the same:they consist of two 90° pulses.The difference is in the timeinterval between pulses, the TR(see page 47). Look at figure 52with the T1-curves (going uphill!)of two different tissues. If wesend in the second pulse after along time, TRlong, both tissues

have regained longitudinalmagnetization. With a TRlong, thesaturation recovery sequence(the protons have relaxed, aresaturated), the signal is in-fluenced by the proton density(Do you recall the stories withthe short trousers and