Introduction to MRI PhysicsIan MillerJuly 11, 2007

Goal of Todays LectureRelate the concepts of MRI physics to things that engineers and neurophysiologists already understandLay the groundwork for more detailed understanding of more complicated imaging techniquesFast spin echoEcho planar imagingVolume imaging3D time of flightDiffusion

Why this is an Intimidating TopicThere are a myriad of basic physics principles involved, each of which is individually important and hard to skip overNeed to simultaneously consider two scalessingle particlesaggregates of billions of particlesThere are multiple dimensions involved to keep straightThe math is complicated for non-engineers, and most of it is vector-basedIts easy to convince yourself you get it

Organization of DiscussionReview of Relevant Basic Physical PrinciplesMagnetismResonanceImage CreationT1 and T2Anatomy of an MR ScannerFuture Topics

Current is the Flow of Charged ParticlesAbbreviated Isodium ions123456

Every Current Creates a Magnetic FieldThe current and the magnetic field have to be perpendicular at all points. ThereforeStraight currents magnetic field loops surrounding themCurrent loops have straight magnetic fields going through themIB

Thermal Energy is Stored as Molecular MotionAt 0 K, all molecular motion ceases.As heat is added, the molecules move around, absorbing the heat in various ways:The second law of thermodynamics requires that all available mechanisms of thermal energy storage be usedFor simpler molecules, the available options are fewer

Protons are Spinning ChargesProtons have charge and are constantly spinningThe charge can be thought of as distributedThis is a magnetic moment

PrecessionPrecession refers to a change in the direction of the axis of a rotating object.torque-freetorque-inducedIt occurs when spinning objects experience a moment outside the plane of rotation

Electromagnetic Radiation is Just LightIts all made up of photonsIt all moves at the same speedThe difference between light we see (visible electromagnetic radiation) and any other type is the frequency at which the photon oscillates

Light Absorption by e- is QuantizedRecall valence shell electron theory from high school chemistryYou can get an electron to jump up to the next level by supplying energy at the exact wavelength required

Absorption Spectra Show Quantizationvisible lightThe parts that are missing were absorbed by the electrons

Emission Spectra Show QuantizationThe requirement for the precise amount of energy needed is quantization

Exponential Change is Convenient to StudyExponential change occurs when the rate of change of a quantity is proportional to the quantity itselfk can bePositive (exponential growth)Negative (exponential decay)We should love exponential change because it is relatively easy to studyIf you plot the quantity against time, k can be readily calculated with a few data points, and there is only one degree of freedomYou often already know two boundary conditionsq at time zeroq at time infinityYou only need one more!

Recap of Review MaterialCurrent is the Flow of Charged ParticlesEvery Current Creates a Magnetic FieldPerpendicular at all points to the currentThermal Energy is Stored as Molecular MotionProtons are Spinning ChargesProtons have a current loopProtons have a magnetic moment along the axis of rotationPrecessionOccurs when a spinning object experiences a moment out of the plane of rotationElectromagnetic Radiation is Just LightLight Absorption by particles is QuantizedAbsorption Spectra Show QuantizationEmission Spectra Show QuantizationExponential Change is Convenient to StudyNow we need to scale up to the bulk / macroscopic scale

Magnetic Resonance ImagingAt rest, all protons spin (and translate) because of the presence of thermal energy. The proton of a single hydrogen atom in the vacuum of space will spin for this reason.Entropy dictates that the spins within a group of protons are not organizedGoing from a single proton to a group of protons will yield all possible orientations (which sum to zero)Net Magnetic Field (M)

MRI: Application of a Magnetic FieldNow lets return to what happens with a proton when you apply an external magnetic fieldThere are two effects hereAlignment of spins with the external magnetic fieldPrecession, because the moment experienced by the proton is out of the plane of rotationThey are related, but different

MRI: Determinants of Spin RateThe speed of precession of a spinning body in a field is called the Larmor frequency, and we know a few things about itZero when B0 = 0Increases as magnetic field increasesWe could do an experiment and plot the relationship between B0 and precessional frequencyFor protons wL is approximately 42 MHz/TeslaB0

MRI: Scaling up to PopulationsPopulation of ProtonsSingle ProtonNo External FieldExternal Field = B0

SimplificationWe cant stop a proton from spinning, so lets simplify our diagram

MRI: Scaling up to PopulationsIn a big population of protons, more line up with the field than against, but there is a distribution of bothThermodynamics will tell us what the ratio is

Difference in Energy LevelsNet = 0This is 500 ppm (small!)MRI works because we have Avagadros numbers of protons

Weve Seen This BeforeThe excitation of proton spins is a quantized systemSo what is the frequency (v) needed to cause this excitation?

MRI: Combining Precession and QuantaGyromagnetic ratio = gamma = 42.58 MHz/TThe excitation frequency (for an individual proton) is going to depend on the magnetic field (the individual proton) experiencesThis is the Resonance frequencyMRISlope = gyromagnetic ratio

Understanding Resonance by AnalogyThe proton is like a tetherballIf you hit the tetherball at random intervals, its net vector is randomIf you hit the tetherball at exactly the right interval (equal to its period of rotation around the pole), each hit is additive and makes the ball go higher and higherThink about the different scales: single tetherball vs. billions of tetherballs

MRI: Identifying the EMF of Interest

SimplificationWeve used B0 enough that we know what it is: a homogeneous external magnetic fieldwill now be

Recipe for an NMR ExperimentPut sample in big magnetic fieldTransmit radio waves into sample (saturate the protons)Turn off radio wave transmitterReceive radio waves re-transmitted by subject (relaxation)Emission experimentWho cares? (what are the applications of spectra?)Immediately recognized that it could tell us about the local magnetic environment of hydrogen protonsYou get a spectrum because each hydrogen atom has a different local environment

Optimizing the NMR ExperimentParallelizing the process: shooting the whole spectrum at onceWe would like toTake a complex EMF wave(Group of photons with different Frequencies)Break it up into component frequenciesUse components to predict identityWe dont have a prism for radio wavesEnter the Fourier TransformPut in amplitude-time dataGet out amplitude-frequency data

Optimizing the NMR ExperimentA prism is an example of a fourier transformSo is the cochlea

Lauterburs InsightConventional NMR used spectra to make inferences about local magnetic perturbations in a uniform magnetic fieldIf the magnetic field was instead made to vary with position, then the resonant frequency spectrum would instead tell you about location in a uniform population of protonsGreat idea

MRI: Slice SelectionThe Larmor frequency is dependent on B0, the external magnetic field

By varying B0 over the subject, we can choose a frequency that will only excite a particular part of the subjectDifferent values of B0 will tune the photons to require different energies (w)If we only give one frequency of EMF, only one slice will be excited

MRI: Slice SelectionNow we have an excited plane of protonsWe reset B0 so that the field is uniformWe wait for the energy to be re-transmitted as a radio signalThe results are not very excitingThe whole signal is at the frequency we put inIt starts loud, and exponentially decaysZXY

Questions?

MRI: What We Have So FarWe have selectively charged a slab of brain with radiofrequency EMFWe turned off the magnet, and got signals back from all over the slabWhat we need is to know where each signal came fromRight now, all we can see is the net magnetization vector, but we can see it in several directions: x, y, zTherefore we can measure signal averaged over the whole sliceThats not a very interesting picture

A Trick Necessary to ContinueThe energy absorbed by an excited particle is determined by the field it is acting against in order to become excitedElectrons: attraction with nucleusSpinning top: gravityProtons in NMR: magnetic fieldNote that the last one is very easily manipulated

Changing the Rules in MidstreamBy changing the strength of the magnetic field (re-writing the rules of attraction in mid-stream), the protons can be manipulated on the flyIncrease the field to increase precession speedIncrease the field to increase their resonance frequencyConsider increasing gravity on a spinning top

MRI: Getting Coordinates in Plane (X)We need to revisit Lauterburs idea with the trick we just learned in order to use frequency to map location Once we get the spins saturated, we can vary B0 over xXB0 still points in the same direction, but make it stronger on one side of the patient than the otherThis is changing the rules in midstream: the protons are already saturated / excited, and now were altering the field on themWe know from our simple experiments that the protons exposed to the weaker field will precess less quickly

MRI: Getting Coordinates in Plane (X)Protons will spontaneously revert to the lower energy stateProtons at x=0 will be relaxing in a strong field, and give off high-frequency EMFProtons at x=1 will be relaxing in a weak field, and give off low-frequency EMFThen we can use the FT to separate the frequencies and identify the signal strength at each x-coordinate

MRI: Getting Coordinates in Plane (X)All frequencies in the output signal come at once, and is a plot of signal strength per unit timeNow, the frequency of the emission tells us the aggregate signal for each x-column

MRI: Getting Coordinates in Plane (Y)Tying the x coordinate to the frequency is called frequency encodingIt would be nice if we could just do the same thing with the Y direction, but we cantSince magnetic field vectors add, putting a second gradient in the y direction is indistinguishable from doing a single gradient at an angleNo new information is captured, and the Fourier Transform cant distinguish them unless the frequencies are unique

A Transient Gradient Changes the PhaseIf we change the field strength on a magnet that is already precessing, we can make its precession change speedIf we increase it again, it speeds back upB0This is what we mean when we say that two protons are out of phase

MRI: Getting Coordinates in Plane (Y)Instead, we will introduce a gradient in the y direction temporarilyThis slows changes the speed for a moment, but then the frequency returns to what it had beenHolding back some spins in this way creates a phase shift in the spins, which we can exploit later

MRI: Getting Coordinates in Plane (Y)This technique gives us an extra degree of freedomThe Fourier transform does not know how to process phase information, but it does preserve itWe then do a second Fourier transform in order to obtain the information we wantLets use an example to understand the 2D Fourier Transform

The 2-D Fourier TransformPlot A-t

The 2-D Fourier TransformPlot A-t

MRI: What we End Up WithWe now have a plot of signal as a function of time at each individual voxelWe know that the signal will decay unequally in different tissues, so we get signal-vs-position plots at multiple time points, calculate the rate of decay, and give that pixel a shade near white if the decay constant is large, and a shade near black if the decay constant is shortIn actuality, the phase-encoding step is done first, because the magnetic gradient it requires is transient. The frequency-encoding step is done last, because it needs to be active when the protons relax (the readout gradient)

Energy Accounting 101It is possible to exhaustively inventory where all of the energy of the RF pulse goes (1st law of thermodynamics)heatSpin alignment (work)Spin alignment (work)the universe (as seen by the physicist)protons (spins)everything else (the lattice)

MRI: Details of the ExcitationWe can choose how much to excite the protons in the planeA big EMF pulse can knock all the spins into the x-y planeAn even bigger EMF pulse can knock all the spins onto the z axis90 Pulse180 PulseOr anything in between

Measuring the Net Magnetization VectorThe net magnetization vector can be measured directly by using orthogonal radio antennas.ZXYThis will allow the vector within each voxel (which weve just learned how to identify) to be measured in x and y

MRI: Details of the DecayIf we start with a 180 pulse, the decay is exponential and goes from -1 to 1 (two data points are known)

MRI: Details of the DecayIf we perform any pulse except 180 pulse, then all protons will get knocked into x-y plane, and precess thereInitially, they will all be in-phase, because they are all knocked away from Z-axis at the same time in the same directionWith time, they will de-phase due to two factorsInteractions with neighboring protons (random effects)Imperfect homogeneity of B0 (nonrandom effects)This is spin-spin relaxation

MRI: Details of the DecayDe-phasing is when the signal is lost because it averages itself out and becomes noiseHere is a visual example of dephasingThere are ways to reverse this process, and any sequence which does so will be called an echo sequenceOnce the signal is completely dephased, we have randomnessEven so, a non-zero net vector in the z-direction may still exist

Revisiting Energy AccountingheatSpin alignment (work)Spin alignment (work)protons (spins)everything else (the lattice)Radiofrequency inRadiofrequency outSpin-Spin relaxationT1 relaxationT2 relaxation

MRI: Details of the DecayWe have seen two types of recovery toward equilibriumMz recovery starts out low and recovers exponentially back toward one (because z equilbrium is to line back up with B0)It happens with all pulse strengthsIt reflects energy loss to surrounding moleculesRandom interactions (changes moment to moment, noise)Nonrandom interactions (is static for a given molecule, bias)Mxy recovery starts out maximal and exponentially decays toward zeroIt happens with all pulse strengths except 180It reflects energy loss back to the universethe rate constant for this process is called T1the rate constant for this process is called T2

Energy Accounting 501heatSpin alignment (work)random effectsRadiofrequency inRadiofrequency outstatic effectsT1 relaxationT2 relaxationT2*

T2 Effectsrandom effectsstatic effectsT2 relaxationT2*T2 relaxationEchoBecause the static interactions are static, they can be reversed by the 180 degree pulsation

Another Analogy

Anatomy of a ScannerFour main hardware componentsMain magnetRF systemMagnetic field gradient systemComputer system.

What Weve CoveredReviewed the most fundamental rules that govern MR phenomenaIdentified how to excite selected photons using supermagnets and radio wavesIdentified how to manipulate the excited photons in order to encode positional informationFrequency encodingPhase encodingBecome familiar with 2D Fourier transforms

Future Topics to ExploreMechanisms of contrastProton DensityT1, T2, T2* in more detailAnisotropyFlowDiffusionTensor mappingIV ContrastPulse Sequence Diagram InterpretationSequence selection, costs and benefits

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