Principles of MRI Physics and Engineering

Principles of MRI Physics and Engineering Allen W. Song Brain Imaging and Analysis Center Duke University

Magnetic resonance imaging, commonly known as MRI, can non-invasively provide high resolution anatomical images of human structures, such as brain, heart and other soft tissues. It is used routinely in clinical diagnosis. Functional MRI advances from the traditional static scans to image dynamic time course of the brain signal during specific tasks. It is widely used now in studying the working mechanism of the human brain. Clinical application is mainly seen in presurgical planning.

MRI  Cool (and Useful) Pictures axial coronal sagittal 2D slices extracted from a 3D image [resolution about 111 mm]

Synopsis of MRI 1) Put subject in big magnetic field 2) Transmit radio waves into subject [2~10 ms] 3) Turn off radio wave transmitter 4) Receive radio waves re-transmitted by subject • Manipulate re-transmission with magnetic fields during this readout interval [10-100 ms: MRI is not a snapshot] 5) Store measured radio wave data vs. time • Now go back to 2) to get some more data 6) Process raw data to reconstruct images 7) Allow subject to leave scanner

Lecture Components I) Magnetic fields and magnetization, fundamental ideas about NMR signal II) How to form an image, introduction to k-space III) MRI contrast mechanisms, various imaging techniques

Part I Magnetic Fields And Magnetization, Fundamental of NMR Signal

Magnetic Fields, Magnetization, NMR Signal Generation

Shimming gradient rf coil rf coil main magnet main magnet Transmit Receive Control Computer

Things needed for a typical MRI scanner • Strong magnetic field, usually from superconducting magnets. • RadioFrequency coils and sub-system. • Gradient coils and sub-system. • Shimming coils and sub-system. • Computer(s) that coordinate all sub-systems.

Magnetic and Electromagnetic Fields • Magnetic fields generate the substance we “see”: magnetization of the H protons in H2O • Magnetic fields also let us manipulate magnetization so that we can make a map [or image] of its distribution inside the body’s tissue • Static magnetic fields change slowly (< 0.1 ppm / hr): main field; static inhomogeneities • RF fields are electromagnetic fields that oscillate at Radio Frequencies (tens of millions of times per second) • transmitted radio waves into subject • received signals from subject • Gradient magnetic fields change quickly (switching up to thousands of times per second)

Vectors and Fields • Magnetic field B and magnetization M are vectors: • Quantities with direction as well as size • Drawn as arrows .................................... • Another example: velocity is a vector (speed is its size) • Vector operations: dot product AB cosq cross product AB sinq • Magnetic field exerts torque to line magnets up in a given direction • direction of alignment is direction of B • torque proportional to size of B [units=Tesla, Gauss=10–4 T]

[Main magnet and some of its lines of force] [Little magnets lining up with external lines of force] Main Magnet Field Bo • Purpose is to align H protons in H2O (little magnets)

Common nuclei with NMR property • Criteria: • Must have ODD number of protons or ODD number of neutrons. • Reason? • It is impossible to arrange these nuclei so that a zero net angular • momentum is achieved. Thus, these nuclei will display a magnetic • moment and angular momentum necessary for NMR. • Examples: • 1H, 13C, 19F, 23N, and 31P with gyromagnetic ratio of 42.58, 10.71, • 40.08, 11.27 and 17.25 MHz/T. • Since hydrogen protons are the most abundant in human body, we use • 1H MRI most of the time.

A Single Proton m There is electric charge on the surface of the proton, thus creating a small current loop and generating magnetic moment m. The proton also has mass which generates an angular momentum J when it is spinning. J + + + Thus proton “magnet” differs from the magnetic bar in that it also possesses angular momentum caused by spinning.

Magnetic Moment B B I L m= tmax / B = IA W L F t = mB = m B sinq F = IBL t = IBLW = IBA Force Torque

J m r v Angular Momentum J = mw=mvr

m = gJ where g is the gyromagnetic ratio, and it is a constant for a given nucleus

Similarity between a spinning proton and a spinning magnetic bar N m J + + + + + + + S

Protons in Free Space What happens if they are in a magnetic field ?

Magnetic Bar in a Magnetic Field N Bo N S S Static magnetic bar Spinning magnetic bar

Protons in a Magnetic Field Bo Parallel (low energy) Anti-Parallel (high energy) Spinning protons in a magnetic field will assume two states. If the temperature is 0o K, all spins will occupy the lower energy state.

Net Magnetization Bo M

Basic Quantum Mechanics Theory of MR • Small B0 produces small net magnetization M • Thermal motionstry to randomize alignment of proton magnets • Larger B0 produces larger net magnetization M, lined up with B0 • At room temperature, the population ratio is roughly 100,000 to 100,006 per Tesla of B0

Basic Quantum Mechanics Theory of MR The Energy Difference Between the Two States D E = hn • D E = 2 mz Bo • n = g/2p Bo known as larmor frequency Eqn. [3.9] - [3.16] g/2p = 42.57 MHz / Tesla for proton

Basic Quantum Mechanics Theory of MR Knowing the energy difference allows us to use electromagnetic waves with appropriate energy level to irradiate the spin system so that some spins at lower energy level can absorb right amount of energy to “flip” to higher energy level.

Basic Quantum Mechanics Theory of MR Spin System Before Irradiation Bo Lower Energy Higher Energy

Basic Quantum Mechanics Theory of MR The Effect of Irradiation to the Spin System Lower Higher

Basic Quantum Mechanics Theory of MR Spin System After Irradiation

Classical Description of Magnetization: Precession • Magnetic field causesMto rotate (or precess) about the direction of Bo at a frequency proportional to the size of Bo — 42 million times per second (42 MHz), per Tesla of Bo.To visualize the rotation, the magnetization M is tipped away from the Bo direction. Bo • If M is not parallel to B, then • it precesses clockwise around • the direction of B. • However, “normal” (fully relaxed)situation has M parallel to B, which means there won’t be any • precession • N.B.: part of M parallel to Bo (Mz) does not precess

A Mechanical Analogy • A gyroscope in the Earth’s gravitational field is like magnetization in an externally applied magnetic field

Derivation of precession frequency • = m× Bo • = dJ / dt J = m/g dm/dt = g (m× Bo) m(t) = (mxocos gBot + myosin gBot) x + (myocos gBot - mxosin gBot) y + mzoz This says that the precession frequency is the SAME as the larmor frequency

How do we detect magnetization? We need to perturb it. Analogy: you have to lift the object to see how much it weighs.

B0+B1 B1 How to perturb M so it is not Parallel to B? • A way that does not work: • Turn on a second big magnetic field B1perpendicular to main B0 (for a few seconds) • Then turn B1 off; M is now not parallel to magnetic field B0 • This fails because cannot turn huge (Tesla) magnetic fields on and off quickly • But it contains the kernel of the necessary idea: A magnetic field B1 perpendicular to B0 B0 • M would drift over to be aligned with sum of B0and B1

Nutation Time = 2–4 ms RF Coil: Transmitting B1 Field • Left alone, M will align itself with Bo in about 2–3 s • So don’t leave it alone: apply (transmit) a magnetic field B1 that fluctuates at the precession frequency and points perpendicular to B0 (how do we achieve this? – by making a coil) • The effect of the tiny B1is to cause M to spiral away • from the direction of the • static B field • B110–4 Tesla • This is called resonance • If B1 frequency is not close to resonance, B1has no effect

Another Mechanical Analogy: A Swingset • Person sitting on swing at rest is “aligned” with externally imposed force field (gravity) • To get the person up high, you could simply supply enough force to overcome gravity and lift him (and the swing) up • Analogous to forcing M over by turning on a huge static B1 • The other way is to push back and forth with a tiny force, synchronously with the natural oscillations of the swing • Analogous to using the tiny RF B1 to slowly flip M over g

Rotating Frame (compared to Laboratory Frame) wo Laboratory Frame Rotating Frame

Spin Excitation using Rotating Frames Reference M q = gB1t B1 M q Notice that the nutation becomes simple rotation in the rotating frame

What if the RF field is not synchronized? Using the swingset example: now the driving force is no longer synchronized with the swing frequency, thus the efficiency of driving the swing is less. In a real spin system, there is a term called “effective B1 field”, given by B1eff = B1 + Dw/g where Dw = wo – we Dw/g B1eff B1

RF Coil: Signal Receiver • When excitation RF is turned off, M is left pointed off at some angle toB0[flip angle] • Precessing part of M [Mxy] is like having a magnet rotating around at very high speed (at RF frequencies) • Will generate an oscillating voltage in a coil of wires placed around the subject — this is magnetic induction

RF Coil: Signal Receiver • This voltage is the RF signal whose measurements form the raw data for MRI • At each instant in time, can measure one voltage V(t), which is proportional to the sum of all transverse Mxy inside the coil • Must find a way to separate signals from different regions

Various RF Coils • Separated by function: Transmit / receive coil (most common) Transmit only coil (can only excite the system) Receive only coil (can only receive MR signal) • Separated by geometry Volume coil (low sensitivity but uniform coverage) Surface coil (High sensitivity but limited coverage)

Relaxation Characteristics About the NMR Signal

Relaxation: Nothing Lasts Forever • In absence of external B1, M will go back to being aligned with static field B0— this is called relaxation • Part of M perpendicular to B0shrinks [Mxy] • This part of M is called transverse magnetization • It provides the detectable RF signal • Part of Mparallel to B0 grows back [Mz] • This part of M is called longitudinal magnetization • Not directly detectable, but is converted into transverse magnetization by externally applied B1

Relaxation Times and Rates • Times: ‘T’ in exponential laws like e–t/T • Rates: R = 1/T [so have relaxation like e–Rt] • T1: Relaxation of Mback to alignment with B0 • Usually 500-1000 ms in the brain [lengthens with bigger B0] • T2: Intrinsic decay of the transverse magnetization over a microscopic region ( 5-10 micron size) • Usually 50-100 ms in the brain [shortens with bigger B0] • T2*: Overall decay of the observable RF signal over a macroscopic region (millimeter size) • Usually about half of T2 in the brain[i.e., faster relaxation]

T2* Relaxation S = So * e –t/T2*

Material Induced Inhomogeneities Will Affect T2* • Adding a nonuniform object (like a person) to B0 will make the total magnetic field B nonuniform • This is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external field • Diamagnetic materials produce negative B fields • Paramagnetic materials produce positive B fields • Size about 10–7B0 = 1–10 Hz change in precession f • Which makes the precession frequency nonuniform, affecting the image intensity and quality For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimming • Nonuniformities in B bigger than voxel size affect whole image • Nonuniformities in B smaller than voxel size affect voxel “brightness”

Frequency and Phase • RF signals from different regions that are at different frequencies will get out of phase and thus tend to cancel out • Phase = the tin cos(t) [frequency f =/2]

Sum of 500 Cosines with Random Frequencies Starts off large when all phases are about equal Decays away as different components get different phases High frequency gray curve is at the average frequency

T2* relaxation (decay) and NMR Signal • Random frequency differences inside intricate tissue environment cause RF signals (from Mxy) to dephase • Measurement = sum of RF signals from many places • Measured signal decays away over time [T2*40 ms at 1.5 T] • At a microscopic level (microns), Mxy signals still exist; they just add up to zero when observed from outside (at the RF coil) • Contents of tissue can affect local magnetic field • Signal decay rate depends on tissue structure and material • Measured signal strength will depend on tissue details • If tissue contents change, NMR signal will change • e.g., oxygen level in blood affects signal strength

Hahn Spin Echo: Retrieving Lost Signal • Problem: Mxy rotates at different rates in different spots • Solution: take all the Mxy’s that are ahead and make them get behind (in phase) the slow ones • After a while, fast ones catch up to slow ones  re-phased! Fast & slow runners Magically “beam” runners across track Let them run the same time as before

Principles of MRI Physics and Engineering