Principles of MRI Physics and Engineering

Principles of MRI Principles of MRI Physics and EngineeringPhysics and Engineering

Principles of MRI Principles of MRI Physics and EngineeringPhysics and Engineering

Allen W. SongAllen W. Song

Brain Imaging and Analysis CenterBrain Imaging and Analysis Center

Duke UniversityDuke 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 inclinical 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 studyingthe working mechanism of the human brain. Clinicalapplication is mainly seen in presurgical planning.

MRI Cool (and Useful) Pictures

2D slices extracted from a 3D image2D slices extracted from a 3D image[resolution about 1[resolution about 1111 mm]1 mm]

axialaxial coronalcoronal sagittalsagittal

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 make an image,

introduction to k-space

III) MRI contrast mechanisms,

various imaging techniques

Part IPart I

Magnetic FieldsMagnetic FieldsAnd Magnetization, And Magnetization,

Fundamental of NMR SignalFundamental of NMR Signal

Magnetic Fields, Magnetization, Magnetic Fields, Magnetization, NMR Signal GenerationNMR Signal Generation

Transmit Receive

rfcoil

rfcoil

mainmagnet

mainmagnet

gradientShimming

ControlComputer

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 Gradient magnetic fields change quickly (switching up to

thousands of times per second): 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

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)

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 Field Bo

Purpose is to align H protons in H2O (little magnets)

[Little magnets lining up with external lines of force]

[Main magnet and some of its lines of force]

Common nuclei with NMR property•Criteria:Criteria: Must have ODD number of protons or ODD number of neutrons.Must have ODD number of protons or ODD number of neutrons.

Reason?Reason? It is impossible to arrange these nuclei so that a zero net angularIt is impossible to arrange these nuclei so that a zero net angular momentum is achieved. Thus, these nuclei will display a magneticmomentum is achieved. Thus, these nuclei will display a magnetic moment and angular momentum necessary for NMR.moment and angular momentum necessary for NMR.

Examples:Examples: 11H, H, 1313C, C, 1919F, F, 2323N, and N, and 3131P with gyromagnetic ratio of 42.58, 10.71, P with gyromagnetic ratio of 42.58, 10.71, 40.08, 11.27 and 17.25 MHz/T. 40.08, 11.27 and 17.25 MHz/T.

Since hydrogen protons are the most abundant in human body, we useSince hydrogen protons are the most abundant in human body, we use11H MRI most of the time.H MRI most of the time.

A Single Proton

++++

++

There is electric charge There is electric charge on the surface of the on the surface of the proton, thus creating a proton, thus creating a small current loop and small current loop and generating magnetic generating magnetic moment moment ..

The proton also has The proton also has mass which mass which generates angenerates anangular momentumangular momentumJJ when it is when it is spinning.spinning.

JJ

Thus proton “magnet” differs from the magnetic bar in that itThus proton “magnet” differs from the magnetic bar in that italso possesses angular momentum caused by spinning.also possesses angular momentum caused by spinning.

= = J where J where is the gyromagnetic ratio is the gyromagnetic ratio

Similarity between a spinning proton and a spinning magnetic bar

N

S

+ +

+ + +

+

+

m

Protons in Free Space

What happens if they are in a magnetic field ?

Magnetic Bar in a Magnetic Field

Bo N

S

N

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.Spinning protons in a magnetic field will assume two states.If the temperature is 0If the temperature is 0o K, all spins will occupy the lower energy state. K, all spins will occupy the lower energy state.

Net Magnetization

BoM

T

BcM o

Small B0 produces small net magnetization M

Thermal motions try 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 MRBasic Quantum Mechanics Theory of MR

The Energy Difference Between the Two States

Eh where Bo / 2known as larmor frequency

= 42.57 MHz / Tesla= 42.57 MHz / Tesla


Knowing the energy difference allows us to useelectromagnetic waves with appropriate energy level to irradiate the spin system so that some spins at lower energy level can absorb right amount ofenergy to “flip” to higher energy level.


Spin System Before Irradiation

BoLower Energy

Higher Energy


The Effect of Irradiation to the Spin System

Lower

Higher


Spin System After Irradiation


If M is not parallel to B, thenit precesses clockwise aroundthe direction of B.

However, “normal” (fully relaxed) situation has M parallel to B, which means there won’t be anyprecession

Precession of Magnetization M Magnetic field causes M to 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.

N.B.: part of M parallel to Bo (Mz) does not precess

BoBo

Classical Mechanics Theory of MRClassical Mechanics Theory of MR

A Mechanical Analogy A gyroscope in the Earth’s gravitational field is like

magnetization in an externally applied magnetic field


How to Make M not be Parallel to B? A way that does not work:

Turn on a second big magnetic field B1 perpendicular 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

B1

B0+B1

M would drift over to be aligned with sum of B0 and B1


The effect of the tiny B1 is to cause M to spiral away from the direction of the static B field B110–4 Tesla This is called resonance If B1 frequency is not close to resonance, B1 has no effect

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)

Time = 2–4 ms


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

gg


Rotating Frame (compared to Laboratory Frame)

Rotating FrameRotating Frame Laboratory FrameLaboratory Frame


Spin Excitation using Rotating Frames Reference

MM

BB11

Notice the disappearance of the Bo term in rotating frameNotice the disappearance of the Bo term in rotating frame

MM

= = BB11


What if the RF field is not synchronized?

Using the swingset example: now the driving force is no longer Using the swingset example: now the driving force is no longer synchronized with the swing frequency, thus the efficiency of synchronized with the swing frequency, thus the efficiency of driving the swing is less.driving the swing is less.

In a real spin system, there is a term called “effective B1 In a real spin system, there is a term called “effective B1 field”,field”,given by given by

BB1eff1eff = = BB11 + + //where where

= = oo – – e e

BB11

BB1eff1eff//


RF Coil: Signal Receiver

When excitation RF is turned off, M is left pointed off at some angle to B0 [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)

Gradient Coils: Spatially Nonuniform B:

Extra static magnetic fields (in addition to B0) that vary their intensity in a linear way across the subject

Precession frequency of M varies across subject

x-axis

f60 KHz

Left = –7 cm Right = +7 cm

Gx = 1 Gauss/cm = 10 mTesla/m = strength of gradient field

Centerfrequency

[63 MHz at 1.5 T]

A 3-D gradient field (dB/dx, dB/dy, dB/dz) would A 3-D gradient field (dB/dx, dB/dy, dB/dz) would allow a unique correspondence between the spatial allow a unique correspondence between the spatial location and the magnetic field. Using this information,location and the magnetic field. Using this information,we will be able to generate maps that contain spatial we will be able to generate maps that contain spatial information – images.information – images.

Gradient Coils

Gradient coils generate varying magnetic field so that spins at different location precess at frequencies uniqueto their location, allowing us to reconstruct 2D or 3Dimages.

X gradient Y gradient Z gradient

x

y

z

x

z z

x

y y

Spatial Encoding – along Spatial Encoding – along xx

xx

Spatial Encoding of the MR Signal

0.8

w/o encoding w/ encoding

ConstantMagnetic Field

VaryingMagnetic Field

Spatial Encoding of the MR Signal

Fourier Transform

Spatial Encoding – along Spatial Encoding – along yy

yy

Relaxation CharacteristicsRelaxation CharacteristicsAbout the NMR SignalAbout 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 B0 shrinks [Mxy]

This part of M is called transverse magnetization

It provides the detectable RF signal

Part of M parallel 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 M back 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 S = So * e –t/T2*–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 10–7B0 = 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 t in cos(t) [frequency f = /2]

Sum of 500 Cosines with Random Frequencies

Starts off large when all phases are about equal

High frequency gray curve is at the average frequency

Decays away as different components get different phases

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 & slowFast & slowrunnersrunners

Magically “beam”Magically “beam”runners across trackrunners across track

Let them run theLet them run thesame time as beforesame time as before

The “magic” trick: Flip of the magnetization M

Apply a second B1 pulse to produce a flip angle of 180 about the y-axis (say)

Time between first and second B1 pulses is called TE/2

“Echo” occurs at time TE

Spin EchoSpin Echo::

ExciteExcite

PrecessPrecess & dephase& dephase

180180 flip flip

PrecessPrecess & rephase& rephase

T2 Relaxation (Decay)

Spin echo doesn’t work forever (TE can’t be too big) Main reason: water molecules diffuse around randomly

• About 5-10 microns during 10-100 ms readout window

They “see” different magnetic fields and so their precession frequency changes from fast to slow to fast to ................

This process cannot be reversed by the inversion RF pulse• Time scale for irreversible decay of Mxy is called T2

S = So * e-t/T2

T1 Relaxation

Longitudinal relaxation of Mz back to “normal” (T1)

Caused by internal RF magnetic fields in matter

Thermal agitation of H2O molecules

Can be enhanced by magnetic impurities in tissue

S = So (1-et/T1)

Proton Density Weighted ImageProton Density Weighted Image

T1 Weighted ImageT1 Weighted Image

T2 Weighted ImageT2 Weighted Image

Factors Influencing Relaxation Rates

• Magnetic impuritiesMagnetic impurities * In general, it will shorten the relaxation time such as T2*,* In general, it will shorten the relaxation time such as T2*, T2 and T1T2 and T1

• Local physiological and chemical environment changesLocal physiological and chemical environment changes * For example, bounded water molecules will have shorter* For example, bounded water molecules will have shorter T2 then free water moleculesT2 then free water molecules

• Strength of the magnetic fieldsStrength of the magnetic fields * Usually stronger field prolongs T1, however, shortens T2* * Usually stronger field prolongs T1, however, shortens T2* and T2 due to increased susceptibility-induced magnetic and T2 due to increased susceptibility-induced magnetic inhomogeneitiesinhomogeneities

Contrast Agents that Affects Relaxation Rate

Drugs containing certain impurities can alter T1, T2, and T2* — contrast agents (e.g., CuSO4, Gd-DTPA)

Principles of MRI Physics and Engineering

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