Basic Physical Principlesof MRIJames Voyvodic, Ph.D.Brain Imaging and Analysis Center

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 subject0 5) Convert measured RF data to image

Many factors contribute to MR imagingQuantum properties of nuclear spinsRadio frequency (RF) excitation propertiesTissue relaxation propertiesMagnetic field strength and gradientsTiming of gradients, RF pulses, and signal detection

What kinds of nuclei can be used for NMR?Nucleus needs to have 2 properties:SpinchargeNuclei are made of protons and neutronsBoth have spin Protons have chargePairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin Good MR nuclei are 1H, 13C, 19F, 23Na, 31P

Hydrogen atoms are best for MRIBiological tissues are predominantly 12C, 16O, 1H, and 14NHydrogen atom is the only major species that is MR sensitiveHydrogen is the most abundant atom in the bodyThe majority of hydrogen is in water (H2O)Essentially all MRI is hydrogen (proton) imaging

Nuclear Magnetic Resonance Visible Nuclei

1.psd

A Single Proton+++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 anangular momentumJ when it is spinning.JmThus proton magnet differs from the magnetic bar in that italso possesses angular momentum caused by spinning.

Magnetic MomentIBFLF = IBLBLWt = IBLW = IBA m = tmax / B = IA t = m B = m B sinqForceTorque

Angular MomentumJ = mw=mvr

m = g J

g is the gyromagnetic ratiog is a constant for a given nucleusThe magnetic moment and angular momentum are vectors lying along the spin axis

How do protons interact with a magnetic field?Moving (spinning) charged particle generates its own little magnetic fieldSuch particles will tend to line up with external magnetic field lines (think of iron filings around a magnet)Spinning particles with mass have angular momentumAngular momentum resists attempts to change the spin orientation (think of a gyroscope)

Ref: www.simplyphysics.com

2.psd

3.psd

The energy difference between the two alignment states depends on the nucleusD E = 2 mz Bo

D E = h n

n = g/2p Bo

known as Larmor frequency g/2p = 42.57 MHz / Tesla for proton

Resonance frequencies of common nucleiNote: Resonance at 1.5T = Larmor frequency X 1.5

4.psd

MRIX-Ray, CTElectromagnetic Radiation Energy

5.psd

MRI uses a combination of Magnetic and Electromagnetic FieldsNMR measures the net magnetization of atomic nuclei in the presence of magnetic fieldsMagnetization can be manipulated by changing the magnetic field environment (static, gradient, and RF fields)Static magnetic fields dont change (< 0.1 ppm / hr):

The main field is static and (nearly) homogeneousRF (radio frequency) fields are electromagnetic fields that oscillate at radio frequencies (tens of millions of times per second)Gradient magnetic fields change gradually over space and can change quickly over time (thousands of times per second)

*

Radio Frequency Fields RF electromagnetic fields are used to manipulate the magnetization of specific types of atoms This is because some atomic nuclei are sensitive to magnetic fields and their magnetic properties are tuned to particular RF frequencies Externally applied RF waves can be transmitted into a subject to perturb those nuclei Perturbed nuclei will generate RF signals at the same frequency these can be detected coming out of the subject

The Effect of Irradiation to the Spin SystemLowerHigher

Basic Quantum Mechanics Theory of MR

Spin System After Irradiation

Basic Quantum Mechanics Theory of MR

Net magnetization is the macroscopic measure of many spins

Bo

M

Net magnetizationSmall B0 produces small net magnetization MLarger B0 produces larger net magnetization M, lined up with B0Thermal motions try to randomize alignment of proton magnets At room temperature, the population ratio of anti-parallel versus parallel protons is roughly 100,000 to 100,006 per Tesla of B0

Quantum vs Classical PhysicsOne can consider the quantum mechanical properties of individual nuclei, but to consider the bulk properties of a whole object it is more useful to use classical physics to consider net magnetization effects.

To measure magnetization we must perturb itWe can only measure magnetization perpendicular to the B0 field Need to apply energy to tip protons out of alignmentAmount of energy needed depends on nucleus and applied field strength (Larmor frequency)The amount of energy added (duration of the RF pulse at the resonant frequency) determines how far the net magnetization will be tipped away from the B0 axis

A 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 swingAnalogous to using a tiny RF B1 over a period of time to slowly flip M over

g

If M is not parallel to B, then it precesses clockwise around

the direction of B. Normal (fully relaxed) situation has M parallel to B, and therefore does not precess PrecessionThis is like a gyroscope

Derivation of precession frequencyThis says that the precession frequency is the SAME as the larmor 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

7.psd

8.psd

Recording the MR signalNeed a receive coil tuned to the same RF frequency as the exciter coil.Measure free induction decay of net magnetizationSignal oscillates at resonance frequency as net magnetization vector precesses in spaceSignal amplitude decays as net magnetization gradually realigns with the magnetic fieldSignal also decays as precessing spins lose coherence, thus reducing net magnetization

NMR signal decays in timeT1 relaxation Flipped nuclei realign with the magnetic fieldT2 relaxation Flipped nuclei start off all spinning together, but quickly become incoherent (out of phase)T2* relaxation Disturbances in magnetic field (magnetic susceptibility) increase the rate of spin coherence T2 relaxationThe total NMR signal is a combination of the total number of nuclei (proton density), reduced by the T1, T2, and T2* relaxation components

9.psd

10.psd

T2* decaySpin coherence is also sensitive to the fact that the magnetic field is not completely uniformInhomogeneities in the field cause some protons to spin at slightly different frequencies so they lose coherence fasterFactors that change local magnetic field (susceptibility) can change T2* decay

Different tissues have different relaxation times. These relaxation time differences can be used to generate image contrast.T1 - Gray/White matterT2 - Tissue/CSFT2* - Susceptibility (functional MRI)

*