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Basic Physical Principles of MRI. James 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 subject 0

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basic physical principles of mri
Basic Physical Principlesof MRI

James Voyvodic, Ph.D.

Brain Imaging and Analysis Center

synopsis of mri
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 imaging
Many factors contribute to MR imaging
  • Quantum properties of nuclear spins
  • Radio frequency (RF) excitation properties
  • Tissue relaxation properties
  • Magnetic field strength and gradients
  • Timing of gradients, RF pulses, and signal detection
what kinds of nuclei can be used for nmr
What kinds of nuclei can be used for NMR?
  • Nucleus needs to have 2 properties:
    • Spin
    • charge
  • Nuclei are made of protons and neutrons
    • Both have spin ½
    • Protons have charge
  • Pairs 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 mri
Hydrogen atoms are best for MRI
  • Biological tissues are predominantly 12C, 16O, 1H, and 14N
  • Hydrogen atom is the only major species that is MR sensitive
  • Hydrogen is the most abundant atom in the body
  • The majority of hydrogen is in water (H2O)
  • Essentially all MRI is hydrogen (proton) imaging
a single proton
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 an

angular momentum

J when it is spinning.





Thus proton “magnet” differs from the magnetic bar in that it

also possesses angular momentum caused by spinning.


Magnetic Moment





m= tmax / B

= IA




t = mB

= m B sinq


t = IBLW = IBA








Angular Momentum

J = mw=mvr


The magnetic moment and angular momentum are vectors lying along the spin axis

m = gJ

g is the gyromagnetic ratio

g is a constant for a given nucleus

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

The energy difference between

the two alignment states depends on the nucleus

  • D E = 2 mz Bo

D E = hn

  • n = g/2p Bo

known as Larmor frequency

g/2p = 42.57 MHz / Tesla for proton

resonance frequencies of common nuclei
Resonance frequencies of common nuclei

Note: Resonance at 1.5T = Larmor frequency X 1.5

mri uses a combination of magnetic and electromagnetic fields
MRI uses a combination of Magnetic and Electromagnetic Fields
  • NMR measures the net magnetization of atomic nuclei in the presence of magnetic fields
  • Magnetization can be manipulated by changing the magnetic field environment (static, gradient, and RF fields)
  • Static magnetic fields don’t change (< 0.1 ppm / hr):

The main field is static and (nearly) homogeneous

  • RF (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

Basic Quantum Mechanics Theory of MR

The Effect of Irradiation to the Spin System




Basic Quantum Mechanics Theory of MR

Spin System After Irradiation

net magnetization
Net magnetization
  • Small B0 produces small net magnetization M
  • Larger B0 produces larger net magnetization M, lined up with B0
  • Thermal motionstry 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 physics
Quantum vs Classical Physics

One 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 it
To measure magnetization we must perturb it
  • We can only measure magnetization perpendicular to the B0 field
  • Need to apply energy to tip protons out of alignment
  • Amount 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
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 swing
    • Analogous to using a tiny RF B1 over a period of time to slowly flip M over


  • 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

This is like a gyroscope


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

recording the mr signal
Recording the MR signal
  • Need a receive coil tuned to the same RF frequency as the exciter coil.
  • Measure “free induction decay” of net magnetization
  • Signal oscillates at resonance frequency as net magnetization vector precesses in space
  • Signal amplitude decays as net magnetization gradually realigns with the magnetic field
  • Signal also decays as precessing spins lose coherence, thus reducing net magnetization
nmr signal decays in time
NMR signal decays in time
  • T1 relaxation – Flipped nuclei realign with the magnetic field
  • T2 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 relaxation
  • The total NMR signal is a combination of the total number of nuclei (proton density), reduced by the T1, T2, and T2* relaxation components
t2 decay
T2* decay
  • Spin coherence is also sensitive to the fact that the magnetic field is not completely uniform
  • Inhomogeneities in the field cause some protons to spin at slightly different frequencies so they lose coherence faster
  • Factors 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 matter
  • T2 - Tissue/CSF
  • T2* - Susceptibility (functional MRI)