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 subject0 5) Convert measured RF data to image

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

MRI uses a combination of Magnetic and Electromagnetic Fields NMR measures magnetization of atomic nuclei in the presence of magnetic fields Magnetization can be manipulated by manipulating the magnetic fields (this is how we get images) 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

Electromagnetic Radiation Energy X-Ray, CT MRI

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 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

Nuclear Magnetic Resonance Visible Nuclei

Why do protons interact with a magnetic field? Moving (spinning) charged particle generates its own little magnetic field Spinning particles with mass have angular momentum

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

Angular Momentum J = mw=mvr m v r J

g is the gyromagnetic ratio g is a constant for a given nucleus The magnetic moment and angular momentum are vectors lying along the spin axis m = g J g is the gyromagnetic ratio g is a constant for a given nucleus

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]

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)

[Main magnet and some of its lines of force] [Little magnets lining up with external lines of force]

Ref: www.simplyphysics.com

Net Magnetization Bo M

Net magnetization Small B0 produces small net magnetization M Larger B0 produces larger net magnetization M, lined up with B0 Thermal 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

The Energy Difference Between the Two Alignment States D 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 nuclei

To measure magnetization we must perturb it Need to apply energy to tip protons out of alignment aligned with magnetic field is lowest energy aligned opposite magnetic field is next lowest energy state Amount of energy needed depends on nucleus and applied field strength (Larmor frequency)

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

Spin System After Irradiation Basic Quantum Mechanics Theory of MR Spin System After Irradiation

Precession 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

RF Coil: Transmitting B1 Field To tip spins in the static B0 field we 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 B1 is to cause M to spiral away from the direction of the static B0 field B110–4 Tesla If B1 frequency is not close to resonance, B1 has no effect

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 the tiny RF B1 to slowly flip M over g

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 rate of spin coherence T2 relaxation NMR signal is a combination of the total number of nuclei (proton density), minus the T1 relaxation and T2 relaxation components

Different tissues have different relaxation times

Relaxation times are important for generating image contrast T1 - Gray/White matter T2 - Tissue CSF T2* - Susceptibility (functional MRI)

MRI Scanner

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.

MRI scanner components

Using NMR signals for imaging Need to prolong and amplify the decaying signal Need to know the spatial location of the tissue generating the signal

The decaying NMR signal can be recovered by realigning spins Spin Echo Imaging Gradient Echo Imaging

Spatial location is identified by using spatially varying magnetic fields Proton resonance with uniform magnetic field Proton resonance with axial field gradient

It is actually spatial frequency, not physical location, that is scanned Gradients cause spins to spread out and realign at different times Bands of tissue with uniform spacing will realign together MRI scanning systematically samples the strength of the signal at different spatial frequencies Horizontal sampling (Kx) Vertical sampling (Ky)

MRI scanner collects spatial frequency data (in k-space) Horizontal spatial frequency density Vertical spatial frequency density

A 2-dimensional Fourier transform mathematically converts from spatial frequency to reconstructed MR images

The versatility of MRI arises from the different types of tissue contrast that can be generated by manipulating parameters TR – adjusting the time between acquisitions affects T1 relaxation TE – adjusting the time between refocusing pulses affects T2 and T2* relaxations Timing of gradients affects sampling in k-space Additional gradient pulses before the RF pulse can enhance specific tissue properties Chemical agents can further enhance image contrast