MRI Physics: Just the Basics An Introduction to MRI Physics and Analysis Michael Jay Schillaci, PhD Monday, February 4th, 2008

Overview Background Magnetic Fields in an MR System Forces Causes and Effects of Magnetism Quantum Theory - Larmor Frequency Brain Physiology Magnetic Fields in an MR System Main and Gradient Coils RF Coils and Spatial Encoding Gradient and Spin Echo Sequences

Background

Fields in General: Gravity Fields are covariates of motion When a ball falls… We refer to “gravity”… *Actual cause is force of attraction of the mass of ball to the mass of Earth through the “field of gravity”…

Fields in General: Electricity When a particle rises… We refer to “electricity”… *Actual cause is force of attraction of the charge of particle to the charge of Capacitor through the “field of electricity”…

The Causes of Magnetism Macroscopic View Current in wire Field is “around” wire Depends on current Depends on distance Microscopic View Moment of atom Field is “about” nucleus Depends on material

Properties of Atomic Nuclei Nuclei have two properties: Spin (conceptual, not literal) Charge (property of protons) Nuclei are made of protons and neutrons Both have spin values of ½ Protons have charge Pairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin A nucleus has the NMR Property if it has both angular momentum and a magnetic moment. Such nuclei have an odd number of protons or an odd number of neutrons.

Kinds of Magnetism Ferromagnetic materials (e.g., Iron) Both attract and repel other magnets Create own field Paramagnetic materials (e.g., Gadolinium) Attracted toward magnets Align with other fields Diamagnetic materials (e.g., Water) Repelled by magnets Anti-align with other fields

Protons align with a magnetic field…

The Effects of Magnetism Two ways to assess effects of magnetic fields: Determine Magnetic Force Forces move objects Field is a covariate of force Determine Magnetic Energy Density Energy heats objects Field is correlated with energy

Basic Quantum Theory Radiation is absorbed Radiation is emitted Energy increases Radiation is emitted Energy decreases Lower Higher

Magnetic Precession Static Field “splits” states Zeeman splits high/low energy states RF Field “rotates” moments Precession Frequency M = net (bulk) magnetization M B0 m ~ 1 ppm excess in spin-up state creates the net Magnetization… B0 m NMR Parameters B0=1T* B0 m = g J dJ / dt = m × Bo dm/dt = g (m × Bo) * For comparison: In the Earth’s magnetic field ( 0.00005 T ), hydrogen precesses at ~2100 Hz.

Larmor Frequency Energy Difference Frequency Equate differences E = Eup – Edown = mz Bo - (-mz Bo ) = 2 mz Bo B0 m B0 m Larmor Equation E = hv0 = 2 mz Bo = 2(1/2 h /2p g) B0

Electromagnetic Energy Quantum Mechanics governs state transitions Energy of transition Planck’s constant Energy values X-Ray, CT Excites Electrons MRI Excites Protons

Brain Physiology - Chemistry Energy of Fields Heats Brain Tissue Drives Chemistry Energy covaries with the wavelength Higher energy breaks bonds Medium energy vibrates molecules Lower energy rotates molecules

Material Dependence Magnetization varies with field, temperature and material Magnetic susceptibility alters the local field Conductivity Susceptibility

Brain Physiology – Empirical Brain Conductivity Measure conductivity of 20 human brains Less than 10 hours after death Results Conductivity depends on frequency: 1.39 S/m (0.14 S/m) at 900 MHz 1.84 S/m (0.16 S/m) at 1,800 MHz fmri-fig-06-02-0.jpg

Brain Physiology – Measures Energy Density Conductivity Relationship

Magnetic Fields in an MR System

USC Trio – Siemens 3T MRI

Protons in no magnetic field In the absence of a strong magnetic field, the spins are oriented randomly. Thus, there is no net magnetization (M).

Transverse Magnetization Bo Bo Longitudinal Axis (z direction) B is used for magnetic fields. B0 is the scanner’s main field. Transverse Plane (xy plane)

In a magnetic field, protons can take either high- or low-energy states

The difference between the numbers of protons in the high-energy and low-energy states results in a net magnetization (M) and gives rise to the Larmor Equation.

Main Field Field Characteristics Generated by Helmholtz Coils B M Field Characteristics Generated by Helmholtz Coils Currents are parallel (same direction) Field along MRI axis a a Coil 2 Coil 1

Gradient Field Field Characteristics Created by Maxwell Pair BG Field Characteristics Created by Maxwell Pair currents are anti-parallel (opposite direction) Field along MRI axis b b Coil 2 Coil 1

Total (Static) Field Total Field Sum of Main and Gradient Fields In practice a “shim” field is also used to “flatten” the field. B0=BM+BG ΔB0 ~ 1mT Gradient field decreases total Gradient field increases total

Spatial Encoding - Gradient Field varies (almost) linearly Change in field = DB0 Frequency depends on position (z) Field depends on material Image Resolution Strong Gradient → High Resolution Weak Gradient → Low Resolution DB0= 0.018 T Dz = 0.16 m

RF Fields - Generation Galois Coils Transverse RF Field Rotating frame Radio Frequency Transmitter, w0 Rotating frame Total field given by Receiver currents are anti-parallel Induced field is perpendicular BC Receiver BC -z r +x Transmitter wo wo FT t Dw = 1/ t

Radiofrequency Coils Defined by their function: Transmit / receive coil (most common) Transmit only coil (can only excite the system) Receive only coil (can only receive MR signal) Defined by geometry Volume coil (low sensitivity but uniform coverage) Surface coil (High sensitivity but limited coverage) Phased-array coil (High sensitivity, near-uniform coverage)

Origin of the MR Signal During Excitation (to) During Excitation (t1) The amount of current oscillates at the (Larmor) frequency of the net magnetization. Before Excitation After Excitation fmri-fig-03-17-0.jpg Excitation tips the net magnetization (M) down into the transverse plane, where it can generate current in detector coils (i.e., via induction).

Gradient Echo Imaging Assume perfect “spoiling” -transverse magnetization is zero before each excitation: Spin-Lattice (T1) Relaxation occurs between excitations: Assume steady state is reached during repeat time: Spoiled gradient rephases the FID signal at echo time: Maximize signal: Ernst Angle

Pulse Sequence Parameters GE imaging complex effects maximum SNR typically between 30 and 60 degrees long TR sequences (2D) increase SNR with increased flip angle short TR sequences (TOF & 3D) decreased SNR with increased flip angle

Basic Spin Echo Sequences (SE) The refocusing pulse allows us to recover true T2. Image from http://www.e-mri.org/cours/ Includes interactive adjustment of T1/T2 T2 T2*

The Spin Echo Sequence Actual Signal 1 Spin echo sequence applies a 180º refocusing pulse half way between 90º pulse and measurement. This pulse eliminates phase differences due to artifacts, allowing measurement of pure T2. Dramatically more signal with Spin Echo. T2 Signal T2* 0.5 TE 0.5 TE Time

Image Formation   Integrate magnetization to get MRI signal Select a z “slice” and form image of XY plane variations Contrast from difference in magnetization Image at several times Scanner acquires K-Space weights Construct image and average slices Horizontal density Vertical density  

T1 & T2 Weighting T1 Contrast T2 Contrast Magnetization is given by Echo (TE) at T2 min Repeat (TR) at T1 max T2 Contrast Echo (TE) at T2 max Repeat (TR) at T1 min Magnetization is given by T1 Contrast Weighting TR TE Max T1 Contrast Min T2 Contrast T2 Contrast Weighting TE TR Min T1 Contrast Max T2 Contrast

Static Contrast Images Examples from the Siemens 3T T1 and T2 Weighted Images T1 Weighted Image (T1WI) (Gray Matter – White Matter) T2 Weighted Image (T2WI) (Gray Matter – CSF Contrast)

Pulse and Field Effects Images adapted from: http://www.mri.tju.edu/phys-web/1-T1_05_files/frame.htm Pulse and Field Effects RF pulse determines “flip angle” Rotation determines amount of magnetization measured Field strength determines resolution Increased magnetization leads to increased signal q B0 = 1.5 T Muscle Tissue Difference B0= 0.2 T