BME 595 - Medical Imaging Applications Part 2: INTRODUCTION TO MRI Lecture 1 Fundamentals of Magnetic Resonance Feb. 16, 2005 James D. Christensen, Ph.D. IU School of Medicine Department of Radiology Research II building, E002C [email protected]317-274-3815
Magnetic resonance imaging (MRI) is a test that uses a magnetic field and pulses of radio wave energy to make pictures of organs and structures inside the body. In many cases, MRI gives different information about structures in the body than can be seen with an X-ray, ultrasound, or computed tomography (CT) scan. MRI also may show problems that cannot be seen with other imaging methods
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BME 595 - Medical Imaging ApplicationsPart 2: INTRODUCTION TO MRI
Lecture 1 Fundamentals of Magnetic Resonance
Feb. 16, 2005
James D. Christensen, Ph.D.IU School of Medicine
Department of RadiologyResearch II building, E002C
Main Components of a Scanner• Static Magnetic Field Coils• Gradient Magnetic Field Coils• Magnetic shim coils• Radiofrequency Coil• Subsystem control computer
• Data transfer and storage computers• Physiological monitoring, stimulus display, and
behavioral recording hardware
Transmit Receive
rfcoil
rfcoil
mainmagnet
mainmagnet
gradientShimming
ControlComputer
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 properties
•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.
Angular Momentum
JJ = m = m=m=mvvrrmm
vvrr
JJ
magnetic moment magnetic moment = = JJwherewhere is the gyromagnetic ratio, is the gyromagnetic ratio,and it is a constant for a given nucleusand it is a constant for a given nucleus
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 The proton also has mass which has mass which generates angenerates anangular angular momentummomentumJJ when it is when it is spinning.spinning.
JJ
Thus proton “magnet” differs from a magnetic bar in that itThus proton “magnet” differs from a magnetic bar in that italso possesses angular momentum caused by spinning.also possesses angular momentum caused by spinning.
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.
Protons align with fieldOutside magnetic field
randomly oriented
• spins tend to align parallel or anti-parallel to B0
• net magnetization (M) along B0
• spins precess with random phase• no net magnetization in transverse plane• only 0.0003% of protons/T align with field
Inside magnetic field Mz Mxy = 0longitudinal
axis
transverseplane
Longitudinalmagnetization
Transversemagnetization
M
Net Magnetization
BoM
TBcM o
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 is roughly 100,000 to 100,006 per Tesla of B0
The Boltzman equation describes the population ratio of the two energy states:
N-/N+ = e –E/kT
Energy Difference Between States
Energy Difference Between States
Eh E = 2 z Bo
/2known as Larmor frequency
/2= 42.57 MHz / Tesla for proton= 42.57 MHz / Tesla for proton
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
Basic Quantum Mechanics Theory of MRBasic Quantum Mechanics Theory of MR
The Effect of Irradiation to the Spin System
Lower
Higher
Basic Quantum Mechanics Theory of MRBasic Quantum Mechanics Theory of MR
Spin System After Irradiation
Basic Quantum Mechanics Theory of MRBasic Quantum Mechanics Theory of MR
Precession of the quantum expectation value of the magnetic momentPrecession of the quantum expectation value of the magnetic momentoperator in the presence of a constant external field applied along the Z axis.operator in the presence of a constant external field applied along the Z axis.The uncertainty principle says that both energy and time (phase) or The uncertainty principle says that both energy and time (phase) or momentum (angular) and position (orientation) cannot be known with momentum (angular) and position (orientation) cannot be known with precision simultaneously. precision simultaneously.
Precession –Precession – ClassicalClassical
= = ×× B Bo torque = dJ / dt J = /
d/dt = ( × Bo)
(t) = ((t) = (xocos cos BBot + t + yosin sin BBot) t) xx + ( + (yocos cos BBot - t - xosin sin BBot) t) yy + + zozz
A Mechanical Analogy of Precession
• A gyroscope in the Earth’s gravitational field is like magnetization in an externally applied magnetic field
Equation of Motion: Block equation
T1 and T2 are time constants describing relaxation processes caused by interaction with the local environment
RF Excitation:
On-resonance
Off-resonance
RF ExcitationExcite Radio Frequency (RF) field
• transmission coil: apply magnetic field along B1 (perpendicular to B0)• oscillating field at Larmor frequency• frequencies in RF range• B1 is small: ~1/10,000 T• tips M to transverse plane – spirals down• analogy: childrens swingset• final angle between B0 and B1 is the flip angle
B1
B0
Transversemagnetization
Signal Detection via RF coil
Signal Detection
Signal is damped due to relaxation
Relaxation via magnetic field interactions with the local environment
Spin-Lattice (T1) relaxation via molecular motion
T1 Relaxation efficiency as function of freq is inversely related to the
density of states
Effect of temperature Effect of viscosity
Spin-Lattice (T1) relaxation
Spin-Spin (T2) Relaxation via Dephasing
Relaxation
Relaxation
T2 Relaxation
Efffective T2 relaxation rate:
1/T2’ = 1/T2 + 1/T2*
Total = dynamic + static
Spin-Echo Pulse Sequence
Spin-Echo Pulse Sequence
Multiple Spin-Echo
HOMEWORK Assignment #1
1) Why does 14N have a magnetic moment, even though its nucleus contains an even number of particles?
2) At 37 deg C in a 3.0 Tesla static magnetic field, what percentage of proton spins are aligned with the field?
3) Derive the spin-lattice (T1) time constant for the magnetization plotted below having boundary conditions: Mz=M0 at t=0 following a 180 degree pulse; M=0 at t=2.0 sec.