MRI Notes

Medical Technology: Magnetic Resonance Imaging (MRI)

Timeline of MR Imaging

  • 1924: Pauli suggests nuclear particles may have angular momentum (spin).

  • 1937: Rabi measures the magnetic moment of the nucleus and coins the term "magnetic resonance."

  • 1946: Purcell shows that matter absorbs energy at a resonant frequency.

  • 1946: Bloch demonstrates that nuclear precession can be measured in detector coils.

  • 1959: Singer measures blood flow using NMR in mice.

  • 1972: Damadian patents the idea for a large NMR scanner to detect malignant tissue.

  • 1973: Lauterbur publishes a method for generating images using NMR gradients.

  • 1973: Mansfield independently publishes a gradient approach to MR.

  • 1975: Ernst develops 2D-Fourier transform for MR; NMR is renamed MRI.

  • 1985: Insurance reimbursements for MRI exams begin.

  • 1990: Ogawa and colleagues create functional images using endogenous, blood-oxygenation contrast.

  • MRI scanners become clinically prevalent.

Nobel Prizes for Magnetic Resonance

  • 1944: Isidor Isaac Rabi (Physics) - Measured magnetic moment of nucleus.

  • 1952: Felix Bloch and Edward Mills Purcell (Physics) - Basic science of NMR phenomenon.

  • 1991: Richard Ernst (Chemistry) - High-resolution pulsed FT-NMR.

  • 2002: Kurt Wüthrich (Chemistry) - 3D molecular structure in solution by NMR.

  • 2003: Paul Lauterbur & Peter Mansfield (Physiology or Medicine) - MRI technology.

MRI Equipment

  • Key components include a shield, magnet, gradient coils, and RF coil.

  • A strong magnet (e.g., 4T magnet) is essential.

  • Gradient coils are inside the magnet.

  • RF coils are used to transmit and receive radiofrequency signals.

  • Other components: Gradient amplifier, RF detector, pulse programmer, digitizer, RF amplifier, RF source.

MRI Diagnostics

  • MRI is ideally suited for soft tissue problems, analogous to how X-rays are for dense tissue (bone).

  • Applications:

    • Diagnosing multiple sclerosis (MS).

    • Diagnosing brain tumors.

    • Diagnosing spinal infections.

    • Visualizing torn ligaments in the wrist, knee, and ankle.

    • Visualizing shoulder injuries.

    • Evaluating bone tumors and herniated discs in the spine.

    • Diagnosing strokes in their earliest stages.

MRI Disadvantages

  • Extreme precautions are needed to keep metallic objects out of the room.

  • People with pacemakers cannot be safely scanned.

  • Claustrophobia can be an issue for some patients.

  • The machine makes loud hammering noises.

  • Some people may be too large to fit inside the magnet.

  • Patients must hold very still for extended periods (up to 90 minutes).

  • MRI systems are expensive; scans cost approximately 500-800 Euro.

Magnetic Field Strength in MRI

  • Imaging: 0.2 T to 2.0 T

  • Spectroscopy: 2.0 T to 7.0 T

  • Categories:

    • Low field: 0.2 - 0.5 T

    • Intermediate: 0.5 - 1.5 T

    • High field: 1.5 - 4.0 T

    • Ultra-high field: > 4.0 T

  • Earth’s magnetic field: 0.5 Gauss = 5 \times 10^{-5} Tesla

  • Conversion: 1 Tesla = 10,000 Gauss

Magnetism

  • Magnetic monopoles do not exist (as far as we know).

  • In a strong magnetic field, nuclei act like tiny dipole magnets, aligning with or against the field.

Protons and Magnetic Moment

  • A single proton has an electric charge, creating a small current loop and generating a magnetic moment \mu. The proton also possesses mass, which generates angular momentum J when spinning.

  • Thus, a proton "magnet" differs from a magnetic bar by also possessing angular momentum caused by spinning.

Energy (Spin) States

  • Protons (hydrogen nuclei) have two spin states and precess about the field direction.

Protons in a Magnetic Field B_0

  • Spinning protons in a magnetic field assume two states: parallel (low energy) and anti-parallel (high energy).

  • At 0^\circ K, all spins would occupy the lower energy state.

Nuclei and Spin

  • All nuclei have spin – multiples of \frac{1}{2}.

  • Combined with charge, this creates a magnetic moment.

  • A nucleus with odd spin acts like a small dipole magnet.

  • If a nucleus has S spin states, the moment (magnet) has 2S+1 stable states in an external magnetic field.

  • Hydrogen (proton): S = \frac{1}{2} => 2 states.

Common Nuclei with NMR Properties

  • Criteria: Must have an odd number of protons or neutrons.

  • Reason: Prevents arrangement into a zero net angular momentum.

  • Examples: ^1H, ^{13}C, ^{19}F, ^{23}Na, and ^{31}P.

  • Hydrogen protons are most abundant in the human body, making ^1H MRI most common.

  • NMR = Nuclear Magnetic Resonance

Alignment of Spins in a Magnetic Field

  • Spins tend to align parallel or anti-parallel to B_0.

  • Net magnetization (M) is along B_0.

  • Spins precess with random phase.

  • Only approximately 0.0003\%\Tesla align with the field.

Magnetic Field Strength and Proton Alignment

  • For a 3T external magnetic field, there are only about 10 per million more protons parallel than anti-parallel.

  • Millions of protons exist, providing a useful magnetic field.

  • Smaller fields result in fewer excess protons and poorer signal-to-noise ratio (SNR), necessitating very large magnetic fields.

NMR / MRI Principle

  • Nuclei are bombarded with Radiofrequency (RF) energy.

  • At certain resonant frequencies, protons flip to the high energy state.

Basic Quantum Mechanics of MRI

  • Illustrates the spin system before and after irradiation, showing transitions from lower to higher energy states.

NMR / MRI Frequencies

  • Common nuclei used in MRI: ^1H, ^{13}C, ^{19}F, ^{23}Na, and ^{31}P with gyromagnetic ratios of 42.58, 10.71, 40.08, 11.27, and 17.25 MHz/Tesla.

  • Probing with different RF energy frequencies builds a spectrum of the sample's composition.

Exciting the Spin System

  • Apply short, high-intensity radio waves at a frequency close to the Larmor frequency.

  • This is called the B1 field, oriented perpendicular to and rotating about the B0 field. Magnitude of B1 ≈ 10^{-5} B0.

  • In a coordinate system rotating at or close to the Larmor frequency, this results in a rotation of the magnetization away from the direction of the external magnetic field – precession.

Mechanical Analogy of Precession

  • A gyroscope in Earth’s gravitational field resembles magnetization in an externally applied magnetic field.

Signal Detection via RF Coil

  • RF coils detect signals emitted by the precessing nuclei.

Signal Detection and Fourier Transform

  • The signal is damped due to relaxation.

  • Fourier Transform converts the time-domain signal to a frequency-domain spectrum.

T1 Relaxation

  • T1 relaxation is the process by which the net magnetization (M) returns to its initial maximum value (M_0).

  • T1 is the time required for the z-component of M to reach (1 - \frac{1}{e}) or about 63\% of its maximum value (M_0).

  • T1 values in biological materials range from a few tenths of a second to several seconds.

  • Longitudinal relaxation is modeled as an exponential growth curve with time constant T1. M reaches 63\% of its maximum value (M_0) at t = T1 and is nearly maximal at t = 5 \times T1.

The Relaxation Constant T1

  • T1 – the spin-lattice relaxation time: corresponds to the time required for the system to return to 63% of its equilibrium value after a 90° pulse.

T1 Relaxation Summary

  • T1 is the time constant for re-growth of longitudinal magnetization (M_z).

  • Synonyms: Spin-lattice relaxation, thermal relaxation, longitudinal relaxation.

  • Requires energy transfer from spins to the environment (