Magnetic Resonance Imaging: How Does an MRI Work?

MRI: How it Works

Introduction to MRI

Magnetic Resonance Imaging (MRI) is a powerful imaging technique that utilizes a strong magnet to produce detailed pictures of the inside of the body. Unlike X-rays or CT scans, MRI doesn't use ionizing radiation. It relies on the principles of nuclear magnetic resonance (NMR) to generate images. An MRI scanner contains three major components: a strong magnet, gradient coils, and radiofrequency (RF) coils. The technology leverages the quantum mechanical properties of atomic nuclei to create images.

Nuclear Magnetic Resonance (NMR)

NMR is the phenomenon where certain atomic nuclei absorb and re-emit radiofrequency energy when placed in a magnetic field. Not all nuclei participate in NMR; it depends on their properties. The strength of the magnetic field and the specific radio frequencies used are crucial for NMR to occur.

The NMR Experiment: A Step-by-Step Overview

1. Alignment: Certain atomic nuclei behave like tiny bar magnets. In the presence of a strong magnetic field, these nuclei align with the field, similar to how a compass needle aligns with the Earth's magnetic field.

2. Excitation: An MRI scanner sends a radiofrequency (RF) pulse into the body to knock the nuclei out of alignment with the main magnetic field. This pulse disrupts their equilibrium.

3. Precession and Signal Detection: The nuclei, now out of alignment, begin to precess (wobble) around the magnetic field lines. This precession generates its own radiofrequency signal, which the MRI scanner detects.

4. T2 Relaxation: The emitted RF signal from the nuclei doesn't last forever. It gradually dies away as the nuclei lose coherence. The time it takes for the signal to decay is called T2 relaxation. Different tissues have different T2 relaxation times, providing a basis for tissue contrast in MRI images.

5. T1 Relaxation: After being knocked out of alignment, the nuclei eventually realign with the main magnetic field. The time it takes for them to realign is called T1 relaxation. Different tissues also have different T1 relaxation times, contributing to image contrast.

6. Repetition: The process of knocking spins over, detecting their emitted signals, and waiting for them to realign is repeated many times until sufficient signal is acquired to create a diagnostically useful image.

The Larmour Equation

The Larmour equation is fundamental to understanding NMR and MRI:

\Omega = \gamma B

Where:

• \Omega is the precession frequency of the nucleus.

• \gamma is the gyromagnetic ratio, a constant specific to the nucleus.

• B is the strength of the magnetic field.

The equation shows that the precession frequency ([[Omega]]) is directly proportional to the magnetic field strength (B). Doubling the magnetic field strength doubles the precession frequency and the required NMR radiofrequency.

Components of an MRI Scanner

1. Main Magnet: The outermost layer of the MRI scanner houses the main magnet, which is often a superconducting magnet. It produces a strong, homogeneous magnetic field (B0 field), typically 10,000 to 100,000 times the strength of the Earth's magnetic field. The magnet is always on and is a significant safety concern due to its strong pull on ferromagnetic materials.

2. Gradient Coils: Located inside the main magnet, the gradient coils alter the B field in three dimensions (X, Y, and Z) by producing smaller magnetic fields. These coils are crucial for spatial localization of the RF signal, enabling the creation of 3D images. They also contribute to different image contrasts, such as in diffusion or flow imaging. The gradient coils are responsible for the loud knocking and buzzing sounds produced during an MRI scan.

3. RF Coils: The innermost layer contains the RF coils, which transmit the RF tipping pulse into the tissue and detect the subsequent signal emitted from the tissue. They act as radio antennas, delivering a homogeneous radio signal. The gradients and RF coils work in a precisely timed concert to excite the nuclei in a specific location within the body and detect the resultant signal echoes. The RF coils are designed to deliver a very homogeneous radio signal to tissue.

Safety Considerations

MRI uses radiofrequency waves, which are non-ionizing, making it a safe imaging modality that can be used serially and in pediatric patients without significant concerns. However, the strong magnetic field poses a risk. Ferromagnetic objects can be pulled into the magnet with great force, potentially causing injury. Therefore, careful screening of patients and personnel entering the MRI suite is essential.

Hydrogen Nuclei in MRI

Clinical MRI primarily targets hydrogen nuclei (protons) due to their abundance in the body, high gyromagnetic ratio, and presence in nearly every organ. Since the body is about 70% water (H_2O), hydrogen nuclei are readily available for imaging.

Properties of Protons

Protons possess mass, electric charge, and spin. Spin is a quantum mechanical property that gives protons two key characteristics:

1. Angular Momentum: Protons behave as if they are spinning, possessing intrinsic angular momentum.

2. Magnetic Moment: Protons act like tiny bar magnets due to their intrinsic magnetic moment. The magnetic moment is related to the particle's spin quantum number and the gyromagnetic ratio (\gamma).

Precession in a Magnetic Field

When a proton is placed in a magnetic field (B), its magnetic moment tries to align with the field. However, because the proton has angular momentum, it precesses about the magnetic field lines, similar to a spinning top precessing under the influence of gravity. This precession is the basis of the NMR phenomenon.

Signal Detection

A coil of wire (RF coil) placed near the precessing proton detects a changing magnetic flux. This changing flux induces a voltage in the wire, according to Lenz's law. The induced voltage is the signal detected by the MRI scanner.

The signal follows a sinusoidal (or cosinusoidal) pattern with a specific frequency (\Omega), which is the precession frequency of the proton.

Factors Affecting Signal Intensity

The intensity of the detected NMR signal depends on several factors:

• Number of Particles (N): More spins lead to a greater collective magnetic field and a higher signal.

• Flip Angle (\theta): The angle between the spin and the magnetic field. The more perpendicular the angle, the higher signal, which places a {sin \theta in front of our signal equation.

• Gyromagnetic Ratio (\gamma): Nuclei with different gyromagnetic ratios precess at different frequencies.

• Magnetic Field Strength (B): Higher magnetic fields result in higher precession frequencies and greater signal amplitudes, following Lenz's law.

The overall signal amplitude (A) combines all these parameters.

Signal Dynamics and T2 Relaxation

Initially, the spins are coherent, meaning they are all in sync and pointing in the same direction. However, this coherence doesn't last due to variations in the local magnetic fields experienced by each spin. Some spins precess slightly faster, and some precess slightly slower, leading to dephasing and a loss of signal. The signal decays exponentially, described by:

Signal = A \cdot cos(\Omega t) \cdot e^{-t/T2}

Where:

• A is the initial signal amplitude.

• \Omega is the precession frequency.

• t is time.

• T2 is the T2 relaxation time, representing how quickly the signal decays.

The decaying exponential plot is called the free induction decay (FID).

T2 Weighting

Tissues with short T2 relaxation times (e.g., bone, lungs) lose coherence quickly, while tissues with long T2 relaxation times (e.g., water, blood) maintain coherence longer. By varying the echo time (TE), which is the time at which the signal is detected after excitation, the MRI technician can manipulate tissue contrast.

• Short TE: Provides less T2 contrast, as the signals from different tissues haven't had enough time to decay significantly.

• Long TE: Provides more T2 contrast, as the differences in T2 relaxation times become more apparent.

A T2-weighted image displays each voxel (3D pixel) based on how quickly the spins dephase in that voxel. Bright voxels indicate slow dephasing, while dark voxels indicate rapid dephasing. Thus, resulting image presents an anatomic map of tissue.

Spin Density Images

If the echo time (TE) is set to 0, the signal intensity primarily depends on the number of protons in the tissue. This is called a spin density image. Spin density images don't show much contrast in the brain but can be useful in other organs.

T1 Relaxation

Simultaneous with T2 dephasing, the spins also start to realign with the main magnetic field. This process is called T1 relaxation and is slower than T2 dephasing.

The realignment curve is described by:

M(t) = M_0 \cdot (1 - e^{-t/T1})

Where:

• M(t) is the magnetization at time t.

• M_0 is the equilibrium magnetization (Boltzmann magnetization).

• T1 is the T1 relaxation time.

T1 Weighting

Different tissues exhibit different T1 relaxation times. T1 weighting is achieved by manipulating the repetition time (TR), where

• TR This is the amount of time the scanner waits in between excitations
  Tissues with short T1 relaxation times realign quickly and appear bright in T1-weighted images, while tissues with long T1 relaxation times realign slowly and appear dark.

TR and TE

The terms TR and TE refer to the time of repetition, and the time of Echo respectively. These two terms are intrinsic properties for the tissues, whereas TR and TE are parameters chosen by the MRI tech and how the scan will detect the T1 and T2.

Total Magnetization Vector

The total magnetization vector of the spins can be decomposed into two components:

• Longitudinal Component: grows at a rate T1 following excitation

• Transverse Component: decays at a rate T2 following excitation

The transverse component is what produces detectable signal, while the longitudinal component represents the magnetization available for the next excitation.

Rotating Reference Frame

To simplify the analysis, a rotating reference frame is used, which rotates at the precession frequency of the nuclei. In this frame, the excitation process and the behavior of the magnetization vectors are easier to describe mathematically.

Excitation in the Rotating Frame

Spins are tipped into the transverse plane by sending a radiofrequency pulse (B1) perpendicular to the main magnetic field (B0) at the same Larmour frequency ([[Omega]]) as the precessing spins. The amount of flip angle is dependent on the time that the pulse lasts.

The Signal Equation

The general expression for the detected signal, after accounting for T1 and T2 relaxation effects, is:

Signal \propto SpinDensity \cdot (1 - e^{-TR/T1}) \cdot e^{-TE/T2}

Boltzmann Magnetization and Thermal Equilibrium

Spin 1/2 nuclei (like protons) exist in two energy states: aligned with the magnetic field (lower energy) or anti-aligned (higher energy). For NMR to work, there must be an unequal number of spins in these two states. The distribution of spins between these states follows the Boltzmann factor. The number of spins in one particular state is

N = N_{total} \cdot P(state)

Polarization

Only mismatched spins contribute to the NMR signal. The fraction of spins that are mismatched is called polarization (P), defined as:

P = \frac{N{up} - N{down}}{N_{total}}

Where:

• [[N]]up is the number of spins in the higher energy state.

• [[N]]down is the number of spins in the lower energy state.

• [[N]]total is the total number of spins

If we consider Einstein's notes:
The energy difference between the two states is\bar{h}{\Omega}, then the fraction of spins which participate in NMR is

P = \frac{\gamma \bar{h} B}{2kT}

Where:

• \gamma is the gyromagnetic ratio.

• \bar{h} is planck's constant divided by 2\pi.

• B is the external magnetic field.

• k is Boltzmann's constant.

• T is the temperature in Kelvin.

Only a tiny fraction of spins (about 3.4 parts per million at 1 Tesla and body temperature) contribute to the NMR signal, making NMR an insensitive technique and can now be expressed as the full expression:

Signal \propto N \cdot \frac{\gamma \bar{h} B}{2kT} \cdot (1 - e^{-TR/T1}) \cdot e^{-TE/T2}

Hyperpolarization

Hyperpolarization is a technique used to increase the polarization of certain nuclei far beyond the Boltzmann equilibrium. Noble gases like helium-3 and xenon-129 can be hyperpolarized up to 50%, leading to a significant increase in signal. This allows for imaging of the gas within the lungs, providing functional information.

Next Steps

Future discussions will cover spatial encoding, gradient schemes, spin echoes, gradient echoes, Fourier theory, and k-space to explain how MRI images are produced.