Biomedical Imaging: Magnetic Resonance Imaging (MRI)

Vocabulary practice flashcards covering the physical principles, equations, pulse sequences, spatial encoding gradients, k-space mechanics, and contrast weighting of Magnetic Resonance Imaging (MRI).

Magnetic Resonance Imaging (MRI)

A major non-invasive medical imaging modality that uses a strong static magnetic field, magnetic field gradients, and radiofrequency (RF) pulses to create anatomical and physiological images by imaging hydrogen nuclei ($^1H$ protons) found in water and fat molecules.

Nuclear Spin

A fundamental physical property of subatomic particles and atomic nuclei, analogous to electric charge or mass, which exists in integer or half-integer multiples of $1/2$ ($\text{or } \frac{1}{2}$) and produces a magnetic dipole when associated with a moving electrical charge.

Gyromagnetic Ratio ($\gamma$)

A proportionality constant specific to a given atomic nucleus that relates its precession frequency to the strength of the external magnetic field. For a hydrogen proton ($^1H$), $\gamma = 42.58\,\text{MHz/T}$ (commonly rounded to $42.6\,\text{MHz/T}$).

Bulk Magnetization ($M_0$)

The net macroscopic magnetic vector produced by the vector sum of individual nuclear magnetic moments per unit volume aligning with a strong static external magnetic field ($B_0$) at thermal equilibrium.

Larmor Equation

The governing equation $f = \gamma B_0$, which states that the precession frequency ($f$, or Larmor frequency) of a nuclear spin is directly proportional to the gyromagnetic ratio ($\gamma$) and the strength of the external magnetic field ($B_0$).

Larmor Frequency ($f_0$)

The rate at which nuclear magnetic moments precess around the direction of an external static magnetic field ($B_0$); for example, hydrogen protons precess at approximately $63.9\,\text{MHz}$ in a $1.5\,\text{T}$ magnetic field.

Resonance

The physical condition achieved when an applied radiofrequency (RF) pulse oscillates at the exact Larmor precession frequency of the nuclei, enabling the net magnetization vector to absorb energy and rotate away from the longitudinal axis.

Flip Angle ($\alpha$)

The angle through which the net magnetization vector is tipped away from the longitudinal ($z$) axis toward the transverse ($x\text{-}y$) plane during RF excitation, mathematically defined by $\alpha = 2\pi\gamma B_1\tau$, where $B_1$ is the RF magnetic field strength and $\tau$ is pulse duration.

$90^\circ$ RF Pulse

An RF excitation pulse that rotates the net magnetization vector by exactly $90^\circ$ from the longitudinal axis into the transverse ($x\text{-}y$) plane, setting the transverse component $M_{xy}$ equal to $M_0$.

$180^\circ$ RF Pulse

An RF pulse with twice the duration or power of a $90^\circ$ pulse that inverts the longitudinal magnetization to $-M_0$ or mirrors the dephased transverse spin vectors across an axis to initiate spin rephasing.

Free Induction Decay (FID)

The transient, oscillating, and exponentially decaying electrical voltage induced in a receiver coil immediately after an RF excitation pulse as transverse spins dephase.

Bloch Equations

A system of macroscopic differential equations that model the time-dependent evolution of the net magnetization vector components ($M_x$, $M_y$, $M_z$) in the presence of applied magnetic fields, incorporating $T_1$ and $T_2$ relaxation rates.

Longitudinal Relaxation ($T_1$ Relaxation)

The thermal or spin-lattice relaxation process by which the longitudinal magnetization component ($M_z$) recovers back to its equilibrium value ($M_0$) through energy exchange with the surrounding molecular lattice, following $M_z(t) = M_0\left(1 - e^{-t/T_1}\right)$.

$T_1$ Relaxation Time

The time constant required for the longitudinal magnetization ($M_z$) to regrow to approximately $63\%$ of its final equilibrium value ($M_0$) following RF excitation.

Transverse Relaxation ($T_2$ Relaxation)

The spin-spin relaxation process by which transverse magnetization ($M_{xy}$) decays irreversibly due to random microscopic variations in local magnetic fields causing dephasing among neighboring spins, following $M_{xy}(t) = M_0 e^{-t/T_2}$.

$T_2$ Relaxation Time

The time constant required for the transverse magnetization ($M_{xy}$) to decay to approximately $37\%$ of its initial post-excitation amplitude.

$T_2^*$ (T2-Star) Relaxation

The effective transverse relaxation decay caused by the combined effects of true spin-spin interactions ($T_2$) and static magnetic field inhomogeneities ($\Delta B$), governed by the relationship $\frac{1}{T_2^*} = \frac{1}{T_2} + \gamma\Delta B$.

Tissue Relaxation Parameters ($T_1$ and $T_2$)

Inherent tissue-specific time constants; for example, at $1.5\,\text{T}$, skeletal muscle exhibits $T_1 = 870\,\text{ms}$ and $T_2 = 47\,\text{ms}$, fat exhibits $T_1 = 260\,\text{ms}$ and $T_2 = 84\,\text{ms}$, gray matter exhibits $T_1 = 920\,\text{ms}$ and $T_2 = 101\,\text{ms}$, and white matter exhibits $T_1 = 790\,\text{ms}$ and $T_2 = 92\,\text{ms}$.

Slice Selection Gradient ($G_z$)

A linear magnetic field gradient applied along the $z$-axis simultaneously with an RF pulse to vary Larmor frequencies along the patient's body axis, selectively exciting only a specific anatomical slice matching the RF bandwidth.

RF Bandwidth

The range of transmitted frequencies within an RF pulse that, together with the slope of the slice-selection gradient ($G_z$), defines the thickness of the excited anatomical slice.

Phase Encoding Gradient ($G_y$)

A magnetic field gradient applied momentarily along the $y$-axis prior to signal readout that imparts a position-dependent phase shift to protons across different rows within the selected slice.

Frequency Encoding Gradient ($G_x$)

A magnetic field gradient (also known as the readout gradient) applied along the $x$-axis during echo signal sampling, causing proton precession frequencies to vary linearly by column position across the slice.

Gradient Coils

Specialized electromagnetic coils ($G_x$, $G_y$, $G_z$) configured within an MRI bore to produce controlled linear variations in the main magnetic field along three orthogonal directions for spatial encoding.

Spin Echo (SE) Sequence

A standard MRI pulse sequence consisting of a $90^\circ$ excitation pulse followed after time interval $\tau = \text{TE}/2$ by a $180^\circ$ refocusing pulse, producing a refocused spin echo signal at $\text{TE} = 2\tau$ while eliminating static field inhomogeneity dephasing.

Repetition Time ($\text{TR}$)

The duration between successive $90^\circ$ RF excitation pulses applied to the same slice, determining the amount of longitudinal ($T_1$) recovery that occurs between cycles.

Echo Time ($\text{TE}$)

The time elapsed from the center of the initial $90^\circ$ RF excitation pulse to the peak of the formed spin echo signal, controlling the degree of transverse ($T_2$) decay.

k-Space

An array or matrix representing the 2D spatial frequency domain in which raw digitized MRI echo signals are stored; each line in the matrix corresponds to a separate phase-encoding step.

Central k-Space

The region near the center of the k-space matrix that holds low spatial frequency data, which determines the overall contrast, brightness, and general shapes within the reconstructed image.

Peripheral k-Space

The outer border regions of the k-space matrix that hold high spatial frequency data, which determines image edge sharpness, fine detail, and spatial resolution.

2D Fourier Transform (2DFT)

The mathematical algorithm applied to k-space raw data to transform spatial frequency information into a reconstructed two-dimensional spatial-domain anatomical image.

$T_1$-Weighted Image

An MRI sequence acquired with a short $\text{TR}$ ($< 600\,\text{ms}$) and a short $\text{TE}$, where tissues with rapid longitudinal regrowth (short $T_1$, such as fat) appear hyperintense (bright) and tissues with slow regrowth (long $T_1$, such as CSF) appear hypointense (dark).

$T_2$-Weighted Image

An MRI sequence acquired with a long $\text{TR}$ ($> 600\,\text{ms}$ or $> 1500\,\text{ms}$) and a long $\text{TE}$, where tissues with slow transverse dephasing (long $T_2$, such as CSF, edema, and lesions) appear hyperintense (bright) and tissues with fast dephasing (short $T_2$, such as muscle) appear dark.

Proton Density ($PD$)-Weighted Image

An MRI sequence acquired with a long $\text{TR}$ (minimizing $T_1$ effects) and a short $\text{TE}$ (minimizing $T_2$ effects), producing image contrast predominantly dictated by differences in tissue proton concentration ($N(H)$).

MRI Image Contrast Matrix

A operational framework matching sequence parameters to tissue weighting: short $\text{TR}$ / short $\text{TE}$ produces $T_1$ contrast; long $\text{TR}$ / long $\text{TE}$ produces $T_2$ contrast; long $\text{TR}$ / short $\text{TE}$ produces Proton Density contrast; and short $\text{TR}$ / long $\text{TE}$ yields poor diagnostic contrast.