Physics of MRI: How an MRI Scanner Works
Magnetic Resonance Imaging (MRI) is based on the principles of nuclear magnetic resonance (NMR), which involves the interaction of atomic nuclei with a strong magnetic field and radiofrequency (RF) pulses. Below is a detailed explanation of the physics behind MRI.
1. Fundamental Principles of MRI
MRI primarily exploits the magnetic properties of hydrogen nuclei (protons), as hydrogen is abundant in the human body (mainly in water and fat).
A. Nuclear Magnetic Resonance (NMR)
- Protons have spin: Hydrogen nuclei (protons) possess an intrinsic property called spin, which creates a tiny magnetic field.
- Alignment in a Magnetic Field: When placed in a strong magnetic field (B₀), these proton spins align either parallel (low energy) or anti-parallel (high energy) to the field.
- Net Magnetization Vector: Since slightly more protons align parallel than anti-parallel, a net magnetization vector (M₀) forms along the direction of B₀.
B. Larmor Frequency and Precession
- Precession: Protons do not stay fixed in place; instead, they rotate (or “precess”) around the magnetic field axis at a specific frequency known as the Larmor frequency (ω₀).
- Larmor Equation: ω0=γB0\omega_0 = \gamma B_0 where:
- ω0\omega_0 is the Larmor frequency (in MHz),
- γ\gamma is the gyromagnetic ratio (42.58 MHz/T for hydrogen),
- B0B_0 is the magnetic field strength (in Tesla).
C. RF Excitation and Resonance
- Applying an RF Pulse: When a radiofrequency (RF) pulse at the Larmor frequency is applied perpendicular to B₀, protons absorb energy and tip away from alignment with the field.
- Flip Angle: The RF pulse rotates the magnetization vector (typically by 90° or 180°).
- Resonance: The energy absorption occurs only at the Larmor frequency, a phenomenon known as resonance.
2. Relaxation Processes and Signal Detection
After the RF pulse is turned off, the protons return to their original alignment with B₀, releasing absorbed energy in a process called relaxation.
A. T1 Relaxation (Longitudinal Relaxation)
- Definition: T1 relaxation refers to the time it takes for the net magnetization vector to recover along the main field direction (B₀).
- Exponential Recovery: Mz(t)=M0(1−e−t/T1)M_z (t) = M_0 \left( 1 – e^{-t/T_1} \right)
- Tissue Dependence: Different tissues have different T1 times (fat has a short T1, cerebrospinal fluid (CSF) has a long T1).
B. T2 Relaxation (Transverse Relaxation)
- Definition: T2 relaxation refers to the dephasing of proton spins in the transverse plane due to spin-spin interactions.
- Exponential Decay: Mxy(t)=Mxy(0)e−t/T2M_{xy} (t) = M_{xy}(0) e^{-t/T_2}
- Tissue Dependence: T2 is shorter in tissues with high molecular interactions (muscle, white matter) and longer in fluids (CSF).
C. T2 Decay (Magnetic Inhomogeneities)*
- T2 (T2-Star) Relaxation*: Represents additional dephasing caused by inhomogeneities in the magnetic field.
- Faster decay than T2: Since it includes both spin-spin interactions and external magnetic field variations.
3. Image Formation: Spatial Encoding
A. Magnetic Field Gradients
To generate images, MRI scanners use additional magnetic fields (gradients) to encode spatial information along three axes:
- Slice Selection (Z-axis gradient)
- A gradient magnetic field is applied so that only protons at a specific Larmor frequency are excited, selecting a slice of tissue.
- Frequency Encoding (X-axis gradient)
- A gradient changes the Larmor frequency along one axis, allowing differentiation of signals based on frequency.
- Phase Encoding (Y-axis gradient)
- A different gradient introduces a phase shift to differentiate signals along the remaining axis.
B. Fourier Transform and k-Space
- Raw MRI data is collected in k-space (a spatial frequency domain).
- 2D or 3D Fourier Transform (FFT) is used to reconstruct the final MRI image.
4. MRI Contrast Mechanisms
Different MRI sequences manipulate T1, T2, and proton density to enhance contrast:
- T1-Weighted Imaging (T1-WI): Short TR (Repetition Time) & Short TE (Echo Time); best for anatomy.
- T2-Weighted Imaging (T2-WI): Long TR & Long TE; best for pathology (fluid appears bright).
- Proton Density (PD) Imaging: Intermediate TR & TE; emphasizes tissue density.
- Diffusion-Weighted Imaging (DWI): Sensitive to water movement, useful for stroke detection.
- Functional MRI (fMRI): Measures blood oxygenation levels to study brain function.
5. Advanced MRI Techniques
- Fast Spin Echo (FSE): Faster imaging by acquiring multiple echoes in one TR cycle.
- Echo Planar Imaging (EPI): Very rapid imaging, used in fMRI and DWI.
- Magnetic Resonance Spectroscopy (MRS): Analyzes tissue chemical composition.
- Diffusion Tensor Imaging (DTI): Maps white matter tracts in the brain.
6. Summary of MRI Physics
| Step | Description |
|---|---|
| Proton Alignment | Protons align with B₀ when placed in a magnetic field. |
| Precession & Larmor Frequency | Protons precess at a frequency ω₀ = γB₀. |
| RF Excitation | An RF pulse tips the magnetization vector, exciting protons. |
| Relaxation (T1 & T2) | Protons return to equilibrium, releasing signals. |
| Spatial Encoding | Magnetic gradients allow localization of signals in 3D. |
| Signal Detection & Reconstruction | Fourier Transform processes raw k-space data into an image. |
MRI is a highly sophisticated imaging modality that leverages quantum mechanics, electromagnetic theory, and signal processing to produce detailed anatomical and functional images.