1. Principles of Electrical Induction and Electromagnets

• Ampere’s Law: An electric current ($I$) moving through a conductor generates a magnetic field ($B$). The field strength is directly proportional to the current, expressed as $B \propto \mu_0 I$.

• Electromagnets: By coiling a wire and passing a current through it, a nearly uniform magnetic field is created inside the coil. This field mimics that of a bar magnet but can be controlled by the intensity of the current.

• Faraday-Lenz Law: Relative motion between a magnetic field and a coil induces a voltage. In MRI, the precessing magnetic fields of protons induce a high-frequency alternating voltage in the receiver coils.

2. NMR Components and Working Procedures

• Components of Standard NMR:

  1. Main Magnet: A powerful magnet that creates a strong external magnetic field ($B_z$) to align proton spins.

  2. Radiofrequency (RF) Coils: These act as both a transmitter (delivering pulses at the resonate frequency) and a detector (receiving the signal emitted by the sample).

• Working Procedure:

  1. The sample is placed within the external magnetic field ($B_z$).

  2. A short RF pulse is applied to the sample, causing energy absorption.

  3. The decaying electromagnetic signals emitted by the sample are detected and measured to determine chemical properties or tissue types.

3. Proton Precession and Larmor Frequency

• Spin and Precession: Protons ($H-1$) have a net positive charge and an intrinsic spin, which creates a small magnetic field ($B<em>p$). When placed in a strong external field ($B</em>z$), they do not just align; they precess (rotate) around the axis of the external field due to torque.

• Larmor Frequency Calculation: The frequency of this precession, known as the Larmor Frequency ($F_L$), depends on the strength of the external field:

  • General Formula: $F<em>L = \gamma B</em>z$

  • For Hydrogen ($H-1$): The gyromagnetic ratio ($\gamma$) is approximately $42.58 \text{ MHz/T}$. Thus, $F<em>L = 42.58 \times B</em>z$.

4. Resonant Absorption and Spin Flips

• Energy States: Protons in a magnetic field occupy two states: low-energy (spin up/parallel) and high-energy (spin down/anti-parallel).

• Resonant Absorption: When an RF photon with an energy corresponding exactly to the Larmor frequency hits a proton, the proton absorbs the energy and "flips" from the low-energy state to the high-energy state.

• Spontaneous Decay: Once the RF source is removed, the protons tend to return to their original low-energy state, releasing the absorbed energy.

5. Longitudinal and Transverse Magnetic Fields

• Longitudinal Magnetic Field ($B_L$): This arises from the net alignment of proton spins parallel to the external field. It is oriented along the z-axis. It is typically very small and difficult to detect while the main magnet is on.

• Transverse Magnetic Field ($B_T$): This is generated when an RF pulse is applied. The pulse causes the spins to precess in phase and tips the net magnetization into the xy-plane (transverse plane). This precessing transverse field is what induces the signal in the RF receiver coils.

6. Spin-Lattice (T1) and Spin-Spin (T2) Relaxation

• Spin-Lattice Relaxation ($T1$):

  • Refers to the recovery of the longitudinal field ($B_L$) as protons exchange thermal energy with the surrounding "lattice" (environment).

  • $T1$ is the time required for $B_L$ to recover to $63\%$ of its original value. In human tissues, this ranges from $0.3$ to $2.0$ seconds.

• Spin-Spin Relaxation ($T2$):

  • Refers to the decay of the transverse field ($B_T$) due to the loss of phase coherence between protons.

  • $T2$ is the time required for $B_T$ to decay to $37\%$ of its maximum value. It is influenced by atomic homogeneity and ranges from $30$ to $150 \text{ ms}$ in tissues.