3.2 Tissue Characteristics and Relaxation

The Concept of Relaxation

Immediately after the radiofrequency (RF) excitation pulse is turned off, the Net Magnetization Vector (NMV) is in the transverse plane, and the hydrogen protons are precessing in phase. The system is in a high-energy, unstable state. The process by which the hydrogen protons lose this absorbed energy and return to their original thermal equilibrium (aligned parallel to the external magnetic field B0) is known as relaxation.

Relaxation consists of two independent and simultaneous processes:

1. Longitudinal Recovery (T1 Relaxation): The recovery of magnetization along the longitudinal axis (z-axis).
2. Transverse Decay (T2 Relaxation): The decay of magnetization in the transverse plane (xy-plane).

Longitudinal Recovery (T1 Relaxation)

Longitudinal recovery, also known as T1 relaxation or spin-lattice relaxation, is the process where hydrogen protons release their absorbed energy to the surrounding molecular environment, known as the lattice. As the protons lose energy, they transition from the high-energy anti-parallel state back to the low-energy parallel state. This energy transfer allows the longitudinal magnetization (Mz) to grow back toward its original equilibrium value (M0).

The mathematical behavior of longitudinal recovery follows an exponential growth curve:

Mz(t) = M0 × (1 - e^(-t/T1))

Where T1 is the specific T1 relaxation time of the tissue. T1 is defined as the time it takes for the longitudinal magnetization to recover to 63% of its original value after a 90-degree RF pulse. Because this recovery is exponential, it takes approximately five times the T1 value (5 × T1) for a tissue to achieve nearly 100% longitudinal recovery.

The efficiency of T1 relaxation depends on how closely the molecular tumbling frequency of a tissue matches the Larmor precessional frequency. If the molecular tumbling rate matches the Larmor frequency, energy transfer is highly efficient, resulting in a short T1 relaxation time:

• Fat: Fat molecules are large, heavy, and packed tightly together, which causes them to tumble relatively slowly. This slow tumbling frequency closely matches the Larmor frequency of hydrogen (63.87 MHz at 1.5 T). Consequently, fat transfers energy to its lattice very efficiently, giving it a short T1 relaxation time (approximately 200–300 ms at 1.5 T).
• Water/CSF: Water molecules (such as in cerebrospinal fluid) are small, spaced far apart, and tumble extremely rapidly. Their tumbling frequency is much higher than the Larmor frequency. Energy transfer is inefficient, giving water a long T1 relaxation time (approximately 3000–4000 ms at 1.5 T).

Transverse Decay (T2 Relaxation)

Transverse decay, also known as T2 relaxation or spin-spin relaxation, is the decay of transverse magnetization (Mxy) due to the loss of phase coherence. Unlike T1 relaxation, which involves energy transfer to the lattice, T2 relaxation is caused by interactions between the magnetic fields of neighboring protons (spin-spin interactions).

As protons precess in the transverse plane, their magnetic fields interact, causing some protons to speed up slightly and others to slow down. This causes the protons to fan out and lose their phase coherence. As dephasing occurs, the net transverse vector (Mxy) shrinks.

The mathematical behavior of T2 decay follows an exponential decay curve:

Mxy(t) = Mxy(0) × e^(-t/T2)

Where T2 is the T2 relaxation time of the tissue. T2 is defined as the time it takes for the transverse magnetization to decay to 37% of its initial value (meaning 63% of the phase coherence has been lost). T2 decay is exponential, and it takes approximately five times the T2 value (5 × T2) for transverse magnetization to decay completely to zero.

T2 relaxation depends on molecular packing and the frequency of spin-spin interactions:

• Fat: Fat molecules are tightly packed, allowing frequent and efficient spin-spin interactions. This causes rapid dephasing and a short T2 relaxation time (approximately 60–80 ms at 1.5 T).
• Water/CSF: Water molecules are widely spaced and move rapidly, which averages out the local magnetic field variations. Spin-spin interactions are infrequent, resulting in a long T2 relaxation time (approximately 2000–3000 ms at 1.5 T).

T2* Decay vs. Pure T2 Decay

In a clinical scanner, transverse magnetization decays much faster than the rate predicted by pure T2 relaxation. This rapid decay is called T2* (T-two star) decay.

T2* decay is the combination of two distinct dephasing effects:

1. True T2 Decay (Spin-Spin Relaxation): Caused by random, time-dependent molecular interactions. This decay is irreversible.
2. Inhomogeneity Dephasing: Caused by static variations in the magnetic field. These variations include imperfections in the main magnet (B0 inhomogeneities), chemical shift between fat and water, and magnetic susceptibility differences at tissue boundaries (e.g., bone-soft tissue interfaces). Because these field variations are static and fixed in space, their dephasing effects are deterministic and can be reversed (refocused) using a 180-degree RF pulse.

The relationship is expressed as:

1/T2* = 1/T2 + 1/T2_inhom

Because T2* includes both effects, T2* is always significantly shorter than true T2 (typically under 40 ms).

Proton Density (PD)

Proton density (or spin density) represents the concentration of mobile hydrogen protons per unit volume of tissue. Proton density determines the maximum possible longitudinal magnetization (M0) that a tissue can achieve. Tissues with a high concentration of mobile hydrogen protons (like CSF or kidneys) have a high proton density and can produce a strong MR signal. Tissues with a low concentration of mobile hydrogen (like air or cortical bone) have a low proton density and produce very little signal.

It is important to note that proton density only measures mobile hydrogen protons (found in fluids and soft tissues). Hydrogen atoms that are tightly bound within large, solid macromolecules (such as in the matrix of cortical bone) cannot tumble. Their spin-spin interactions are so rapid that their T2 decay occurs within microseconds—long before the scanner can begin collecting data. Consequently, cortical bone appears black on all MRI pulse sequences due to a lack of detectable mobile protons.

Tissue Relaxation and Density Properties