T2 Relaxation in MRI

What is T2 Relaxation?

In MRI, T2 relaxation (also known as transverse relaxation) refers to the process where hydrogen protons, after being disturbed by an RF (radiofrequency) pulse, lose phase coherence with each other.

While T1 relaxation describes how protons realign with the magnetic field, T2 describes how they lose their synchronized spinning or "phase coherence" in the transverse plane (the plane perpendicular to the main magnetic field).

Example: Imagine a group of spinning tops. If you spin them all at the same speed at first, they stay in sync. Over time, they start spinning at different speeds due to slight differences, and they lose their synchronized movement. This loss of synchronization is similar to T2 relaxation.

The Physical Process of T2 Relaxation

During T2 relaxation, the hydrogen protons begin to lose their alignment with each other in the transverse plane. Initially, after an RF pulse, the protons are all aligned and spinning together. But as time passes, small variations in the local magnetic field cause each proton to spin at slightly different rates. This leads to the loss of phase coherence, and the MRI signal starts to decay.

The rate at which this loss of coherence occurs is determined by the T2 time, which is different for different tissues in the body. Tissues with a short T2 time lose coherence quickly, while tissues with a long T2 time maintain coherence for a longer period.

Mathematics Behind T2 Relaxation

The mathematical description of T2 relaxation is based on an exponential decay of the signal. The magnetization of the protons in the transverse plane decays exponentially over time. This can be expressed by the equation:

\[ M(t) = M_0 \cdot e^{-t/T2} \] where: - \( M(t) \) is the magnetization at time \( t \), - \( M_0 \) is the initial magnetization, - \( T2 \) is the transverse relaxation time, - \( t \) is the time elapsed after the RF pulse.

This equation shows that the magnetization decays exponentially as time progresses, and the rate of decay depends on the tissue’s T2 time. A shorter T2 time means faster decay, and a longer T2 time means slower decay.

Why T2 Relaxation Matters in MRI

T2 relaxation is important because it helps define how tissues appear in T2-weighted MRI images. Tissues with longer T2 times, like water-rich tissues (e.g., brain or muscle), tend to have a stronger signal and appear brighter on T2-weighted images. On the other hand, tissues with shorter T2 times, such as bone or fat, lose their signal more quickly and appear darker on T2-weighted images.

Example: In T2-weighted MRI scans, the brain (which has a long T2 time) appears bright, while bones (with a very short T2) appear dark.

Examples of T2 Relaxation in Different Tissues

Tissue	T2 Time (ms)
Brain	80-100 ms
Muscle	40-50 ms
Fat	30-40 ms
Bone	0-10 ms

As shown in the table above, brain tissue has a relatively long T2 time compared to fat and bone. This is why brain tissue shows up much brighter on T2-weighted images, while bone (with a very short T2) shows up as dark.

How T2 Relaxation Affects MRI Imaging

T2 relaxation is used to create T2-weighted MRI images, which are particularly useful for detecting abnormalities such as inflammation, tumors, and lesions. Tissues that retain their signal for a longer time (long T2) are highlighted in T2-weighted images, which is useful for visualizing structures like the brain, spinal cord, and muscles.

MRI technicians can adjust the scan parameters (e.g., echo time \( TE \)) to emphasize the T2 decay and create clear, high-contrast images.

Example: In a T2-weighted image of the brain, a stroke might appear as a bright area because the tissue has a longer T2 time and retains the signal, while surrounding healthy tissue appears darker due to shorter T2 times.

Summary

T2 relaxation is an essential concept in MRI that explains how hydrogen protons lose their phase coherence in the transverse plane over time. It describes how the MRI signal decays and is influenced by the T2 time of different tissues. Understanding T2 relaxation is crucial for interpreting T2-weighted MRI images and diagnosing medical conditions.