Intuition for T1 vs T2 weighting in MRI
Published:
The overall signal intensity (S) of a spin echo sequence is: \(S = K \cdot [H] \cdot (1 - e^{-TR/T1}) \cdot e^{-TE/T2}\)
Where,
- $K$ is a scaling factor
- $[H]$ is the spin (proton) density
- $TR$ and $TE$ are the repetition and echo times, respectively
- $T1$ determines the rate at which the protons return to their normal spin, while
- $T2$ determines the rate at which the protons either reach equilibrium or go out of phase with each other.
- the exponential terms $e^{-x}$ are the T1 or T2 weighting terms
The table below summarizes how this equation helps us understand the effects of short and long TE and TR on MRI contrast.
- Naturally, $e^{-x} \in [0, 1]$
- When $e^{-x} \approx 1$, the effect of the term on signal intensity is negligible
- As such, the effects of T1 or T2 on signal intensity increase when their respective exponential terms decrease, i.e. approach zero
| Effect on T1 | Effect on T2 | |
|---|---|---|
| ↓ TE | x | $e^{-TE/T2} \rightarrow 1$, so T2 effects will decrease. |
| ↑ TE | x | $e^{-TE/T2} \rightarrow 0$, so T2 effects will increase |
| ↓ TR | $(1 - e^{-TR/T1}) \rightarrow 0$, so T1 effects will increase | x |
| ↑ TR | $(1 - e^{-TR/T1}) \rightarrow 1$, so T1 effects will decrease | x |
Another way to understand the effect of TE on T2-weighting is to consider the signals generated by two tissues with different T2 values. When TE is short, the echo occurs when there has been little time for T2-decay to have taken place and hence the tissues are not differentiated. If TE is long, the relative differences in signal decay between the two tissues become more noticeable, and hence more “T2-weighting.”