Active motor threshold (AMT) is simply the threshold for motor cortex excitability while the muscle is being contracted rather than at rest (RMT). They are very highly correlated and cortical excitability is generally a bit higher when the muscles are active (i.e., AMT is lower than RMT). You're probably fine using either one in your study assuming you're planning on stimulating part of the motor cortex, but like most experimental design choices, you should choose what seems more relevant to your task. Are your subjects going to be moving a lot? Are they going to primarily be sitting there at rest? What have previous studies that are similar to yours used?

Here's a paper that compared resting and active motor thresholds and various stimulation protocol that you might find useful: Article Comparison of transcranial magnetic stimulation measures obt...

Connor Spiech thanks for answering!My research has mainly measured MEP in the resting state, so rMT should be sufficient. Just curious about the meaning of aMT, I saw someone in youtube saying that since rmt cannot be detected in people with movement disorders, a more sensitive amt is used, I don't know if this statement is correct? Can it be said that amt is a supplementary version of rmt?Or we can say we introduce amt when we cannot detect rmt due to brain defect or muscle contraction.

The reason why a resting motor threshold wouldn't be as appropriate for people with movement disorders is that their hand (or whatever motor area is being thresholded) might be moving rather than actually resting. Since their muscles are more engaged, it would thus be better to just have them fully flex their hand while you find their motor threshold. The only difference between active and resting motor thresholds is whether they're flexing the muscle or resting it so it's just two sides of the same coin; you're measuring their corticospinal excitability in two different states of activity.

Connor Spiech Thank you very much for your answer, really help me a lot！