How do I align a 38400 one dimensional lines with a broad peak?

We are aquiring a one dimensional, non phase encoded line in our small animal MRI scanner every 50 ms for 32 minutes in order to see if there are any intensity differences at particular points of the spinal cord of mice.

Since the spinal cord is moving a little because of the breathing we have to realign these lines so the movement is cancelled out. The array we aquire is 128 (our spatial resolution) times 38400 (our temporal resolution) with the spinal cord being about 20 points of the 128. These 20 points are not always in the same position and need to be realigned but we do not have any distinct peaks - just the sudden signal increase at the beginning and the sudden signal drop of at the end of the spinal cord.

Can this be done with msalign?