For a single run, the use of 3 parameters provides a GLM analysis equivalent to the original SRTM (Lammertsma 1996). Other acronyms for linear SRTM include MRTM (Ichise 2003) and LSRRM (Alpert 2003). If k2' is set as a global constant, then this is MRTM2 (Ichise 2003). Files for describing a single scan using each type of analysis are shown below.
LSRRM or MRTM MRTM2
96 0. # [number time points] [k2'] 96 0.25 # [number time points] [k2']
1 R1 constant # event 1, constant value 1 R1 constant # k2=R1*k2' above
0 # start at 0, end at end-of-run 0
a k2 constant # required k2, because k2'=0 A k2a constant
A k2a constant # k2a, from which BP is calculated
In some case, one might want a time dependence on k2a; when using 3 constant parameters, this again is LSRRM. This could be added to either file above. A time dependence in k2a starting at 30 minutes into a scan can be added as below. In the example, the constant k2a term is applied to the entire scan, and the gamma time dependence is applied starting at 30 minutes and continuing to the end of the run.
LSRRM without variable k2, or MTRM2 plus time dependence
96 0.25 # [number time points] [k2']
1 R1 constant # k2=R1*k2' above
A k2a constant
B k2a gamma # normalized gamma = t/tau * exp(1-t/tau)
30 25 # start at time=30 minutes, use tau=25 minutes
Finally, one could choose to employ a basis set of time-dependent parameters like gamma functions (Normandin 2012). One would specify a series of gamma functions with different tau values but the same starting time. Alternatively, one could employ a basis set of sigmoidal functions, or some other user-specified basis set (e.g., B-spline basis functions) implemented through the table file associated with the run. In practice, only one or a very few time-dependent terms will provide optimal chi2/DOF.