- Although only a "reference-region" overlay is required in principle, also use a "target-region" overlay corresponding to a high-binding region. At the beginning of analysis ("srtm glm.dat" from the unix line), the reference region is analyzed to give the chi-squared per degree of freedom and other parameters. This enables one to adjust parameters to minimize the chi2/DOF, which is important when using a time variation in a parameter such as k2a. Run the program ("srtm glm.dat") to view the chi2/DOF for the target region, kill the program and adjust the parameter of interest (e.g., tau in a gamma or sigmoid function for k2a), run again, and repeat until a best value is obtain. Then run to completion.
- An odd "feature" of this GLM is that BP is in the denominator of k2a, but BP generally is the parameter of interest. This means that k2a, rather than BP, is the parameter (together with an error bar) that is determined directly by GLM. To perform fixed-effects analyses across sessions, one can test time-dependent k2a values in the conditions.
- Because BP is a parameter of interest, in this implementation BP has been elevated to be a “pseudo-GLM parameter” (don’t look for this on Wikipedia - it’s my own invention, for better or worse). By convention, each GLM parameter of type “k2a” has a BP value associated with it. For a constant k2a value, the value is simply BP = k2/k2a - 1 if k2 is fit for every voxel, or R1/tau2’/k2a -1 when the time constant for the reference region is fixed. For a non-constant k2a value, the associated BP value is the value that occurs at the extrema of the function. For a sigmoidal function, this is the end of the run. For a gamma function, it is either the minimum/maximum of the gamma function, or the the end of the run if this occurs prior to the extrema. Using this convention, one can treat BP
a GLM parameter in many respects. A condition that is “AB”, where A is a baseline (constant) k2a parameter and B is a gamma-variate k2a parameter, will produce a “BP” value that is A+B, where the B value is the “dynamic binding potential” that occurs at the extrema of the gamma function. Accordingly, a map of displacement in BP units (with error bars, appropriate for use in a 2nd-level GLM) can be generated by the condition A-B, with positive values indicating displacement. However, the appropriate fixed-effects p-values for displacement are NOT associated with condition “A-B”, but with condition “B” alone, at least if one uses the typical approach of defining k2a as a constant value throughout the run plus a time-varying value that begins at some point well into the run. Whether or not one should base analyses on values of k2a or BP is not clear. Parameter k2a is determined by GLM with smaller relative error than BP (a derived quantity), but changes in BP produce relatively smaller changes in k2a assuming constancy of the other parameters.__like__