A Complex fMRI Activation Model With a Temporally Varying Phase

Recently Rowe and Logan (2004) introduced a complex fMRI activation model in which multiple regressors were allowed, hypothesis tests were formulated in terms of contrasts, and the phase was directly modeled as a fixed unknown quantity which may be estimated voxel by voxel. This model was shown to achieve higher detection power over the usual magnitude-only normal model especially at decreased signal-tonoise ratios. Here, we extend this model to allow for a dynamic rather than constant phase. It is seen that this dynamic phase complex fMRI model has identical regression coefficients and activation F-statistics as that of the magnitude-only model although derived with the phase included. It is also seen that the maximum likelihood estimate of the variance in this model is not consistent.