Figure 1.

Schematic of the ME-fMRI signal model and the ME-SPFM algorithm. From left to right: An activity-inducing signal (∆a(t)) is convolution with the hemodynamic response (ℎ(t)) resulting in the activity-induced hemodynamic signal or BOLD responses (i.e. $\mathrm{\Delta }{R}_2^{*}(t)$). The convolution step can be modelled as multiplying the activity inducing signal with a Toeplitz matrix whose columns are shifted HRFs every TR. Percentage signal changes of the fMRI signal acquired at TE_k can be modelled as the sum of the hemodynamic signal scaled by TE_k (i.e. $-T{E}_k\mathrm{\Delta }{R}_2^{*}(t)$), fluctuations of the net magnetization (∆ρ(t)), and other noisy sources (e.g. thermal noise) (∆n(t)). The percentage signal changes of all echoes (or their MEICA denoised versions) are concatenated and input to ME-SPFM algorithm, which solves a regularized least squares problem, to obtain estimates of the activity inducing signal.