Simplified Signal Equations for Spoiled Gradient Echo MRI

INTRODUCTION: This work presents simplified signal equations for spoiled gradient echo (SPGR) imaging that, to the authors' knowledge, has not been published. The framework introduces an exponential time constant TA, which reflects magnetization loss from the rf pulse. This framework is then used for to consider image SNR and T1 contrast. THEORY: Image SNR can be approximated as the product of (SNR/spin)*(spins/voxel), the first term derived from spin physics, and the second representing voxel volume (resolution) and proton density. This abstract focuses on the first term, which will be called SNRspin. This work also sets many constant terms to one without loss of generality. The longitudinal magnetization loss each TR from a flip angle α is cos(α); this magnetization loss, along with T1 recovery, affects the signal and determines T1 contrast in an image, and can be equated to an exponential signal loss using a time constant TA, i.e. cos(α) = e [1] If one varies α and TR according to Eq. [1] in order to keep a constant TA, T1 contrast remains equivalent; this is illustrated in Fig. 1.