Rose model in MRI: noise limitation on spatial resolution and implications for contrast enhanced MR angiography

Introduction The relationship between noise and detectable spatial resolution is described by the Rose Model: the differentiation of a single voxel from the noise background requires a minimum signal-to-noise ratio (SNR) per voxel of 4 (1,2). This model has been widely used as a guide in x-ray imaging. This study assesses its implication for MRI and develops a guideline forkspace sampling. In k-space, the signal falls off rapidly with k-space radius whereas the noise power is constant over the entire frequency range (2). Increasing the sampled volume of k-space increases resolution at the expense of decreased image SNR. When the SNR is reduced to the Rose limit (-4), the detectable resolution ceases to increase. This noise limit on detectable spatial resolution indicates that there is a cutoff k-space radius corresponding to maximum resolution and optimal scan time. Optimizing k-space and scan time is particularly important for contrast enhanced MRA (CEMRA). Many techniques such as timing, undersampling and view ordering have been developed to maximize the contrast enhancement at the k-space center (3). How big is the center of k-space? The Rose model is used to answer this question. Methods and results Rose model The original Rose criterion requires direct measurement of the voxel SNR (statistical properties) and the voxel conspicuity (human observation). The former criterion can be considered as a statistical test for a hypothesis that the probability distribution of the signal intensity in one voxel is significantly different from that of the background. The probability distribution can be obtained from many repeated experiments, which are not realistic to perform. To overcome this problem, a uniform phantom can be imaged once, and the statistical distribution can be estimated from the voxel intensities over a large area of the uniform phantom. Such statistical analysis provides a link to express the Rose criterion in k-space. To measure signal and noise in k-space, two nominally identical acquisitions m,(k) and mZ(k) were obtained from a uniform spherical phantom. Complex subtraction of the measurements, and taking the mean-square average within an annulus of radius k, in k-space yields the RMS noise, o(k,). o(k$ = % while taking the mean-square values from a single measurement gives the RMS signal, S(k). S(kJ2 = o(kJ2 Figure 1 shows the measured k-space SNR for a 5 12x5 12 acquisition from a uniform spherical phantom using a body coil and a fast gradient echo sequence. As the acquisition moves towards the edge of k-space (from b to e), the kSNR =S(k,)/ o(kJ decreases as approximately kre3”, the voxel SNR (vSNR) decreases, and the histograms of noise and signal broaden and overlap. The detected image resolution (phantom edge) first increases with sampled k,, (from b to c, where there is no overlap between noise and signal histograms) and then starts to be noise limited (d, 9.8% overlap, and e, 28.8% overlap). The image quality of e is substantially inferior to c&d.; The optimal detected resolution (-1.5 mm) is achieved somewhere between c&d;, corresponding to vSNR 4 and kSNR 0.05. The same cutoff kSNR value was also obtained using a head coil with a 3-fold increase in detected optimal resolution