Recovery of chemical estimates by field inhomogeneity neighborhood error detection (REFINED): fat/water separation at 7 tesla.

Magnetic resonance imaging (MRI) fat quantification can be used for monitoring several physiological and disease processes, including fatty infiltration of the liver (hepatic steatosis)(1, 2) and heart(3, 4), as well as for automatic analysis of adipose(5) and brown adipose(6) volumes. Mouse models are ideal for studying the effects of genes, diet, exercise and therapeutics on lipid stores, so we are developing MRI methods for performing fat quantification on such models. Dixon methods have been useful for monitoring changes in the lipid content of tissues. This class of methods uses multiple acquisitions with varying echo time shifts to elicit varying phase differences between fat and water(7). The chemical parameters are then estimated by modeling the signal as a function of the phase differences caused by the chemical and field inhomogeneity shifts(8). However, since these phase differences are modeled as complex exponentials, the multiplication of the two complex exponentials results in a periodic cost function with multiple minima per period(9, 10). This creates an ambiguity in the estimation of the chemical parameter maps that can lead to a local “swap” of fat and water, where the fat estimate appears in the water parameter map, and vice versa. Many attempts have been made to resolve the ambiguity using the a priori knowledge of B0 field map (ψ) smoothness, based on the observation that real magnetic fields do not have discontinuities. Region-growing schemes(11–14) have been used to generate initial guesses at each pixel. However, these algorithms are prone to error propagation, since the initialization at a pixel depends on the previously solved pixels. Another approach to using the a priori knowledge of field smoothness is to formulate the cost function with a Markov Random Field (MRF) prior(Equation 1): ψ=argmin(∣Scomputed(ψ,TE)-Ssignal(TE)∣2︸datacost+μ∑j∈Nwq,j∣ψq-ψj∣2︸smoothnesscost) (1) where μ is a weighting constant (empirically determined), and w is the inverse of the Euclidean distance between the current pixel of interest (q) and a neighboring pixel (j). This formulation can then be solved using a number of network algorithms such as Iterated Conditional Modes (ICM)(15, 10), Graph Cuts(16, 17), or Loopy Belief Propagation(18). The MRF formulation enforces local smoothness, but this does not necessarily ensure correct decomposition of fat and water because of what we call “clumping errors”: regions that have sufficient cohesiveness to result in partial swaps (part of the image) or complete swaps (the entire image). Partial swaps of water and fat occur when portions of the chemical parameter maps are swapped relative to one another. This happens because each of these regions has sufficient spatial cohesiveness to overcome the smoothness penalties at the borders between the regions (Figure 1). Partial swaps leave demarcations in the B0 field map wherever a swap occurs. In contrast, complete swaps occur when the MRF formulation results in a globally smooth B0 field map, but the estimation in every pixel converges to an incorrect minimum, resulting in a chemical swap at every pixel. Complete swaps may not leave discontinuities in the B0 field map to indicate that an error has been made. Open in a separate window Figure 1 B0 field map with clumping errors. When clumping errors are made, the swapped regions (arrows) appear piecewise constant, while the unswapped region (any part of the mouse caudal to the apex of the visible lung and the phantom) also appears similarly piecewise constant. The variation between regions is much higher than the variation within each region. We found it useful to categorize two types of partial swap regions: those that are circumscribed by other regions (“holes”, solid arrows), and those that touch the edge (“edge groups”, dashed arrows).