Voxel spread function method for correction of magnetic field inhomogeneity effects in quantitative gradient-echo-based MRI

Abstract

Purpose: Macroscopic magnetic field inhomogeneities adversely affect different aspects of MRI images. In quantitative MRI when the goal is to quantify biological tissue parameters, they bias and often corrupt such measurements. The goal of this article is to develop a method for correction of macroscopic field inhomogeneities that can be applied to a variety of quantitative gradient-echo-based MRI techniques.

Methods: We have reanalyzed a basic theory of gradient echo MRI signal formation in the presence of background field inhomogeneities and derived equations that allow for correction of magnetic field inhomogeneity effects based on the phase and magnitude of gradient echo data. We verified our theory by mapping effective transverse relaxation rate in computer simulated, phantom, and in vivo human data collected with multi-gradient echo sequences.

Results: The proposed technique takes into account voxel spread function effects and allowed obtaining virtually free from artifacts effective transverse relaxation rate maps for all simulated, phantom and in vivo data except of the edge areas with very steep field gradients.

Conclusion: The voxel spread function method, allowing quantification of tissue specific effective transverse relaxation rate-related tissue properties, has a potential to breed new MRI biomarkers serving as surrogates for tissue biological properties similar to longitudinal and transverse relaxation rate constants widely used in clinical and research MRI.

Keywords: MRI; gradient echo; magnetic field inhomogeneities; magnetic susceptibility.

Figure 1

The voxel spread function as a function of the distance from a given voxel to the neighboring voxel (0, 1, 2, 3, 4) and the parameter q (range from 0 to 2). Left panel – the original voxel spread function, Eq. [18]; right panel – the voxel spread function for Hanning filtered data, Eq. [26].

Figure 2

Frequency profile through the 1D object used in simulation (left panel) and a corresponding frequency gradient (right panel). The frequency profile was adopted from human data and measured going anterior → posterior through the center of an imaging slice shown in Fig. 6.The square is a representative point used for illustrations in Fig. 3.

Figure 3

Example of the data (circles) corresponding to the point indicated by the square in Fig. 2, where the field gradient is very steep. Left panels (A and C) represent magnitude data and corresponding F-functions; right panels (B and D) represent phase data and their linear fits to initial portion. A and B - no filter, C and D - Hanning filtered data. Red lines in A and C show the F-function calculated with m ranging from −2 to 2, per Eq. [23]; Blue line in A corresponds to the F-function calculated with m ranging from −8 to 8. Data are plotted against the parameter q introduced in Eq. [14].

Figure 4

R2^* profiles of the simulated data. Dotted line shows R2* profile resulting from mono-exponential fitting without F-function, solid line - with F-function, Eq. [32]. Since signal in simulated data decays only due to field inhomogeneities, the true R2^* should be zero. Application of the F-function gives very good results except for points at the edges, where the background field gradient is maximal.

Figure 5

Example of the images obtained from the phantom study without (left panel) and with (right panel) correction for the macroscopic magnetic field inhomogeneities. The upper row represents R2^* maps and the lower row represents signal intensity maps S(0). Data were analyzed after applying Hanning filter.

Figure 6

Example of the data obtained from a human subject. Left image – signal intensity map, middle and right images – R2^* map obtained without and with correction for field inhomogeneities, respectively. Data were analyzed after applying Hanning filter.

Figure 7

Distribution of the frequency gradients in x (A), y (B), and z (C) directions measured in human brain. The vertical axes of the histograms are # of pixels in the brain, and horizontal axes are gradients of frequencies in the brain in ppm/cm. Dash lines enclose a range of the gradients where the error in estimating F-function is less than 1% (q < 0.3) under our experimental condition with maximal TE = 44 ms and resolution of 1×1×3 mm³.