Elsevier

NeuroImage

Volume 60, Issue 1, March 2012, Pages 818-829
NeuroImage

Correction of gradient echo images for first and second order macroscopic signal dephasing using phase derivative mapping

https://doi.org/10.1016/j.neuroimage.2011.11.083Get rights and content

Abstract

Gradient echo techniques are often hampered by signal dephasing due to macroscopic phase perturbations because of system imperfections (shimming) or object induced perturbations of the magnetic field (hemorrhagic lesions, calcified tissue, air–tissue interfaces). Many techniques have been proposed to reduce the effects of macroscopic phase variations. Among these techniques are tuned pulse sequences, fitting techniques and reconstruction algorithms. These methods, however, suffer from one or more of the following drawbacks: they require longer acquisition times, require additional acquisitions, compensate only locally, can only be applied to multi-gradient echo data or may result in inaccurate results.

In this work a generally applicable post-processing technique is presented to evaluate and compensate signal alterations invoked by first and second order macroscopic phase incoherences. In this technique, the derivatives of the signal phase are determined by applying the Fourier derivative theorem on the complex data. As a result, the phase derivatives are obtained without phase unwrapping and without compromising the resolution. The method is validated for single and multi-echo acquisitions by experiments on a co-axial cylinder phantom with known macroscopic field disturbances. The potential of the method is demonstrated on a multi-gradient echo acquisition on the head of a human volunteer. In general a first order correction is shown to be sufficient, however higher order correction is found to be beneficial near sharp transitions of the magnetic field.

Highlights

► Dephasing due to macroscopic phase incoherence degrades gradient-echo images. ► Multi-echo and single-echo dephasing is evaluated by a Taylor expansion of the phase. ► Signal incoherence is corrected without loss of resolution or extra acquisitions. ► Largest R2*-corrections (3 s 1) in the brain occur near the skull and air cavities. ► Second order correction improves first order corrected data at sharp transitions.

Introduction

Gradient echo MR imaging is routinely used for many purposes, for example, for assessing treatment response (Dahnke and Schaeffter, 2005, Nijsen et al., 2004, Seppenwoolde et al., 2005), for imaging and tracking of devices during MR-guided interventions (Peters et al., 2009, Seevinck et al., 2011, Varma et al., 2009), and for depiction of disease, e.g., in Parkinson's disease, cancer, and stroke (Conijn et al., 2011, Dennie et al., 1998, Haacke et al., 2004, Ordidge et al., 1994, Sedlacik et al., 2008, Seevinck et al., 2010, Wood et al., 2005, Wu et al., 2009). The choice for gradient echo sequences for such applications is usually motivated by advantages in terms of imaging speed, power deposition and sensitivity to mesoscopic field inhomogeneities (R2). These advantages result from the absence of a 180° refocusing pulse as is employed in spin echo acquisitions.

The absence of a 180° refocusing pulse can result in desired and in undesired effects. Discrimination between desired and undesirable signal dephasing effects is situation dependent and usually performed by a radiologist or researcher. As regards the undesired effects, the gradient echo signal is degraded by macroscopic phase perturbations. Macroscopic field inhomogeneities, which are characterized by changes of the magnetic field over distances larger than the voxel size (Baudrexel et al., 2009, Volz et al., 2009), include system imperfections, e.g. incorrect shimming, object induced magnetic field disturbances (hemorrhagic lesions, calcified tissue) and field inhomogeneities at extremities of the body (e.g. at the back of the head) (Moerland et al., 1995). More extreme examples of macroscopic field inhomogeneities are typically observed near air tissue interfaces e.g. near the lungs or at the nasal cavity. With regard to the desired effects, the available contrast (R2*) can be applied to study mesoscopic field inhomogeneities. Mesoscopic field inhomogeneities are variations of the magnetic field on the order smaller than the voxel-size, but larger than the diffusion length. These inhomogeneities are usually caused by susceptibility differences within tissue, for example due to micro-calcifications, by the deoxygenation of blood, due to microbleeds and near T2-contrast agents. Despite the difference in order at which they affect the signal, the effects of mesoscopic field inhomogeneities and macroscopic field inhomogeneities are not easily separated. Because macroscopic field distortions are generally proportional to the field-strength and considering the tendency to employ increasingly strong main magnetic field strengths for MR imaging, undesirable macroscopic phase effects constitute an increasingly large problem.

During the last two decades many techniques have been proposed to reduce the effects of macroscopic magnetic field inhomogeneities. Among these techniques are tuned pulse sequences, fitting techniques and reconstruction algorithms. Tuned signal acquisition techniques are usually designed to overcome (a part of) the undesired effects of the macroscopic field inhomogeneities on the signal. Examples are the utilization of extra local gradients (Deichmann et al., 2002, Posse et al., 2003, Seppenwoolde et al., 2003), adaption of the excitation pulse (Baudrexel et al., 2009, Stuber et al., 2007) and tuning of the encoding gradients (Jung et al., 2010, Zhang, 1994, Zheng and Price, 2007). These techniques usually require precise tuning for effective compensation, lengthen acquisition times, and compensate in a limited number of directions or compensate locally, while introducing signal dephasing in other areas. Fitting techniques on the other hand do not try to compensate, but fit the signal with a model that includes the macroscopic signal dephasing (Baudrexel et al., 2009, Dahnke and Schaeffter, 2005, Fernandez-Seara and Wehrli, 2000Yang et al., 2010). The fitting techniques can therefore be applied to multi-gradient echo data only. Since these methods can only be applied to multi-echo data, they are unsuitable for a number of applications that use the R2 contrast but acquire only one or two gradient echoes (Conijn et al., 2011, Haacke et al., 2004, Sedlacik et al., 2008). Furthermore, since these fitting algorithms introduce additional fitting parameters on a limited number of data points, the procedure may end up in a local minimum or result in inaccurate results (Baudrexel et al., 2009, Fernandez-Seara and Wehrli, 2000). The third approach consists of reconstruction algorithms which reduce the effects of macroscopic phase perturbations by applying a field and a (R2-) relaxation-map during delayed (iterative) reconstruction. Although these reconstruction techniques can be applied to single-echo data, they require extra acquisitions to determine the field-map and relaxation-map. Especially field mapping is difficult and increases the acquisition time. Furthermore, the reconstruction methods lengthen the reconstruction time significantly because of the number of reconstructions required during the iterative process of reconstruction (Chen et al., 2008, Knopp et al., 2009, Schomberg, 1999, Volz et al., 2009).

In this work a generally applicable post-processing technique is presented to evaluate and compensate signal alterations invoked by first and second order macroscopic phase incoherences. In this technique, the derivatives of the signal phase are determined by applying the Fourier derivative theorem on the complex data. As a result, the phase derivatives are obtained without phase unwrapping and without compromising the resolution. The method is validated for single and multi-echo acquisitions by experiments on a co-axial cylinder phantom with known macroscopic field disturbances. Furthermore experiments on gels containing Holmium loaded microspheres are carried out to demonstrate that the technique corrects for macroscopic signal dephasing effects, while leaving the mesoscopic signal dephasing unaffected. The potential of the method is demonstrated on a multi-gradient echo acquisition of the head of a human volunteer.

Section snippets

The phase derivative

The phase of a complex (MR) signal is defined as:P=arg[s]=arctan[IR]with R, I the real and imaginary signal, respectively. The arctan function is the four quadrant arctangent function, whose values are restricted to the (− π, π]-interval. Through the arctangent-operation any value of the true phase outside the (− π, π]-interval is wrapped into this interval, creating a black and white stripe (wrapping) pattern around local field distortions. To obtain the true field or field derivatives, which

Infinite cylinder phantom

For qualitative and quantitative validation of the correction method a coaxial cylinder phantom was used. The phantom had a known susceptibility difference between the inner cylinder and outer annular region. The phantom consisted of a plastic container with a diameter and height of 10 cm. The container was filled with a 17.4 mM Holmium(III)-doped agarose gel, with a volume susceptibility of 0.3 ppm (Bakker and de Roos, 2006). The container was placed upright near the scanner isocenter with its

Results

Since the phase derivatives form the basis of the correction algorithm (Eqs. (7), (8)), the phase derivatives were validated first, using the infinite cylinder phantom. Typical results for the signal magnitude and the signal phase and the first and second order phase derivatives (both in the three orthogonal directions), for a coronal slice through the cylinder, are shown in Fig. 2. The signal magnitude shown in Fig. 2a shows a ring of reduced signal intensity near the inner cylinder. The

Discussion

In this work a generally applicable post-processing technique has been presented to evaluate and compensate for signal perturbations invoked by first and second order macroscopic phase incoherence. The derivatives of the signal phase are determined by applying the Fourier derivative theorem on the complex data. As a result, the phase derivatives are obtained without phase unwrapping and without compromising the resolution. The correction can be applied on single-echo as well as on multi-echo

Acknowledgments

Grant sponsor: Dutch Technology Foundation STW; Grant number: 06648 is gratefully acknowledged.

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