Correction of gradient echo images for first and second order macroscopic signal dephasing using phase derivative mapping
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: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.
References (44)
- et al.
Selection of voxel size and slice orientation for fMRI in the presence of susceptibility field gradients: application to imaging of the amygdala
NeuroImage
(2003) - et al.
Application of k-space energy spectrum analysis to susceptibility field mapping and distortion correction in gradient-echo EPI
NeuroImage
(2006) - et al.
Compensation of susceptibility-induced BOLD sensitivity losses in echo-planar fMRI Imaging
NeuroImage
(2002) - et al.
Recovery of signal loss due to an in-plane susceptibility gradient in the gradient echo EPI through acquisition of extended phase-encoding lines
Magn. Reson. Imaging
(2010) - et al.
Unwrapping magnetic resonance phase maps with Chebyshev polynomials
Magn. Reson. Imaging
(2009) - et al.
Single-shot T2⋆ mapping with 3D compensation of local susceptibility gradients in multiple regions
NeuroImage
(2003) - et al.
Investigation of the influence of carbon dioxide concentrations on cerebral physiology by susceptibility-weighted magnetic resonance imaging (SWI)
NeuroImage
(2008) - et al.
Reduction of susceptibility-induced signal losses in multi-gradient-echo images: application to improved visualization of the subthalamic nucleus
NeuroImage
(2009) - et al.
MRI R2 and R2⋆ mapping accurately estimates hepatic iron concentration in transfusion-dependent thalassemia and sickle cell disease patients
Blood
(2005) - et al.
Concerning the preparation and use of substances with a magnetic susceptibility equal to the magnetic susceptibility of air
Magn. Reson. Med.
(2006)
Dephased MRI.
Magn. Reson. Med.
Phase gradient mapping as an aid in the analysis of object-induced and system-related phase perturbations in MRI
Phys. Med. Biol.
Rapid single-scan T2⋆-mapping using exponential excitation pulses and image-based correction for linear background gradients
Magn. Reson. Med.
The Fourier Transform and its Applications
Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients
Magn. Reson. Med.
Cerebral microbleeds on MR imaging: comparison between 1.5 and 7T
Am. J. Neuroradiol.
Limits of detection of SPIO at 3.0 T using T2⋆ relaxometry
Magn. Reson. Med.
NMR imaging of changes in vascular morphology due to tumor angiogenesis
Magn. Reson. Med.
Postprocessing technique to correct for background gradients in image-based R2⋆ measurements
Magn. Reson. Med.
Magnetic Resonance Imaging: Physical Principles and Sequence Design
Susceptibility weighted imaging (SWI)
Magn. Reson. Med.
Phase derivative analysis in MR angiography: reduced V-enc dependency and improvement vessel wall detection in laminar and disturbed flow
J. Magn. Reson.
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