The challenge of bias‐free coil combination for quantitative susceptibility mapping at ultra‐high field

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Magnetic susceptibility describes the magnetization of a sample when placed in an external magnetic field. The quantification of magnetic susceptibility based on MRI phase measurements has gained a lot of interest because it may yield quantitative information on myelin composition and iron, copper, and calcium content in the brain 1. Quantitative susceptibility mapping (QSM) provides a unique gray/white matter contrast 5, and has the potential to deliver novel insights into tissue composition in health and disease 6. As calcium has a lower magnetic susceptibility than water, QSM can be used to visualize microbleeds 8 and differentiate them from microcalcifications 9. Additionally, it can be used to measure iron stores 7 in normal aging 10, Huntington's disease 12, multiple sclerosis 6, Alzheimer's disease 15 and Parkinson's disease 16. The novel contrast generated using QSM may also enhance image‐guided planning of electrode placement in deep brain stimulation 18.
Quantitative and qualitative magnetic susceptibility MRI profit from the use of ultra‐high field scanners, in which improvements in glioma treatment response assessment 19, microbleed detection 20, and multiple sclerosis lesion characterization 21 have been demonstrated compared with lower field strength results. A problem at ultra‐high field, however, is the optimal channel combination of phase data in the absence of a volume reference coil with which to correct for spatially dependent phase offsets. With the term phase offset, we summarize the difference in phase between two channels, which consist of a constant and a spatially dependent term: There is a common offset for every channel caused by JOURNAL/mrim/04.02/01445475-201801000-00010/math_10MM1/v/2017-12-21T175206Z/r/image-png phase, eddy currents, gradient delay effects, and a phase offset that is different for every channel, caused by cable length and receive sensitivity JOURNAL/mrim/04.02/01445475-201801000-00010/math_10MM2/v/2017-12-21T175206Z/r/image-png22. At lower field strengths, these offsets can be corrected for using a homogeneous volume reference coil measurement (i.e. a body transmit coil, but this technology is currently not available at 7 Tesla (T). Transceive coils with inhomogeneous transmit and receive profiles are available for some MRI systems and allow the correction of phase offsets. However, transceive elements are not available in some custom coils; therefore, we investigated ways that do not rely on transceive coils to correctly combine phase data.
Other methods for combining phase data have been proposed and are widely used, but the problem is that none of them is ideal for single‐echo applications and quantitating susceptibility at ultra‐high field: The simplest method, homodyne filtering 25, will result in a loss of low spatial frequency features, thereby affecting quantitation in susceptibility mapping. Phase matching methods 28 fail in large objects and contain undefined contributions to the phase 23, which also makes these methods suboptimal for accurate QSM. Other methods are based on phase difference between echoes 32 or temporal phase evolution 37 and require multi‐echo data, which are not always available. Methods, such as sensitivity encoding (SENSE) 38, could optimally combine data from multiple coils using a single echo, but without a homogenous volume reference coil, the required coil sensitivity maps cannot be generated easily.
A recent solution to the phase combination problem ‐ combining phase data using a short echo‐time reference scan (COMPOSER) ‐ can approximate phase offsets by using a phase reference scan at a very short echo time 39. The phase offset for each channel can then be subtracted from every channel before complex valued channel data can be summed to form a single image. Notably, it is important to use a short echo time relative to JOURNAL/mrim/04.02/01445475-201801000-00010/math_10MM3/v/2017-12-21T175206Z/r/image-png of the tissue of interest to limit the reduction in phase contrast and quantitation bias.

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