Correlation distance dependence of the resonance frequency of intermolecular zero quantum coherences and its implication for MR thermometry

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The proton resonance frequency (PRF) method has become one of the most widely used methods for MR thermometry, thanks to the large, linear temperature dependence of the water‐resonance frequency (−0.01 ppm/°C) that, in vivo, is virtually independent of tissue types 1. A number of factors have been known to undermine the accuracy of PRF‐based thermometry methods, such as macroscopic magnetic field inhomogeneities, motion, and field drift 2. Several approaches have been devised to correct for these effects through the use of an internal, temperature‐independent reference. In tissues in which lipid protons are present, for example, the almost‐temperature‐independent 3 resonance frequency of the methylene protons is typically used as an internal reference 4. By using the methylene resonance frequency as a reference, the correction of the water‐resonance frequency can then be done on a voxel scale, either by using spectroscopy‐based methods 5, by examining the phase change between images acquired at different temperatures 9, or by using chemical‐shift‐based, water–fat separation methods 11, which generally allow for a considerable reduction of voxel size.
To remove macroscopic field inhomogeneities at a scale much smaller than the resolution achievable with common MRI techniques, people sought to use the signal generated from intermolecular multiple‐quantum coherences (iMQCs) 13. The iMQC signal is generated by exceedingly small long‐range dipolar interactions among spins that reside in different molecules 16, and sometimes even in different compartments 17. In the past, these signals have been used for a wide range of imaging and spectroscopy applications, which include contrast enhancement in MRI experiments 19, and suppression of temporal 24 and spatial inhomogeneities 13. The removal of macroscopic field inhomogeneities via iMQCs is typically accomplished by the selection of a specific order of coherence, the intermolecular zero‐quantum coherences (iZQCs), even though, in general, with a proper design of the pulse sequence any other coherence can be used for such a purpose 27.
One of the prominent features of iZQC is that its signal naturally evolves at the resonance frequency difference between the two correlated spins. This property alone would not reduce the effect of magnetic‐field inhomogeneities that exists within a voxel, if it were not for the fact that the bulk of the iZQC signal actually originates from spins that are a “correlation distance” apart. The correlation distance is a “user‐controlled” parameter that can be changed by simply altering the strength of the magnetic‐field gradient pulses used for coherence pathway selection. This distance defines the average distance between the correlated spins from which most of the iZQC signal comes from, and it can be selected to be as large as a few millimeters or as small as few hundreds of micrometers, at which point the magnetic‐field inhomogeneity or susceptibility gradients present on a larger scale are effectively removed. This property of iZQCs, and specifically the signal generated by water–methylene iZQC coherences, has been used to enhance the accuracy of PRF thermometry 31, or as an attempt to measure absolute temperature in fatty tissues 33.
However, water and fat spins do not mix and typically reside in different tissue/cell compartments. In addition, water and fat have different magnetic susceptibilities. This means that microscopic susceptibility gradients that are always present at water–fat interfaces on a scale comparable to the correlation distance cannot be completely removed. In this paper, we analyze how susceptibility gradients affect the water–methylene iZQC resonance frequency and discuss the conditions under which the susceptibility gradients' dependence of the iZQC resonance frequency is eliminated.

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