T he British Journal of Radiology, 71 (1998), 704–707

© 1998 The British Institute of Radiology

Commentary

Signal-to-noise ratio in MRI T W REDPATH, PhD, FInstP Department of Bio-Medical Physics and Bio-Engineering, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK

Clinical MRI quality depends crucially on the signal-to-noise ratio (SNR) available from the system transducer, in this case the receiving coil, which yields a small radiofrequency (RF) voltage when nuclear magnetic dipoles are excited to precess within it. The latest MR scanners have considerably higher SNR than the prototype machines of the late 1970s and early 1980s, owing to the use of higher field strength magnets and to improvements in RF receiving coil design. However, modern imaging techniques often demand very high speed and spatial resolution, so that the highest possible SNR is still required to avoid poor image quality. In this commentary, the physics underlying the variation of SNR with static field strength will be briefly reviewed, practical methods of optimizing SNR will be outlined, including a discussion of the principles of quadrature and phased-array RF coils, and methods of measuring SNR for acceptance testing and quality assurance will be discussed.

Signal-to-noise ratio and static magnetic field strength The arguments presented in this section are based on the electromotive forces (EMFs) induced in RF receiving coils. EMF is measured in volts. The voltage measured across the terminals of a coil tuned with a capacitor is approximately Q times any EMF produced in it, owing to the voltage multiplication effect of coil tuning (Q is the Q factor of the RF coil). Thus, tuning amplifies both signal and noise EMFs. However, the ratio of the signal EMF to the noise EMF remains the same whether the coil is tuned or not. It is therefore simpler not to base SNR arguments on coil Q factors, or on the size of observed voltages across the terminals of tuned coils, but on consideration of the physics underlying the relative sizes of signal and noise EMFs. This avoids the need to consider specifically the reduction of coil Q when the patient is placed inside the coil. RF eddy currents within the patient’s conducting tissue are therefore dealt Received 5 January 1998 and in revised form 6 March 1998, accepted 20 March 1998. 704

with not by their effect on coil Q factors, but by a more fundamental consideration of the electrical noise EMF which they induce in the receiving coil. The nuclear magnetic resonance (NMR) signal EMF induced in the receiving coil increases as the square of the Larmor frequency f , in other words 0 as the square of B , the static magnetic field 0 strength [1]. This increase is due to two separate and independent factors. Firstly, the separation of the energy levels of spin-up and spin-down protons is proportional to B , so that their population 0 difference is larger at high values of B . Since the 0 ratio of the energy difference to thermal energy is very small, the population difference increases in direct proportion to B , as does the size of the 0 nuclear magnetic dipole moment. Secondly, the Larmor frequency at which the dipole moment precesses is proportional to B so that the rate of 0 change of flux linked to the RF coil also increases in proportion to f . Therefore, by Faraday’s law 0 of electromagnetic induction, the signal produced by a dipole magnetic moment of constant magnitude, will increase in proportion to its precession frequency. The combination of these two factors gives the f 2 dependence. 0 Noise in the MR image is caused by the thermally driven Brownian motion of electrons within the body’s conducting tissue, and within the receiving coil itself. This noise is sometimes called Johnson noise. At mid and high fields, the patient will be the dominant noise source unless the coil is very small. The patient noise EMF is caused by random RF currents circulating round a number of eddy current loops, thus producing randomly varying magnetic fields which induce noise voltages in the RF receiving coil. The current amplitude flowing in these loops is, to a first approximation, reasonably independent of frequency, since Johnson noise is white, and the impedance of the loops is approximately resistive. Since only the narrow bandwidth around the Larmor frequency is used for signal observation, only noise voltages in this narrow frequency band produce noise in the image. As the Larmor frequency increases, so does the frequency of the eddy currents which produce the image noise. Therefore, by Faraday’s law of electromagnetic induction, the noise EMF T he British Journal of Radiology, July 1998

Commentary: Signal-to-noise ratio in MRI

increases in proportion to f , since the flux linkage 0 is changing faster for the same eddy current amplitude [2]. This argument also shows that a well fitting RF receiving coil, closely coupled to the precessing magnetization should be used to optimize SNR as a large signal will be induced in the coil; and the smallest possible tissue volume is ‘‘seen’’ by the coil, thus reducing noise. Good coils are also designed to minimize the quasielectrostatic capacitive interaction with the patient, which allows additional noise from the random electronic motion to degrade the image [3]. At imaging frequencies below about 10 MHz or so, especially with small coils, the resistance of the coil winding itself, rather than the patient, can be the dominant source of Johnson noise. In this case, significant gains in SNR can be achieved either by cooling the coil winding to reduce its resistance and hence the noise it generates, or by eliminating coil resistance altogether by using a high temperature superconductor (HTS) to form the winding [4]. Immersion in liquid nitrogen is the usual method of cooling. Its boiling point is 77 K, and it is much cheaper and easier to handle than liquid helium. The rapid increase of signal with field strength is the only factor contributing to improved conventional image quality at high field. All other factors work against it, with two notable exceptions. MRI of brain function (fMRI) is based on blood oxygenation level dependent (BOLD) contrast. This is much stronger at very high field strengths than at 1 or 1.5 tesla, so that very high field strength imaging is often used. In spectroscopic imaging, the absolute frequency separation of chemically shifted lines is proportional to B , so that it is 0 often easier to resolve metabolites at higher field strengths. However, for conventional imaging, the penalties to be paid for increased B are: noise 0 levels increasing at least linearly with f as outlined 0 above; increased chemical shift artefacts; significantly higher RF power deposition and tissue heating, increasing as the square of f for a particu0 lar pulse sequence; reduced longitudinal relaxation time (T ) contrast as tissue T values approach that 1 1 of pure water; RF magnetic field inhomogeneity effects due to eddy current and wavelength effects; and higher capital, installation and running costs [5]. Thus, at best, SNR will increase linearly with magnetic field strength. In practice, to maintain the chemical shift effect at a constant number of pixels, the frequency encoding bandwidth used has to increase in proportion to B , thus reducing the 0 gain in SNR with frequency to only a √f depen0 dence. Furthermore, once decreasing tissue conductivity and increasing T are taken into account, 1 it can be argued that the real gain in SNR with f 0 is even less (the first effect causes the patient to generate more noise than expected, and the second T he British Journal of Radiology, July 1998

reduces the number of signal averages possible in a given time, as field strength is increased) [5].

Optimizing signal-to-noise ratio For a particular scanner, the user can optimize SNR by appropriate choice of sequence, spatial resolution and receiving coil. Once the sequence has been chosen it is essential to choose an appropriate field-of-view, matrix size and slice thickness. If these parameters are chosen to make the voxel volume so small as to give an inadequate SNR, then image smoothing may be unable to correct the error. Edelstein et al [6] argued that MRI is unlike transmission and emission tomography in this respect, as with those techniques, poor SNR resulting from image acquisition at too high a spatial resolution can be retrieved by image smoothing. As the underlying noise level increases as the square root of the acquisition bandwidth per pixel Df, it is important to choose as low a value as is practical. However, too low a bandwidth results in chemical shift artefacts and geometric distortion. Following the introduction of surface coils [7] which optimize SNR over a small superficial volume of interest, further innovations in RF coil design have improved sensitivity. The main ones to note are: the introduction of circularly polarized (CP) (i.e. quadrature) coils [8]; highly homogeneous RF field CP ‘‘birdcage’’ designs [9]; and most recently, phased array RF coils [10]. Quadrature coils can give a √2 improvement in SNR by acquiring the signal independently through two orthogonally orientated coils, or through two modes of the same coil. This is achieved because the noise voltages in each coil are more or less uncorrelated, while the signals can be added after appropriate phase-shifting. Phased array coils take this approach further, with multiple overlapping RF receiving coils arranged so that they operate independently, by virtue of their having negligible mutual inductance. Signals are collected and images computed separately from each coil, before they are merged, using a variety of possible algorithms, into a composite image. This approach gives similar SNR to that available from each coil individually, but over a much bigger field-of-view. It could be said that they give the SNR of a surface coil, but the coverage of a conventional coil. However, at the centre of the body or head, it is well known that a surface coil will not give good results, so that at depth, a phased array coil will not be superior to a conventional quadrature coil by virtue of its multicoil technology, but only by virtue of its fitting the patient more closely, thus minimizing the volume of tissue from which eddy current noise is received. In effect, to image at depth, the signals 705

T W Redpath

from all coil elements have to be added together, and with it all of the noise, so that the array is being synthesized by the image merging software into a conventional CP coil. For tissue at the surface of the patient, SNR could in theory be improved virtually indefinitely if coil noise is ignored. This could be achieved simply by making the phased array coil elements smaller and smaller, so that each coupled more strongly to the precessing superficial magnetization, with minimal noise being picked up from the tiny volume of tissue seen by the coil element. In practice, cost and engineering complexity limits this approach. When combining signals from two or more elements of a phased array RF coil, it is important to realize that the SNR performance of the array can be degraded if noise from different elements is correlated. Consider a tissue region which is approximately equidistant from two coil elements, so that it gives rise to roughly the same signal size in both. Combining the signals from both elements will roughly double the signal in this region, while the combined noise will increase by √2 if it is completely uncorrelated, so that SNR will be improved by about √2. If the noise is completely correlated no improvement in SNR will be seen, as both signal and noise will be doubled on combining the outputs from the two elements. There is some controversy regarding theoretical aspects of noise correlation, with Jesmanowicz and Hyde convinced that noise cannot be correlated if elements have no mutual inductance [11]. Others argue that noise correlation is possible even if mutual inductance is zero [10, 12]. Redpath [13] has derived a formula for the degree of correlation based on the measurement of voltage feed through from one element to another. In my opinion, Jesmanowicz and Hyde’s position could probably be reconciled with that of other authors if, instead of basing their arguments on zero mutual inductance, they based it on zero voltage feed through from one element to the other, with patient or loading phantom in position within the coil array. This is because Jesmanowicz and Hyde appear to be under the misapprehension that zero mutual inductance between elements implies that the coils cannot interact. However, as argued by Redpath [13], this is not the case. Zero mutual inductance only implies that the coils will not interact if the patient is absent. In practice, however, provided phased array coils are designed according to the principles outlined by Roemer et al [10], noise correlation does not appear to significantly degrade phased array coil performance.

Measuring signal-to-noise ratio The projection method of SNR measurement was proposed with the aim of bringing some order 706

to comparisons between different scanners and manufacturers [14]. Previously, manufacturers had used a multiplicity of phantoms, pulse sequences and voxel volumes to measure SNR, with the technique sometimes biased to favour their equipment. The projection protocol uses a single-shot, spin echo sequence with non-selective RF pulses to give a one-dimensional projection of the signal from a syringe or test tube of water onto its axis. In some scanners, this sequence is not available, so that this method has not found general acceptance. The method has the advantage of giving the SNR per unit volume of water, normalized to 1 Hz receiver bandwidth. As a result, comparisons are straightforward, and are unaffected by slice profile and longitudinal relaxation time (T ) effects. However, the result is still strongly 1 dependent on the amount of RF loading used when making the measurement. Loading refers to the use of saline, or some other electrically conducting material, to stimulate the effects of eddy currents in the patient. Loading, therefore, introduces eddy current noise which reduces the measured SNR. Recently, McRobbie has proposed making SNR measurements using a standard phantom with known relaxation times, and a loading annulus of known electrical conductivity and geometry so that RF loading effects are standardized [15]. Conventional selective two-dimensional spin echo images are acquired with measurements normalized to unit volume and 1 Hz bandwidth. For accurate results this method still requires a knowledge of slice profile. The strength of the method is that the maximum possible SNR achievable for the phantom can be calculated for conventional RF coils, providing the RF field can be assumed to be homogeneous over the whole phantom, for comparison with the measured result. The calculation of the maximum achievable SNR assumes that the RF coil itself is noiseless. For transmit–receive coils, the maximum SNR achievable from any patient or test object can be estimated from the net forward power needed to produce a 90° RF pulse of known shape [16]. The advantage of this approach is that no assumptions need to be made about RF homogeneity, or about the size, shape or composition of the patient or phantom being imaged, as detailed knowledge of RF loading is not needed. Furthermore, the SNR estimated from the forward power measurement does include noise coming from the coil itself, as well as that from the patient or phantom. For quality assurance and acceptance testing transmit– receive coils, often the most frequently used coils on many systems, a combination of the standard phantom method of SNR measurement and the forward power method would appear to have T he British Journal of Radiology, July 1998

Commentary: Signal-to-noise ratio in MRI

advantages, in that considerable prior knowledge of the expected result is available.

Discussion It is surprising that, given MRI has been in clinical use since the early 1980s, there is not a widely accepted method of performing SNR measurements for acceptance testing and quality assurance. This problem needs to be addressed. As a first step, manufacturers should include a nonselective one-dimensional projection spin echo sequence [14] in the standard imaging library, for SNR testing. The standard phantom [15] and power measurement techniques [16] appear to offer the basis of standard SNR measuring protocols. Some MR applications, such as ultra fast imaging, and some quantitative techniques, demand the highest possible SNR, and therefore are best done on high field systems. For conventional imaging, the variation of SNR with magnetic field strength is less strong than is often supposed. However, for spectroscopic and functional brain imaging, high field has particular advantages.

Acknowledgment The author is grateful to the Aberdeen Royal Hospitals NHS Trust for their continuing support of clinical MRI research at Aberdeen Royal Infirmary.

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