## Artifacts Due To Magnetic Field Nonuniformity

During MR imaging the magnetic field in the object can be nonuniform for various reasons including nonuniformity of the external magnetic field, presence of metal implants and spatial variations in magnetic susceptibility of the object. Magnetic field nonuniformity causes two major types of artifacts in MR images: geometric distortion and signal loss due to intravoxel dephasing [1-7],

### Geometric Distortion

To describe geometric distortion caused by magnetic field non-uniformity, it is convenient to express the magnetic field in the specimen as a sum of two terms:

where B0 is uniform and B' is a function of coordinates. Because MR imaging is typically performed in a very homogeneous magnetic field such that |B'| <c |B0|, the components of B' perpendicular to B0 can be neglected because they cause only a minor perturbation of Larmor frequencies of spins. Thus, we can assume that B' = kB', where k is the unit vector in the direction of B0.

For simplicity we will confine our discussion to the case of 2D gradient-echo imaging considered in Chapter 3. The magnetic field B' gives rise to the spatially-varying phase of the transverse magnetization <j> = Jt, where J = 7B'. A general equation describing the signal acquired in the presence of T2 relaxation and dephasing of spins caused by the field inhomogeneity B' can be written as

S(kx, ky) = J J Mxy(x, y)ej^+jkyy+jJ(t+TE)-{t+TE)/T2 ^ ^ (612)

where kx = 7Gxt and ky = *yGytph\ Gx and Gy are the readout and phase-encoding gradients, respectively; t = nrw and n changes from —N/2 to N/2 - 1; TE is the echo time (see Chapter 3). To simplify our analysis we neglect T2 relaxation and assume that B' can be approximated as a sum of constant and linear terms: B' = a + G'xx + G'yy + G'zz. Using these assumptions we obtain from (6.1.2)

Geometric distortion is produced by intrinsic field gradients G'x, G'y and G'z that alter the dependence of Larmor frequencies of spins on their actual locations in the specimen. By examining (6.1.3) we can conclude that the image distortion can be described by the following: spatially varying image displacement in the readout direction by SB'/Gx, magnification in the readout direction and weighting of the image intensity by the factor (1 + G'x/Gx)~l. The strength of the readout gradient is typically high enough to allow only minor geometrical distortion in conventional MR imaging. However in some cases, non-uniformity of the magnetic field can be large enough (e.g., due to the presence of metal objects ) to cause significant degradation of images.

Another artifact caused by magnetic field nonuniformity is distortion of the slice profile. In Chapter 2 we have shown that spatially selective excitation in a uniform magnetic field creates a nonzero transverse magnetization in a slice of material with thickness defined by the bandwidth of the excitation pulse and the applied gradient. Assuming that 2uib is the excitation bandwidth and Gz is the slice-select gradient, we obtain that the boundaries of the slice are: Zi = —ujh/{~(Gz) and z2 = ojb/{^Gz) (see Chapter 2). In the presence of a magnetic field inhomogeneity, B\x,y,z), the slice boundaries are defined by the following equations:

From Eq. (6.1.4) it follows that magnetic field nonuniformity gives rise to nonplanar slices of varying thickness. The degree of slice distortion depends on magnetic field nonuniformity and slice-select gradient: a large B' or small Gz can result in significant distortions of the slice profile.

It should be noted that no image distortion due to magnetic field inhomogeneities exists in the phase-encoding direction. Consequently, distortion free images can in principle be acquired by using phase encoding in three orthogonal directions. However, this acquisition technique is rarely used because it is prohibitively slow.

### Intravoxel Dephasing

Magnetic field inhomogeneities cause dephasing of nuclear spins during data acquisition. Spin dephasing in turn leads to a loss of NMR signal. The resulting effect is a noticeable reduction in image intensity (Figure 6.1). Mathematically, the signal loss is defined by the factor ejuJ TE averaged over the voxel volume. It is instructive to consider the effect of intravoxel dephasing in the presence of an isotropic gradient, G'x = G'y — G'z, in a cubic voxel, A3x. In this case the reduction in image intensity is given by the factor where A to = 7 G^ Ax/2. For example, an isotropic gradient of 1 ppm/cm causes a loss of more than 50% of the signal in gradient-echo imaging at 1.5Tesla with TE of 30 msec and 2 mm3 voxel size. The good news is that decreasing voxel size and shortening echo time reduces loss of sind(A ujTE)

(AivTE) Phase encoding Phase encoding a b

Figure 6.1. Images of a uniform phantom in (a) and (b) were acquired using a gradient-echo pulse sequence with the same imaging parameters. Visible reduction in image intensity in (b) is due to a metal paper clip placed in the vicinity of the phantom.

signal. The bad news is that by decreasing voxel size we proportionally reduce SNR in images.

Equation (6.1.5) is interesting because it clearly indicates that magnetic field inhomogeneities generally cause a nonexponential decay of signal as a function of echo time in gradient-echo imaging. In many instances this decay can be significant enough to cause a drastic reduction in image intensity (Figure 6.1). It is therefore important that the effect of magnetic field nonuniformity can be minimized by acquiring spin-echo signals. Because of the reduced dephasing of spins, the resulting spin-echo images generally have better contrast than gradient-echo images. ## Staying Relaxed

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