Magnetic susceptibility effects can be modeled using a susceptibility gradient term. If the susceptibility gradient is primarily in the through-plane direction, as is the case for axial slices superior to the air cavities in the brain, the image I
) generated with a slice-select RF pulse at TE can be written as
is the spatially varying through-plane susceptibility gradient and p
) is the slice profile. Phase cancellation from integrating across the slice will produce signal loss in I
The standard z-shim method reduces the signal loss artifact by applying an additional compensation gradient
along the slice-select direction. If
, where T
is the length of
, the dephasing at (x0
) produced by the susceptibility gradient at TE will be canceled. Due to the spatial variation of
, the compensation gradient
has to be incremented using multiple steps such that a series of images are acquired with varying degree of z-shim. The final corrected image is a combination of all of the individual shimmed images. The gradient steps can be incremented using separate excitations or with multiple echoes. Both approaches lead to increased scan times.
A compensation gradient can also be created by time shifting the RF pulse relative to the slice-select gradient. Following the excitation k
-space formalism (22
), in the presence of a slice-select gradient Gz
a shift in time Δt
applied to the RF waveform B1
) creates a phase term:
For example, shows plots of a centered RF wave-form and the same pulse shifted 300 µs back in time. This pulse produces a Δz = 5-mm-thick slice with a Gz = 20 mT/m slice-select gradient. The through-plane phase produced by this pulse is γGzΔzΔt = 8 radians. shows the simulated slice profile and through-plane phase of the shifted pulse. Theoretically, one could duplicate the standard gradient-compensated z-shim method by applying several scans using RF pulses with a range of time shifts. However, this would incur an increase in scan time to obtain a combination of z-shims.
Fig. 1 a: A centered slice-select RF pulse (solid line) and the same pulse shifted 300 µs back in time (dashed line). b: The slice profile (solid line) and through-plane phase (dashed) created by the shifted RF pulse. The slice-select gradient (not shown) (more ...)
We propose a simultaneous z-shim method for multiple transmitter applications. Using this approach, each of j
transmitters applies a pulse with a unique Δtj
. The summation of z-shims occurs automatically with the parallel transmission. Assuming linearity, the resultant image can be written by
) is the transmitter sensitivity. The efficacy of the technique will in part be a function of the locations of the susceptibility artifacts, coil positions, overlap in sensitivities, and pulse superposition effects.
As a simple demonstration, a Bloch equation simulation of an oval-shaped object I(x,y) with a circular region of through-plane susceptibility gradient is shown in . Four transmitters with sensitivities that varied linearly from 1 to 0, successively rotated 90°, were used. shows I(x,y) excited with unshifted pulses on all four transmitters. Note the signal loss artifact in the circular region. shows the same slice excited by four transmitters with the pulse on the top transmitter time shifted to cancel the through-plane gradient. The circular region now has recovered magnitude; however, there is reduced magnitude in the surrounding areas. This is due to the fall-off in sensitivity from the other transmitters as well from a degradation of the slice profile when shifted and unshifted pulses are superimposed. shows a simulated slice profile from overlapping pulses with different time shifts. Note the zeros in the profile due to phase cancellation, as well as the narrower profile. In the limit of uniform sensitivities, all pixels will have similar slice profile issues as well as increased SAR.
Fig. 2 a: Bloch equation simulation of an image excited by four transmitters (one on each side) using unshifted RF pulses. A through-plane gradient added to a circular region produces a void in the image. b: The same image excited by four transmitters with the (more ...)