Chapter 3: Theoretical Background for Dynamic Chemical Shift Imaging
3.2 Rapid CSI from a Multi-Gradient Echo Acquisition: From Theory to
Fundamentally, several conditions must be met in order to image the spatial distribution of hydrogen protons for MRTI. A strong magnetic field, B0, is needed in order to align a small majority of protons with the field. Radiofrequency (RF) pulses at the resonance frequency, ω, are used to tip the spin population. As the population relaxes back to equilibrium with the magnetic field, a small voltage is measured in an RF-tuned receiver coil which is perpendicular to B0.
In the laboratory frame of reference in the absence of gradients and relaxation effects, the signal from a 3D spin system, ρ(x,y,z), in a given volume, V, can be described as
32
( , , )
( ) ( , , ) i x y z t V
S t ∝
∫∫∫
ρ x y z e−ω dV (3.1)To spatially localize the signal, gradients are used that spatially vary the magnetic field over the sample.
For an acquisition in the axial plane, the z-direction is assigned as the slice- selection direction. A gradient is applied in this direction in conjunction with the bandwidth-limited RF excitation pulse. This creates a planar distribution of spins described by 0 0 / 2 ( , , ) / 2 ( , , ) ( , , ) z z i x y z t z z I x y t ρ x y z e ω dz +∆ − −∆ =
∫
(3.2)where z0 is the center of the slice and ∆z is the slice thickness. The z-dependence in ω can be related to the magnetic field, B0, and the slice encoding gradient, Gz, where
0
( )
z B G zz
ω =γ + (3.3)
After the RF pulse, the spins in I can be localized spatially using gradients and encoded in k-space. The relationship between a location in k-space at time, t, and the gradients in the x and y directions is given by
0
( ) ( )
t
33 In the collection of data in k-space, a phase encoding gradient moves collection of data to one line in k-space. This is followed by a frequency encoding gradient that is applied during the signal readout.
Mathematically, the signal at a location in k-space, S(kx,ky) can be given by
dydx e e y x k k S ix kx iy ky y x
∫∫
− − ∝ ρ 2π 2π ) , ( ) , ( (3.5)It is important to note that this equation gives the spatial frequency domain of the spin distribution and a 2D Fourier transform can be used to represent the data in the spatial domain (74).
Figure 3-1 displays the pulse sequence diagram for a fast gradient echo acquisition typically used for standard CPD MRTI. A small flip angle RF pulse is used during encoding of the slice selection gradient, Gz. The polarity of Gz is then switched to account for de-phasing of the transverse magnetization. The frequency encoding gradient, Gx, is turned on to move across k-space. Gy is then applied for the phase encoding before the positive gradient of Gx encodes the signal. A Gz gradient is then applied to dephase residual transverse magnetization.
34 Figure 3-1 Pulse sequence diagram for a fast gradient-recalled echo (FGRE) acquisition
This represents a balanced pulse and gradient schematic for a high spatiotemporal CPD acquisition. Note that one echo is collected per TR.
In this research, the fast gradient-recalled echo (FGRE) acquisition was modified to provide multiple echoes per TR for encoding the chemical shift (Fig. 3-2). As with FGRE, the sequence is compatible with parallel acquisition techniques, such as SENSE, to increase the speed of acquisition (94) and can acquire images in interleaved slice acquisition mode or in a sequential slice acquisition mode with RF spoiling to cancel out any residual transverse magnetization before the next TR period by modulating the phase between successive RF pulses. Note that the TR is kept constant so there is no loss in
35 spatiotemporal resolution compared to CPD from a FGRE acquisition. The ETL and ESP are set in order to collect the selected number of echoes within the TR.
Figure 3-2 Pulse sequence diagram of a 2D unipolar MGE acquisition
The phase encoding gradient only pulses once per echo train. The frequency-encoding gradient can be implemented in bipolar or unipolar mode. In the unipolar sequence shown above, when each echo is acquired in a positive gradient readout, the free induction decay (FID) is sampled.
The sequence can be run using unipolar readout gradients with time-optimized rewinder (i.e. flyback) gradients as shown in Figure 3-2 or using bipolar readout gradients. In bipolar gradient mode, negative polarity readout data is time reversed in k- space prior to image reconstruction by Fourier transformation. Also in bipolar gradient mode, N/2 spectral ghosting caused by timing errors between the positive and negative readouts can be corrected by applying a calculated linear phase shift to the images reconstructed from every other echo time (95). The moments of the signal are calculated
36 in k-space. The phase shift is measured by the differences in the moment between odd and even echoes in the bipolar readout (Figue 3-3).
Figure 3-3 Differences between bipolar and unipolar readout gradients with N/2 correction
Bipolar and unipolar readout acquisitions were performed on an agar phantom. Due to timing errors between odd and even echoes, the bipolar readout gradient is susceptible to N/2 ghosts (top left). These timing errors can be corrected by calculating the phase change in k-space (top right). Unipolar readout gradients are immune to these errors but using unipolar gradients comes at an expense of larger ESP and lower SNR (96).
37 We made two fundamental changes in the conventional acquisition strategy for fast CSI acquisitions. First, the echo-spacing (ESP) parameter was increased in order to facilitate use of lower readout bandwidths to provide higher SNR. In the case of previous 3.0T CSI acquisitions, restraints on the ESP have usually resulted in the use of multiple interleaved echo-trains in order to avoid aliasing (47). Because of the relaxed ESP associated with this technique we can acquire multiple echoes within one TR acquisition thus increasing the spatial and temporal resolution compared to previous CSI acquisitions for MRTI. This causes aliasing of the lipid peak. However, in MRTI we are only interested in the change in the lipid PRF and not the absolute position when measuring temperature changes.
The second modification was to collect only the number of echoes that would fit into the TR period of our standard CPD MRTI sequence. The artifacts associated with this undersampling required innovative processing in order to resolve the lipid signal as outlined in the following section.
To increase sensitivity, uncertainties in the PRF as a function of acquisition parameters need to be determined. It is important to note that in PRF mapping, the frequency difference, which is directly proportional to temperature, is not constrained to TE=T2*, in contrast to CPD. For an homogenous voxel,
( )
( )
/ 1 / 2* ∆f / 1 1 CNR sin 1 cos TR T TE T A TR T e f SNR e e θ θ − − − − ∝ ∆ ⋅ ∝ ⋅ ⋅ − ⋅ (3.6)38 which means that the sensitivity of measuring frequency changes is directly proportional to the SNR of the source image from a gradient echo acquisition. This gives an image metric where the sensitivity of the frequency changes can be measured and verified using the spectral analysis technique as described in the next section.