Stephen J. Riederer1, Eric A. Borisch1, Adam T. Froemming1, Soudabeh Kargar1, Akira Kawashima1, and Joshua D. Trzasko1
1Radiology, Mayo Clinic, Rochester, MN, United States
Synopsis
A new method is
described in which slice profile in 2D multi-slice acquisition is corrected for
with k-space-based processing, restoring resolution along the slice select
direction. When used with multiple
multi-slice acquisitions the method may allow isotropic 3D resolution. The method is described, and preliminary
results from phantom and prostate MRI exams are presented.
Purpose
Two-dimensional (2D) multi-slice
T2-weighted spin-echo (T2SE) acquisition is used in essentially 100% of
clinical prostate MRI exams. However,
slice thickness is typically 3–6× coarser than inplane resolution and can limit
interpretation. This is often accounted
for by acquiring 2D multi-slice images in two or three of the orientations:
axial (A), coronal (C), sagittal (S). Directly
acquired 3D T2SE images are typically compromised by reduced resolution and
contrast1. The purpose
of this work is to describe how multi-slice images can be used to form a 3D
data set. The novel aspect is that
transforming the acquired multi-slice data along the slice direction into k-space
allows correction of the slice profile, enabling improved resolution.Methods
The approach is illustrated in Figure 1. Figure 1A shows a set of slices acquired in a 2D multi-slice scan with slice selection along Z. The inplane sampling is r, the slice thickness T, and the slice-to-slice spacing S. For illustration assume T:r is 4:1 and S>T. The idea of the approach is to transform the acquired slice information along Z while maintaining the signals in kX−kY space. Assuming frequency encoding is along kX, only the kY−kZ plane is shown (Fig. 1B). Full sampling of k-space is assumed to extend from -1/2r to +1/2r in both directions. The rect-like slice thickness T imposes a sinc-like low-pass filter of width 2/T along kZ, with the shaded passband shown. Sampling slices at spacing S along Z causes the passband signals to be replicated at intervals of 1/S along kZ, shown as the dashed horizontal lines, creating aliasing.
The reconstruction can be expressed mathematically. Define →k as the desired, unknown, high resolution k-space data vector of size N (assumed here to be along Z) for a specific (kX,kY). The multi-slice process subjects →k to slice-select-based modulation and shifted replications, both expressed as matrices. This is further down-sampled to match the number M of slices along Z (M<N). This can be expressed as:
F⋅→z=D⋅{A0+A−1+A+1+…}⋅B⋅→k
where F is the M-point Fourier transform, →z the M×1 acquired data vector along Z, D is the M×N down-sampling matrix, Ai express the replications at offsets i(1/S) due to the k-space aliasing (with A0 the identity matrix IN), and B is the N×N diagonal matrix describing the k modulation due to slice selection. Inversion of Eq. 1 yields an estimate of →k.
The algorithm of Eq. 1 was tested experimentally in T2SE images of a phantom and of subjects having a prostate MRI exam (for which multi-slice images in A, C, and S orientations are typically all acquired). In the experiments the acquired images were contiguous; i.e. S=T. Also, the algorithm was extended by taking multi-slice data from two orientations (A and C), applying Eq. 1 individually to each and combining results for improved kY-kZ coverage (Fig. 1C).
Results
Results from a
human prostate study using a single multi-slice T2SE set (axial) are shown in
Figure 2. Figure 2A shows one of the
acquired images. The axial images were
stacked and a sagittal section through the line shown in (A) is presented in
(B), showing clear stair-stepping. Use
of the new algorithm of Eq. 1 yields the result in (C) which improves the
apparent resolution. This is similar to
zero padding as might be expected with use of a single set of contiguous
slices. Use of axial and sagittal
multi-slice sets in a phantom is illustrated in Figure 3. The line in the axial section (A) identifies
the target coronal section. Images of
that section formed from stacked axial and sagittal acquired slices are shown
in (B) and (C) respectively, both showing stair-stepping. Figure 3D shows the same section formed
synthetically from both sets. Note the
improved sharpness along the inplane directions with markedly diminished
stair-stepping artifact without perceptible contrast loss.Discussion
We have presented a
new approach for generating 3D images from 2D multi-slice data. The novel element is k-space-based correction
for slice profile, a correction going beyond zero padding2. The k-space approach provides considerable flexibility vs. image-space-based
super-resolution techniques3. Figure 3 illustrated usage when multiple orientations are used. The method is also applicable to multi-NEX
acquisition in which the time spent for averaging could be exchanged with
overlapped slices (S<T), reducing the aliasing along kZ. This could possibly eliminate the coronal and
sagittal T2SE image sets in prostate MRI. The method is applicable to other 2D multi-slice acquisitions such as
DWI as well as other regions of the body.Acknowledgements
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