Fourier Spliced Pencil Imaging. Oliver Heid. Institute of Diagnostic Radiology, University of Bern, CH-3010 Bern, Swizerland. Introduction. The observation of a ...
Fourier Spliced Pencil Imaging Oliver Heid Institute of Diagnostic Radiology, University of Bern, CH-3010 Bern, Swizerland
Introduction RF
The observation of a small subregion in a larger object with a high time resolution, e.g. in real-time flow measurements in vessels, is a typical task in MRI. One technique proposed so far acquires a 2D image of the complete object by a fast method, usually Echo Planar Imaging (EPI) [1]. The region of interest is selected in an image postprocessing step. A different method uses a 2D spatially selective rf pulse to excite a ‘pencil’ containing the point of interest, which is scanned by a single readout gradient in pencil direction [2]. To achieve a given spatial resolution, both methods are shown to require comparable measurement times. We want to propose a hybrid Fourier Spliced Pencil (FSP) technique offering a significant improvement in time resolution to both of these methods without any concessions to spatial resolution.
AQ
. .. . ..... ..... ...... .... .... .... ...... ..... ..... ...... ...... ...... ...... ...... ...... .... ... .... ... .... ... .... ... .... .. .. ..... ..... ..... ..... .....
GR
GP
GS
. .... .... .... .... .... .... .... .... .......... .. .. .. .. .. .. .. .. .. .... .... .... .... .... .. ..... ... ..... ... ..... ... ..... ... ..... .. ..... ..... ..... ..... ..
Fig. 1: Fourier Spliced Pencil (FSP) imaging sequence.
achieved for
Theory
M=
Aquiring an Echo Planar Imaging (EPI) image data set by N k-space lines takes a time of roughly TEPI = tRF + N × tADC . tRF denotes the total time required to transmit an rf pulse and tADC is the time necessary to acquire an echo. For the 2D pencil excitation (PE) method incorporates a gradient scheme resembling time-reversed EPI, a similar expression results for the total measurement time TPE = N × tRF + tADC for a N subpulse zig-zag trajectory excitation and an aliasing distance to pencil width ratio of N : 1. The details of k-space traversal, e.g. a spiral instead of a meander trajectory, does not change the situation markedly. Our approach is to excite a coarse pencil and to ‘splice’ the pencil by means of an EPI-like 2D readout module. Let us assume a 2D rf pulse exciting a pencil with an aliasing distanceto-width ratio of M : 1, the readout module has to resolve the N fine structure of the pencil only, which can be done with L = M k-space lines. The key idea behind this Fourier Spliced Pencil (FSP) method is to choose the free parameter M to minimize the total measurement time representing the sum of the rf excitation and the readout durations TFSP = M × tRF +
N × tADC , M
but keeping a constant resolution, which is given by the product, N = M × L. By a convexity argument, the minimum of the measurement time TSPM can be derived to be √ √ TFSP = 2 N × tRF × tADC
r
N × tADC . tRF √
For tRF ≈ tADC , the time improvement is 2N . For higher resolution, the improvement is quite substantial, e.g. a factor of ≈ 5 for N = 128.
Implementation and Results We implemented a Fourier Spliced Pencil (FSP) imaging sequence on a conventional Siemens Magnetom VISION equipped with a 24 mT /m gradient strength, 600 µs rise time gradient set. Both the rf pulse train and the echo readout acted upon a trapezoidal gradient waveform with 1200µs half waves. To achieve the desired isotropic 2.2 mm resolution at a 280 × 280 mm aliasing distance, the excitation pulse incorporated 9 Gaussian rf subpulses. The readout k-space consisted of 10 lines with slightly asymmetric encoding. The total measurement time of 24 ms represented an improvement by a factor of about 5 compared to an EPI sequence with similar resolution.
Discussion The proposed Fourier Spliced Pencil (FSP) imaging sequence allows to track a small subregion in a larger object with a significantly higher repetition rate than the 2D methods proposed so far. The imaging time approaches the domain of the fastest 1D methods known (RACE, [3]).
References [1] Poncelet P.,J. Phys. C 10, L55-L58, 1992. [2] Hardy C.J. et al.,SMRM XI, 107, 1992. [3] M¨ uller E. et al.,SMRM VII, 729, 1988.
