Fast 3D Imaging Using Variable-Density Spiral Trajectories With Applications to Limb Perfusion Jin Hyung Lee, 1 * Brian A. Hargreaves, 1 Bob S. Hu, 2 and Dwight G. Nishimura 1 Variable-density k-space sampling using a stack-of-spirals tra- jectory is proposed for ultra fast 3D imaging. Since most of the energy of an image is concentrated near the k-space origin, a variable-density k-space sampling method can be used to re- duce the sampling density in the outer portion of k-space. This significantly reduces scan time while introducing only minor aliasing artifacts from the low-energy, high-spatial-frequency components. A stack-of-spirals trajectory allows control over the density variations in both the k x –k y plane and the k z direc- tion while fast k-space coverage is provided by spiral trajecto- ries in the k x –k y plane. A variable-density stack-of-spirals tra- jectory consists of variable-density spirals in each k x –k y plane that are located in varying density in the k z direction. Phantom experiments demonstrate that reasonable image quality is pre- served with approximately half the scan time. This technique was then applied to first-pass perfusion imaging of the lower extremities which demands very rapid volume coverage. Using a variable-density stack-of-spirals trajectory, 3D images were acquired at a temporal resolution of 2.8 sec over a large volume with a 2.5  2.5  8 mm 3 spatial resolution. These images were used to resolve the time-course of muscle intensity following contrast injection. Magn Reson Med 50:1276 –1285, 2003. © 2003 Wiley-Liss, Inc. Key words: variable-density; spiral; 3D; perfusion; first-pass In MRI, for a given gradient system constraint and acqui- sition bandwidth, scan time becomes proportional to the number of points sampled in k-space. Conventionally, the number of points sampled is determined by the Nyquist sampling rate given the field of view (FOV) and spatial resolution requirements. This gives a lower limit on scan time, and in many MRI applications, particularly those requiring 3D imaging, scan time is a limiting factor. One way to reduce the scan time beyond the scan time limitation imposed by the Nyquist criterion is to under- sample in k-space. However, undersampling inevitably results in either aliasing or lower resolution. Different approaches have been used to overcome this problem us- ing a priori knowledge. They include parallel imaging methods (1, 2), unaliasing by Fourier-encoding the over- laps using the temporal dimension (UNFOLD) (3), partial k-space reconstruction methods (4 – 6), keyhole imaging (7,8) and variable-density k-space sampling. Variable-den- sity sampling uses the knowledge that most of the energy of an image is concentrated at low spatial frequencies. Therefore, by allocating more of the sampling points near the k-space origin, reasonable image quality can be achieved with fewer sampling points compared to the case in which k-space is sampled uniformly. Variable-density k-space trajectories have been used pri- marily for fast imaging (9 –12), reduction of aliasing arti- facts (13–15), motion artifacts (16), off-resonance artifacts (17), and chemical shift imaging artifacts (18). Marseille et al. (9) employed nonuniform phase encodes to reduce imaging time. Scheffler and Hennig (10) proposed the use of undersampled PR trajectories, which are inherently sampled with variable-density, to reduce scan time. Peters et al. (11) used the undersampled PR trajectories to reduce scan time for angiography applications. Spielman et al. (12) used variable-density spiral trajectories to increase the temporal resolution of fluoroscopy. Nayak and Nishimura (13) tried randomizing the k-space trajectory to reduce artifacts by making the artifacts noncoherent. Tsai and Nishimura (14) studied variable-density spiral trajectories to reduce aliasing artifacts from objects outside the FOV. Cline et al. (15) designed logarithmic k-space trajectories to reduce aliasing artifacts. Liao et al. (16) described the use of variable-density spiral trajectories to reduce motion artifacts by oversampling in the low-spatial-frequency re- gion. Stochastic k-space trajectories were used by Scheffler et al. (17) to reduce the off-resonance artifacts by random- izing the distribution of the off-resonance signal. Variable- density spirals were also used by Adalsteinsson et al. (18) for spatial side lobe reduction in chemical-shift imaging. Compared to other imaging modalities, variable-density sampling is more practical in MRI because sampling points are arbitrarily determined by the gradient wave- forms. Therefore, no additional hardware is required to enable variable-density sampling. The gradient waveforms can be modified to choose sampling points in k-space as long as the trajectory is still smooth. Consequently, under- sampling can be done selectively in a very flexible manner. Here we propose the use of variable-density sampling applied to the stack-of-spirals trajectory to significantly reduce 3D scan time while maintaining reasonable image quality. The stack-of-spirals trajectory (19, 20) consists of spiral trajectories in the k x –k y plane and phase encoding in the k z direction. Since the combination of the spiral tra- jectory and the phase encoding allows flexible control over the density variation, it is particularly suitable for vari- able-density k-space sampling. The proposed technique was demonstrated with phantom images and applied in vivo to the problem of assessing limb perfusion. MRI, with its excellent spatial resolution, is an ideal tool for assessing peripheral perfusion. Methods such as BOLD and T 1 measurement of perfusion (21, 22) have been de- 1 Magnetic Resonance Systems Research Laboratory, Department of Electri- cal Engineering, Stanford University, Stanford, California. 2 Division of Cardiovascular Medicine, Palo Alto Medical Foundation, Palo Alto, California. Grant sponsors: National Institutes of Health; GE Medical Systems; Grant sponsor: California Tobacco-Related Disease Research Program; Grant num- ber: 9RT-0024. *Correspondence to: Jin Hyung Lee, Packard Electrical Engineering, Room 210, 350 Serra Mall, Stanford University, Stanford, CA 94305-9510. E-mail: ljinhy@mrsrl.stanford.edu Received 28 May 2003; revised 30 July 2003; accepted 11 August 2003. DOI 10.1002/mrm.10644 Published online in Wiley InterScience (www.interscience.wiley.com). Magnetic Resonance in Medicine 50:1276 –1285 (2003) © 2003 Wiley-Liss, Inc. 1276