3D Steady-State Diffusion-Weighted Imaging with Trajectory Using Radially Batched Internal Navigator Echoes (TURBINE)

3D Steady-State Diffusion-Weighted Imaging with Trajectory Using Radially Batched Internal Navigator Echoes (TURBINE) Jennifer A. McNab, Daniel Gallichan, Karla L. Miller Oxford Centre for Functional Magnetic Resonance Imaging of the Brain, University of Oxford, Oxford, UK Corresponding Author: Jennifer A. McNab Oxford Centre for Functional Magnetic Resonance Imaging of the Brain John Radcliffe Hospital Headington, Oxford OX3 9DU, United Kingdom E-mail: jmcnab@fmrib.ox.ac.uk Word Count: 2798 Running Head: Steady-State Diffusion-Weighted Imaging with TURBINE 1

Abstract While most DWI is acquired using single-shot diffusion-weighted spin-echo (DW-SE) EPI, steadystate DWI is an alternative method with the potential to achieve higher-resolution images with less distortion. Steady-state DWI is, however, best suited to a segmented 3D acquisition and thus requires 3D navigation to fully correct for motion artifacts. In this paper, a method for 3D motioncorrected steady-state DWI is presented. The method uses a unique acquisition and reconstruction scheme named Trajectory Using Radially Batched Internal Navigator Echoes (TURBINE). Steady-state DWI with TURBINE uses slab-selection and a short EPI read-out each TR. Successive EPI read-outs are rotated about the phase-encode axis. For image reconstruction, batches of cardiac-synchronized read-outs are used to form 3D navigators from a fully-sampled central k- space cylinder. In vivo steady-state DWI with TURBINE is demonstrated in human brain. Motion artifacts are corrected using refocusing reconstruction and TURBINE images prove less distorted compared to 2D single-shot DW-SE-EPI. Keywords: diffusion, steady-state, motion-correction; 2

Introduction Diffusion-weighted imaging (DWI) is sensitive to the self-diffusion of water molecules. In brain tissue, biological membranes and barriers hinder the diffusion of water along certain orientations, thereby rendering DWI an effective method to non-invasively interrogate tissue microstructures. DWI is used routinely in the clinical diagnosis of acute stroke [1] and to differentiate between cysts and other neurological lesions [2]. More recently the neuroscience community has capitalized on multi-orientation DWI measurements to study the orientation and structural properties of white matter pathways [3]. There remain, however, several technical challenges that limit the utility of DWI including the need for increased resolution and reduced distortions. At the current standard resolution of around 8 mm 3 small stroke lesions may not be detectable. For diffusion tensor imaging and tractography a combination of white matter (WM) and grey matter (GM) within each voxel give rise to an ambiguous mixture of putatively anisotropic diffusion in WM and isotropic diffusion in GM. Decreased voxel sizes should also limit the incidence of intra-voxel crossing or kissing fibres, situations which can also give rise to ambiguity. Severe distortions are also a serious problem for conventional 2D single-shot diffusion-weighted spin echo (DW-SE) EPI. The long EPI read-out is prone to distortions caused by susceptibility differences at air-tissue interfaces and with the increasing trend towards higher static magnetic field strengths, these susceptibility artifacts are exacerbated. Parallel imaging can be used to reduce the time to acquirea single-shot image [4] thereby providing the potential to improve resolution and/or reduce distortions at the cost of some loss in SNR. However, current techniques are in practice limited to accelerations of 2-3. Recently, steady-state DWI with a heavily segmented 3D acquisition has been shown to be an efficient method for achieving high resolution (0.8 mm isotropic), low distortion DWI in fixed human brains [5, 6]. Steady-state DWI accumulates signal from multiple echoes that are generated across several TRs and thereby builds a strong sensitivity to diffusion with relatively small gradient areas and short imaging times [7 9]. These benefits would be useful for in vivo applications as well. However, applying the same 3D segmented steady-state DWI pulse sequence in vivo leads to severe artifacts due to the inherent sensitivity to motion (both bulk and physiological) which corrupts 3

phase encoding when combining separately-acquired k-space segments. It is for this reason that standard DWI methods (i.e. 2D DW-SE-EPI) acquire all data required to form an image in a single-shot. A compelling method for correcting motion-induced phase errors in 2D is to acquire a low resolution, full field-of-view (FOV) image, called a navigator image, along with each k-space segment. The low frequency phase information from the navigator image can be used to correct for phase offsets between separately acquired k-space segments [10, 11]. These data can accurately measure 2D rigid body movement, provided the centre of k-space does not shift outside the covered region. However, cardiac pulsation causes brain tissue to deform in a largely non-linear way and thus more recent work has extended this concept to include correction of non-linear motion. Non-linear phase offsets can be measured with 2D navigators, provided the phase offsets vary sufficiently slowly to be well-described by the low-resolution navigator. The simplest reconstruction operates in image space and removes the phase measured by the navigator from the (potentially aliased) highresolution image data [12,13]. Self-navigating trajectories such as Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconsturction (PROPELLER) [12], Self-Navigated Interleaved Spiral (SNAILS) [14] and EPI with Keyhole (EPIK) [15, 16] are highly efficient methods of 2D navigation because they acquire the 2D navigator and the outer k-space segment in a single readout. However, the aforementioned techniques are for 2D imaging, whereas steady-state DWI is best suited to a 3D acquisition such that the steady-state does not need to be re-established with each slice. The challenge in developing a 3D navigated pulse sequence is that it would take a prohibitively long time to acquire all the data needed for a 3D navigator along with each k-space segment. A disproportionate amount of time spent acquiring the navigator compared to the associated k-space segment renders the pulse sequence highly inefficient. As a solution to this problem we propose the use of a multi-shot navigator. Using multiple read-outs to form a navigator is perhaps counterintuitive, but if the majority of motion effects are due to cardiac pulsation then these effects should be highly reproducible and able to be captured using multiple acquisitions. We thus propose that using the very rapid steady-state DWI pulse sequence, it may be sufficient to form a 3D navigator 4

from multiple read-outs acquired during a similar portion of the cardiac cycle. Along these lines we present an implementation of steady-state-dwi that uses slab-selection and a novel k-space trajectory named Trajectory Using Radially Batched Internal Navigator Echoes (TURBINE). This pulse sequence is tested in healthy volunteers and compared with standard 2D DW-SE-EPI to highlight the reduced levels of distortion. Methods Pulse Sequence The steady-state DWI TURBINE pulse sequence (Fig. 1a) selectively excites a slab and acquires an EPI read-out each TR with phase-encoding along the same orientation as the slab-selection. The EPI read-out fully samples the phase-encoding orientation (Fig. 1b) and for successive TRs the EPI read-outs are rotated about the phase-encoding/slab-select axis (Fig. 1cd) such that they sample a k-space volume the shape of a Swedish snuff box. By acquiring multiple averages and monitoring a pulse oximeter and scanner triggers, batches of EPI blades acquired during a similar portion of diastole and with equal angular spacing are formed. The angular spacing for each batch of cardiac-synchronized blades was chosen such that the central cylinder corresponds to a full-fov navigator with 10 mm 10 mm resolution in the radially sampled plane. Acquisition All data were acquired on a Siemens 3T MRI (TIM Trio) using a transmit-receive head coil, in accordance with the ethics review board at our institution. 3D steady-state DWI TURBINE data were acquired on 11 healthy volunteers. Three different experiments are presented in this paper. The first experiment aimed to demonstrate the signal that could be restored using the TURBINE image reconstruction. 3D steady-state DWI TURBINE data were acquired in a healthy 28 year old male using three different parameter sets. slab-selection, TE/TR = 28/46 ms, flip angle = 37, FOV read FOV phase = 210 mm 31.5 mm, slab thickness = 29 mm, EPI matrix = 140 21, 224 k-space radial-encoding positions, resolution = 1.5 mm isotropic, diffusion gradient = 5.3 ms 38 mt/m (providing equivalent attenuation to a diffusion-weighted spin echo with b = 556 s/mm 2 ), 46 averages, time per volume = 10.3 s. 5

The goal of the second experiment was two-fold: 1) to test steady-state DWI with TURBINE with a larger diffusion-encoding gradient area and 2) to test the reproducibility of repeated measurements. For this experiment data were acquired in a healthy 33 year old female using TE/TR = 27/41 ms, flip angle = 37, FOV read FOV phase = 210 mm 26 mm, slab thickness = 25.8 m, EPI matrix = 120 16, 192 k-space radial-encoding positions, resolution = 1.75 mm isotropic, diffusion gradient = 7.5 ms 38 mt/m (providing equivalent attenuation to diffusion-weighted spin echo with b = 935 s/mm 2 ), 6 sets of 15 averages, time per volume = 7.9 s. The third experiment aimed to compare 2D single-shot DW-SE-EPI and 3D steady-state DWI TURBINE. Data were acquired in a healthy 31 year old female. Cardiac-gated 2D DW-SE-EPI data were acquired with TE/TR = 97/4200 ms, partial Fourier = 6/8, BW = 1654 Hz/pixel, b = 1000 s/mm 2, 10 averages. 3D steady-state DWI TURBINE data was acquired using TE/TR = 25/41 ms, flip angle = 37, slab thickness = 39 mm, diffusion gradient = 5.3 ms 38 mt/m, 10 averages, BW = 992 Hz/pixel. Both pulse sequences used FOV read FOV phase = 212 mm 212 mm, voxel size = 2 mm 2 mm 2 mm and acquired 21 coronally oriented slices with diffusion-encoding along anterior-posterior orientation in 1 minute, 15 seconds. Note that for all steady-state DWI data, the TE is defined as the time between the RF pulse and the read-out. Pulse oximeter and scanner triggers were recorded for all steady-state DWI experiments in order to synchronize cardiac pulses with the data acquisition. Image Reconstruction All TURBINE images were reconstructed offline. Image analysis was performed using custom software written in MATLAB v7.4 (MathWorks Inc.). The common even-odd EPI artifact [17] was correct for using three non-phase-encoded reference lines that were acquired between the RF pulse and the diffusion-encoding gradient each TR. Retrospective cardiac gating was performed by eliminating EPI blades acquired less than 150 ms following or 50 ms prior to a cardiac trigger. A zero-order phase correction was also performed on each EPI blade (i.e. the phase at the centre of k- space was removed from each data point in the EPI acquisition). This zero-order phase-correction was intended to remove the effects of bulk, rigid-body shifts, so that once the EPI blades were combined to form navigators, only cardiac-induced phase-offsets would remain. One would expect 6

rigid body rotations to induce a linear phase-ramp across the image-space data, however, no such effects were detected and thus no rotational corrections were applied. Batched sets of 16 EPI blades with equal angular spacing and acquired during a similar portion of diastole were combined (Fig. 2). Cardiac timing for each EPI blade was measured as the delay between the most recent pulse oximeter trigger and the start of data acquisition. For each set of 16 equally spaced angular positions, the number of cardiac synchronized batches was equal to the number of averages acquired. Using this scheme, some EPI blades were used in more than one batch and some were not used at all. For each 3D interleave the 16 EPI blades were gridded onto a 2 Cartesian grid using sampling density compensation and a sinc convolution of window width 5. After gridding, two copies of each k-space interleave were retained. One copy was 3D inverse Fourier transformed to generate an aliased 3D image volume which includes both high and low frequency information. The second copy was k-space filtered using a Hanning window with full-width-at-half-maximum = 0.15 to retain only the low frequency information. The filtered data were then 3D inverse Fourier transformed to form the 3D navigator with in-plane resolution of 10 mm 10 mm and through-plane resolution equal to the full resolution of the acquisition (i.e. 1.5 mm or 2 mm for the data sets presented here). The 3D navigators and image interleaves were used to perform refocusing reconstruction in image space [13], which consists of multiplying the 3D image interleaves by the complex conjugate of their 3D navigators and then summing the corrected image interleaves to produce the final image. A diagram of an essentially identical image reconstruction pipeline can be found in Figure 6 of Pipe et. al. 2002 [12]. There are two main differences between TURBINE image reconstruction and PROPELLER image reconstruction. Firstly, instead of the k-space strip that is used in each stage of the PROPELLER reconstruction, TURBINE uses a batch of cardiac-synchornized EPI blades as shown in Fig. 1d. Secondly, for TURBINE all the FFTs and filters are in 3D whereas for PROPELLER they are in 2D. Results Figure 3 shows images acquired with 3D steady-state DWI with TURBINE that have been re- 7

constructed in three different ways. In left column of Fig. 3 TURBINE data has been gridded and inverse Fourier transformed but the retrospective cardiac gating and refocusing reconstruction has not been applied. In the middle column of Fig. 3 TURBINE data has been reconstructed by first removing any EPI blades that were acquired during systole and then inverse Fourier transforming the data but still not applying the refocusing reconstruction. Finally in the right column of Fig. 3 TURBINE data has been retrospectively cardiac-gated by removing EPI blades acquired during systole and then performing the full refocusing reconstruction pipeline as described in the image reconstruction section. When no cardiac-gating or motion-correction is applied, images with diffusion-encoding along left-right and anterior-posterior orientation don t show any apparent motion artifacts. The majority of the artifacts arise when diffusion-encoding is applied along the superior-inferior orientation and this is consistent with previous 2D imaging results [13]. After removal of data acquired during systole, the images do not improve (Fig. 3 (middle column)), in fact a reduction in SNR is the only noticeable effect. After the refocusing reconstruction is applied there is a significant amount of signal restored in the superior-inferior diffusion-encoded image. However, a comparison of signal values in four gray matter regions where we would expect largely isotropic diffusion, reveals that, on average, signal values in the S-I diffusion-encoded image are still 32% lower than in the L-R and A-P diffusion-encoded images. Figure 4 displays steady-state DWI TURBINE images acquired with a larger diffusion-encoding gradient area (attenuation equivalent to DW-SE with b = 935 s/mm 2 ) and reconstructed using the refocusing reconstruction. Sequentially acquired images show excellent reproducibility. The coefficient of variation maps (Fig. 4 right column) show increased variation in areas of low signal (e.g. CSF which is highly attenuated) and reduced variation in regions of high signal (e.g. white matter tracts running orthogonal to the diffusion-encoding gradient) but do not indicate any unexpected instabilities. Matched 2D single-shot DW-SE-EPI and 3D steady-state DWI with TURBINE data (Fig. 5) highlight the reduction in distortions that can be achieved using steady-state DWI with TURBINE. For 2D single-shot DW-SE-EPI distortions are particularly apparent around the temporal lobe and are so so severe it would be difficult to match tissue in these regions with the same tissue in a 8

conventional structural image. Discussion The efficiency of steady-state imaging methods is best capitalized using 3D imaging such that the steady-state does not need to be re-established for each slice. However, 3D segmented DWI is a challenging problem due to the inherent sensitivity of DWI to bulk and physiological motion and the amount of data required to fully correct motion effects in three dimensions. Here we have presented a novel solution to this problem using a new pulse sequence called steady-state DWI with TURBINE. We have presented the first steady-state diffusion-weighted images with 3D navigation. To achieve this, the peculiar concept of a multi-shot navigator has been introduced and its feasbility demonstrated. Cardiac pulsation creates the most tissue deformation along the superior-inferior orientation [18,19] and our data shows that diffusion-encoding along the superior-inferior axis is indeed the most problematic (Fig. 3). However, for diffusion-encoding along left-right and anterior-posterior orientations the TURBINE images don t show any apparent motion artifacts. If physiological brain motion is primarily along the S-I orientation it may not seem obvious why a 3D navigator is required. A 3D navigator is required if we expect brain motion to create a gradient of phase along all three orientations. Phase variation in image space along a particular orientation will cause a shift in the centre of k-space along that same orientation and if we do not have a navigator that encompasses the orientation along which we have phase variation then the centre of k-space can shift outside of the navigator resulting in uncorrectable motion artefacts. While previous studies [18,19] have found that brain motion consists primarily of displacement along the S-I axis, these studies also indicate that the motion primarily affects the mid-brain. It is the variation in the amount of displacement experienced by the mid-brain relative to the surrounding tissue that causes phase variations along all three axes and therefore necessitates a 3D navigator. In addition to physiological motion, we speculate that the severe drop-out observed in the frontal 9

brain regions in uncorrected S-I diffusion-encoded images (Fig.??) is due to rigid body motion. For a person lying in the scanner we would epxect there to be rotation about the L-R axis but with adequate padding minimal rotation about the S-I or A-P orientations. Rotation of the head about the L-R axis would cause both the frontal brain regions and inferior-posterior brain regions (i.e. the cerebellum which is not encompassed y the slab we acquired) to be displaced significantly along the S-I orientation and therefore result in significant drop-out in these regions when we are diffusion-encoding along S-I. The reconstruction scheme presented here combines EPI blades that were acquired during a similar portion of diastole in different heart beats to form 3D navigators. An alternative method in which EPI blades acquired during the diastolic portion of the same cardiac cycle were combined to form 3D navigators was also tested. Acquiring one navigator per heart-beat is feasible from an acquisition stand-point (i.e. the data required for one 3D navigator takes 700 ms and thus can be acquired within the quiet portion of a single cardiac cycle). However, in our experience refocusing reconstruction did not improve image quality when combining data from the same cardiac cycle. This could be due to residual motion during diastole, which although not as severe as systole, still causes significant phase offsets. There are of course many additional ways in which the EPI blades could be combined. For example, a higher priority could be given to cardiac synchronization by allowing the angular spacing to vary a small amount and/or leaving out EPI blades where an appropriately synchronized read-out is not available. Once an optimal method for combining batches of EPI blades is determined, it will likely be beneficial to implement prospective cardiac gating since the retrospective gating becomes less effective if fewer averages are acquired. Prospective gating will, however, necessitate dummy scans between cardiac triggers in order to maintain the steady-state throughout [13]. A different number of EPI blades could also be used to form the 3D navigators. In this study, 16 EPI blades was chosen in order to achieve an in-plane navigator resolution similar to that which had been used successfully in 2D imaging [13]. A different image reconstruction approach that may also be worth exploring is an appropriate version of magntiude-only filtered back projection [20]. With the severity of susceptibility artifacts proportional to main magnetic field strength, diffusion- 10

weighted image quality has suffered as methods have been ported largely unchanged from 1.5T to 3T. Field inhomogeneities cause errors in spatial encoding in the vicinity of susceptibility differences. Long k-space read-outs such as single-shot EPI are particularly vulnerable to susceptibility artifacts because they allow spins to accrue more artifactual phase resulting in a greater spatial encoding error. As expected the shorter read-outs used by TURBINE result in reduced distortions (Fig. 5), a highly desirable characteristic when attempting to study detailed anatomical connections and/or match DWI to T 1 or T 2 -weighted images. One major difference between the 2D single-shot DW- SE-EPI data and the 3D steady-state DWI TURBINE data presented in Figure 5 is how we would expect distortions to propagate. Distortions are primarily expected along the phase-encode axis which for DW-SE is along an in-plane axis whereas for TURBINE phase-encoding is along the through-plane axis (i.e. anterior-posterior for the images in Fig. 5). Regardless of this difference, it is clear that the distortions are reduced when using TURBINE. In addition to reduced distortions, a 3D segmented pulse sequence also has the potential to achieve very small isotropic voxels. Unlike 2D imaging which is usually limited to a through-plane resolution of around 2 mm due to technological constraints associated with thin slice selection, a 3D segmented pulse sequence is limited only by SNR/time contraints. In order to reduce total raw data size, the data presented here was acquired with a single channel coil and thus further SNR gains are expected when a multi-channel coil is used. While the refocusing reconstruction significantly improves the quality of the S-I diffusion-encode images, we expect the lower signal values measured in the S-I diffusion-encoded images compared to diffusion-encoding along L-R or A-P to be problematic for DTI and tractography since there would be a consistent bias towards the S-I orientation when estimating the orientation of maximum diffusivity. Therefore, in its current implementation steady-state DWI with TURBINE is limited to the detection of changes to isotropic diffusion and future work will be aimed at resolving these signal discrepancies such that DTI and tractography may be feasible. One way in which TURBINE image quality may be further improved is through the use of a full least squares reconstruction. Refocusing reconstruction ignores the final step of the least-squares reconstruction which is the application of the unmixing operator to the refocused image [13]. The 11

unmixing operator removes motion-induced aliasing by a linear combination that removes coupling between voxels. If our images contain significant aliased energy, a full least squares reconstruction could provide considerable further improvement to image quality. The challenge is to find a way to invert the large mixing matrix, which has a minimum size of N 2 N 2 where N 2 corresponds to the number of points in your image. In our case, even if we were to calculate one phase-encoded slice at a time, the size of our mixing matrix would be 19600 19600 which requires a minimum of 1.4 GB of memory to store. The problem, however, is mathematically similar to a non-cartesian SENSE reconstruction [21, 22] and thus an iterative scheme such as the conjugant-gradient reconstruction which has been proposed for multicoil reconstructions may offer a solution. TURBINE is currently limited to a slab thickness of only a few centimeters, but there are several ways in which brain coverage could be extended. Parallel imaging could be used and/or a variable density k-space trajectory such as EPIK [15, 16] would permit a larger slab at the same resolution whilst still enabling formation of the 3D navigator using the more densely sampled k-space centre. Alternatively, multiple slabs could be stitched together to cover the full brain volume. From an implementation perspective, for steady-state imaging, gradients are generally played out as quickly as possible in order to keep the TR short. Steady-state DWI wth TURBINE currently uses the maximum possible gradient amplitude (38 mt/m) to achieve a diffusion-encoding gradient in only 5.3 ms. Such rapid ramping of the gradients makes the pulse sequence close to peripheral nerve stimulation (PNS) limits. The Siemens scanner issues a stimulation warning prior to commencing the scan and 3 of the 10 volunteers felt they may have experienced some PNS. Thus, the design of highly efficient DWI methods needs to consider such physiological restrictions. A concern often raised about steady-state DWI is that its signal properties are unconventional. The steady-state DWI signal is generated from multiple echoes across several TRs. This type of signal formation results in a weighted combination of b-values (i.e. a different b-value for each contributing echo) and a complicated, non-linear dependency on not only the diffusion-encoding gradient area but also flip angle, TR, T 1 and T 2 [23]. It has been shown previously, however, that the signal model for steady-state DWI is robust and permits quantitative measures of diffusion if T 1 and T 2 measurements are made [6,24]. Additionally, it has been shown that the principal diffusion 12

orientation can be determined even without T 1 and T 2 measures, thereby permitting tractography applications without any additional data acquisition [6]. Conclusion In conclusion, this study presents a unique and promising approach towards 3D segmented DWI. Steady-state DWI has long been recognized as an efficient diffusion imaging method, but the segmented nature of the pulse sequence combined with a strong sensitivity to motion has thus far prevented its adoption to mainstream applications. It is our hope that, with further refinements, the TURBINE acquisition and reconstruction scheme may provide a viable option for harnessing the benefits of steady-state DWI and thus provide an alternative DWI method that will push the boundaries of what can currently be achieved. Acknowledgments Funding for this work was provided by the UK Multiple Sclerosis Society, Royal Academy of Engineering and the Engineering and Physical Sciences Research Council. The authors would like to acknowledge helpful discussions with Dr. Matthew Robson. References 1. Chien D, Kwong KK, Gress DR, Buonanno FS, Buxton RB, Rosen BR. MR diffusion imaging of cerebral infarction in humans. American Journal of Neuroradiology 1992;13:1097 1102. 2. Tsuruda JS, Chew WM, Moseley ME, Norman D. Diffusion weighted MR imaging of the brain: value of differentiating between extraaxial cysts and epidermoid tumors. American Journal of Neuroradiology 1990;11:925 931. 3. Basser PJ, Mattiello J, Le Bihan D. MR diffusion tensor spectroscopy and imaging. Biophysics Journal 1994;66:259 267. 13

4. Bammer R, Auer M, Keeling SL, Augusting M, Stables LA, Prokesch RW, Stollberger R, Moseley ME, Fazekas F. Diffusion tensor imaging using single-shot SENSE-EPI. Magnetic Resonance in Medicine 2002;48:128 136. 5. McNab JA, Miller KL. Sensitivity of diffusion weighted steady-state free precession to anisotropic diffusion. Magnetic Resonance in Medicine 2007;60:405 413. 6. McNab JA, Jbabdi S, Deoni SCL, Douaud G, Behrens TEJ, Miller KL. High resolution diffusion-weighted imaging in fixed human brain using diffusion-weighted steady-state free precession. NeuroImage 2009;doi:10.1016/j.neuroimage.2009.01.008. 7. Kaiser R, Bartholdi E, Ernst RR. Diffusion and field-gradient effects in NMR Fourier spectroscopy. Journal of Chemical Physics 1974;60:2966 2979. 8. LeBihan D. Intravoxel incoherent motion imaging using steady-state free precession. Magnetic Resonance in Medicine 1988;7:346 351. 9. Wu E, Buxton R. Effect of diffusion on the steady-state magnetization with pulsed field gradients. Journal of Magnetic Resonance 1990;90:243 253. 10. Butts K, Pauly J, decrespigny A, Moseley M. Isotropic diffusion-weighted and spiral-navigated interleaved EPI for routine imaging of acute stroke. Magnetic Resonance in Medicine 1997; 38:741 749. 11. Atkinson D, Porter DA, Hill DL, Calamante F, Connelly A. Sampling and reconstruction effects due to motion in diffusion-weighted interleaved echo planar imaging. Magnetic Resonance in Medicine 2000;44:101 109. 12. Pipe J, Farthing V, Forbes K. Multishot diffusion-weighted FSE using PROPELLER MRI. Magnetic Resonance in Medicine 2002;47:42 52. 13. Miller KL, Pauly JM. Nonlinear phase correction for navigated diffusion imaging. Magnetic Resonance in Medicine 2003;50:343 353. 14

14. Liu C, Bammer R, Kim DH, Moseley ME. Self-navigated interleaved spiral (SNAILS): application to high-resolution diffusion tensor imaging. Magnetic Resonance Imaging 2004;52:1388 1396. 15. Zaitsev M, Zilles K, Shah NJ. Shared k-space echo planar imaging with keyhole. Magnetic Resonance in Medicine 2001;45:109 117. 16. Nunes RG, Jezzard P, Behrens TEJ, Clare S. Self-navigated multishot echo-planar pulse sequence for high-resolution diffusion-weighted imaging. Magnetic Resonance in Medicine 2005; 53:1474 1478. 17. Bruder H, Fischer H, Reinfelder H, Schmitt F. Image reconstruction for echo planar imaging with nonequidistant k-space sampling. Magnetic Resonance in Medicine 1992;23:311 323. 18. Enzmann DR, Pelc NJ. Brain motion: measurement with phase-contrast MR imaging. Radiology 1992;185:653 660. 19. Poncelet BP, Wedeen VJ, Weisskoff RM, Cohen MS. Brain parenchyma motion: measurement with cine echo-planar MR imaging. Radiology 1992;185:645 651. 20. Trouard TP, Theilmann RJ, Altbach MI, Gmitro AF. High-resolution diffusion imaging with DIFRAD-FSE (diffusion-weighted radial acquisition of data with fast spin echo) MRI. Magnetic Resonance in Medicine 1999;42:11 18. 21. Pruessmann KP, Weiger M, Bornert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magnetic Resonance in Medicine 2001;46:638 651. 22. Liu C, Moseley ME, Bammer R. Simultaneous phase correction and SENSE reconstruction for navigated multi-shot DWI with non-cartesian k-space sampling. Magnetic Resonance in Medicine 2005;54:1412 1422. 23. Buxton R. The diffusion sensitivity of fast steady-state free precession imaging. Magnetic Resonance in Medicine 1993;29:235 243. 24. Deoni S, Peters T, Rutt B. Quantitative diffusion imaging with steady-state free precession. Magnetic Resonance in Medicine 2004;51:428 433. 15

Figure Captions Figure 1: a) Pulse sequence diagram for steady-state DWI using TURBINE. The bottom line (G SS/P E ) represents the axis along which slab-selection and phase-encoding are applied. G θ represents the read-out axis which is rotated about the slab-select/phase-encode axis for successive TRs. b-d) The TURBINE k-space trajectory. An EPI read-out as shown in b) is acquired each TR. Successive EPI read-outs, as shown in c) and d), are rotated about the slab-select/phase-encoding axis which in this case is k z. Figure 2: Diagrams showing how EPI read-outs were combined to form 3D navigators. Each navigator consisted of 16 EPI read-outs with equal angular spacing. The image in a) describes the data available to form 3D navigators at a particular set of angular positions. For each angular k-space position, multiple averages were acquired. The colour scale represents when each EPIread-out was acquired with respect to the cardiac cycle, as determined by the delay in time from the most recent measured cardiac trigger. Black pixels indicate data acquired during systole that has been discarded. The particular average that is used for the EPI read-out with the lowest angular position (i.e. starting at the positive k x -axis) determines the cardiac synchronization for a particular batch of EPI-read-outs that will form a 3D navigator. The reconstruction software then searches for EPI-readouts at the appropriate positions that were acquired during the same portion of the cardiac cycle. The symbols in a) indicate EPI-read-outs that were combined to form one navigator for this set of positions. In b) the angular positions of these EPI-read-outs are plotted using the same colour code as in a). c-d) and e-f) show two further examples of data combined to form navigators for different angular positions and different cardiac timings. Figure 3: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row), anterior-posterior (middle row) and superior-inferior (bottom row). Columns left to right show the effects of cardiac gating and refocusing reconstruction. Figure 4: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row), anterior-posterior (middle row) and superior-inferior (bottom row). In the first column, 6 sequentially acquired images are shown. The middle column shows the average of the 6 images shown in 16

the left column. The right column shows the coefficient of variation map for the 6 images in the left column. Figure 5: A comparison of coronal images at 2 mm isotropic resolution acquired with 2D singleshot DW-SE-EPI (left column) and 3D steady-state DWI with TURBINE (right column) in the same healthy volunteer. (a-d) depict the same coronal slice acquired without diffusion-weighting (ab) and with diffusion-weighting (c-d). (e-h) depict a different coronal slice again without diffusion weighting (e-f) and with diffusion weighting (g-h). 17

!! TR! RF! G Diff! G! "!!!!!"! G#! x-y! G z! $! SS/PE %! &! '! Figure 1: a) Pulse sequence diagram for steady-state DWI using TURBINE. The bottom line (G SS/P E ) represents the axis along which slab-selection and phase-encoding are applied. G θ represents the read-out axis which is rotated about the slab-select/phase-encode axis for successive TRs. b-d) The TURBINE k-space trajectory. An EPI read-out as shown in b) is acquired each TR. Successive EPI read-outs, as shown in c) and d), are rotated about the slab-select/phase-encoding axis which in this case is k z. 18

Figure 2: Too long to fit on this page, see Figure Captions section. 19

No gating No correction Cardiac Gated No correction Cardiac Gated Refocusing Recon R-L A-P S-I Figure 3: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row), anterior-posterior (middle row) and superior-inferior (bottom row). Columns left to right show the effects of cardiac gating and refocusing reconstruction. 20

Repetitions 1-6 Average Coefficient of Variation 1 R-L 0 1 A-P 0 1 S-I 0 Figure 4: Steady-state-DWI-TURBINE images with diffusion encoding along right-left (top row), anterior-posterior (middle row) and superior-inferior (bottom row). In the first column, 6 sequentially acquired images are shown. The middle column shows the average of the 6 images shown in the left column. The right column shows the coefficient of variation map for the 6 images in the left column. 21

Figure 5: A comparison of coronal images at 2 mm isotropic resolution acquired with 2D single-shot DW-SE-EPI (left column) and 3D steady-state DWI with TURBINE (right column) in the same healthy volunteer. (a-d) depict the same coronal slice acquired without diffusion-weighting (a-b) and with diffusion-weighting (c-d). (e-h) depict a different coronal slice again without diffusion weighting (e-f) and with diffusion weighting (g-h). 22