Dynamic Imaging with Multiple Resolutions Along Phase-Encode and Slice-Select Dimensions

Transcription

1 Dynamic Imaging with Multiple Resolutions Along Phase-Encode and Slice-Select Dimensions Lawrence P. Panych, Lei Zhao, Ferenc A. Jolesz and Robert V. Mulkern Departments of Radiology, Brigham and Women s Hospital and Children s Hospital, Boston MA Harvard Medical School Running Title: Dynamic multi-resolution imaging Address correspondence to: Lawrence P. Panych, Ph.D. Department of Radiology Brigham and Women s Hospital 75 Francis Street Boston, Massachusetts Tel. (617) Fax (617) Submitted for publication to Magnetic Resonance in Medicine, September Revised December, Accepted for publication, February 8, 2001 (MRM ).

2 ABSTRACT An implementation is reported of an imaging method to obtain Multiple Resolutions along Phase and Slice-select dimensions. The method, referred to as MURPS, enables dynamic imaging of focal changes using a graded, multi-resolution approach. MURPS allows one to trade spatial resolution in part of the volume for improved temporal resolution in dynamic imaging applications. A unique method of Hadamard slice encoding is used, enabling the varying of the phase encode and slice resolution while maintaining a constant effective TR throughout the entire 3-dimensional volume. MURPS was implemented using a gradient recalled echo sequence and its utility was demonstrated for MR temperature monitoring. In the preliminary work presented in this paper, it has been shown that changes throughout a large volume can be effectively monitored in times that would normally only permit dynamic imaging in one or a very few slices. Key words: Dynamic multi-resolution imaging, Temperature monitoring, Hadamard encoding, Spatially selective RF excitation, non-fourier encoding, Adaptive imaging. ACKNOWLEDGEMENTS Work performed with support from Whitaker Foundation Transitional Funding Grant TF and from NIH grants, R29-CA70314, P01-CA67165 and R01-NS The authors wish to acknowledge Dr. Seung-Schik Yoo for his assistance with some of the experimental work and to acknowledge Dr. Kullervo Hynynen and Nathan McDannold for the useful discussions on applications of the method for temperature mapping. A preliminary account of this work was reported at the Eighth Scientific Meeting of the ISMRM in Denver, Colorado, April 1-7, 2000.

3 Panych et al 1 I INTRODUCTION Dynamic MR imaging methods for monitoring of spatially localized changes usually involve reducing volume coverage to improve temporal resolution. This is a good tradeoff when changes are clearly limited to a small, well-defined volume-of-interest. In some applications, however, such as monitoring the progress of heating in focused ultrasound or interstitial laser surgery, this tradeoff is less than ideal because changes are not restricted to a well-defined volume. To achieve a reasonable temporal resolution, it then becomes necessary to monitor a relatively small volume-of-interest comprising very few slices where the dominant change is experienced. Changes may occur in other slices throughout the volume but, in the interests of temporal resolution, they may not be monitored. Here we propose a graded, multi-resolution image acquisition as an alternative to the all or nothing approach. In a standard acquisition, the parameters affecting spatial resolution - slice thickness and number of phase encodes - are constant for all slice acquisitions. For example, if it is determined that 3 millimeter slices and 256 phase encodes are necessary to spatially resolve changes in one slice, the same parameters must be used for all slices, thereby limiting the volume that can be imaged. If, however, slice thickness and phase-encode resolution were varied within an acquisition, we reason that it will be possible to effectively monitor changes throughout a much larger volume without sacrificing temporal resolution. This depends, of course, on whether or not the requisite spatial resolution to resolve changes is also variable throughout the volume. For applications such as temperature mapping this is indeed the case. Sharp and rapid temperature changes occur close to the source of energy deposition, however, in regions distant from the source, the changes are slower and more spatially diffuse. In previous work, we and others have investigated multi-resolution approaches based on non-fourier encoding with wavelets ([1]-[9]). In wavelet encoding, RF pulses were designed to excite spatial profiles shaped like wavelet functions. The special features of the wavelet transform make it particularly suitable for reconstructing images with spatially variable resolution and this led us to propose adaptive imaging strategies based on multi-resolution wavelet encoding [2]. Our previous work with wavelets involved variation of resolution in a single RF select direction only. Imaging methods have been reported by other groups that also involve expansions

4 Panych et al 2 in terms of non-fourier basis functions with spatially variable resolution ([10]-[14]). In these methods, variable resolution is achieved through a non-uniform sampling of k-space in phase-encoding directions combined with a special reconstruction method that projects the selected Fourier basis set onto the non-fourier basis functions. We propose a method to obtain Multiple Resolutions along Phase and Slice-select dimensions (MURPS). In the MURPS approach, resolution parameters are constant within any single slice, however, both slice thickness and phase-encode resolution are varied for different slices. By reducing the number of phase encodes and increasing the slice thickness for some slices, we are able to directly trade reduced spatial resolution in some parts of the volume for an overall increase either in temporal resolution or in volume coverage. Currently MURPS is being developed for MR temperature monitoring but it also has potential for use with other applications such as fmri and other dynamic contrast studies. II METHODS Multi-resolution encoding method Here we describe a MURPS imlementation for acquiring seven slices, each with variable slice thickness and variable phase-encode resolution but with constant effective TR. The drawing at the top of Fig.1 demonstrates the MURPS acquisition schematically with each block in the drawing representing a view of a voxel in the slice-phase plane. The seven slices are arranged horizontally. For simplicity, only a small number of voxels are shown in the phase-encoding direction (ie. the vertical direction in the drawing). In the frequency-encoding direction (through-plane in Fig.1) the resolution is constant for all slices. Ideal excitation profiles for the seven slices are shown below the drawing in Fig.1. The table at the bottom of Fig.1 lists parameters that were used in some of our experiments. In this example, a relatively thin (eg. 5mm) center slice (labeled A ) was acquired at full in-plane resolution. In an application such as the monitoring of heating by focused ultrasound, this slice should be placed so as to cover the location of maximum energy deposition. For two neighboring slices ( B1 and B2 ), slice thicknesses were increased (eg. to 10mm) and phase-encode resolution was reduced by a factor of 2. For the outer four slices ( C1, C2, C3 and C4 ), slice thicknesses were again varied and phase-encode resolution reduced by another factor of 2.

5 Panych et al 3 In the MURPS implementation described here, the B and C slices are separately Hadamard encoded ([15]-[18]) to enable a reduced number of phase encodes in the outer slices while still maintaining a fixed TR for all slices. Figure 2 shows the encoding scheme for the first twelve TR periods. After every three TR periods, the entire imaging volume (A,B, and C slices) is excited once, thus the effective TR throughout the volume is 3*TR. At the end of the twelve TR periods, as shown in Fig.2, slice A has been excited four times and four phase encodes of the slice have been collected. The volume covered by the B slices has also been excited four times in the twelve TR periods. However, because reconstruction of the B slices requires two separate Hadamard encodes (B1+B2, B1-B2), only two phase encodes can be collected in the same time period that slice A is phase encoded four times. The volume covered by the C slices is also excited four times in the twelve TR periods. Because reconstruction of the C slices requires four separate Hadamard encodes (C1+C2+C3+C4, C1-C2+C3-C4, C1+C2-C3-C4, C1-C2-C3+C4), only one phase encode can be collected in the same time period that slice A is phase encoded four times and the B slices are phase encoded twice. Note that with this scheme, there is a relationship between the number of phase encodes and the Hadamard encoding factor. The reduction in the number of phase encodes is inversely proportional to the Hadamard encoding factor so that the product of the number of phase encodes and the Hadamard encoding factor is constant for all slices. For example, when the number of phase encodes acquired for a slice is 1/4 the full resolution case, then 4 slices are Hadamard encoded. Likewise if the number of phase encodes is reduced by 1/2, the number of Hadamard encoded slices is 2. This relationship is necessary in order to maintain a constant effective TR for all slices. There is no such restriction on the slice thickness. We are free to set slices to any convenient thickness. As shown in the table of Fig.1, it is not even necessary to maintain constant slice thickness within a group of Hadamard encoded slices (eg. the C group). In MURPS, signal-to-noise ratio (SNR) varies between slices according to slice thickness, number of phase encodes, and number of Hadamard encodes. The SNR in any slice with respect to slice A is equal to (S/S A ) (H P A )/P, where S is the slice thickness, P is the number of phase encodes, and H is the number of Hadamard encodes. S A is the thickness of the slice A and P A is the number of phase encodes for the slice. Since there is no Hadamard encoding of slice A, H A =1 and is not included

6 Panych et al 4 in the equation. As discussed above, the product of the number of phase encodes and the Hadamard encoding factor is constant for all slices, so that P = P A /H, thus, the relative SNR in any slice with respect to slice A is simply equal to H (S/S A ). A 2D spoiled gradient-echo (SPGR) sequence was modified for the MURPS implementation as follows. First, the sequence was altered so that a set of arbitrary RF pulses (as defined in external files) could be preloaded and then different RF pulses used for each excitation. Twelve pulses designed to excite the profiles shown in Fig.2 were computed on a workstation and preloaded into the imager. Each of the 12 RF pulses (of 5.12 millisecond duration and 30 o flip angle) was used in succession with the sequence repeating after every 12 excitations. The imaging pulse sequence was further modified to execute a phase-encoding order as denoted in Fig.2 for the first 12 excitations. On each set of excitations, the phase-encoding order was simply equal to the order from the previous set of excitations plus { 4,2,1,4,2,1,4,2,1,4,2,1 }. The phase-encode ordering for each TR period was programmed directly in the pulse sequence although it is also possible to read the order from an external file. Brain imaging experiments The seven-slice multi-resolution MURPS acquisition scheme, described in the previous section, was implemented on our 1.5T Signa LX system (GE Medical Systems, Milwaukee, WI) and used to acquire a set of slices from a human volunteer after obtaining informed consent according to institutional review protocol. Seven slices of varying thickness and in-plane resolution were acquired in an interleaved fashion using the modified SPGR sequence (TR/TE, 30/8.6 msec). Slice A was acquired at full in-plane resolution (256x256 acquisition matrix, 240mm FOV) and at a thickness of 5mm. The B slices were acquired at 1/2 the phase-encode resolution (256x128 acquisition matrix) and the C slices were acquired at 1/4 the phase-encode resolution (256x64 acquisition matrix). The B and C slices were 2 or 3 times the thickness of the center slice. As shown in the table of Fig.1, with this scheme, voxel volume increases in graded steps from 5mm 3 in the center slice to 60mm 3 in the outer slices. The total time for encoding the seven multi-resolution slices is 3*N*TR, where N is the number of phase encodes collected for slice A (ie. 256 in the brain imaging experiments). The total volume covered is 7.5cm x 24cm x 24cm. To cover the same volume with 5mm slices at the highest in-plane resolution would require 15*N*TR. Thus, the temporal resolution

7 Panych et al 5 is increased 5-fold over what it would be at full spatial resolution. Or, for the same temporal resolution, there is a 5-fold increase in volume coverage with MURPS over a standard acquisition at constant full spatial resolution. A straightforward tradeoff is made, decreasing spatial resolution in some parts of the volume in order to increase either temporal resolution or volume coverage. Temperature mapping experiments MURPS was implemented on a Signa 1.5T LX system for dynamic temperature monitoring using the proton resonant shift method ([19]-[21]). A glass tube was inserted into the center of an orange and placed in the MRI system. A catheter with attached syringe was inserted into the glass tube so that hot water could be injected into the tube at the start of imaging. A doped water phantom was also placed within the imaged volume in order to monitor changes due to slow drift of the static magnetic field during the experiment. The method of acquisition was as described in the previous sections with resolution parameters as follows: Numbers of phase encodes in the A, B and C slices respectively were 120, 60, and 30 and slice thicknesses were 80% of those used in the brain imaging experiments (ie. 4mm in the center slice, A, and 12mm in the edge slices, C1 and C4). A dynamic series of images was acquired at the rate of one set of 7 multi-resolution slices every 12.6 seconds over a period of approximately 1 hour. Each set of multi-resolution slices was reconstructed and phase difference images were computed by performing a complex division of the image set at each time point with the final image set in the dynamic series, then taking the phase of the result. For each voxel, a time series of 252 phase difference values was obtained. These were then converted directly to temperature change given a reported shift in the proton resonance of approximately ppm per o C of change [21]. Prior to conversion from phase to temperature values, the phase was unwrapped using a library function in Matlab (The Mathworks, Natick, MA) that removes abrupt wrap-around phase changes. The average phase was also measured in a volume-of-interest in the unheated doped water phantom in order to separate phase changes due to heating from the background drift in phase due to static magnetic field changes.

8 Panych et al 6 III RESULTS Brain imaging experiments The upper part of Fig.3 shows seven reconstructed axial brain slice images using MURPS. The variable resolution is evident across the volume with highest resolution (and lower SNR) in slice A and lowest resolution in slices C1 and C4. Note the uniform contrast behavior throughout the volume. The total volume covered in 23 seconds is 7.5mm x 240mm x 240mm. At full resolution (5mm 3 voxels) 115 seconds would be required to cover the same volume. The table at the bottom of Fig.3 gives the theoretical and experimental SNR of the MURPS slices with respect to slice A. There is a relatively close agreement between the theoretical SNR values and those determined experimentally, thus validating our expression for the variation in SNR between MURPS acquired slices. A reference set of 15 slices of 5mm thickness covering the same volume as above was also acquired. Phase-encode resolution was 256 for this set. The slices were acquired sequentially with a TR of 90 milliseconds so as to match the T1-weighting of the multi-resolution set (where the effective TR was 3 30 = 90 milliseconds). From this reference set of slices, virtual slices were created by averaging appropriate slices to simulate the thicker slices in the MURPS set and then filtering the images in the phase-encode direction. As expected, the virtual set is very similar to the MURPS result except for a few understandable differences. Because the reference set was acquired sequentially, in-flowing spins were not saturated and blood vessels in the virtual image set appear bright. In MURPS, the entire volume is excited every 3 shots, minimizing the inflow effect from vessels. Other minor contrast differences are likely due to slightly different flip angle settings in the two acquistions. There is also a small but noticeable dark artifact in the frontal region of slice C4 in the MURPS result (see arrow). We attribute this to susceptibility induced losses in the slice direction due to the relatively large slice thickness. Note that it does not appear in the corresponding virtual slice because the image was created by averaging thinner slices. The left side of Fig.4 shows mid-brain slices for axial, sagittal and coronal orientations after creating an interpolated data set from the seven original MURPS slices. The interpolated slices were obtained using an interpolation function in Matlab. For comparison, we also created a comparable interpolated data set from the 15 reference

9 Panych et al 7 slice images and mid-brain slices for the 3 orientations are shown on the right of Fig.4. The coronal slice on the left shows variable resolution in both phase and slice directions causing it to appear slightly more isotropically smoothed than the sagital slice which has variable resolution only in the slice direction. The dark streaks in the sagital view on the left are due to thin horizontal features that are not broadened because the vertical is the frequency-encoded direction. The features are however, very poorly resolved in the slice direction, giving the streaked appearance. The central axial slice is, as expected, virtually identical with respect to resolution in the two sets. It should be noted that the interpolated images in Fig.4 do not provide any additional information that does not also exist in Fig.3. Rather, these interpolated data sets are presented only to demonstrate the tradeoffs that are made when using MURPS to increase temporal resolution or volume coverage. Temperature mapping experiments The left side of Fig.5 shows 3-plane views of an interpolated data set computed from seven magnitude multi-resolution MURPS images of the phantom (orange with tube of hot water). Voxel sizes varied from 2x2x4 mm in the center slice to 2x8x12 mm in the edge slices. Temperature difference maps in 3-plane views were computed and are also shown in Fig.5 (right side). The temperature maps are obtained from phase difference images using the linear relationship between the phase change (after unwrapping) and temperature change. The maps in Fig.5 show the temperature difference at the beginning of the cooling period with respect to the baseline temperature at the end of the cooling period. As expected, the largest temperature change occurs close to the hot water tube. The images clearly demonstrate the ability of the multi-resolution acquisition method to depict temperature change throughout a large, 3-dimensional volume. Figure 6 shows a segmented gray-scale representation of the temperature changes ocurring over a 30 minute period along one column through the phantom in each of the seven MURPS slices. The maps are segemented into 4 regions of temperature change; [T < 2 o ], [2 o T < 4 o ], [4 o T < 10 o ], and [T 10 o ] which are represented in the figure by successively lighter shades of gray with white representing the highest temperature region. The position of the column in each slice is shown at the right in Fig.6. The columns are displayed side-by-side for each time point so that the horizontal direction represents time and the vertical direction represents space.

10 Panych et al 8 Figure 6 demonstrates temperature change with time in each of these slices along the column indicated in the right-hand panel. The figure demonstrates that, as expected, the time lag to reach peak temperature is a function of the slice distance from the hot water tube (which is located in slice A ) and that temperature changes are more spatially and temporally diffuse in regions further away from the heat source. It should be noted that the data shown in Fig.6 is only a small fraction of that available from the complete MURPS data set. IV DISCUSSION In this work we present MURPS, a multi-resolution imaging scheme for dynamic imaging with variable slice thickness and phase-encode resolution. The MURPS method allows one to trade spatial resolution in part of the volume for improved temporal resolution or increased volume coverage in dynamic imaging applications. MURPS was implemented using a modified SPGR sequence and its utility was demonstrated for MR temperature monitoring. In the preliminary work presented in this paper, we have shown that temperature changes throughout a large volume can be effectively monitored in times that would normally only permit monitoring in one or a very few slices. The potential for use of MURPS with other applications where we have applied a multi-resolution imaging approach, such as in fmri [22] and in dynamic contrast studies [4], is currently under investigation. The MURPS implementation described here uses Hadamard slice encoding, enabling the varying of the phase-encode resolution while maintaining constant effective TR. This is achieved when the product of the number of phase encodes and the Hadamard encoding factor is constant for all slices. Sequential, non-hadamard MURPS acquisitions are also possible (ie, all phase encodes for one slice are acquired before acquisition of another slice begins). Therefore, constant effective TR can be achieved without Hadamard encoding with the advantage that the temporal resolution of each slice acquisition can be varied along with spatial resolution. A fully sequential acquisition, however, is only time efficient for short TR applications and signal-to-noise would suffer in regions of medium and long T1. It is also possible to design a non-hadamard MURPS implementation that combines both sequential and interleaved acquisitions. For example, if N/4 phase encodes of slices [A,B1,C1] are followed by N/4 phase encodes of [A,B1,C2], followed in turn

11 Panych et al 9 by N/4 phase encodes of [A,B2,C3] and, then, N/4 phase encodes of [A,B2,C4], we would achieve the same effective TR as Hadamard MURPS along with a variable number of phase encodes in the A, B, and C slices. The absence of Hadamard encoding in this scheme has the advantage of avoiding potential peak power problems and the need to design special RF pulses. These advantages, however, would have to be weighed against several disadvantages. SNR per unit time in Hadamard MURPS would be 100% and 40% higher respectively in the C and B slices compared to the non-hadamard implementation. Furthermore, in the non-hadamard MURPS acquisition, several extra dummy excitations would be needed to allow for signal equilibrium to be reached in the B and C slices. In addition, the temporal sampling window is not constant for all sets of slices, as it is for Hadamard MURPS. Hadamard encoding may introduce some constraints in terms of peak RF power. This was not a problem in our work, however, due to the fact that a gradient echo sequence with relatively short TR was used so that flip angles in the range of 30 0 were sufficient. For spin-echo imaging, peak power constraints are more severe and the implications need to be investigated. Because of the flip angles used, we did not expect distortions in the Hadamard profiles due to non-linear effects. When higher flip angles are used, however, special RF design methods must be employed with Hadamard MURPS to insure that the desired profiles are excited[23]. SNR varies considerably between MURPS slices due to the large variation in voxel sizes. In the implementation reported here, SNR in the central, high-resolution slice is the same as would be obtained in a normal high-resolution acquisition for an equivalent TR. In the MURPS acquisition, however, the SNR increases as we move away from the central slice and it is a full 12 times greater in the outer slices than in the central slice. Generally, because changes tend to become much smaller as we move away from the focal volume-of-interest, an important advantage of MURPS is that it provides increasing SNR to enable more accurate measures of the changes where they tend to be small. It should be noted that MURPS is not pulse sequence dependent and, in principle, it is possible to implement it for any kind of sequence including fast imaging approaches such as echo-planar imaging. Also, although we implemented MURPS using seven multi-resolution slices, any number of variations is possible. It is not necessary, for example, to limit oneself to a single high resolution slice located at the center of the imaged volume. Slices can be arranged in any fashion with one, two or

12 Panych et al 10 more high resolution slices mixed with other slices of varying thickness. Further, it is not even necessary that slices be contiguous. Because RF pulses are designed off-line and read by the pulse sequence prior to scanning, it is easy to provide a flexible choice of slice thickness and location. We are currently investigating dynamically adaptive approaches where such a choice is made on-line during a dynamic scan session [22]. Finally, MURPS is compatible with other dynamic imaging methods that involve reconstructing information from a reduced number of phase encodes, thereby raising the possibility of hybrid approaches. For example, combining MURPS with keyhole approaches [24] involves a minimum of modifications - simply replacing the appropriate data from a high resolution static baseline dataset with the multi-resolution dynamic data obtained in MURPS. Extended keyhole-type methods such as TRICKS [25, 26] which segment k-space into regions with different update rates can also be combined with MURPS by redesigning the phase-encode acquisition scheme within individual slices. Constrained reconstruction methods such as RIGR ([27]-[29]) and related methods [30] use low order phase encodes to reconstruct higher resolution dynamic data based on assumptions about the dynamics and can also be combined with MURPS to reconstruct data in the slices where we have reduced phase encoding. More complex methods that involve non-uniform k-space sampling, such as Locally Focused MRI ([11]-[14]), are also compatible because MURPS does not require the use of any particular set of reduced phase encodes. Combining MURPS with Locally Focused MRI would enable variable resolution imaging within individual slices as well as between slices, further extending the multi-resolution capability of both methods.

13 Panych et al 11 Figure Captions Figure 1: The upper drawing is a schematic depiction of voxel sizes in the slice and phase-encoding directions for a seven-slice MURPS acquisition method. The lower drawing is of excitation profiles for the seven MURPS slices. The table lists resolution parameters for the seven-slice MURPS scheme used in brain imaging experiments. Figure 2: Hadamard encoding profiles used for acquisition of data to reconstruct seven MURPS slices as shown in Fig.1. From top to bottom, a different profile is used in succession on each of 12 successive TR periods. This sequence of profiles is used repeatedly for 3*N TR periods where N is the number of phase encodes collected for slice A. The order of phase encoding is shown for the first 12 TR periods. Figure 3: At top are seven brain slices acquired using the MURPS method. See Fig.1 for a description of resolution parameters. The seven slices cover a volume of 24x24x7.5 centimeters. The vertical is the frequency-encode direction and horizontal is the phase-encode direction. Below the MURPS set are images of virtual slices created from a reference set of 15 slices of 5 mm thickness and phase-encode resolution of 256 that cover the same total volume as the 7 slices above. The virtual slices were created by averaging appropriate 5 mm slices to simulate the thicker slices and by filtering the images in the phase-encode direction. The table below the images gives the theoretical and experimental SNR of each MURPS slice with respect to slice A. Relative SNR is equal to H (S/S A ) where S is the slice thickness, H is the Hadamard encoding factor, and S A is the thickness of slice A. Figure 4: Left: Mid-brain slices for axial, sagittal and coronal orientations after creating an interpolated data set from the MURPS slices shown at the top of Fig.3. Right: Mid-brain slices for axial, sagittal and coronal orientations after creating an interpolated data set using fifteen 5 mm slices covering the same volume as the seven MURPS slices. Figure 5: Left image set: 3-plane views of interpolated data set obtained from magnitude images of a phantom (orange with hot water tube inserted in center) acquired using the MURPS method. Right image set: 3-plane views of interpolated temperature difference maps for the period just after injection of hot water into the

14 Panych et al 12 tube. The maps show the temperature change in o C with respect to baseline temperature. White represents the hottest temperature as shown on the scale at the far right. Figure 6: Evolution of heat over a 30 minute period along one (8 centimeter wide) plane cutting through the phantom in all seven MURPS slices. The location of the plane is shown in the set of slice reference images on the right side of the figure. The maps are segemented into 4 temperature regions that are represented in the figure by successively lighter shades of gray (See color legend at bottom). White represents the hottest temperature region.

15 Panych et al 13 Slice Direction Phase Encode Direction C1 C2 B1 A B2 C3 C4 Slice Encoding Label C1 C2 B1 A B2 C3 C4 Slice Thickness (mm) Phase Encodes Voxel Size (mm 3 ) Figure 1:

16 Panych et al 14 Slice Encode Phase Encode TR A B1+B2 C1+C2+C3+C4 A B1 B2 C1 C2+C3 C4 A B1+B2 C1+C2 C3 C4 A B1 B2 C1 C2 C3+C Figure 2:

17 Panych et al 15 C1 C2 B1 A B2 C3 C4 Slice Label C1 C2 B1 A B2 C3 C4 Relative thickness, S/S A Hadamard encoding factor, H SNR/SNR A (theoretical) SNR/SNR A (experimental) Figure 3:

18 Panych et al 16 S L I C E F R E Q U E N C Y SLICE PHASE SLICE PHASE Magnitude Images Figure 4: Temperature Difference Maps S L I C E Temperature ( 0 C) F R E Q 30 U E N C Y SLICE PHASE SLICE PHASE Figure 5:

19 Panych et al 17 1 C1 2 C2 Slice Number 3 B1 A 4 5 B2 6 C3 7 C Time (minutes) Figure 6:

20 Panych et al 18 References [1] L.P. Panych, P.D. Jakab, and F.A. Jolesz. An implementation of wavelet encoded MRI. J. Magn. Reson. Imag., 3: , [2] L.P. Panych and F.A. Jolesz. A dynamically adaptive imaging algorithm for wavelet encoded MRI. Magn. Reson. Med., 32: , [3] L.P. Panych, P. Saiviroonporn, G.P. Zientara, and F.A. Jolesz. Digital wavelet encoded MRI - a new wavelet encoding methodology. In Proc. ISMRM, page 1989, [4] K. Shimizu K, L.P. Panych LP, R.V. Mulkern RV, S.-S. Yoo SS, R.B. Schwartz, R. Kikinis, and F.a. Jolesz. Partial wavelet encoding: a new approach for accelerating temporal resolution in contrast-enhanced MR imaging. J Magn Reson Imaging, 9: , [5] D.M. Healy and J.B. Weaver. Two applications of wavelet transforms in magnetic resonance imaging. IEEE Trans. Inform. Theory, 38: , [6] J.B. Weaver, Y. Xu, D.M. Healy, and J.R. Driscoll. Wavelet-encoded MR imaging. Magn. Reson. Med., 24: , [7] N. Gelman and M.L. Wood. Wavelet encoding for three-dimensional gradientecho MR imaging. Magn. Reson. Med., 36: , [8] N. Gelman and M.L. Wood. Wavelet encoding for improved SNR and retrospective slice thickness adjustment. Magn. Reson. Med., 39: , [9] R.D. Peters and M.L. Wood. Multilevel wavelet-transform encoding in MRI. J Magn. Reson. Imag., 6: , [10] Y. Cao and D.N. Levin. MR imaging with spatially variable resolution. J Magn. Reson. Imag., 2: , [11] Y. Cao, D.N. Levin, and L. Yao. Locally focused mri. Magn Reson Med, 34: , [12] L. Yao L, Y. Cao Y, and D.N. Levin. 2d locally focused mri: applications to dynamic and spectroscopic imaging. Magn Reson Med, 36: , 1996.

21 Panych et al 19 [13] V.Y. Kuperman, S.K. Nagle, and D.N. Levin. Locally focused mri of interventions. J Magn Reson Imaging, 8: , [14] V.Y. Kuperman, S.K. Nagle, M.T. Alley, G.H. Glover, and D.N. Levin. Locally focused contrast-enhanced carotid mra. J Magn Reson Imaging, 9: , [15] C. Oh, H.W. Park, and Z.H. Cho. Line-integral projection reconstruction (LPR) with slice encoding techniques: Multislice regional imaging in NMR tomography. IEEE Trans.Med.Imag, MI-3: , [16] L. Bolinger and J.S. Leigh. Hadamard spectroscopic imaging (HSI) for multivolume localization. J. Magn. Reson., 80: , [17] G. Goelman, V. Harihara Subramanian, and J.S. Leigh. Transverse hadamard spectroscopic imaging techniques. J. Magn. Reson., 89: , [18] O. Gonen, F. Arias-Mendoza, and B. Goelman. 3D localized in vivo 1 H spectroscopy of human brain using a hybrid of 1D-Hadamard with 2D-chemical shift imaging. Magn.Reson.Med., 37: , [19] J. De Poorter, C. De Wagter, Y. De Deene, C. Thomsen, F. Stahlberg, and E. Achten. Noninvasive mri thermometry with the proton resonance frequency (prf) method: in vivo results in human muscle. Magn Reson Med, 33:74 81, [20] A.H. Chung, K. Hynynen, V. Colucci, K. Oshio, H.E. Cline, and F.A. Jolesz. Optimization of spoiled gradient-echo phase imaging for in vivo localization of a focused ultrasound beam. Magn Reson Med, 36: , [21] C.J. Lewa and J.D. Certaines. Body temperature mapping by magnetic resonance imaging. Spect Lett, 27: , [22] S.-S. Yoo, C.R.G. Guttmann, L. Zhao, C.R.G. Guttmann, and L.P. Panych. Real-time adaptive functional MRI. Neuroimage, 10: , [23] C.H. Cunningham and M.L. Wood. Method for improved multiband excitation profiles using the Shinnar-Le Roux transform. Magn. Reson. Med., 42:577 84, 1999.

22 Panych et al 20 [24] J.J. van Vaals, M.E. Brummer, M.T. Dixon, H.H. Tuithof, H. Engels H, R.C. Nelson, B.M. Gerety BM, J.L. Chezmar, and J.A. den Boer. keyhole method for accelerating imaging of contrast agent uptake. J Magn Reson Imaging, 3:671 5, [25] F.R. Korosec, R. Frayne, T.M. Grist, and C.A. Mistretta. Time-resolved contrast-enhanced 3D MR angiography. Magn Reson Med, 36: , [26] C.A. Mistretta, T.M. Grist, F.R. Korosec, R. Frayne, D.C. Peters, Y. Mazaheri, and T.J. Carrol. 3D time-resolved contrast-enhanced MR DSA: advantages and tradeoffs. Magn. Reson. Med., 40: , [27] Z.-P. Liang and P.C.Lauterbur. An efficient method for dynamic magnetic resonance imaging. IEEE T Med Imag, 13: , [28] A.G. Webb, Z.P. Liang ZP, R.L. Magin, and P.C. Lauterbur. Applications of reduced-encoding MR imaging with generalized-series reconstruction (RIGR). J Magn Reson Imaging, 3: , [29] S. Chandra, Z.P. Liang ZP, A. Webb, H. Lee, H.D. Morris, and P.C. Lauterbur. Application of reduced-encoding imaging with generalized-series reconstruction (RIGR) in dynamic MR imaging. J Magn Reson Imaging, 6: , [30] C. Oesterle and J. Hennig. Improvement of spatial resolution of keyhole effect images. Magn Reson Med, 39: , 1998.