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Innovative physics boosts MRI speed, cuts CT dose


Recent advances in fast imaging have provided radiologists with tools for simplified scanning and improved diagnosis. Real-time diagnostic capability gives radiologists unprecedented freedom to uncover pathology and measure its extent and severity. Multislice CT captures hundreds of slices per second, freezing motion and creating mammoth files of data for reconstruction into diagnostically relevant renderings of organs, bone, vessels, and disease.

Recent advances in fast imaging have provided radiologists with tools for simplified scanning and improved diagnosis. Real-time diagnostic capability gives radiologists unprecedented freedom to uncover pathology and measure its extent and severity. Multislice CT captures hundreds of slices per second, freezing motion and creating mammoth files of data for reconstruction into diagnostically relevant renderings of organs, bone, vessels, and disease. Three-D, time-resolved, contrast-enhanced MR angiography reduces the need for careful timing of the contrast injection relative to data acquisition and provides dynamic flow information that clearly depicts late filling and other physiologically significant information.

High spatial and high temporal resolutions must be achieved simultaneously for applications like time-resolved MRA. But producing a finely resolved image quickly is difficult with Cartesian k-space acquisition and phase encoding, the way most MR images are now produced. When phase encoding is employed, matrix size is proportional to imaging time. Some combinations of spatial and temporal resolution are impossible to achieve in reasonably short imaging times.

Although scientists from around the world have made significant progress in developing faster pulse sequences and incorporating techniques such as parallel imaging, these have been implemented primarily within the context of Cartesian imaging using phase encoding in one or two dimensions.

A fundamental departure from the Cartesian techniques that have dominated MRA since its inception is needed to product ultrafast, high-resolution MR images.


The original acquisition and reconstruction geometry that the late Paul Lauterbur, Ph.D. proposed for MRI1 was similar to the strategy developed for early x-ray CT. For MRI, the approach involves a series of signal readouts that follow radial trajectories that all pass through the center of k-space. This strategy was set aside, however, in favor of a Cartesian-based rectilinear scan of k-space, similar to what occurs in a television raster scan. Rectilinear scanning reduced the need for system accuracy and required 50% fewer readouts than the radial approach.

Both techniques are governed by the Nyquist theorem, which specifies in mathematical terms how many signal samples are required for an exact reconstruction. The minimum signal sampling requirement defines the shortest possible image acquisition time.

The Cartesian approach requires that phase encoding be performed in one direction for 2D imaging or two directions for 3D imaging. Unfortunately, spatial resolution achieved through this process is proportional to the number of phase encodings. Extremely long imaging times are required to produce high-resolution images.

Recently, parallel imaging strategies, such as SMASH2 and SENSE,3 have been introduced to reduce the number of phase encodings by exploiting redundancies in data sets acquired with multiple coils. Typically, acceleration factors of 2 to 4 are possible, although somewhat higher acceleration factors have been achieved in selected applications. This increase in speed is accompanied by a loss in signal-to-noise ratio. SNR falls by more than a factor of 2 when acceleration rises by a factor of 4.

Phase encoding poses a serious limitation for MRA and other applications for which high resolution and high frame rates are both desirable. Development efforts beginning in 1995 have aimed at reducing or eliminating phase encoding with undersampled radial imaging techniques:4-7

  • Demonstration that undersampled 2D radial scanning could be used to image moving joints with tolerable streaking artifacts, shown by Volker Rasche, Ph.D., and colleagues4 from Philips in 1995;

  • Confirmation that undersampled radial imaging could be used for high-resolution, small field-of-view, streak-free imaging because streak artifacts associated with undersampling start at a finite distance from the signals generating the streaks, demonstrated by Klaus Scheffler, Ph.D., director of MR physics at the University of Basel in Switzerland, and Juergen Hennig, Ph.D., director of medical physics at the University of Freiburg in Germany in 1998;5

  • Realization that the same speed advantage could be achieved in full field-of-view MRA because the streaks were tolerable for acceleration factors on the order of 4 to 6, illustrated by Dana C. Peters, Ph.D., then at the University of Wisconsin, Madison;6 and

  • Subsequent understanding that by extending the undersampling to 3D, the streak artifacts were much more effectively distributed, and that significantly higher undersampling factors-on the order of 100-could be achieved, explained by physicist Dr. Andrew Barger, Walter Block, Ph.D., and colleagues at the University of Wisconsin, Madison.7

Interest in the radial acquisition method is growing because of properties that make it fundamentally different from Cartesian acquisition. As with MSCT, in which the spatial resolution is determined by the number of x-ray detectors, the spatial resolution of a radial MR acquisition is determined by the number of readout points, not by the number of projection angles or views that are obtained. Undersampled radial acquisition violates the Nyquist theorem by acquiring fewer than the recommended number of views but preserving spatial resolution.


As shown in Figure 1, the k-space trajectory (left) of 3D vastly undersampled isotropic imaging with projections (VIPR) for the ungated phase-contrast MRA (right) is radically different from Cartesian acquisition. By undersampling by a factor of 36, an image that would have taken two hours to produce using Cartesian encoding is produced in only five minutes.

As demonstrated by Kevin M. Johnson of the University of Wisconsin, Madison, gated phase-contrast VIPR exams using undersampling factors of 230 can acquire 20 time frames in a single cardiac cycle (Figure 2). The phase-contrast VIPR exam was completed in just 12.5 minutes, or about 145 times faster than the 29 hours that would have been needed to produce the same 384 x 384 x 384-pixel matrix exam using conventional Cartesian methods.

Although the intrinsic speed of VIPR reduces the typical advantage pursued with parallel imaging, the use of multiple coil technology may be very promising when the partially parallel imaging with localized sensitivities (PILS) technique8 is used to limit the potential VIPR streak artifacts to regions around individual coils. One study9 implemented an MR coronary artery acquisition using a 32-coil VIPR sequence. This approach, which incorporates motion correction capabilities inherent in the VIPR data set, holds much promise. If motion correction techniques prove adequate, it might be possible to obtain images approaching the quality of those in Figure 2 in the coronary arteries, which, when combined with its other attributes, would make MRI more competitive with cardiac CTA.

The high-resolution anatomic and flow information contained in phase-contrast imaging provides another new tool for evaluation of the significance of vascular stenoses. Navier Stokes equations have been applied to measure pressure gradients in large arteries such as the aorta. With time-resolved phase-contrast VIPR, this application can now be extended to smaller arteries such as the carotids.10,11 To fully realize the benefits of this, software that will enable rapid measurements with a minimum of user interaction must be developed.


A fundamentally new reconstruction technique called highly constrained back projection (HYPR) produces even greater acceleration factors than VIPR.12 It greatly improves phase-contrast MRA acquisition times and boosts the acquisition speeds of contrast-enhanced MRA and other exams in which a variable is sequentially changed.13,14 In CT, the new approach reduces patient radiation exposure five- to 10-fold for perfusion and other time-resolved exams.15,16

HYPR was conceived shortly after the 2005 International Society for Magnetic Resonance in Imaging meeting and was stimulated by previous ideas about exploiting the redundancy of information in imaging sequences17-19 and by an ISMRM plenary talk by Jurgen Hennig, Ph.D., a professor of medical physics at the University of Freiberg. He described a hypothetical example showing how images can be updated using a single k-space point if every point in an image volume had the same time dependence, a condition we have come to refer to as the Hennig limit.

The question arose as to how many k-space measurements would be required to update an image series if a priori information regarding the image signal distribution were available and the degree of spatiotemporal correlation were substantial, even if not perfect. For sparse data sets or data sets with high temporal correlation, surprisingly few k-space measurements are needed, if a radically unconventional back-projection reconstruction method is used.

The HYPR reconstruction concept is described in Figure 3. Interleaved undersampled projection sets, reconstructed with conventional filtered back projection, show severe streak artifacts. By summing these images, a well-sampled composite image with few streaking artifacts can be generated. The composite image helps maintain high resolution for a series of images, though only a few projections are actually acquired in each time frame. The demonstration of this tactic in the illustration provided by the University of Wisconsin's Yijing Wu and Pat Turski in Figure 3 shows that this is possible by multiplying the weighting image of a few projections acquired at a specific time point by the composite imaging. SNR is acquired from the entire examination. This composite image is multiplied by a weighting image formed from the few projections acquired in each time frame. The HYPR time frame is the product of the composite image and the weighting image.20


The speed advantages of the 3D radially acquired VIPR sequence and the HYPR reconstructions method can be applied with multiplicative benefit in the case of phase-contrast imaging where the data set is sparse but temporal correlation from image to image is substantial. In this application, an ECG-gated phase-contrast VIPR examination is acquired and reconstructed using HYPR. A phase-contrast VIPR exam was completed in 12.5 minutes and captured true 76-msec time frames. In a more recent study, Julia Velikina, assistant scientist in the medical physics department at the University of Wisconsin, Madison, reported a phase-contrast HYPR VIPR exam finished in four minutes obtained true 50-msec time frames with a 384 x 384 x 384-pixel matrix.21 The same 3D exam of the internal carotid arteries performed with nonaccelerated Cartesian phase encoding would have taken 39 hours. The phase-encoding process was completely eliminated with phase-contrast VIPR. This time-saving feature, combined with the acceleration provided by HYPR, produced an undersampling factor of 928.22

HYPR can also be combined with time-resolved imaging of contrast kinetics (TRICKS), a commercially available contrast-enhanced MRA technique to increase frame rate and resolution. Conventional TRICKS uses two phase-encoding dimensions. Using TRICKS processing in the slice direction and radial acquisition in-plane results in a variant called PR HYPR TRICKS, which provides a 40-fold improvement over TRICKS (a 10-fold increase in temporal resolution and fourfold improvement in spatial resolution).22


The short duration of the time frames associated with first-pass contrast-enhanced imaging limits the SNR and spatial resolution that can be achieved. This problem is evident during standard time-resolved contrast-enhanced MRA, but it is addressed with PR HYPR TRICKS, which produces much higher SNR and spatial resolution by combining undersampled radial acquisition and HYPR processing.

More improvement is possible, however. For true subsecond frame times, a VIPR acquisition can be used to achieve high isotropic spatial resolution. The SNR restored by HYPR processing can be enhanced further by using a phase-contrast scan on the order of five to six minutes, as shown in Figure 1, to provide the composite image used for HYPR processing. When this is done, the SNR of the entire phase-contrast scan is transferred to each of the subsecond time frames in the contrast-enhanced MRA scan.23 This provides contrast-enhanced MRA images of unprecedented small voxel size and high SNR. Additionally, the phase-contrast information obtained in the separate phase-contrast scan provides physiological information on flow direction and magnitude and can be used to calculate trans-stenotic pressure gradients.

Figure 5 shows three views (A, B, and C) of a single first-pass HYPR flow time frame with 320 x 320 x 320 isotropic resolution and a true frame time of 0.5 seconds. Also shown are the corresponding images with velocity information encoded (D, E, and F). It is important to realize that the phase-contrast composite image contains no temporal information and has a negligible effect on the temporal resolution of the time frames depicting the injected contrast passage. In this example, the frame time is basically the time required to collect 150 VIPR projections, representing an undersampling factor of 1072 relative to the 160,849 projections required by the Nyquist criterion. The use of the phase-contrast scan and HYPR processing permits time frame formation without view-sharing during contrast inflow and results in temporal and spatial resolution simply not achievable with the Cartesian technique.


Researchers initially assumed that HYPR would not provide advantages in the presence of motion because of the need for the composite image to provide a relatively sharp spatial constraint. Recent work by Julia Velikina24 has shown that HYPR can provide substantial acceleration in the depiction of cardiac motion. The faster acquisition time can be used to reduce the breath-hold period or to acquire more slices.


Undersampling could also help cut the radiation exposure from time-resolved CT applications such as perfusion CT and time-resolved CTA. An undersampled set of projections could be acquired during each gantry rotation and applied to HYPR to reconstruct the images and preserve the SNR. The CT data acquisition algorithm is identical to the one used during MRI acquisition.15,16

Figure 5 shows a comparison with one of 46 frames of a time-resolved CTA scan. To test the feasibility of low-dose HYPR CTA, images from a clinical time-resolved CT exam were retrospectively reconstructed using just 1/46 of the x-ray dose actually used for the scan.17 Thirteen of 600 acquired x-ray projections per gantry rotation were supplied, courtesy of James Pipe, Ph.D., a bioengineer at Barrows Neurological Institute in Phoenix, in connection with a reconstruction contest. Image quality was judged to be acceptable by a panel of radiologists. The standard CT reconstruction image, also using 1/46 of the total x-ray dose, is on the left; the HYPR CT image is shown on the right.

HYPR is especially valuable for speeding the acquisition of a time-resolved series of images, as in MRA, but it can accelerate diffusion tensor imaging and other functional applications as well.

To demonstrate the impact of HYPR on diffusion tensor imaging, a simulation was performed at the University of Wisconsin, Madison, by associate professor Andrew Alexander, Ph.D., and research assistant Jee Eun Lee. It involved a Cartesian acquisition of 100 images having variable diffusion-encoding directions that were resampled into small numbers of radial projections. Projections associated with each diffusion-encoding direction were interleaved so that composite images could be formed using images surrounding the diffusion-encoding direction of the HYPR image to be reconstructed.15

The acceleration factors provided by HYPR depend on the sparsity of the information in the image and on the degree of temporal correlation between various portions of the image. If there is complete temporal correlation, the sparsity requirements vanish. Similarly, if the image is very sparse, in the sense that the image contains a low density of signal containing pixels, the correlation requirements are relaxed.

For many applications, HYPR in its basic form appears to capture the required clinical information. In situations where these requirements are not fulfilled, as reported in a study presented in Switzerland last year by Mark Griswold of Case Western Reserve University,25 HYPR can be applied iteratively in a process in which reconstructed HYPR projections are compared with the actually acquired projections. Differential sets of projections are iteratively used to refine the HYPR result. This can improve the HYPR result, especially when quantitative results are desired.

This approach promises to extend HYPR to more applications. At the University of Wisconsin-Madison, research assistant Rafael O'Halloran and assistant professor of medical physics Sean Fain, Ph.D., have reported on the iterative use of HYPR with the iterative emission tomography algorithm OSEM.26 The combination appears to refine the basic HYPR results for applications requiring greater accuracy in the reconstructed images. This is particularly useful when trying to distinguish the waveforms from two very closely spaced vessels with different time dependences. These iterative approaches also permit the use of composite images of longer duration leading to increased signal-to-noise benefits.

Several options for normalizing the HYPR weighting image have been introduced. In the original HYPR paper, the weighting image was formed as a sum of the ratio of projections blurred by the unfiltered backprojection process. Yuexi Huang and Graham Wright, Ph.D., from the University of Toronto reported on the formation of the weighting image as the ratio of a blurred time frame and a blurred composite image.27 A closely related approach was reported by Feng Huang from Invivo28 and by Kevin M. Johnson of the University of Wisconsin.29 The blurred image ratio approach makes HYPR more easily adaptable to nonradial acquisitions and eliminates the need for back projection. However, the use of undersampled radial acquisition is a very powerful element of the combined undersampling/HYPR accelerations that have been achieved.


It is difficult to predict when all these techniques will be released for general use. Reconstruction times for phase-contrast pressure gradient imaging are still quite long, and sophisticated new software is needed to display the large amount of time-resolved data produced by the sequences. Reconstruction of contrast-enhanced angiographic series with 40 times the present amount of data is also a challenge. The use of highly parallel computing will help, but more development is needed.

Ultimately, there is little doubt that vastly undersampled data acquisition and reconstruction, inspired by HYPR, VIPR, and other ultrafast imaging techniques in development today, will lead to real-time, high-resolution MRI and low-dose MSCT.

More than 60 individuals at the University of Wisconsin are involved with research covered in this article. The author specifically acknowledges the contributions of Dr. Tom Grist, chair of radiology, and the following researchers: Pat Turski, Howard Rowley, Quill Turk, Darren Lum, Beverly Aagaard Kienitz, Scott Reeder, Vic Haughton, and Kim Newrhee.


  • Lauterbur PC. Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature 1973;242:190-191.

  • Sodickson DK, Griswold MA, Jakob PM. SMASH Imaging. Magn Reson Imaging Clin N Am 1999;7(2):237-254.

  • Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999;42(5):952-962.

  • Rasche V, de Boer RW, Holz D, Proksa R. Continuous radial acquisition for dynamic MRI. Magn Reson Med 1995;34(5):754-761.

  • Scheffler K, Hennig J. Reduced circular field-of-view imaging. Magn Reson Med 1998;40(3):474-480.

  • Peters DC, Grist TM, Korosec FR, et al. Undersampled projection reconstruction applied to MR angiography. Magn Reson Med 2000;43(1):91-101.

  • Barger AV, Block WF, Toropov Y, et al. Time-resolved contrast-enhanced imaging with isotropic resolution and broad coverage using an undersampled 3D projection trajectory. Magn Reson Med 2002;48(2):297-305.

  • Johnson KM, Lum D, Wieben O, et al. 7D flow and anatomical imaging at 3T with PC VIPR. Presented at 18th International Conference on Magnetic Resonance Angiography, Basel, Switzerland; Sept. 13-15, 2006.

  • Griswold MA, Jakob PM, Nittka M, et al. Partially parallel imaging with localized sensitivities (PILS). Magn Reson Med 2000;44(4):602-609.

  • Stehning C, Bornert P, Nehrke K, et al. Free-breathing whole-heart coronary MRA with 3D radial SSFP and self-navigated image reconstruction. Magn Reson Med 2005;54(2):476-480.

  • Turk AS, Johnson KM, Lum D, et al. Physiologic and anatomic assessment of a canine carotid artery stenosis model with phase contrast vastly undersampled isotropic projection imaging (PC-VIPR). In press: Am J Neuroradiol, 2007.

  • Lum D, Johnson K, Wieben O, et al. Intracranial phase contrast MRA with vastly under-sampled isotropic projection reconstruction (PC-VIPR): initial experience at 3.0 tesla. Presented at annual meeting of the International Society for Magnetic Resonance in Medicine, Seattle; May 6-12, 2006.

  • Mistretta CA, Wieben O, Velikina J, et al. Highly constrained backprojection for time-resolved MRI. Magn Reson Med 2006;55(1):30-40.

  • Perry JO, Wieben O, Mistretta CA, et al. Scan time reduction in spectroscopic imaging using HYPR. Presented at annual meeting of the International Society for Magnetic Resonance in Medicine, Seattle; May 6-12, 2006.

  • Alexander A, Lee J, Mistretta CA. Diffusion tensor imaging with highly constrained backprojection (HYPR). Presented at annual meeting of the International Society for Magnetic Resonance in Medicine, Seattle; May 6-12, 2006.

  • Supanich M, Chen G, Rowley H, et al. Factor of ten dose reduction in CT perfusion imaging. Presented at annual meeting of the American Association of Physicists in Medicine, Orlando, FL; July 30-Aug. 3, 2006.

  • Velikina J, Johnson K, Wieben O, et al. Response to CTA undersampled data reconstruction challenge. Presented at the ISMRM Workshop on Non-Cartesian Trajectories, Sedona AZ; Feb. 25-28, 2007.

  • Liang ZP, Madore B, Glover GH, Pelc NJ. Fast algorithms for GS-model-based image reconstruction in data-sharing Fourier imaging. IEEE Trans Med Imaging 2003;22(8):1026-1030.

  • Tsao J, Boesiger P, Pruessmann KP. k-t BLAST and k-t SENSE: dynamic MRI with high frame rate exploiting spatiotemporal correlations. Magn Reson Med 2003;50(5):1031-1043.

  • Huang Y, Gurr D, Wright G. Time-resolved 3D MR angiography by interleaved biplane projections. Abstract 1707, Presented at annual meeting of the International Society for Magnetic Resonance in Medicine, Miami; May 7-13, 2005.

  • Velikina J, Johnson KM, Mistretta CA, Wieben O. PC HYPR VIPR: a rapid acquisition method for 3D phase contrast. Presented at ISMRM Workshop on Flow and Motion: Imaging Assessment of Cardiovascular and Tissue Mechanics, New York, NY; July 13-16, 2006.

  • Wu Yijing, Turski P, Newrhee K, Mistretta CA. Subsecond 3D time resolved contrast enhanced cerebrovascular MRA using undersampled radial k-space trajectories and highly constrained projection reconstruction (HYPR). In press: AJNR, 2007.

  • Velikina J, Johnson K, Wieben O , et al. First pass HYPR flow: time-resolved CE-MRA with 322-fold undersampling and a phase contrast HYPR composite providing 4-fold SNR restoration per time frame. Presented at the ISMRM Workshop on Non-Cartesian Trajectories, Sedona AZ; Feb. 25-28, 2007.

  • Velikina J, et al. An application of HYPR and McKinnon-Bates algorithms to fast cardiac imaging. Presented at 18th International Conference on Magnetic Resonance Angiography, Basel, Switzerland; Sept. 13-15, 2006.

  • Griswold M, et al. More optimal HYPR reconstructions using a combination of HYPR and conjugate-gradient minimization. Presented at 18th International Conference on Magnetic Resonance Angiography, Basel, Switzerland; Sept. 13-15, 2006.

  • O'Halloran RL, Holmes JH, Fain SB. Abstract: Iterative reconstruction of time-resolved images using highly constrained back-projection (HYPR). Presented at the ISMRM Workshop on Non-Cartesian Trajectories, Sedona AZ; Feb. 25-28, 2007.

  • Huang Y, Wright GA. HYPR signal behavior in time resolved MR angiography. Presented at 18th International Conference on Magnetic Resonance Angiography, Basel, Switzerland; Sept. 13-15, 2006.

  • Huang F. Image ratio constrained reconstruction. Presented at the ISMRM Workshop on Non-Cartesian Trajectories, Sedona, AZ; Feb. 25-28, 2007.

  • Johnson KM, Velikina J, Wu Y, et al. Improved waveform fidelity using local HYPR reconstruction. In press: Magn Reson Med, 2007.

Dr. Mistretta is a professor of medical physics, radiology, and biomedical engineering at the University of Wisconsin, Madison. Research is supported by grants and technical support from the National Institutes of Health and GE Healthcare.

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