Dynamic magnetic resonance inverse imaging using linear constrained minimum variance beamformer

This application is a continuation-in-part of U.S. patent application Ser. No. 11/84,091 filed on Jul. 11, 2006 and entitled “Dynamic Magnetic Resonance Inverse Imaging”, which claims the benefit of U.S. Provisional Patent Application Ser. No. 60/745,218, filed Apr. 20, 2006. This application further claims the benefit of U.S. Provisional Patent Application Ser. No. 60/927,357 filed on May 3, 2007, and entitled “Dynamic Magnetic Resonance Inverse Imaging Using Linear Constrained Minimum Variance Beamformer”.

This invention was made with United States government support awarded by the following agencies: NIH R01 HD040712, NIH R01 NS037462, and NIH P41 RR14075. The United States has certain rights in this invention.

The field of the invention is nuclear magnetic resonance imaging (MRI) methods and systems. More particularly, the invention relates to dynamic studies in which a series of MR images are acquired at a high temporal resolution.

When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B₀), the individual magnetic moments of the excited nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B₁) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, M_z, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment M_t. A signal is emitted by the excited nuclei or “spins”, after the excitation signal B₁ is terminated, and this signal may be received and processed to form an image.

When utilizing these “MR” signals to produce images, magnetic field gradients (G_x, G_y and G_z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.

The measurement cycle used to acquire each MR signal is performed under the direction of a pulse sequence produced by a pulse sequencer. Clinically available MRI systems store a library of such pulse sequences that can be prescribed to meet the needs of many different clinical applications. Research MRI systems include a library of clinically proven pulse sequences and they also enable the development of new pulse sequences.

The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space”. Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. Most pulse sequences sample k-space in a roster scan-like pattern sometimes referred to as a “spin-warp”, a “Fourier”, a “rectilinear” or a “Cartesian” scan. The spin-warp scan technique is discussed in an article entitled “Spin-Warp MR Imaging and Applications to Human Whole-Body Imaging” by W. A. Edelstein et al., Physics in Medicine and Biology, Vol. 25, pp. 751-756 (1980). It employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of MR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (2DFT), for example, spatial information is encoded in one direction by applying a phase encoding gradient (Gy) along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient (G_x) in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT pulse sequence, the magnitude of the phase encoding gradient pulse G_y is incremented (ΔG_y) in the sequence of measurement cycles, or “views” that are acquired during the scan to produce a set of k-space MR data from which an entire image can be reconstructed.

There are many other k-space sampling patterns used by MRI systems These include “radial”, or “projection reconstruction” scans in which k-space is sampled as a set of radial sampling trajectories extending from the center of k-space as described, for example, in U.S. Pat. No. 6,954,067. The pulse sequences for a radial scan are characterized by the lack of a phase encoding gradient and the presence of a readout gradient that changes direction from one pulse sequence view to the next. There are also many k-space sampling methods that are closely related to the radial scan and that sample along a curved k-space sampling trajectory rather than the straight line radial trajectory. Such pulse sequences are described, for example, in “Fast Three Dimensional Sodium Imaging”, MRM, 37:706-715, 1997 by F. E. Boada, et al. and in “Rapid 3D PC-MRA Using Spiral Projection Imaging”, Proc. Intl. Soc. Magn. Reson. Med. 13 (2005) by K. V. Koladia et al and “Spiral Projection Imaging: a new fast 3D trajectory”, Proc. Intl. Soc. Mag. Reson. Med. 13 (2005) by J. G. Pipe and Koladia.

An image is reconstructed from the acquired k-space data by transforming the k-space data set to an image space data set. There are many different methods for performing this task and the method used is often determined by the technique used to acquire the k-space data. With a Cartesian grid of k-space data that results from a 2D or 3D spin-warp acquisition, for example, the most common reconstruction method used is an inverse Fourier transformation (“2DFT” or “3DFT”) along each of the 2 or 3 axes of the data set. With a radial k-space data set and its variations, the most common reconstruction method includes “regridding” the k-space samples to create a Cartesian grid of k-space samples and then perform a 2DFT or 3DFT on the regridded k-space data set. In the alternative, a radial k-space data set can also be transformed to Radon space by performing a 1DFT of each radial projection view and then transforming the Radon space data set to image space by performing a filtered backprojection.

To reduce the time needed to acquire data for an MR image multiple NMR signals may be acquired in the same pulse sequence. The echo-planar pulse sequence was proposed by Peter Mansfield (J. Phys. C.10: L55-L58, 1977). In contrast to standard pulse sequences, the echo-planar pulse sequence produces a set of NMR signals for each RF excitation pulse. These NMR signals can be separately phase encoded so that an entire scan of 64 views can be acquired in a single pulse sequence of 20 to 100 milliseconds in duration. The advantages of echo-planar imaging (“EPI”) are well-known, and this method is commonly used where the clinical application requires a high temporal resolution. Echo-planar pulse sequences are disclosed in U.S. Pat. Nos. 4,678,996; 4,733,188; 4,716,369; 4,355,282; 4,588,948 and 4,752,735.

A variant of the echo-planar imaging method is the Rapid Acquisition Relaxation Enhanced (RARE) sequence which is described by J. Hennig et al in an article in Magnetic Resonance in Medicine 3,823-833 (1986) entitled “RARE Imaging: A Fast Imaging Method for Clinical MR.” The essential difference between the RARE (also called a fast spin-echo or FSE) sequence and the EPI sequence lies in the manner in which NMR echo signals are produced. The RARE sequence, utilizes RF refocused echoes generated from a Carr-Purcell-Meiboom-Gill sequence, while EPI methods employ gradient recalled echoes.

Other MRI pulse sequences are known which sample 2D or 3D k-space without using phase encoding gradients. These include the projection reconstruction methods known since the inception of magnetic resonance imaging and again being used as disclosed in U.S. Pat. No. 6,487,435. Rather than sampling k-space in a rectilinear, or Cartesian, scan pattern by stepping through phase encoding values as described above and shown in FIG. 2, projection reconstruction methods sample k-space with a series of views that sample radial lines extending outward from the center of k-space as shown in FIG. 3. The number of projection views needed to sample k-space determines the length of the scan and if an insufficient number of views are acquired, streak artifacts are produced in the reconstructed image. There are a number of variations of this straight line, radial sampling trajectory in which a curved path is sampled. These include spiral projection imaging and propeller projection imaging.

Recently, parallel MRI scanning methods using spatial information derived from the spatial distribution of the receive coils and a corresponding number of receiver channels has been proposed to accelerate MRI scanning. This includes the k-space sampling methods described in Sodickson D K, Manning W J, “Simultaneous Acquisition Of Spatial Harmonics (SMASH)” Fast Imaging With Radiofrequency Coil Arrays”, Magn. Reson. Med. 1997;38(4):591-603, or Griswold M A, Jacob P M, Heidemann R M, Nittka M, Jellus V, Wang J, Kiefer B, Hasse A, “Generalized Autocalibrating Partially parallel Acquisitions (GRAPPA)”, Magn. Reson. Med. 2002;47(6):1202-1210, or Pruessmann K P, Weiger M, Scheidegger M B, Boesiger P, “SENSE: Sensitivity Encoding For Fast MRI”, Magn. Reson. Med. 1999;42(5):952-962, all of which share a similar theoretical background. Parallel MRI accelerates image data acquisition at the cost of reduced signal-to-noise ratio (SNR). The temporal acceleration rate is limited by the number of coils in the array and the number of separate receive channels, and the phase-encoding schemes used. Typically, acceleration factors of 2 or 3 are achieved.

Mathematically, the attainable acceleration in parallel MRI is limited by the available independent spatial information among the channels in the array. The parallel MRI image reconstruction manifests itself as a problem in solving an over-determined linear system using this spatial information. Therefore, advances in the coil array design with more coil elements and receiver channels can increase the acceleration rate when using the parallel MRI technique. Recently, optimized head coil arrays have been extended from 8-channel as described in de Zwart J A, Ledden P J, Kellman P, van Gelderen P, Duyn J H, “Design Of A SENSE-Optimized High-Sensitivity MRI Receive Coil For Brain Imaging”, Magn. Reson. Med. 2002;47(6):1218-1227, to 16-channel as described in de Zwart J A, Ledden P J, van Gelderen P, Bodurka J, Chu R, Duyn J H, “Signal-To-Noise Ratio And Parallel Imaging Performance Of A 16-Channel Receive-Only Brain Coil Array At 3.0 Tesla”, Magn. Reson. Med. 2004;51(1):22-26, as well as 23 and 90-channel arrays as described in Wiggins G C, Potthast A, Triantafyllou C, Lin F-H, Benner T, Wiggins C J, Wald L L, “A 96-Channel MRI System With 23- and 90-Channel Phase Array Head Coils At 1.5 Tesla”, 2005; Miami, Fla., USA, International Society for Magnetic Resonance in Medicine, p. 671.

As described recently by McDougall M P, Wright S M, “64-Channel Array Coil For Single Echo Acquisition Magnetic Resonance Imaging”, Magn. Reson. Med. 2005;54(2):386-392, a dedicated 64-channel linear planar array was developed to achieve 64-fold acceleration using a single echo acquisition (SEA) pulse sequence and a SENSE reconstruction method. The SEA approach depends on the linear array layout and localized RF coil sensitivity in individual receiver channels to eliminate the phase encoding steps required in conventional imaging. The challenge of this approach is the limited sensitivity in the perpendicular direction to the array plane and the extension of the methodology to head-shaped geometries.

In co-pending U.S. patent application Ser. No. 11/484,091 filed on Jul. 11, 2006 and entitled “Dynamic Magnetic Resonance Inverse Imaging”, a method is described which is capable of extremely fast data acquisition due to the minimal gradient cycling used for spatial encoding. Similar to the problems encountered when using classical source localization techniques with MEG and EEG data sources, an inverse operator is required to estimate the spatial distribution of signal changes and their associated statistical significance in magnetic resonance lnl. Due to the limited amount of independent information from each RF coil channel and the large number of sources to be estimated, an inverse problem of this type is generally ill-posed, indicating that there exist an infinite number of solutions satisfying the physical relationship between the underlying sources and the detected signals, the so called forward solution. In order to obtain a unique solution, additional constraints must be applied in solving this ill-posed inverse problem.