The field of the invention is magnetic resonance imaging (“MRI”) methods and systems. More particularly, the invention relates to the acquisition and reconstruction of MR images with pulse sequences that employ gradients indicative of motion.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins 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) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx Gy and Gz) 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 NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The prevailing methods used to acquire NMR signals and reconstruct images use a variant of the well known Fourier transform (FT) imaging technique. This technique is discussed in an article entitled “Spin-Warp NMR 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 NMR 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 (Gx) 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 Gy is incremented (ΔGy) in the sequence of views that are acquired during the scan to produce a set of NMR data from which an entire image can be reconstructed. With this method Fourier space, or “k-space”, is sampled along Cartesian coordinates in a scanning pattern such as that shown in FIG. 2A.
To increase the rate at which an image is acquired, image quality may be sacrificed by acquiring fewer phase encoding views, or by using faster pulse sequences that inherently result in lower quality images. With the Fourier transform methods, therefore, there is a trade-off between the number of views that are acquired to achieve the desired image resolution and quality, and the rate at which NMR data for a complete image may be acquired.
MR methods have been developed that encode spin motion into the phase of the acquired signal as disclosed in U.S. Pat. No. Re. 32,701. These form a class of techniques known as phase contrast (PC) methods. Currently, most PC techniques acquire two images, with each image having a different sensitivity to the same velocity component. Images may then be produced by forming either the phase difference or complex difference between the pair of velocity-encoded images. This motion encoding method is used to image flowing blood in what is commonly referred to as phase contrast magnetic resonance angiography (PCMRA).
Phase contrast techniques have also been used to image flow and provide quantitative measurement of blood flow. In flow imaging the motion encoding gradients used during the scan are sensitive to velocity components in two or three orthogonal directions. From the resulting velocity component images, total quantitative flow images can be produced. However, the scan becomes unduly long when four to six fully sampled images must be acquired using different motion encoding gradients.
As described in U.S. Pat. No. 6,188,922 the acquisition of velocity encoded MR data can be shortened by sampling k-space with a series of interleaved projection views. Projection views sample k-space along radial trajectories and it was discovered that far fewer projection views are required to produce a quality image than with phase encoded views that sample k-space along Cartesian coordinates. Such a radial sampling pattern is shown in FIG. 2B.
There are two methods used to reconstruct images from an acquired set of projection views as described, for example, in U.S. Pat. No. 6,710,686. In MRI the most common method is to regrid the k-space samples from their locations on the radial sampling trajectories to a Cartesian grid. The image is then reconstructed by performing a 2D or 3D Fourier transformation of the regridded k-space samples. The second method for reconstructing an MR image is to transform the radial k-space projection views to Radon space by first Fourier transforming each projection view. An image is reconstructed from these signal projections by filtering and backprojecting them into the field of view (FOV). As is well known in the art, if the acquired signal projections are insufficient in number to satisfy the Nyquist sampling theorem, streak artifacts are produced in the reconstructed image.
The standard backprojection method used in MRI is shown in FIG. 3. Each acquired signal projection profile 110 is Fourier transformed and then backprojected onto the field of view 12 by projecting each signal sample 14 in the transformed profile 10 through the FOV 12 along the projection path as indicted by arrows 16. In projecting each signal sample 16 in the FOV 12 we have no a priori knowledge of the subject being imaged and the assumption is made that the NMR signals in the FOV 12 are homogeneous and that the signal sample 14 should be distributed equally in each pixel through which the projection path passes. For example, a projection path 8 is illustrated in FIG. 3 for a single signal sample 14 in one transformed signal projection profile 10 as it passes through N pixels in the FOV 12. The signal value (P) of this signal sample 14 is divided up equally between these N pixels:Sn=(P×1)/N  (1)
where: Sn is the signal value distributed to the nth pixel in a projection path 8 having N pixels.
Clearly, the assumption that the backprojected signal in the FOV 12 is homogeneous is not correct. However, as is well known in the art, if certain corrections are made to each signal profile 10 and a sufficient number of profiles are acquired at a corresponding number of projection view angles, the errors caused by this faulty assumption are minimized and image artifacts are suppressed. In a typical, filtered backprojection method of image reconstruction, 400 projections are required for a 256×256 pixel 2D image and 103,000 projections are required for a 256×256×256 voxel 3D image.
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