Abstract:
In an MRI imaging system each portion of k-space is sequentially scanned, transformed and separately demodulated. Instead of adding the k-space regions, as is the practice in the prior art, the demodulated portions are added, each representing spectral portions of the image. Each k-space portion is scanned with closely spaced lines which substantially satisfy the sampling requirement to avoid aliasing. In this way, distortion resulting from phase changes between k-space scans is avoided.

Description:
CROSS REFERENCE to RELATED APPLICATIONS 
   Not Applicable 
   STATEMENTS REGARDING FEDERALLY SPOSERED RESEARCH or DEVELOPMENT 
   Not Applicable 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates to magnetic resonance imaging systems. In a primary application this invention involves an MRI system that acquires a sequence of portions of the k-space of an image. Each individual portion of k-space is separately transformed and demodulated. The demodulated portions, each representing different spectral portions of the image, are summed. 
   2. Description of Related Art 
   The basic concepts in magnetic resonance are described in a series of papers in the June 1980 series of the IEEE Transactions on Nuclear Science, Vol. NS-27, pp 1220–1255. A detailed description of MRI is given in the paper by W. S. Hinshaw and A. H. Lent, “An introduction to NMR imaging: From the Bloch equation to the imaging equation”, Proceedings of the IEEE, 71(3):338–350, March 1983. 
   In MRI, the acquired data is the k-space or spatial Fourier transform of the image. In high-speed MRI imaging, each excitation is followed by the scan of a portion of k-space. The entire k-space is not scanned for a number of reasons. Firstly, the short imaging period would result in a poor SNR as shown in the journal paper by A. Macovski, “Noise in MRI”, Magn Reson Med 36:494–497, 1996. In addition, attempts at very rapid gradient speeds to cover all of k-space often result in exceeding the FDA dB/dt limits, causing neural stimulation. As a result, typical k-space scans involve a sequence of interleaved spirals or of sequences of parallel lines. The problem with these approaches is that motion or other changes occur between the acquisitions of these sequences. The k-space sequences are added, transformed and demodulated to provide the final image. However, as a result of the changes between sequences, significant artifacts result because of the inconsistent k-space data. Thus each sequence of k-space corresponds to a somewhat different image as a result of these changes. 
   BRIEF SUMMARY OF THE INVENTION 
   An object of this invention is to provide a method of acquiring sequences of k-space data without substantial artifacts. 
   A further object of this invention is to provide MRI images of rapidly moving objects, such as the beating heart, with negligible errors. 
   Briefly, in accordance with the invention, gradient waveforms are generated which provide sequences of closely spaced k-space lines to avoid aliasing. Each of these sequences cover a portion of the image k-space. Each of these sequences are separately transformed and demodulated to provide real-valued images representing spectral portions of the image. These are combined to form the final image. Very-low frequency k-space data is used to facilitate the demodulation process. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete description of the invention reference can be made to the following detailed description of several embodiments thereof which is given in conjunction with the accompanying drawings of which: 
       FIG. 1  is a schematic drawing illustrating an MRI instrument used in an embodiment of the invention. 
       FIG. 2  is a block diagram of the gradient amplifiers used in an embodiment of the invention. 
       FIG. 3  is a graph of gradient waveforms used in an embodiment of the invention. 
       FIG. 4  is an illustration of spiral k-space scan used in the prior art. 
       FIG. 5  is an illustration of a k-space scan used in an embodiment of the invention. 
       FIG. 6  is a block diagram of the signal processing used in an embodiment of the invention. 
       FIG. 7  is an illustration of a spiral scan of a portion of k-space in an embodiment of the invention. 
       FIG. 8  is an illustration of a set of spiral scans in k-space along with a very low frequency scan used in an embodiment of the invention. 
       FIG. 9  is an illustration of a sequence of k-space spirals used in an embodiment of the invention. 
       FIGS. 10A ,  10 B, and  10 C are block diagrams of alternate embodiments of detector systems used in the invention; and 
       FIG. 11  includes illustrations of sequences of parallel line k-space scans used in the invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   An understanding of the broad aspects of the invention can best be had by reference to  FIG. 1 . Here we basically see the structures of an MRI system as described in the book by P. Mansfield and P. G. Morris in “NMR Imaging in Biomedicine”, Academic Press, Inc., Orlando Fla., 1982. Here it is used to image object  11  that is normally a portion of the human body. The magnetic moments in the body are polarized using solenoidal magnet  10 . A set of gradient coils on cylinder  12  provide fields pointed in the same direction as the B 0  field created by magnet  10 . These are made spatially varying to provide imaging information while the magnetic moments are precessing. Using these coils, variations can be made in the x, y, or z axes representing the three gradient fields, all pointing in the B 0  direction. These provide gradient fields as given by:
 
 G   x   =d/dx B   0 
 
G y   =d/dy B   0 
 
 G   z   =d/dz B   0 .
 
These gradient fields are used, while the moments are precessing, to create linear space-varying fields to provide imaging. If a two-dimensional slice is selected, only the two gradient fields in the plane of the slice are required to make an image of the slice. Thus if a slice is created in an xy plane, at some value of z, only G x  and G y  are required. In many cases a 3D set is required of a volume in the body. In that case a slab is selected representing the volume of interest. This is followed by a gradient set in all three axes that cover the desired range of k-space. The resultant signals  13 , representing the spatial frequencies, are received by birdcage coil  14 . They are then processed to create an image as described in the previous references.
 
   In general, for this invention, the basic elements of the MRI instrument are unchanged. The novel features of this invention include changes in the gradient waveforms and in the detection system. 
   As shown in  FIG. 2  the gradient coils  12  are driven by gradient amplifiers  16 . For 2D imaging the X and Y gradients are driven with signals  18  and  20 . As described in the previous references, the k-space values are the integral of these gradient waveforms. For example, as shown in  FIG. 3 , for spiral k-space scans, as described in Meyer CH, B. S. Hu, D. G. Nishimura and A. Macovski, “Fast Spiral Coronary Artery Imaging”, Magn. Reson. Med. 28-2, pp. 202–213, 1992, sinusoids of varying frequency represent the signals  18  and  20  applied to amplifier  16 . 
     FIG. 4  illustrates a spiral k-space scan as used in the prior art. It is normally undesirable to cover all of k-space in a single excitation for a number of reasons. The short acquisition time results in a poor signal-to-noise-ratio. Also, this would require very rapidly changing magnetic fields that can cause undesirable neural stimulation within the body. The FDA has set limits on dB/dt, the rate of magnetic field changes. Here the 2D k-space is covered in three excitations providing scans  54 ,  55 , and  56  that are spatially interleaved. The k-space data of the three scans is collected, summed and processed to provide the desired image. This approach works very well unless a rapidly moving object, such as the beating heart, is being imaged. In that case motion will occur between scans. For example the heart can be in one position for scan  54  and in another for scan  55 . This results in inconsistent k-space data, producing undesirable artifacts in the resultant image. 
   An alternate k-space scan approach is shown in  FIG. 5  and is described in U.S. Pat. No. 5,402,067, Apparatus and method for rare echo imaging using k-space spiral coverage issued to Pauly et al. Here the spirals are in concentric rings  40 ,  42  and  44  rather than being interleaved. Here again, in the presence of motion, the inconsistent data will result in artifacts. However, this k-space format enables an alternate processing scheme which is the subject of this invention. Each concentric spiral,  44 ,  42 , and  44  has closely spaced lines. Therefore each spiral, of itself, can produce image components substantially free of aliasing or inadequate sampling. Thus scan  40 , of itself, can be used to provide the low spatial frequencies of the image. Similarly scan  42  can be used to provide the intermediate spatial frequencies and scan  44  the high spatial frequencies of the image from object  11 . 
   The processing system is illustrated in  FIG. 6 . Signal  13  from the radio frequency pickup coil  14  is stored in storage device  22 . To enable Fourier transformation of the stored signal  21 , it is separated into in-phase and quadrature components I and Q as is done in the prior art. Signal  21  is applied to multipliers  23  where it is multiplied by quadrature versions of the carrier signal at a frequency of ω 0  corresponding to the magnetic field B 0 . These multipliers are followed by low-pass filters  25  in the manner of classic synchronous demodulators as used in the prior art. The complex signal, represented by I and Q, is then Fourier transformed in  24  in a digital computer. Ideally the resultant image signal  32  would be a real image signal capable of being displayed. However, because of a variety of considerations such as regions being somewhat off resonance, magnetic susceptibility changes, etc. the resultant transformed image signal  32  is of the form
 
 I ( x,y )= M ( x,y )exp[ i θ( x,y )]
 
where M(x,y) is the transformed desired magnetic moment amplitude representing the desired image and θ(x,y) represents the various phase departures at each point in the image I(x,y). To deal with these phase errors, existing MRI instruments either use a magnitude detector or a homodyne detector as described in D C Noll, D G Nishimura, A Macovski, “Homodyne Detection in Magnetic Resonance Imaging,” IEEE Trans Med Imag, 10(2):154–163, June 1991. The magnitude detector simply provides the desired image M(x,y). The homodyne detector makes the reasonable assumption that the phase variations θ(x,y) include primarily low-frequency variations. The low frequency portion of the signal is therefore used to extract θ(x,y). Then the signal I(x,y) is multiplied by exp[−iθ(x,y)] to provide the desired M(x,y).
 
   In the prior art, using a k-space scan such as the interleaved spirals of  FIG. 4 , the Fourier transform of the image is filled using the sequence of interleafs, and then transformed to provide the image. Again, as previously discussed, this results in undesirable artifacts due to the motion occurring between k-space sequences. 
   In this invention, each k-space scan is separately detected to provide an image representing a part of the spatial frequency spectrum. Thus a separate image is provided of the low spatial frequencies, medium spatial frequencies and high spatial frequencies. These are then stored and combined in image store  28  to provide the desired image in display  30 . As each new spatial-frequency component is scanned, the resultant component image  34  is used to update the final image in image store  28 . 
   In order to provide real images representing portions of the spatial-frequency spectrum, these should be free of aliasing. Thus the interleaved spirals of  FIG. 4  would be unsuitable since they are each coarse scans that would result in severe aliasing. We therefore choose scans of the type shown in  FIG. 5 , concentric spirals, where each scan represent an image, substantially free of aliasing, of specific spatial frequencies. To avoid aliasing the reciprocal of the line spacing in k-space must relate to the image size. 
   To provide the component images  34 , they must be detected in detector  26  to remove the undesired phase variation θ(x,y).  FIG. 10  illustrates the methods of detection.  FIG. 10A  illustrates a magnitude detector  33 . This detector is suitable for the low frequency portion of the image as represented by scan  40  in  FIG. 5 . However, for the other scans,  42  and  44 , a magnitude detector is unsuitable since the polarity information would be lost. The low frequencies are all positive. However, higher frequency information is bi-polar and the polarity must be preserved. One method of detection which preserves polarity is shown in  FIG. 10B . It requires a very-low frequency reference to deal with the previously described phase variations. The extraction of this low-frequency reference is shown in  FIG. 7A  with a representative associated gradient waveform in  FIG. 7B . For example, for the scan of the high frequencies  44 , a very-low frequency scan  51  is first created. We then use segment  52  to rapidly reach the high frequency region. As shown in  FIG. 7B  the very-low frequency scan  51  is generated by waveform  61 , the traverse in k-space  52  is generated by flat waveform  62  and the high-frequency scan  44  is generated by variable-frequency sinusoid  60 . The X and Y gradient waveforms are similar. 
   The very-low frequency scan  51  is stored to provide signal  36  which is used in the polarity-preserving detector of  FIG. 10B . 
   Here signal  32  is separated into a very-low spatial frequency signal  36  and a high spatial frequency signal  37  for example by using a digital filter  35 . A conjugate phase signal  39 , exp−i[θ(x,y)] is extracted in  31  by conventional methods including the arc tangent of Q/I or the signal divided by its magnitude. This conjugate phase signal is multiplied by the complex signal  37  to remove the phase component θ(x,y) to provide a real-valued bi-polar image of the high frequencies M h (x,y)  34 . 
   An alternate detector approach is illustrated in  FIG. 10C  Here the extracted very-low spatial frequency signal  36  is added to the high-spatial frequency signal  37 . This addition assures that the sum  45  will be positive. If desired a scaled version of  36  can be added to further insure that 45 is positive. The magnitude of this sum is taken in magnitude detector  33  to remove the phase factor. The added low spatial-frequency signal  36  is then subtracted in  38  to provide the desired bi-polar signal  34 . 
   S 
   As shown in  FIG. 6 , the detected signals are sequentially applied to updated image store  28  where each new acquisition replaces the previous one of the same spectral content. The latest updated image is then displayed in  30 . 
   The system as described thusfar will substantially avoid the motion artifacts. What may remain is a subtle motion blurring that is common to motion pictures. However, the resultant dynamic image may experience a problem that may be labeled “flash”. This is illustrated in  FIG. 9 . For example, the image is made up of three sequential scans in group  77  providing the low  70 , intermediate  71  and high  72  frequencies. Each displayed image shows the current stored set of values. Note that each spectral portion is updated every three scans. In most practical cases this will be more than three. The low frequency portions  70 ,  73 , and  76  represent the average value or brightness of the final image. Since these are updated every three scans, the brightness change due to scene motion can cause an annoying flash or flicker. For example, scan set  79  contain the brightness due to  73 ; while set  80  has the brightness due to  76 . To avoid this “flash” problem we update the very-low spatial frequencies on each scan. The source of this very-low frequency signal can be the very-low frequency scan  65  in  FIG. 8 . For convenience this can be the same very-low frequency scan used for demodulation shown as  51  in  FIG. 7A . 
   Very-low spatial frequency signal  36  has previously been used to facilitate detection of a bi-polar signal. It can also be used to provide updating of the very-low frequencies on each scan, thus eliminating the flash. Signal  36 , which exists in detector  26 , is passed onto updated image store  28  as shown in the dashed line in  FIG. 6 . This provides rapid updating of the average brightness. 
   Thusfar only spiral scans have been used as illustrations. These could also be concentric circles with close enough spacing to avoid aliasing. Alternatively straight-line scans can be used as shown in  FIG. 9 . Scan  80  illustrates a low-frequency scan using straight parallel lines. This scan is taken separately despite being shown with other scans. The intermediate and high spatial frequency scans are shown as  81  and  82  respectively. In each of these cases very-low frequency scan  83  is added and is used for detection and to avoid flashes in average brightness. 
   In each case the specific scan pattern, as with existing systems, will depend on the desired speed and resolution. However, unlike existing systems, which first add up all Fourier components and then detect the entire image, this system will avoid motion artifacts by adding detected images of specific spectral components. 
   Although all of the scan systems shown have sufficient line density to avoid aliasing, in some cases aliasing can be tolerated while providing increased resolution. For example, the line density in the outer concentric spiral  44  could be made coarser thus extending into higher spatial frequencies. Although this would result in a small amount of high-frequency aliasing, it provides increased resolution. 
   The systems described herein use the typical MRI resolution standards such as 128×128 or 256×256. The inner very-low frequency region used for demodulation and avoiding flash brightness changes is of the order of 10% of the total scan or 13×13 or 26×26. 
   Although image motion was given as a cause of the artifacts in the prior art, a number of other factors can cause changes between k-space acquisitions. These include eddy currents, susceptibility errors and frequency changes. Each of these artifact-causing changes would be reduced by separately demodulating each segment and adding the partial images as described in this invention.