Patent Publication Number: US-9414766-B2

Title: Method for simultaneous multi-slice magnetic resonance imaging using single and multiple channel receiver coils

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application represents the national stage entry of PCT International Application No. PCT/US2011/026250 filed Feb. 25, 2011, which claims the benefit of U.S. Provisional Patent Application Ser. No. 61/308,170, filed on Feb. 25, 2010, and entitled “Method for Simultaneous Multi-Slice Magnetic Resonance Imaging Using Single and Multiple Channel Receiver Coils”, all of which are hereby incorporated herein by reference for all purposes. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with government support under EB007827 awarded by the National Institutes of Health. The government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     The field of the invention is magnetic resonance imaging (“MRI”) methods and systems. More particularly, the invention relates to methods and systems for simultaneous multi-slice MRI, in which either a single or multiple channel receiver coil is employed to simultaneously acquire image data from multiple slice locations. 
     MRI uses the nuclear magnetic resonance (“NMR”) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B 0 ), the individual magnetic moments of the 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 B 1 ) 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 xy . A signal is emitted by the excited nuclei or “spins,” after the excitation signal B 1  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 for the spatial encoding of the signals. 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 raster scan-like pattern sometimes referred to as a “spin-warp,” a “Fourier,” a “rectilinear,” or a “Cartesian” scan; however, other pulse sequences may sample k-space along non-Cartesian trajectories such as radial lines and spirals. 
     Depending on the technique used, many MR scans currently require many minutes to acquire the necessary data used to produce medical images. The reduction of this scan time is an important consideration, since reduced scan time increases patient throughout, improves patient comfort, and improves image quality by reducing motion artifacts. Many different strategies have been developed to shorten the scan time. 
     One such strategy for shortening scan time is referred to generally as “parallel MRI” (“pMRI”). Parallel MRI techniques use spatial information from arrays of radio frequency (“RF”) receiver coils to substitute for the spatial encoding that would otherwise have to be obtained in a sequential fashion using RF pulses and magnetic field gradients, such as phase and frequency encoding gradients. Each of the spatially independent receiver coils of the array carries certain spatial information and has a different spatial sensitivity profile. This information is utilized in order to achieve a complete spatial encoding of the received MR signals, for example, by combining the simultaneously acquired data received from each of the separate coils. Parallel MRI techniques allow an undersampling of k-space by reducing the number of acquired phase-encoded k-space sampling lines, while keeping the maximal extent covered in k-space fixed. The combination of the separate MR signals produced by the separate receiver coils enables a reduction of the acquisition time required for an image, in comparison to a conventional k-space data acquisition, by a factor related to the number of the receiver coils. Thus the use of multiple receiver coils acts to multiply imaging speed, without increasing gradient switching rates or RF power. 
     Two categories of such parallel imaging techniques that have been developed and applied to in vivo imaging are so-called “image space methods” and “k-space methods.” An exemplary image space method is known in the art as sensitivity encoding (“SENSE”), while an exemplary k-space method is known in the art as simultaneous acquisition of spatial harmonics (“SMASH”). With SENSE, the undersampled k-space data is first Fourier transformed to produce an aliased image from each coil, and then the aliased image signals are unfolded by a linear transformation of the superimposed pixel values. With SMASH, the omitted k-space lines are synthesized or reconstructed prior to Fourier transformation, by constructing a weighted combination of neighboring k-space lines acquired by the different receiver coils. SMASH requires that the spatial sensitivity of the coils be determined, and one way to do so is by “autocalibration” that entails the use of variable density k-space sampling. 
     A more recent advance to SMASH techniques using autocalibration is a technique known as generalized autocalibrating partially parallel acquisitions (“GRAPPA”), as described, for example, in U.S. Pat. No. 6,841,998. With GRAPPA, k-space lines near the center of k-space are sampled at the Nyquist frequency, in comparison to the undersampling employed in the peripheral regions of k-space. These center k-space lines are referred to as the so-called autocalibration signal (“ACS”) lines, which are used to determine the weighting factors that are utilized to synthesize, or reconstruct, the missing k-space lines. In particular, a linear combination of individual coil data is used to create the missing lines of k-space. The coefficients for the combination are determined by fitting the acquired data to the more highly sampled data near the center of k-space. 
     Another strategy is to use so-called partial k-space echo-planar imaging (“EPI”), in which the number of acquired k-space lines is reduced and a relatively short echo time (“TE”) is used, thereby minimizing signal dropout. The time required to cover k-space can be further reduced by the use of in-plane SENSE or one of its derivatives. 
     Other methods for decreasing scan time have been developed. For example, methods for the simultaneous acquisition of image data from multiple imaging slice locations, using an array of multiple radio frequency (“RF”) receiver coils, and subsequent separation of the superimposed slices during image reconstruction have be introduced, as described by D. J. Larkman, et al., in “Use of Multicoil Arrays for Separation of Signal from Multiple Slices Simultaneously Excited,”  Journal of Magnetic Resonance Imaging,  2001; 13(2):313-317. This method is limited, however, in that the separation of the multiple slices is rendered difficult by the close spatial proximity of the aliased pixels that must be separated during image reconstruction. For example, if image data is acquired from three slices simultaneously, and with an inter-slice spacing of around 3 cm, then aliasing will be present along the slice-encoding direction, and this aliasing must be undone in order to produce reliable images. The origin of the aliased pixels are only 3 cm apart in space, and it is this spatial closeness of the aliased pixels that makes their separation difficult by standard parallel imaging methods, such as sensitivity encoding (“SENSE”). 
     The difficulties of SENSE, and other similar methods, to properly separate the aliased pixels results from the differences in detection strength among the multiple array coil elements at the locations of the aliased pixels. In particular, the problem is that the detection profiles of the coil array elements are not unique enough on the spatial scale of a few centimeters. As a result, a high level of noise amplification, characterized by a high SENSE g-factor, is present in the separated images. This result is in contrast to the conventional implementation of SENSE methods, in which an undersampled phase encoding scheme produces aliasing along the phase-encoding direction, which is orthogonal to the slice-encoding direction. Moreover, this in-plane aliasing results in pairs of aliased pixels that are separated by one-half of the image field-of-view (“FOV”). For a conventional brain image, the FOV is equal to around 24 cm; thus, when aliasing occurs in the imaging plane, or slice, the distance between aliased pixels is around 12 cm. It is contemplated that it is the four-fold smaller distance between aliased pairs of pixels that results in significant noise amplification in the method disclosed by Larkman. It would therefore be desirable to provide a method for simultaneous multi-slice imaging that is produces less noise amplification than presently available methods, such as the one taught by Larkman. 
     Another notable method for simultaneous multi-slice imaging was described by D. A. Feinberg, et al., in “Simultaneous Echo Refocusing in EPI,”  Magn. Reson. Med.,  2002; 48(1):1-5. In this method, which is termed “SER-EPI,” the RF excitation of the slices is sequential, as opposed to truly simultaneous. A readout gradient pulse is applied between two sequential excitations, and acts to shift the k-space data of one slice relative to the other along the k x -direction, which corresponds to the readout direction in image space. By lengthening the readout window, the k-space data for both slices is captured sequentially. The data can then be cut apart and reconstructed separately. This approach has several downsides, however. Since the excitation is not simultaneous, the two slices do not have identical echo times (“TE”). In fact, the TEs typically differ by about 3 ms. This difference in TE is problematic, in that image intensity and contrast is exponentially dependent on TE. Thus, the two slices are not truly identical in image contrast or intensity. Another limitation of the SER-EPI method is that the lengthened readout needed to capture the shifted k-space data of the second slice increases the total readout duration. In turn, this increased duration increases the B 0  susceptibility distortions included in the resultant EPI images. 
     More recently, the SER-EPI method of Feinberg has been modified to include the approach utilized by Larkman, as described by D. A. Feinberg, et al., in “Multiplexed Echo Planar Imaging for Sub-Second Whole Brain fMRI and Fast Diffusion Imaging,” PLos ONE (5):e15710. This more recently modified method, however, still includes the limitations of the reconstruction technique described by Larkman. 
     Simultaneous multi-slice methods have not gained much traction in conventional imaging since there are alternative parallel imaging methods, such as conventional SENSE and GRAPPA, for accelerating standard image acquisitions. However, as noted above, these methods do not confer the same acceleration benefits on pulse sequences such as EPI as they do on other conventional pulse sequences. Unlike parallel imaging methods such as SENSE and GRAPPA, multi-slice acquisition techniques do not aim to shorten the time spent on reading out k-space data, for example, by reducing the number of phase-encodings. Rather, they aim to acquire signal data from multiple image slice locations per acquisition, such that the number of repetitions of a pulse sequence can be reduced to similarly reduce overall scan time. For example, a three-fold accelerated multi-slice acquisition acquires image data from three image slice locations per each repetition of the EPI sequence. As a result of this simultaneous acquisition, the number of repetitions of an EPI sequence required to cover an imaging volume is reduced, thereby similarly reducing the total acquisition time. 
     It would therefore be desirable to provide a method for simultaneous, multi-slice imaging that allows for a more reliable separation of aliased pixels than currently available methods for simultaneous multi-slice imaging, so that the benefits associated with these techniques can be realized in a clinical setting. It would further desirable to provide such a method that would be amenable to functional MRI (“fMRI”) techniques, including resting state or functional connectivity fMRI. 
     SUMMARY OF THE INVENTION 
     The present invention overcomes the aforementioned drawbacks by providing a method for reconstructing a plurality of images depicting a subject from image data that is simultaneously acquired from a corresponding plurality of slice locations with a magnetic resonance imaging (“MRI”) system. Image data is acquired following the application of radio frequency (“RF”) energy to the plurality of slice locations. The RF energy is tailored to provide a different phase to each of the plurality of slice locations. Reference image data is also acquired for each slice location following the application of RF energy that has the same phase as used to excite the respective slice location for the acquisition of the image data. Aliased images are reconstructed from the image data, and reference images are reconstructed from the reference image data. Using both of these image sets, an unaliased image is produced for each of the plurality of slice locations. Such a method is advantageous for performing functional MRI (“fMRI”) and for acquiring a time series of image frames that covers the entire volume of the brain in a shorter period of time than is capable with previous methods. This advantageous benefit of the method makes it particularly well-suited for performing resting-state fMRI and for assessing functional connectivity. Thus, the herein provided method provides an advantageous imaging method for assessing the functional connectome with fMRI. 
     The foregoing and other aspects and advantages of the invention will appear from the following description. In the description, reference is made to the accompanying drawings which form a part hereof, and in which there is shown by way of illustration a preferred embodiment of the invention. Such embodiment does not necessarily represent the full scope of the invention, however, and reference is made therefore to the claims and herein for interpreting the scope of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an exemplary magnetic resonance imaging (“MRI”) system that employs the present invention; 
         FIG. 2  is a block diagram of an exemplary radio frequency (“RF”) system that forms part of a configuration of the MRI system of  FIG. 1 ; 
         FIG. 3  is a block diagram of an exemplary RF system including a parallel receiver coil array that forms a part of another configuration of the MRI system of  FIG. 1 ; 
         FIG. 4  is a pulse sequence diagram depicting an exemplary pulse sequence employed when practicing some embodiments of the present invention; 
         FIG. 5A  is an exemplary set of four RF pulse profiles in frequency space; 
         FIG. 5B  is an exemplary set of four RF pulse phase profiles corresponding to the RF pulse profiles of  FIG. 5A ; 
         FIG. 5C  is an exemplary composite RF pulse waveform produced by Fourier transforming and combining the RF pulse profiles of  FIG. 5A ; 
         FIG. 5D  is a phase of the composite RF pulse wave of  FIG. 5C ; 
         FIG. 6A  is a pictorial representation of an exemplary data acquisition scheme using multiple slice locations that are simultaneously excited in accordance with some embodiments of the present invention; 
         FIG. 6B  is a pictorial representation of another exemplary data acquisition scheme using multiple slice locations that are simultaneously excited in accordance with some embodiments of the present invention; 
         FIG. 7  is a flowchart setting forth the steps of an exemplary method for simultaneously acquiring image data from multiple slice locations and reconstructing images therefrom; and 
         FIG. 8  is a flowchart setting forth the steps of an exemplary method for calculating and correcting phase drifts in reconstructed aliased images. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring particularly now to  FIG. 1 , an exemplary magnetic resonance imaging (“MRI”) system  100  is illustrated. The MRI system  100  includes a workstation  102  having a display  104  and a keyboard  106 . The workstation  102  includes a processor  108 , such as a commercially available programmable machine running a commercially available operating system. The workstation  102  provides the operator interface that enables scan prescriptions to be entered into the MRI system  100 . The workstation  102  is coupled to four servers: a pulse sequence server  110 ; a data acquisition server  112 ; a data processing server  114 , and a data store server  116 . The workstation  102  and each server  110 ,  112 ,  114  and  116  are connected to communicate with each other. 
     The pulse sequence server  110  functions in response to instructions downloaded from the workstation  102  to operate a gradient system  118  and a radiofrequency (“RF”) system  120 . Gradient waveforms necessary to perform the prescribed scan are produced and applied to the gradient system  118 , which excites gradient coils in an assembly  122  to produce the magnetic field gradients G x , G y , and G z  used for position encoding MR signals. The gradient coil assembly  122  forms part of a magnet assembly  124  that includes a polarizing magnet  126  and a whole-body RF coil  128 . 
     RF excitation waveforms are applied to the RF coil  128 , or a separate local coil (not shown in  FIG. 1 ), by the RF system  120  to perform the prescribed magnetic resonance pulse sequence. Responsive MR signals detected by the RF coil  128 , or a separate local coil (not shown in  FIG. 1 ), are received by the RF system  120 , amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server  110 . The RF system  120  includes an RF transmitter for producing a wide variety of RF pulses used in MR pulse sequences. The RF transmitter is responsive to the scan prescription and direction from the pulse sequence server  110  to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole body RF coil  128  or to one or more local coils or coil arrays (not shown in  FIG. 1 ). 
     The RF system  120  also includes one or more RF receiver channels. Each RF receiver channel includes an RF amplifier that amplifies the MR signal received by the coil  128  to which it is connected, and a detector that detects and digitizes the I and Q quadrature components of the received MR signal. The magnitude of the received MR signal may thus be determined at any sampled point by the square root of the sum of the squares of the I and Q components:
 
 M =√{square root over ( I   2   +Q   2 )}  (1):
 
     and the phase of the received MR signal may also be determined: 
     
       
         
           
             
               
                 
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     The pulse sequence server  110  also optionally receives patient data from a physiological acquisition controller  130 . The controller  130  receives signals from a number of different sensors connected to the patient, such as electrocardiograph (“ECG”) signals from electrodes, or respiratory signals from a bellows or other respiratory monitoring device. Such signals are typically used by the pulse sequence server  110  to synchronize, or “gate,” the performance of the scan with the subject&#39;s heart beat or respiration. 
     The pulse sequence server  110  also connects to a scan room interface circuit  132  that receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit  132  that a patient positioning system  134  receives commands to move the patient to desired positions during the scan. 
     The digitized MR signal samples produced by the RF system  120  are received by the data acquisition server  112 . The data acquisition server  112  operates in response to instructions downloaded from the workstation  102  to receive the real-time MR data and provide buffer storage, such that no data is lost by data overrun. In some scans, the data acquisition server  112  does little more than pass the acquired MR data to the data processor server  114 . However, in scans that require information derived from acquired MR data to control the further performance of the scan, the data acquisition server  112  is programmed to produce such information and convey it to the pulse sequence server  110 . For example, during prescans, MR data is acquired and used to calibrate the pulse sequence performed by the pulse sequence server  110 . Also, navigator signals may be acquired during a scan and used to adjust the operating parameters of the RF system  120  or the gradient system  118 , or to control the view order in which k-space is sampled. The data acquisition server  112  may also be employed to process MR signals used to detect the arrival of contrast agent in a magnetic resonance angiography (“MRA”) scan. In all these examples, the data acquisition server  112  acquires MR data and processes it in real-time to produce information that is used to control the scan. 
     The data processing server  114  receives MR data from the data acquisition server  112  and processes it in accordance with instructions downloaded from the workstation  102 . Such processing may include, for example: Fourier transformation of raw k-space MR data to produce two or three-dimensional images; the application of filters to a reconstructed image; the performance of a backprojection image reconstruction of acquired MR data; the generation of functional MR images; and the calculation of motion or flow images. 
     Images reconstructed by the data processing server  114  are conveyed back to the workstation  102  where they are stored. Real-time images are stored in a data base memory cache (not shown in  FIG. 1 ), from which they may be output to operator display  112  or a display  136  that is located near the magnet assembly  124  for use by attending physicians. Batch mode images or selected real time images are stored in a host database on disc storage  138 . When such images have been reconstructed and transferred to storage, the data processing server  114  notifies the data store server  116  on the workstation  102 . The workstation  102  may be used by an operator to archive the images, produce films, or send the images via a network to other facilities. 
     As shown in  FIG. 1 , the radiofrequency (“RF”) system  120  may be connected to the whole body RF coil  128 , or, as shown in  FIG. 2 , a transmission channel  202  of the RF system  120  may connect to a RF transmission coil  204  and a receiver channel  206  may connect to a separate RF receiver coil  208 . Often, the transmission channel  202  is connected to the whole body RF coil  128  and each receiver section is connected to a separate local RF coil. 
     Referring particularly to  FIG. 2 , the RF system  120  includes a transmission channel  202  that produces a prescribed RF excitation field. The base, or carrier, frequency of this RF excitation field is produced under control of a frequency synthesizer  210  that receives a set of digital signals from the pulse sequence server  110 . These digital signals indicate the frequency and phase of the RF carrier signal produced at an output  212 . The RF carrier is applied to a modulator and up converter  214  where its amplitude is modulated in response to a signal, R(t), also received from the pulse sequence server  110 . The signal, R(t), defines the envelope of the RF excitation pulse to be produced and is produced by sequentially reading out a series of stored digital values. These stored digital values may be changed to enable any desired RF pulse envelope to be produced. 
     The magnitude of the RF excitation pulse produced at output  216  is attenuated by an exciter attenuator circuit  218  that receives a digital command from the pulse sequence server  110 . The attenuated RF excitation pulses are then applied to a power amplifier  220  that drives the RF transmission coil  204 . 
     The MR signal produced by the subject is picked up by the RF receiver coil  208  and applied through a preamplifier  222  to the input of a receiver attenuator  224 . The receiver attenuator  224  further amplifies the signal by an amount determined by a digital attenuation signal received from the pulse sequence server  110 . The received signal is at or around the Larmor frequency, and this high frequency signal is down converted in a two step process by a down converter  226 . The down converter  226  first mixes the MR signal with the carrier signal on line  212  and then mixes the resulting difference signal with a reference signal on line  228  that is produced by a reference frequency generator  230 . The down converted MR signal is applied to the input of an analog-to-digital (“A/D”) converter  232  that samples and digitizes the analog signal. The sampled and digitized signal is then applied to a digital detector and signal processor  234  that produces 16-bit in-phase (I) values and 16-bit quadrature (Q) values corresponding to the received signal. The resulting stream of digitized I and Q values of the received signal are output to the data acquisition server  112 . In addition to generating the reference signal on line  228 , the reference frequency generator  230  also generates a sampling signal on line  236  that is applied to the A/D converter  232 . 
     An alternative configuration of the RF system of  FIG. 2  is shown in  FIG. 3 , to which reference is now made. In this alternative configuration, the RF transmission coil  204  and RF receiver coil  208  are replaced by a coil array  336 , which includes at least one RF transmission coil and a plurality of receiver coils connected through one or more transmit/receive (“T/R”) switches  338 . The signal produced by the subject is picked up by the coil array  336  and applied to the inputs of a set of receiver channels  306 . A pre-amplifier in each receiver channel  306  amplifies the signal by an amount determined by a digital attenuation signal received from the pulse sequence server  110 . The received signal is at or around the Larmor frequency, and this high frequency signal is down converted in a two step process by a down converter. The down converter first mixes the MR signal with a carrier signal on line  312  and then mixes the resulting difference signal with a reference signal on line  328  that is produced by a reference frequency generator  330 . The down converted MR signal is applied to the input of an analog-to-digital (“A/D”) converter that samples and digitizes the analog signal. The sampled and digitized signal is then applied to a digital detector and signal processor  334  that produces 16-bit in-phase (I) values and 16-bit quadrature (Q) values corresponding to the received signal. The resulting stream of digitized I and Q values of the received signal are output to the data acquisition server  112 . In addition to generating the reference signal on line  328 , the reference frequency generator  330  also generates a sampling signal on line  336  that is applied to the A/D converter. 
     A method for accelerating the acquisition of a time course of images with a magnetic resonance imaging (“MRI”) system by way of a simultaneous multi-slice data acquisition is provided. For example, the acquisition of image data with echo planar imaging (“EPI”) or spiral imaging is accelerated by at least two-fold. Such a method is generally applicable to functional MRI (“fMRI”), resting-state fMRI (“R-fMRI”), arterial spin labeling (“ASL”), diffusion weighted image (“DWI”), and other situations where the acquisition of a large number of images are desirable. However, the method may advantageously improve the data acquisition efficiency for any number of other clinical applications, as will be appreciated by those skilled in the art. 
     In the method, groups of image slices, for example two or more slices, are simultaneously excited using a slice-selective tailored pulse that labels each slice by way of a unique radio frequency (“RF”) phase. This method is generally referred to as “parallel slice phase tagging” (“PSPT”). Unraveling of the overlapping slices is accomplished using the RF phase labeling. It is noted that this method can be implemented using either a single channel, or multi-channel, receiver coil. Unraveling of the overlapping slices is further enhanced through the use of “reference slices.” A set of reference slice images is obtained, for example, using the labeling phase assigned to each slice. 
     The PSPT method can be combined with SENSE acceleration, for significantly enhanced overall acceleration. This combination is generally referred to as “two-axis acceleration” (“TAC”), in which one axis is perpendicular to the slice, and the other axis is in the phase-encoding direction, for example. Cross-talk between slices is characterized and reduced by the tailored RF pulse formation and an appropriate slice separation algorithm. Additionally, increasing number of receiver channels in the coil array may reduce cross-talk between the slices. A time course of simultaneously excited slices can be easily registered using, for example, rigid-body as well as affine registration methods. 
     The method provided by the present invention allows for the acquisition of high-resolution functional connectivity data across the whole brain in a clinically reasonable time. Data can be obtained, for example, using R-fMRI with sufficiently thin slices such that intravoxel dephasing and signal drop-out are substantially mitigated. Data can be obtained within a repetition time (“TR”) value of around two seconds, thereby preserving coherency of physiological fluctuations across the whole-brain data set. For EPI time-course methods, parallel acquisition allows a significantly enhanced tradeoff between temporal acceleration and increase of spatial resolution to the advance of neuroscience and diagnosis of human brain disease. 
     An exemplary pulse sequence employed to direct the MRI system to acquire image data simultaneously from multiple slice locations, in accordance with the present invention, is illustrated in  FIG. 4 . Such an exemplary pulse sequence is a gradient-recalled echo planar imaging (“EPI”) pulse sequence. The pulse sequence includes a spatially selective radio frequency (“RF”) excitation pulse  402  that is played out in the presence of a slice-selective gradient  404  in order to produce transverse magnetization in multiple prescribed imaging slices. The slice-selective gradient  404  includes a rephasing lobe  406  that acts to rephase unwanted phase dispersions introduced by the slice-selective gradient  404 , such that signal losses resultant from these phase dispersions are mitigated. 
     The RF excitation pulse  402  is, for example, a composite RF pulse that is tailored to simultaneously excite multiple slice locations, such that the transverse magnetization at each slice location is imparted a different phase. By way of example, and referring now to  FIGS. 5A-5D , a desired slice profile is determined and the Fourier transform of that slice profile is calculated to determine the appropriate RF excitation pulse  402  profile, including the different phase information for the different slice locations. For example, the location and thickness for each desired slice location is selected and used to produce an RF pulse profile for each slice location in frequency space. Additionally, the tip angle of each RF pulse profile can be separately selected. Four such RF pulse profiles are shown in  FIG. 5A , in which each different RF pulse profile has different frequency values and bandwidths associated with it, which correspond to the different spatial locations and slice thicknesses, respectively, that will be excited by the corresponding RF pulse. As shown in  FIG. 5B , each RF pulse profile has a unique phase profile. In general, N such RF pulse profiles and N corresponding phase profiles are produced and then transformed to generate the desired RF pulse waveforms. By way of example, the Fourier transform of the RF pulse profiles in  FIG. 5A  produce four distinct RF pulse waveforms that, when combined, produce a composite RF pulse waveform, such as the one illustrated in  FIG. 5C . The phase of the exemplary RF pulse waveform shown in  FIG. 5C  is illustrated in  FIG. 5D . The composite RF pulse waveform may be obtained by summing the N RF pulse profiles and calculating the Fourier transform of the sum, or, alternatively, by adding the RF pulse waveforms produced by Fourier transforming each of the individual RF pulse profiles. 
     Exemplary phases for a four-slice acquisition include those lying in the first quadrant, that is: zero, thirty, sixty, and ninety degrees. It will be appreciated by those skilled in the art that any number of combinations of phase values may be readily implemented to phase-tag the respective slice locations, however. The individual RF pulses are also used to acquire reference image data, as will be described below. This reference image data, therefore, may be acquired with the same phases as those in the image data acquired following excitation by the composite RF pulse by using individual portions of the composite RF profile. It is noted that each complex-valued composite RF pulse may be formed from a single transmit frequency. 
     Referring again to  FIG. 4 , following excitation of the nuclear spins in the prescribed imaging slice, image data is acquired by sampling a series of gradient-recalled echo signals in the presence of an alternating readout gradient  408 . The alternating readout gradient is preceded by the application of a pre-winding gradient  410  that acts to move the first sampling point along the frequency-encoding, or readout, direction by a prescribed distance in k-space. Spatial encoding of the echo signals along a phase-encoding direction is performed by a series of phase encoding gradient “blips”  412 , which are each played out in between the successive signal readouts such that each echo signal is separately phase-encoded. The phase-encoding gradient blips  412  are preceded by the application of a pre-winding gradient  414  that acts to move the first sampling point along the phase-encoding direction by a prescribed distance in k-space. Together, the pre-winding gradients  410  and  414  act to begin the sampling of k-space at a prescribed k-space location. As is known in the art, the foregoing pulse sequence is repeated a plurality of times while applying a different slice-selective gradient  404  during each repetition such that a plurality of groups of multiple slice locations are sampled. 
     With reference now to  FIGS. 6A and 6B , exemplary groups of multiple slice locations are illustrated. In  FIG. 6A , a first group of slice locations  602  is shown, in which the slice locations are closely grouped together. This close grouping of slice locations is moved sequentially through the desired field-of-view in order to acquire image data throughout the desired field-of-view. For example, the first group of slice locations is moved sequentially through a plurality of group locations until a last group location, indicated by dashed lines  604 . When imaging in regions where significant air-tissue interfaces exist, such as the more inferior regions of the brain, it may be advantageous to use a thinner slice thickness than used for imaging other regions. Thus, as illustrated in  FIG. 6A , a second group of slice locations  606  may be used, in which the slice locations are again closely spaced, but in which the slice thickness of each individual slice location in the group  606  is thinner than those in the first group  602 . Like the first group  602 , the second group of slice locations  606  may be sequentially moved through the field-of-view until a last group location  608  is reached. As shown in  FIG. 6B , the selected slice locations do not need to be closely spaced; rather, each slice location in a group of slice locations may be spaced apart such that subsequent locations of the group of slice locations are interleaved with other group locations. It will be appreciated by those skilled in the art that the preceding examples of multiple slice location groupings and movement are just examples and that many other variations other than those expressly stated herein are possible within the scope of the invention. 
     When acquiring image data from multiple slice locations, it may be advantageous to use high dynamic range receivers that are well-suited for the increased signal associated with the simultaneous excitation of multiple slice locations. Exemplary high dynamic range receivers include, for example, EchoTek™ Series ECDR-GC316 digital receivers manufactured by Mercury Computer Systems, Inc. (Chelmsford, Mass.). 
     Referring now to  FIG. 7 , a flowchart setting forth the steps of an exemplary method for simultaneously acquiring image data from multiple slice locations and reconstructing images therefrom is illustrated. The method begins with the simultaneous acquisition of image data from multiple slice locations, as indicated at step  702 . This image data may be acquired using, for example, the pulse sequence described above. The data acquisition step includes acquiring image data from a plurality of slice locations in groups of multiple slice locations that are acquired simultaneously. In addition, reference image data is acquired during data acquisition. Reference image data is acquired for each receiver coil and for each slice location. Thus, when a single receiver coil is employed, one reference image data set is acquired for each slice location, but when a multi-channel receiver coil array is employed, such as an n-channel receiver coil array, n reference image data sets are acquired for each slice location. 
     From the acquired reference image data, reference images are reconstructed, as indicated at step  704 . These reference images are complex-valued images. In some instances, it may be advantageous to discard the first few reference images in a time course to avoid T 1  relaxation effects. These reconstructed reference images are then averaged to produce an average reference image having an improved signal-to-noise ratio (“SNR”), as indicated at step  706 . For example, the reference images obtained at each slice location from each of the coils in the multi-channel receiver coil array are averaged together to produce an average reference image for that slice location. It is noted that, to some degree, physiological fluctuations may be averaged in this process. From the acquired image data, images are reconstructed, as indicated at step  708 . Because image data was acquired from multiple slice locations simultaneously, these reconstructed images will include aliased signal information that is unaliased in later processes to produce the target images. Before unaliasing, it may be beneficial to remove unwanted phase drifts from the reconstructed images. It is contemplated that these unwanted RF phase drifts are associated with B 0  drifts, and may arise from a bulk susceptibility effect as the body of the subject relaxes toward a stable prone position, or from a heating effect during image acquisition. Thus, phase drifts are calculated and corrected for at step  710 . This phase drift correction process is described in more detail below, and with respect to  FIG. 8 . 
     Referring still to  FIG. 7 , after the reconstructed images have been corrected for phase drifts, the images are unaliased to produce the target images, as indicated at step  712 . In this process, each reconstructed image is unaliased into N images corresponding to the N slice locations simultaneously excited during data acquisition. In general, for each aliased voxel, a complex valued number exists from each of the n receiver channels, and, in addition, the reference images provide unaliased data from the N slices and n channels for that voxel. A system of equations is formed using this information, and may be solved, for example, by singular value decomposition to obtain the desired, unaliased image information. Data are combined across channels in this process, and the procedure is repeated across all voxels in each aliased image 
     The herein described reconstruction method for parallel slice phase-tagging provides the reconstruction of either complex-valued or real-valued images. Complex-valued images preserve temporal phase variations from the reference images. Such phase variations are necessary if advanced statistical methods that require the use of complex-valued data are used, and half Fourier reconstruction additionally requires complex-valued images. However, if standard magnitude images are to be used in statistical analysis, only real-valued images need to be reconstructed. 
     The decision to reconstruct only real-valued images may yield an improvement in the unaliasing process. By solving for only the real component of the deviation from the reference images, the reconstruction process includes half of the number of unknowns with respect to reconstructing complex-valued images. Thus, the separation problem is more overdetermined when only real-valued solutions are desired, yielding an improvement in, for example, a least squares fitting of the separated image information. By reconstructing only real-valued images from the complex-valued phase-tagged image data, a reduction factor of two times the number of coils can be advantageously reached. This reduction is a twofold improvement over previously parallel imaging techniques. 
     As mentioned above, the reconstruction method utilizes reference images that may be acquired, for example, serially with the same pulse sequence used to acquire the multiple slice image data. These reference images contain spatially varying magnitude sensitivity from receiver coil profiles and spatially varying phase from the combined effects of the vector reception field for each specific RF receive channel, local magnetic field properties, and the RF excitation phase. Both the magnitude and phase of these reference images are utilized to separate the aliased images by solving, for example, the following system of equations: 
     
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     S 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                 
                                   - 
                                   
                                     S 
                                     
                                       1 
                                       , 
                                       N 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         N 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     N 
                                   
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         N 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                             
                               ⋮ 
                             
                             
                               ⋱ 
                             
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 
                                   S 
                                   
                                     n 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         n 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   S 
                                   
                                     n 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         n 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                 
                                   S 
                                   
                                     n 
                                     , 
                                     N 
                                   
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         n 
                                         , 
                                         N 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 u 
                                 1 
                               
                             
                           
                           
                             
                               
                                 
                                   u 
                                   ^ 
                                 
                                 1 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 
                                   u 
                                   ^ 
                                 
                                 N 
                               
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               a 
                               1 
                             
                           
                         
                         
                           
                             
                               
                                 a 
                                 ^ 
                               
                               1 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 a 
                                 ^ 
                               
                               n 
                             
                           
                         
                       
                       ) 
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where a n  is the real component of the n th  aliased signal; â n  is the imaginary component of the n th  aliased signal; u N  is the real component of the N th  unaliased signal component, corresponding to the N th  image slice location; û N  is the imaginary component of the N th  unaliased signal component corresponding to the N th  image slice location; S n,N  is the magnitude of the reference image corresponding to the N th  slice location and the n th  receiver coil; and θ n,N  is the phase of the reference image corresponding to the N th  slice location and the n th  receiver coil. For simplicity, Eqn. (3) can be written as:
 
 Su=a   (4);
 
     where S is an encoding matrix containing the reference image magnitude, S n,N , entries and the reference image phase, θ n,N , entries; u is an unaliased image matrix containing the real and imaginary components of the unaliased images, u N  and û N , respectively; and a is an aliased image matrix containing the real and imaginary components of the aliased images, a n  and â n , respectively. 
     By using the reference image magnitude and phase in Eqn. (3), the unaliased images have near unity values that can be scaled by a combination of the reference images to yield an expected spatial contrast. Generally, Eqn. (3) determines the deviation of the magnetization vector in the aliased images from the magnetization vector in the reference images. Optionally, standard partial Fourier interpolation can be performed on the separated images, as indicated at step  714 . In the process for partial Fourier imaging, reference data and acquired data are zero filled and unaliased before performing partial Fourier interpolation. 
     For real-valued reconstructions, an assumption is made that the variation of the phase between the aliased images and reference images is negligible. With this assumption, the unaliased images are assumed to be real-valued, with phases defined entirely by the phases of the reference images. In this situation, Eqn. (3) may be rewritten as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     N 
                                   
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         N 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                 
                                   S 
                                   
                                     1 
                                     , 
                                     N 
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         1 
                                         , 
                                         N 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                             
                               ⋱ 
                             
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 
                                   S 
                                   
                                     n 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         n 
                                         , 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                 
                                   S 
                                   
                                     n 
                                     , 
                                     N 
                                   
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       
                                         n 
                                         , 
                                         N 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 u 
                                 1 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 
                                   u 
                                   
                                       
                                   
                                 
                                 N 
                               
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               a 
                               1 
                             
                           
                         
                         
                           
                             
                               
                                 a 
                                 ^ 
                               
                               1 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 a 
                                 ^ 
                               
                               n 
                             
                           
                         
                       
                       ) 
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     where the even columns of the encoding matrix, S, in Eqn. (3) and the even rows of the unaliased vector, u, in Eqn. (3) have been eliminated. Thus, when solving for a real-valued solution, the above system of equations includes 2n equations for N unknowns, as opposed to the 2n equations for 2N unknowns in Eqn. (3). As long as the number of receiver channels, n, is greater than or equal to twice the number of slice locations in each group of slice locations, that is, 2N, solutions to the real-valued parameterization exist. Through the assumption of real-valued unaliased images, and with the inclusion of the reference image phase in the encoding matrix, this parameterization allows higher accelerations than previously capable for parallel imaging. For example, accelerations up to 2n for coil arrays having n coils is possible. 
     For parallel imaging, the ratio of the signal-to-noise ratios of the separately acquired slices and unaliased slices yields the product of the unaliasing geometry-factor, or g-factor, g, and the square root of the reduction, or acceleration, factor, R: 
     
       
         
           
             
               
                 
                   
                     g 
                     ⁢ 
                     
                       R 
                     
                   
                   = 
                   
                     
                       
                         SNR 
                         Ideal 
                       
                       
                         SNR 
                         Unaliased 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     With the described reconstruction method, the reduction factor is R=1 because the number of k-space lines is not reduced below the Nyquist criterion during acquisition from multiple slice locations. Thus, with the described reconstruction method, the ratio of SNRs of separately acquired to unaliased images is the g-factor: 
     
       
         
           
             
               
                 
                   g 
                   = 
                   
                     
                       
                         SNR 
                         Ideal 
                       
                       
                         SNR 
                         Unaliased 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The g-factor was initially described as a measure of coil covariance. With the addition of RF phase-tagging, it is expanded here to include the magnetization phase from RF excitation and magnetic field shimming. Furthermore, the g-factor can be reduced by increasing the overdetermined nature of the unaliasing problem by solving for only real-valued image values. 
     As described above, the reconstruction method may include the correction of the aliased images for phase drifts resulting from drifts in B 0 , as well as for noise in the G x  and G y  gradients. Referring now to  FIG. 8 , a flowchart setting forth the steps of an exemplary method for calculating and correcting phase drifts in the reconstructed aliased images is illustrated. Generally, the method includes creating a facsimile of an aliased, multi-coil image data by summing the reference images and comparing the result with each aliased image to correct for phase drifts. 
     Thus, the phase drift correction method begins by summing the reference images, as indicated at step  802 . Let the entries in an image time course be designated by:
 
 A   m ( k,l ) e   iφ     m     (k,l)   (8);
 
     where m counts images and k,l enumerates voxel locations x and y. Using this notation, the I, Q sum of the reference images over the n receiver channels for the N th  slice location is given by: 
     
       
         
           
             
               
                 
                   
                     
                       A 
                       0 
                     
                     ⁡ 
                     
                       ( 
                       
                         k 
                         , 
                         l 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       n 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           A 
                           
                             0 
                             , 
                             j 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             , 
                             l 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           ⅇ 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 ϕ 
                                 
                                   0 
                                   , 
                                   j 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   , 
                                   l 
                                 
                                 ) 
                               
                             
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Using the calculated reference image sum, A 0 , phase difference, Δφ m , between the reference image sum, A 0 , and the aliased image for the N th  slice location, A m , are calculated, as indicated at step  804 . This phase difference is represented as:
 
Δφ m ( k,l )=tan −1 ( A   0 ( k,l ) A   m ( k,l ) e   i(φ     m     (k,l)-φ     0     (k,l)) )  (10).
 
     As indicated at step  806 , the next step in the phase drift correction method is to fit polynomials to the calculated phase difference, Δφ m . For example, the following fit is made: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Φ 
                         m 
                       
                       ⁡ 
                       
                         ( 
                         
                           k 
                           , 
                           l 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         a 
                         0 
                       
                       + 
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             a 
                             
                               1 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               k 
                             
                           
                           ( 
                           
                             
                               k 
                               - 
                               
                                 R 
                                 2 
                               
                             
                             R 
                           
                           ) 
                         
                       
                       + 
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             a 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               l 
                             
                           
                           ( 
                           
                             
                               l 
                               - 
                               
                                 R 
                                 2 
                               
                             
                             R 
                           
                           ) 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where R is the resolution of the image; a 0  corresponds to phase drifts arising from, at least in part, the transfer of heat produced in the gradient coils; and a lk  and a 2l  correspond to phase drifts arising from noise in the gradient coils. The result of the fitting process is the calculation of a phase drift correction factor, Φ m , which is subtracted from the aliased images to correct for the phase drifts occurring therein, as indicated at step  808 . This subtraction takes the form of:
 
 I   m ( k,l )= A   m ( k,l ) e   i(φ     m     (k,l)-Φ     m     (k,l))   (12);
 
     where I m  is the m th  phase drift corrected, aliased image in a time course of images. 
     While the foregoing description focused primarily on application using a multi-channel receiver coil array, it will be appreciated by those skilled in the art that multiple slice acquisition can also be realized using a single receiver channel. For example, for two slices having a ninety degree phase difference between them, and assuming an ideal case in which each slice has a uniform phase profile and absolute phase aligned with the in-phase, I, acquisition channel, the first slice would be acquired in the I-channel and the second in the Q-channel. In such a case, twofold acceleration is attainable with a single RF coil. 
     The present invention has been described in terms of one or more preferred embodiments, and it should be appreciated that many equivalents, alternatives, variations, and modifications, aside from those expressly stated, are possible and within the scope of the invention.