Patent Publication Number: US-2023152406-A1

Title: Method and Magnetic Resonance Apparatus for Diffusion Image Acquisition with Motion Offsetting and Navigation-Dependent Segmentation

Description:
BACKGROUND OF THE INVENTION 
     The field of the invention is nuclear magnetic resonance imaging (MRI) methods and systems. More particularly, the invention relates to MR diffusion weighted imaging (DWI). Any nucleus which possesses a magnetic moment attempts to align itself with the direction of the magnetic field in which it is located. In doing so, however, the nucleus precesses around this direction at a characteristic angular frequency (Larmor frequency) which is dependent on the strength of the magnetic field and on the properties of the specific nuclear species (the gyromagnetic constant gamma of the nucleus). Nuclei which exhibit this phenomena are referred to herein as “spins”. 
     When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B 0 ), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. A net longitudinal magnetization M 0  arises in the direction of the polarizing field, but the randomly oriented magnetic components in the perpendicular, or transverse, plane (x-y plane) cancel one another. If, however, the substance, or tissue, is subjected to a magnetic field (excitation field B 1 ) which is in the x-y plane and which is near the Larmor frequency, the net longitudinal magnetization, M 0 , may be rotated, or “tipped” into the x-y plane to produce a net transverse magnetic moment M xy , which is rotating, or spinning, in the x-y plane at the Larmor frequency. The practical value of this phenomenon resides in the signal which is emitted by the excited spins after the excitation signal B 1  is terminated. There are a wide variety of measurement sequences in which this nuclear magnetic resonance (NMR) phenomenon is exploited. 
     When utilizing NMR to produce images, a technique is employed to obtain NMR signals from specific locations in the subject. Typically, the region which is to be imaged (region of interest) is scanned by a sequence of NMR measurement cycles which vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct an “MR” image using one of many well-known reconstruction techniques. To perform such a scan, it is, of course, necessary to elicit NMR signals from specific locations in the subject. This is accomplished by employing magnetic fields (G x , G y , and G z ) which have the same direction as the polarizing field B 0  but which have a gradient along the respective x, y and z axes. By controlling the strength of these gradients during each NMR cycle, the spatial distribution of spin excitation can be controlled and the location of the resulting NMR signals can be identified. MR imaging is widely employed to image samples and a number of anatomical and physiological features in humans and animals. Moreover, diffusion-weighted imaging (DWI) is a powerful MRI technique for probing microscopic tissue structure. 
     SUMMARY OF THE PRIOR ART 
     With regard to diffusion and its measurement using magnetic resonance, it will be recognized that in a pure liquid such as water at room temperature, the individual water molecules are in constant motion due to the phenomenon of thermal agitation. This phenomenon is commonly referred to as “Brownian motion”. The so-called “diffusion coefficient” (herein sometimes referred to as “D”) is a measure of this molecular motion, and it can be determined with magnetic resonance techniques. 
     More particularly, a magnetic field gradient can be used to “tag” atomic level spins in a sample according to their location in space at the time of the application of a first magnetic gradient to the sample. A second gradient, applied at a later time, then serves to probe how far, on average, the individual spins have moved between the time of the first gradient application and the time of the second gradient application. In the ideal case, these magnetic field gradients are applied in brief, strong bursts separated by a common well-defined time period. In practice in clinical magnetic resonance systems, however, the gradients are applied for a moderate duration of several milliseconds or several tens of milliseconds, and the leading edges of the respective bursts are separated by delays of similar, but slightly longer duration. 
     Referring to  FIG.  1   , diffusion weighting of the acquired NMR signal is provided by gradients on each side of a 180° radiofrequency (RF) refocusing pulse. The first and second diffusion gradient lobes are of equal polarity, amplitude, and size (area). Their relative amplitude values along respective axes can be changed to measure diffusion in different directions. The timing parameters δ and Δ refer to the duration of the diffusion gradient pulses and to the separation of their leading edges, respectively. Under these conditions, the diffusion encoding level, i.e., the so-called “b-factor”, is defined by the following relationship: 
         b=γ   2   G   2 δ 2 (Δ−δ/3)
 
     where γ is the gyromagnetic ratio (42.58 MHz/Tesla for protons) and G is the magnetic field gradient amplitude. The diffusion-encoding gradient waveforms are usually optimized for short duration within the constraints of desired diffusion encoding and apparatus-specific gradient amplitude and slew rate limitations. The short duration ensures shortest possible echo time with maximum attainable signal-to-noise ratio (SNR). 
     In an experiment with one gradient pulse placed prior to and the other following the 180° RF inversion pulse of a spin echo sequence (90° RF slice select-TE/2-180° RF inversion-TE/2-signal acquisition), the signal S of the spin-echo measured at echo time TE for isotropic diffusion in a simple diffusion environment like a liquid is given by a mono-exponential relationship: 
         S ( b )= S   0  exp(− bD ).
 
     In this relationship, S 0  depends upon machine constants, the spin-spin relaxation time T 2 , the spin-lattice relaxation time T 1  in any experiment that repeats measurements every repetition time period TR, and the spin density ρ. Specifically, the diffusion coefficient D may be measured by making multiple measurements of S as a function of b, plotting the natural logarithm of S vs. b and then performing a linear regression whose slope provides the experimental measurement of D. Alternatively and preferably, a non-linear least-square regression analysis can be used to directly infer the fitting exponential function without performing the logarithm operation. The value of b is most conveniently varied by keeping the gradient timings fixed and incrementing the amplitude G of the magnetic field gradient. 
     It was quickly realized that in certain organs like the brain, preferred directions of water diffusion exist. More particularly, diffusion along one direction, as selected by the direction of the magnetic field gradient vector could be different than the diffusion along another direction. In the brain, this lack of isotropy of the diffusion coefficient (the so-called “diffusion anisotropy”) was, and is, attributed to the presence of nerve fiber tracts along which water is more free to move than it is in directions perpendicular to these tracts. Indeed, in the light of the phenomenon of restricted or anisotropic diffusion, it generally is agreed in the art that at least three orthogonal directions of the diffusion sensitization gradient (which are independent of the preferred directional diffusion) should be sampled to generate trace images, i.e., maps of a rotationally invariant measure of diffusion. Further, a minimum of six directions must be sampled for each voxel, to determine the preferred direction of diffusion with the diffusion tensor formalism. More advanced formalisms have been developed for use with acquisition protocols that sample much more than six directions. This approach can be useful to detect the presence and orientation of crossing fibers. 
     A DWI pulse sequence suitable for single-shot diffusion imaging is shown in  FIG.  2   . It includes the generation of a spatially and spectrally selective 90° RF excitation pulse  8  which is produced in the presence of a multi-polar pulse group  6  to excite spins in a 2D slice. A 180° RF refocusing pulse  21  is produced in the presence of a slice select gradient pulse  22  to refocus the transverse magnetization. The refocusing pulse is preceded by dephasing gradient pulses  16 ,  18 , and  20  along each of the three gradient axes. Immediately after the refocusing pulse follow rephasing gradient pulses  24 ,  26 , and  28  along each of the three gradient axes. These dephasing and rephasing pulses are required if the MR scan includes the acquisition of images without or with very low diffusion weighting. Diffusion weighting of the NMR signal along each of the respective axes is provided by gradients  10 ,  12  and  14  immediately after the 90° RF excitation pulse and by gradients  30 ,  32  and  34  immediately after the rephasing pulses  24 ,  26 , and  28 . After the completion of the diffusion encoding, gradient pulse  44  along the read direction and gradient pulse  46  along phase encoding direction dephase the signal so that under the influence of read gradient pulses  48  and phase encode pulses  50  all echo signals  52  to reconstruct the 2D image are collected in a single shot. After the echoes have been received, optional crusher gradient signals  54 ,  56 , and  58  can be applied respectively. 
     There are a large number of clinically and scientifically important applications for DWI that relate to tissue water diffusion. These include early detection and characterization of cytotoxic edema caused by cerebral infarction, improved tumor characterization through detection of restricted diffusion within a cellular tumor, and cerebral “tractography” for fiber angle mapping of the cerebral white matter, as well as many others. Within the abdomen, low b-value DWI is commonly used for liver imaging, to cancel the signal from flowing blood in order to improve the conspicuity of liver lesions such as metastases or primary liver tumors. 
     Diffusion weighted imaging is exquisitely sensitive to motion. Large phase shifts from small involuntary patient bulk motion result during the application of diffusion sensitizing gradients with high amplitude and long duration. The movement of a rigid body can be described completely by the provision of the translation vector and the rotation vector. A separation of the phase shifts related to each respective motion vector is helpful to better understand their disturbing effect on the reconstructed image. Object translation introduces a uniform phase shift according to 
       φ( x,y,z )=γ∫ {right arrow over (G)} ( t )· {right arrow over (r)} ( t ) dt  
 
     where {right arrow over (G)}(t) describes the time course of the diffusion gradient (with reversed sign for times prior to the RF refocusing pulse) and {right arrow over (r)} (t) the time dependent translation vector. Accordingly, given the mono-polar diffusion gradient configuration shown in  FIG.  1   , the phase shift φ introduced by an object translation with constant velocity v that shares the same direction as applied magnetic field gradient equals: 
       φ= vγGδΔ 
 
     With typical gradient configurations employed in diffusion imaging experiments, velocities as small as 1 mm/s and below are sufficient to induce 180° phase shifts. Obviously, higher order motion terms, such as acceleration, jerk, etc., also contribute to the observed phase shifts. 
     Object rotation introduces a linear phase shift gradient orthogonal to the rotation axis and the gradient encoding direction. The phase shift is given by 
       φ( x,y,z )=γ· {right arrow over (r)}   0   ∫{right arrow over (G)} ( t )×{right arrow over (θ)}( t ) dt  
 
     where {right arrow over (r)} 0  describes the position with reference to the center of rotation and {right arrow over (θ)} (t) the time dependent rotation vector. 
     Tissue deformation, caused by cardio-vascular pulsations, respiration, or muscle contraction is another source of phase shifts. These phase shifts occur locally and can to some extent be mitigated by timing the acquisition with electrocardiogram (ECG) or respiratory gating. 
     Many MRI pulse sequences rely on multiple excitations and signal acquisitions in order to form a complete k-space matrix prior to Fourier transformation. It should be noted that without diffusion weighting, phase shifts and associated artifacts that result from patient movement during such multi-shot sequences are typically not significant. With diffusion imaging, however, the shot-to-shot variations of motion-related phase shifts severely interfere with spatial encoding and lead to pronounced ghosting and blurring artifacts. The prior art has investigated several approaches of multi-shot diffusion imaging that rely on mitigation and correction of shot-to-shot phase variations. 
     The earliest approach used a second refocusing RF pulse to generate a navigator echo along the readout direction. This navigator echo was used to determine and correct residual zeroth order phase shifts, i.e., only phase shifts related to translation. This was followed by an approach that extended the use of this 1D navigator by also correcting first order phase shifts, i.e., phase shifts related to rotation. Despite such correction, for axial brain scans the reduction of ghosting artifacts was basically only effective with diffusion encoding along the phase encode direction. Subsequent research showed the benefit of combining navigation along the readout direction with velocity compensated diffusion encoding gradients. Although this approach is effective at eliminating velocity related phase shifts, the low performance of the magnetic field gradients available at the time resulted in rather long duration gradient pulses with pronounced sensitivity for higher order motion terms. Another approach shown in  FIG.  3    attained appreciably improved results without velocity compensated gradients by using orthogonal navigator trajectories  36  and  40  along the phase encode and readout direction, respectively. The resulting navigator signals  38  and  42  were used to perform a zeroth order phase correction and a first order phase correction along the phase encode and readout direction, respectively. Slice selection occurred with a basic slice selective 90° RF pulse  9  in the presence of a slice select gradient pulse  7 . A segmented rectilinear k-space trajectory for accelerated readout was used instead of the single line k-space trajectory that was employed in the earlier approaches. Moreover, the k-space trajectory followed the navigator without interposed refocusing RF pulse. All of these early attempts at improving multi-shot DWI relied on ECG gating to attain a minimum level of acceptable image quality. 
     In the subsequent development it was shown how such 1D navigator correction can be incorporated into the hardware of an MR system. A major breakthrough for navigated multi-shot diffusion imaging was the introduction of 2D navigator trajectories that are collected after a refocusing RF pulse. This permitted not only correction the correction of zeroth and first order phase changes, but also of local phase changes caused by tissue deformation. This made multi-shot DWI without ECG gating practical. The most recent advance called multiplexed sensitivity encoding, relies on self-navigation using the echo that is collected for imaging and parallel coil acceleration. Attempts have been made to expand spatial encoding to a 3D volume for improved SNR, generally by using a thin slab acquisition, such that phase variations across the slab are small and can be ignored. 
     From the onset of DWI pulse sequence development for practical use in human subjects, there has been the quest to entirely avoid multi-shot sampling. In this way, ghosting and blurring artifacts that result from shot-to-shot phase variations can be completely eliminated. One such method, which poses only modest requirements for gradient hardware, is line scan diffusion imaging. This method sacrifices multi-shot 2D spatial encoding for single shot 1D read-outs along sequentially excited parallel columns. Early on, however, it was recognized that a read-out trajectory covering the complete k-space matrix for an image in a single shot would be the preferred solution for inherently robust and rapid diffusion imaging. With the widespread availability of magnetic field gradients that provide the high slew rates required for rapid k-space traversal, single-shot diffusion imaging with an echo-planar imaging (EPI) readout as presented in  FIG.  2    has found broad clinical application. However, EPI suffers from inferior spatial resolution, global and local distortions caused by eddy currents and local susceptibility variations, and blurring caused by the T 2 * signal decay during the long readout. To address all these deficiencies, but also to perform a 3D acquisition, a segmented, i.e., multi-shot approach is required. 
     It should be recognized that artifacts caused by diffusion sensitization also occur with single-shot EPI diffusion sequences; the linear phase shift gradient that arises during rotation causes the signal echo to shift in k-space, which can lead to a complete signal loss. This happens more frequently with partial echo sampling, a technique that is used to attain a shorter echo time for improved SNR. Moreover, non-uniform tissue deformation can lead to localized signal loss. Particularly for abdominal and heart diffusion imaging this has been an obstacle which spurred further development to eliminate phase artifacts at the source, i.e., by using motion compensated diffusion sensitizing gradients. 
     The sensitivity of a gradient pulse to motion of order n is given by the moment integral according 
         {right arrow over (M)}   n   =∫{right arrow over (G)} ( t )· t   n   dt  
 
     The basic and most commonly used diffusion encoding gradient waveform as shown in  FIG.  1    relies on mono-polar gradient pulses of equal duration and amplitude on each side of the refocusing 180° RF pulse. After applying this gradient waveform, stationary spins experience no phase shift and therefore the zeroth order moment M 0  is zero. The first order moment M 1  and all higher order moments are non-zero. The simplest motion-compensated diffusion encoding gradient waveform is shown in  FIG.  4    and consists of bipolar pulses of equal duration and amplitude on each side of the refocusing 180° RF pulse. This arrangement only results in nulling of M 0  and the velocity associated moment M 1 . The MOCO gradient waveform shown in  FIG.  5    is the preferred setup for motion-compensated diffusion encoding, since it efficiently achieves nulling of M 0 , the velocity associated moment M 1 , and the acceleration associated moment M 2 . 
     More time-efficient diffusion encoding with M 0 =M 1 =M 2 =0 can be attained with optimized solutions where the gradient pulses on either side of the refocusing pulse are non-symmetrical and non-identical. Such gradient waveforms are preferable, provided the programming environment of the apparatus provides means to install such pulses. An optimization framework to develop such pulses has been presented. 
     The application of a gradient field leads to the generation of concomitant magnetic fields as described by the higher order terms of Maxwell&#39;s equations. Concomitant fields are not typically an issue in diffusion weighted imaging because the M 0  terms on each side of the refocusing pulse cancel out when diffusion encoding gradient waveforms are identical on either side of a refocusing pulse. However, with gradient waveforms that are not symmetrical or identical on either side of a refocusing pulse, the concomitant fields must be considered in order to attain M 0 =0. The M 1  or M 2  moment nulling of motion compensated waveforms applies only to the iso-center. At very high gradient amplitudes the concomitant gradient fields can introduce small, but significant M 1  and M 2  terms that grow with off-center distance. 
     Such motion-compensated diffusion encoding gradient waveforms have been successfully applied in single-shot sequences to obtain largely artifact-free diffusion-weighted images and accurate diffusion coefficient maps of the brain, liver and even moving heart. In particular, it was demonstrated that signal voids that result with conventional mono-polar gradient waveforms in areas of transitory tissue rotation or deformation are effectively eliminated with such motion-compensated gradient waveforms. Thus the purpose of motion-compensated diffusion encoding has been to reduce intra-voxel phase dispersion and related signal loss in areas of non-uniform motion. The reduction of shot-to-shot variations of motion induced phase changes is also substantial but not relevant, since these methods rely on single-shot imaging, where phase coherence between shots is not required. 
     It has been shown that motion-compensated diffusion encoding gradient waveforms can be integrated into preparation sequences of longitudinal magnetization. Images of the longitudinal magnetization can then be generated with conventional imaging sequences, including multi-shot 3D sequences. This approach is inherently robust and requires no phase correction because motion-related phase shifts introduced by the diffusion-encoding gradients are only present during the preparation step. Compared to the conventional diffusion preparation with direct readout of the transversal magnetization the number of RF pulses is doubled, i.e., the preparation sequence requires an initial 90° RF pulse, two 180° refocusing RF pulses, and a final 90° RF pulse to flip back the magnetization vector. This significantly increases the amount of power deposited by the RF field, which will limit the rapid repeated application of the preparation sequence. 
     SUMMARY OF THE INVENTION 
     The present invention exploits the significant reduction of motion-induced phase changes that can be attained with motion-compensated diffusion encoding waveforms for segmented multi-shot diffusion imaging with optional navigation-based phase correction along two or three spatial encoding directions. It has been shown that 1D navigation along the spatial encoding directions is useful to perform segmented diffusion imaging. Such 1D navigation correction is limited to phase changes caused by rigid body translation and rotation and does not result in optimal image quality. Only the correction of local phase changes due to non-uniform tissue deformation will result in optimal image quality. Non-uniform tissue deformation is not only caused by direct muscle contraction, but also by pulsatile expansion of blood vessels. Correction of the consequential spatially non-linear phase changes requires a 2D navigator for 2D encoded multi-shot diffusion imaging and a 3D navigator for 3D encoded multi-shot diffusion imaging. A 3D navigator with sufficient coverage that provides adequate spatial detail in phase information is inherently difficult to implement. The invention is based on the assumption that these local phase changes caused by tissue deformation can sufficiently be offset by motion-compensated diffusion encoding alone. This is especially the case if higher order motion compensated diffusion encoding gradients, such as velocity and acceleration-compensated diffusion encoding gradients, are applied. Any residual zeroth order and first order phase variations caused by rigid body motion can be corrected by simple navigators, such as 1D navigators along each of the spatial encoding directions. These short duration k-space trajectories for navigation are preferably performed immediately after the k-space trajectory for imaging without interposed refocusing pulse. 
     Indeed it can be argued that this concept is more fail-proof than a 2D-navigator, where rotational rigid body movement can lead to a shift of the echo peak outside the limited k-space sampled by the navigator with complete signal loss and consequential inability to perform navigation. With motion-compensated diffusion encoding, the resulting echo peak shift will be smaller and the 1D navigator can readily sample a longer segment of k-space. Since 1D navigation can be performed sequentially along respective encoding directions, without interposed refocusing pulses, there are, unlike the transition from 2D to 3D navigators, no technical difficulties extending the 1D navigation along two directions for 2D imaging to 1D navigation along three directions for 3D imaging. Importantly, particularly when considering a 3D acquisition, the acquisition can be optimized for maximum SNR by using rapid excitation with a flip angle that is larger than 90°. A high-resolution 3D acquisition can advantageously be combined with motion monitoring and retrospective reconstruction-based correction of shot-to-shot dislocations that occur during the scan. The invention is fully compatible with acceleration methods, like parallel coil imaging and compressed sensing. This can be particularly advantageous when performing phase encoding along a third direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a time diagram of a basic diffusion-weighting preparatory experiment without motion compensation; 
         FIG.  2    shows in one diagram over a common time axis the sequence of magnetic field pulses, radiofrequency pulses, and acquired radiofrequency signals for image formation based on a prior art pulse sequence design for a single-shot 2D echo-planar readout using a basic diffusion-weighting preparation without motion compensation as shown in  FIG.  1   ; 
         FIG.  3    shows in one diagram over a common time axis the sequence of magnetic field pulses, radiofrequency pulses, and acquired radiofrequency signals for navigator correction and image formation based on a prior art pulse sequence design for segmented 2D echo-planar readout using a basic diffusion-weighting preparation without motion compensation as shown in  FIG.  1   ; 
         FIG.  4    is a time diagram of a diffusion-weighting preparatory experiment with first order motion compensation; 
         FIG.  5    is a time diagram of a diffusion-weighting preparatory experiment with first and second order motion compensation; 
         FIG.  6    is a high-level block diagram of an illustrative embodiment of a magnetic resonance imaging system suitable for use in the method of present invention; 
         FIG.  7    shows in one diagram over a common time axis the sequence of magnetic field pulses, radiofrequency pulses, and acquired radiofrequency signals for image formation and navigator correction based on a pulse sequence design for segmented 2D or 3D echo-planar signal readout using a diffusion-weighting preparation with first and second order motion compensation as shown in  FIG.  5   . 
     
    
    
     It may be mentioned that the illustrated time diagrams are not drawn to scale, i.e. the individual time sections and the amplitudes are not drawn in accordance with their actual mutual size ratios. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The invention relies on diffusion encoding gradient pulses with motion compensation. Such gradient pulses are inherently less efficient in achieving diffusion encoding, which for given maximum gradient amplitude implies longer encoding time and higher sensitivity to uncompensated higher order motion terms. To decrease the sensitivity to uncompensated higher order motion terms it is beneficial employ higher gradient amplitudes. Thus, the invention is particularly applicable on systems with ultra-high gradient performance, where sequences with motion-compensated diffusion encoding can be realized at comparably short echo times. A b-factor in the order of 1000 s/mm 2  is used for the majority of clinical brain diffusion imaging protocols and on a state-of-the-art system, timings of δ=20 ms and Δ=30 ms can typically be realized with mono-polar gradients. The table below compares gradient amplitude and resulting motion sensitivities of this setup with those for motion-compensated diffusion encoding with equal gradient duration and separation. 
     
       
         
           
               
               
               
               
             
               
                   
               
               
                 b = 1000 s/mm 2 , 
                   
                   
                 MOCO (δ 1  = 7 ms, 
               
               
                 δ = 20 ms, Δ = 30 ms 
                 Mono-polar 
                 Bipolar 
                 δ 2  = 13 ms) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 G (mT/m) 
                 38.7 
                 102.4 
                 120.3 
               
               
                 M1 motion sensitivity* 
                 0.5 
                 None 
                 None 
               
               
                 (mm/s/180°) 
               
               
                 M2 motion sensitivity* 
                 10 
                 19 
                 None 
               
               
                 (mm/s 2 /180°) 
               
               
                 M3 motion sensitivity* 
                 230 
                 255 
                 1026 
               
               
                 (mm/s 3 /180°) 
               
               
                   
               
               
                 *Smaller numbers imply higher motion sensitivity 
               
            
           
         
       
     
     It is known that with partial echo sampling in cooperative normal subjects, involuntary head rotation in the presence of mono-polar diffusion encoding gradient waveforms can result in echo peak shifts that lead to complete signal loss. This implies velocity gradients that introduce phase gradients that exceed many-fold 180° across the field of view. From this observation it can be estimated that involuntary head motion involves velocities up to and beyond 10 mm/s. With this velocity number and magnetic resonance imaging measurements of blood flow acceleration in humans it is estimated that acceleration develops up to and beyond 100 mm/s 2 . From other physical measurements of human motion it is estimated that such velocity and acceleration generates jerk of up to and beyond 1000 mm/s 3 . Accordingly and referring to the motion sensitivity numbers of the table above, it is expected that substantial phase shifts can result, even with the offsetting of first and second order motion-related phase shifts. If not corrected for, these phase shifts would produce significant artifacts in multi-shot diffusion-weighted imaging. 
     The proposed innovation can be used with bipolar or MOCO gradient waveforms for diffusion encoding. The use of MOCO gradient waveforms with M 0 =M 1 =M 2 =0 is preferred, but for equal b-factor and equal maximum gradient amplitude it comes at a slight expense in time efficiency. The more time-efficient, numerically optimized diffusion encoding solutions with M 0 =M 1 =M 2 =0, where the gradient pulses on either side of the refocusing pulse are non-symmetrical and non-identical, should be used, however, if the programming environment of the apparatus provides means to install and execute such pulses. 
     The proposed pulse sequence invention offers several advantages over existing solutions for improved diffusion magnetic resonance imaging. The simplified navigation with 1D navigators is fast and readily incorporated with the standard multi-shot echo-planar readout without the need for generation of a separate echo by means of a refocusing pulse. Unlike methods that rely on self-navigated multiplexed sensitivity encoding, there is no inherent limitation of the segmentation factor, which warrants better distortion suppression. A segmented volume, i.e., segmented 3D acquisition is possible with the simple addition of phase encoding gradients and a 1D navigator along the same direction. Such approach can advantageously be integrated with techniques for motion monitoring and correction of body location changes that occur during the scan. Unlike multi-slice based approaches for compensation of body location changes, the excitation location and the spatial encoding directions do not need to be updated in real-time, since the correction can be applied retrospectively to the 3D k-space data. 
     The pulse sequence invention is fully compatible with acceleration methods, like parallel coil imaging and compressed sensing. Particularly, with a second phase encoding direction that is sampled over multiple separate excitations it can be considered beneficial to achieve a shorter scan time with parallel coil and compressed sensing acceleration along the second phase encode direction. The repeated excitation for 3D sampling can be optimized for maximum SNR by using a large angle excitation with the flip angle set to the supplement angle of the tissue-specific Ernst-angle 
     
       
         
           
             
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     where TR equals the repetition time and T 1  the tissue-specific longitudinal relaxation time. For example, with a 250 ms TR excitation, using a 149° RF flip angle optimized for the 1600 ms T 1  of white matter at 3T, the relative SNR compared to infinite TR is 0.28, which constitutes a 100% improvement over the use of a 90° RF flip angle, for which relative SNR is only 0.14. Hence, the use of a standard 90° RF flip angle would require four averages to attain the same SNR. In brain applications, rapid repeat excitation can also be beneficial to significantly suppress the signal of cerebrospinal fluid, which is a nuisance signal in images generated at long repetition times with conventional multi-slice scans. It is important to note that the application of 3D diffusion imaging with longitudinal magnetization preparation sequences at short repetition times would not permit RF flip angle optimization and would result in undesirably high RF power deposition. 
     The use of gradient coils capable of generating very high magnetic field gradients can increase eddy currents and associated geometric distortions. An inherent advantage of multi-polar diffusion encoding waveforms for motion-compensation is the reduction of eddy currents. Also, the use of a segmented multi-shot scan will reduce resulting distortions in proportion with the segmentation factor. 
     An apparatus and pulse sequence suitable for the practice of this invention, as will be seen from  FIGS.  6  and  7   , includes a magnetic resonance imaging system  60 , generally having a magnet assembly, interface circuitry, and a computer  90 . The magnet assembly includes a very strong magnet  63  that creates a homogeneous magnetic field within and around a sample (e.g. an inert sample or patient). X, Y, and Z magnetic field gradient coils  64 ,  66 , and  68  also form a part of the assembly and are positioned proximate or surrounding the sample  70 . The assembly further comprises one or more RF coils  72 , which are positioned near or around the sample. 
     The interface circuitry  62  includes a gradient waveform generator  74  with a control input connected to the computer and signal outputs connected to the gradient coils  64 ,  66 , and  68 , as well as an RF signal generator  76  with a control input connected to the computer and an output connected to an input of an RF power amplifier  78 . The RF power amplifier has an output connected to an input of an RF switch  80 . The RF switch has an output connected to the RF coil  72  and an output connected to the input of an RF detector  82 . 
     The computer  90  includes computing hardware  92  and storage  94 . The computing hardware can comprise special purpose hard-wired computing circuitry dedicated to magnetic resonance acquisition and image reconstruction, as well as a special programmed general purpose computer for display and user interaction. The storage  94  can include various types of storage, such as disk storage and random access memory. The storage can be used to store data and programs, including programs used to interact with the system&#39;s interface circuitry  62 . The computer has a video output for providing video signals to a display  96 , as well as control outputs connected respectively to control inputs of the gradient waveform generator  74  and the RF signal generator  76 . The computer also has acquisition input operatively connected to an output of the RF detector  82 . 
     In operation, referring to  FIGS.  6  and  7   , the imaging system  60  builds images under the control of the computer  90  according to a multi-shot echo-planar imaging (EPI) sequence. At the beginning of an acquisition sequence for an image, the computer  90  sends a signal to the RF signal generator  76 , which responds by generating a spatially and spectrally selective pulse  108  with a flip angle of 90° or greater. This pulse is amplified by the RF power amplifier  78  and provided to the RF coil  72  via the RF switch  80 . As this pulse is being provided, the computer instructs the gradient waveform generator  74  to drive the Z coil  68  with a multi-polar pulse group  6 . 
     Next, the gradient waveform generator  74  provides a set of gradient pulse groups  110 ,  112 , and  114  for the first part of motion-compensated diffusion encoding respectively to the X, Y, and Z gradient coils  64 ,  66 , and  68 . After the falling edge of the diffusion gradient signals and a wait time, which is inserted if needed to center the echo refocusing for the readout process, the gradient waveform generator  74  provides a set of dephasing gradient pulses  16 ,  18 , and  20  respectively to the X, Y, and Z gradient coils  64 ,  66 , and  68 . Subsequently, a spatially selective 180° refocusing pulse  21  is provided to the RF coil  72 , in much the same way that the spatial-spectral selective pulse was. At the same time, the gradient waveform generator provides a rectangular pulse  22  on the Z gradient coil. Then, the gradient waveform generator  74  provides a set of rephasing gradient pulses  24 ,  26 , and  28  of same amplitude and duration as the dephasing gradient pulses respectively to the X, Y, and Z gradient coils  64 ,  66 , and  68 . Then, the waveform generator provides a set of gradient signals  120 ,  122 , and  124  for the second part of motion-compensated diffusion encoding respectively to the X, Y, and Z gradient coils  64 ,  66  and  68 . Both parts of the motion encoding gradient signals to the X, Y, and Z gradient coils are scaled to attain a desired diffusion weighting and diffusion encoding direction. 
     Once the gradient signals for motion-compensated diffusion encoding are turned off, the gradient waveform generator provides a set of dephasing gradient pulses  130 ,  46 , and  132  respectively to the X, Y, and Z gradient coils  64 ,  66  and  68 . With each new shot, the amplitude of the dephasing gradient pulse  46  is incremented or decremented according to the multi-shot sampling pattern. The dephasing gradient pulse  132  is only used in the case of 3D encoding and is varied according to the sampling pattern along the second phase encoding direction. Then the gradient waveform generator provides gradient pulse group  48  on the X coil  64  for spatial encoding along the frequency encoding direction and at the same time gradient pulse group  50  on the Y coil  66  for spatial encoding along the first phase encoding direction. As a result of this excitation sequence, a train of echoes  52  is received from the slice or volume that was excited by the spatial-spectral selective RF pulse and the 180° RF pulse. The RF coil receives these echoes and provides them via the RF switch  80  to the RF detector, from where the digitized signals are forwarded to the data storage  94 . After completion of the last readout gradient pulse of gradient pulse group  48 , the gradient waveform generator provides a set of rephasing gradient pulses  136  and  138  respectively to the Y, and Z gradient coils  66  and  68 . The amplitude and duration of rephasing gradient pulse  136  is set so that the gradient time integral from the beginning of gradient pulse  46  to the end of gradient pulse  136  equals zero. Meanwhile, the rephasing gradient pulse  138  is of same magnitude and duration, but of opposite polarity as the dephasing gradient pulse  132 . The rephasing gradient pulse  138  is only used in the case of 3D encoding. 
     After completion of the rephasing gradient pulses, the gradient waveform generator provides sequentially gradient pulse groups  140 ,  144 , and  148  respectively to the X, Y, and Z gradient coils  64 ,  66  and  68 . Each of these gradient pulse groups is characterized by a net zero time integral. The rephasing pulse that is required after completion of gradient pulse group  48  is preferably overlapped with the first gradient pulse of gradient pulse group  140 . The sequential application of gradient pulse groups  140 ,  144 , and  148  gives rise to sequential echoes  141 ,  145 , and  149 , respectively. The RF coil receives these 1D encoded echoes and provides them via the RF switch  80  to the RF detector, from where the digitized signals are forwarded to the data storage  94 . After the echoes have been received, optional crusher gradient signals  54 ,  56 , and  58  can be applied respectively to the X, Y, and Z gradient coils  64 ,  66  and  68 . The computer  90  processes the signal data of the image echoes  52 , and navigator echoes  141 ,  145 ,  149 . Image reconstruction can be completed after acquiring all k-space data of a diffusion encoding and then images for this diffusion encoding can be displayed on the display  96 . 
     The new pulse sequence design as presented in  FIG.  7    places the 1D navigator echoes towards the end of the sequence before applying the crusher gradient pulses  54 ,  56 , and  58 . This placement is preferable, since the prior art placement before the readout as presented in  FIG.  3    delays the train of echoes  52  and requires a commensurate addition of wait time before the refocusing 180° RF pulse. This results in a longer echo time and consequently lower SNR. 
     The acquisition proceeds to obtain data for other segments and, if the option is used, for other phase encoding steps along the third encoding direction. The exemplary k-space trajectory shown in  FIG.  7    is advantageous for the reconstruction process, but other k-space trajectories for imaging and navigation, including non-rectilinear k-space trajectories, and k-space trajectories suitable for self-navigation may be considered. This includes also sampling trajectories that span over a plurality of spin-echoes within one shot. 
     Scanning can be performed sequentially for a plurality of diffusion encoding gradient waveforms, a plurality of diffusion encoding gradient amplitudes and a plurality of diffusion encoding directions. These acquisition steps can be performed in arbitrary order, but typically the diffusion gradient amplitude or diffusion encoding direction is changed after completing the acquisition of all k-space data of a slice or volume. However, in order to distribute the load on the gradient power amplifier over time, it may be of interest to complete the acquisition of all amplitudes and directions for one segment and, moreover, to alternate between low and high amplitudes, before proceeding to the acquisition of the next segment. 
     After the completion of sampling all k-space data for one diffusion encoding setting, reconstruction of image data pertaining to this part of the acquisition can be initiated. The processing of a segmented acquisition with phase correction is well described in the MRI literature. The following describes one, but not unique way to perform such processing. 
     In a first step, all navigator signals are analyzed to determine the necessary zeroth and first order phase correction. The first order phase shift along each respective encoding direction is obtained by measuring the echo peak position with respect to the center of each gradient pulse group used to encode the 1D navigator echo. The echo peak position can be estimated by fitting a symmetric function with a single positive peak, such as a parabola or the modulus of a shifted Sinc function to the modulus of the 1D echo signal. The modulus or magnitude M of the received 1D echo signal may be determined at any sampled point by the square root of the sum of the squares of the I and Q components of the complex signal: 
         M =√{square root over ( I   2   +Q   2 )}
 
     After fitting and finding the shift of the peak position, the 1D navigator signal is Fourier transformed into image space and the phase is determined for each position along the profile as follows: 
       φ=arctan( Q/I )
 
     The phase profile in image space is linearly adjusted so that according to the Fourier Shift Theorem, which relates a linear phase in image space to a shift in k-space, the echo peak determined through fitting is shifted to the center of the sampling window. Any residual shift is estimated by fitting a line to the so corrected phase profile via a linear regression weighted by the magnitude of the points along the image space profile. This may require the application of a phase unwrapping algorithm prior to fitting the line. The slope of the fitted line is used to adjust the estimated shift of the echo peak. The first order phase correction term ϕ 1  for motion induced phase errors can then be determined according the Fourier Shift Theorem from this adjusted echo peak shift value. The zeroth order phase correction term ϕ 0  for motion induced phase errors equals the constant term of the line fit applied to the phase profile in image space. The first order phase correction term is determined for each navigator of each shot. The zeroth order phase correction term should ideally be the same for all navigators within a shot, but differences may arise due to eddy currents. Thus it is advisable to use the zeroth order phase correction term of one specific navigator only. 
     The estimation of motion related phase errors for each shot is followed by the actual image reconstruction. The echo signals sampled along the frequency encoding direction x can be directly Fourier transformed. Subsequently the phase φ(x,j) for each spatial position x and each shot j is computed. The zeroth and first order phase term that was obtained with the analysis of the navigator signal along the frequency encoding direction of respective shot j is used to obtain the corrected phase φ c (x,j) by simple subtraction: 
       φ c ( x,j )=φ( x,j )−(ϕ 0,x ( j )+ xϕ   1,x ( j ))
 
     The correction for linear phase shifts determined with the phase-encode navigator profiles is more complicated. According the Fourier Shift Theorem the slope φ 1,y (j) of the y-navigator phase profile predicts the error dk y  in the k y -space positions for all the echoes acquired in the corresponding shot. Analogously, if phase encoding along a second direction is performed, the slope ϕ 1,z (j) of the z-navigator phase profile predicts the error dk z  in the k z -space positions for all the echoes acquired in the corresponding shot. Because the shifts are fractions of a sample point and vary from shot to shot, the data are not actually on a regular grid in respective phase-encode direction, which precludes a discrete Fourier transform. One way to deal with this is to interpolate the k-space data to the Cartesian grid by convolution with a weighted kernel function prior to performing the discrete Fourier transform. Another approach that is preferable, provided sufficient computing resources are available, is the inversion of the experimental image gradient encoding matrix that results from the incorporation of the adjusted k-space positions. This is possible since the measured k-space values for a single column of k y -space signal data, S(k y ,x), together with the adjusted encoding matrix, E(k y +dk y ,y), can be used to compute the ideal diffusion-weighted proton density distribution through 
         ( y   1    . . . y   n   ,x )= S ( k   y1    . . . k   yn   ,x ) E   −1 ( k   y   +dk   y   ,y ) 
     with the encoding matrix being given by 
     
       
         
           
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     This operation can be performed analogously and independently for all k z -space signal data. 
     In conclusion, embodiments of the invention can provide a new and highly practical technique to allow high-resolution DWI with high spatial fidelity and SNR, as well as minimal blurring. In contrast to segmentation methods that rely on 2D navigation, the present method is compatible with simplified 1D navigation, which does not require formation of a separate spin echo. Unlike multiplexed sensitivity-encoding, the segmentation factor is not limited. The method can be used for segmented acquisition in 3D, which can yield substantially better SNR and which is compatible with techniques for correction of body location changes during the scan. As such, it should find broad applications in clinical applications and neuroscience investigations of detailed brain microstructures, where high spatial resolution is required. 
     One skilled in the art will readily appreciate that the present invention is well adapted to carry out the objects and obtain the ends and advantages mentioned, as well as those inherent therein. The present disclosures described herein are presently representative of preferred embodiments, are exemplary, and are not intended as limitations on the scope of the invention. Changes therein and other uses will occur to those skilled in the art which are encompassed within the spirit of the invention as defined by the scope of the claims.