Abstract:
A method of reducing artifacts produced during Fast Spin Echo measurements made using permanent magnet NMR instruments. The method includes applying encoding gradients that do not switch signs throughout the experiment. Prior to the 90° RF pulse, a strong RM gradient pulse is given to produce a dominant and constant residual magnetization. The encoding is done through the combination of encoding gradients with the aid of the 180° RF pulses of the echo train. A first constant encoding gradient is given before the first 180 pulse. Then two variable encoding gradients are provided after each 180 pulse; one applied prior to and one applied subsequent to each acquisition in the echo train.

Description:
FIELD OF THE INVENTION 
       [0001]    This invention relates in general to methods for reducing artifacts in images produced by MRI. It particularly relates to pulse sequences for fast spin echo NMR in permanent magnet MRI systems. 
       BACKGROUND OF THE INVENTION 
       [0002]    Fast Spin Echo (FSE) is a well-known NMR technique. A main source of artifacts in FSE is inaccurate phase gradient areas during the echo train. This inaccuracy is generally due to at least one of two factors. One of them is imperfections in the gradient power amplifier. In particular, the gradient power amplifier can produce inaccurate gradient shapes while switching the sign of the current. A second factor, unique to permanent magnet NMR systems, is residual magnetization (RM). The magnetic field gradients produced during the scan can induce a mirror field on the magnet pole pieces that remains for a significant amount of time (at least several minutes) after the gradients are turned off. This RM is approximately linear in space and adapts the field lines of the field gradient. Its actual value is a function of the gradient strength and of the inherent properties of the magnet. While the specific value of this gradient-dependent RM will vary from magnet to magnet, it is typically on the order of 0.1% of the gradient strength, and need only be measured once for any given magnet. 
         [0003]    Reference is now made to  FIG. 1 , which illustrates a conventional FSE pulse sequence known in the art. The phase encoding along the phase axis G pe  is shown with a pattern of a single echo train of length ETL. For each cycle in the echo train, two gradients are shown, an encoding gradient k i   pe , and a reverse gradient that undoes the phase, −k i   pe ; k=∫ 0   T  G(t)dt, where G is the gradient strength (including the proton&#39;s gyromagnetic ratio) and T is the duration of the gradient pulse. If G is in units of Hz mm −1 , k will be given in units of mm −1 . In order for FSE to work properly, two conditions should be met: 
         [0004]    (1) At each echo point  420  (see  FIG. 2 ), the phase should vary as φ 420   pe =k i   pe ·r pe . 
         [0005]    (2) Between two 180° pulses, the phase φ 420   pe  should be constant. Ideally, φ 420   pe =0, i.e. 
         [0000]      φ 420   pe =( k′   i   pe   −k   i   pe )· r   pe =0.
 
         [0006]    In an NMR/MRI instrument comprising a permanent magnet with pole pieces, in general, neither of these conditions will be fulfilled. After each encoding gradient k i   pe , some RM gradient  100  is produced. Moreover, due to imperfections in the gradient amplifier, the refocusing gradient will not necessarily produce the desired gradient, i.e. one having an identical shape as the encoding gradient but with opposite sign. 
         [0007]    Thus, an FSE pulse sequence that overcomes the aforementioned problems with residual magnetization and that can compensate for imperfections in the gradient amplifier remains a long-felt, yet unmet need. 
       SUMMARY OF THE INVENTION 
       [0008]    It is an object of this invention to provide an FSE pulse sequence that meets this need. The method disclosed herein comprises applying an RM gradient pulse that is given prior to the 90° RF excitation pulse followed by a series of encoding gradient pulses. The first is constant and given before the first 180° pulse, and the others are variable and applied in pairs following each 180° RF pulse, one prior to and one subsequent to each acquisition in the echo train. Relative to the amplitude of the initial RM gradient pulse, the amplitudes of the encoding gradient pulses are all of the same sign but of smaller magnitude. That is, there are no inverted or reversed gradient pulses in the pulse sequence, thereby keeping the RM constant throughout the measurement, where it acts as a small addition to the static field inhomogeneity for which, in preferred embodiments of the invention, activation of linear shim gradients is used to compensate. In addition, retention of the same sign of the gradient throughout the measurement sequence eliminates problems arising from non-idealities in the gradient amplifier. 
         [0009]    It is therefore an object of this invention to disclose a method for reducing artifacts produced during a Fast Spin Echo (FSE) pulse sequence in a nuclear magnetic resonance instrument comprising a gradient power amplifier and a permanent magnet comprising a plurality of pole pieces, said permanent magnet characterized by a gradient-dependent residual magnetization B g , said FSE pulse sequence comprising, in order: a 90° RF pulse  100  characterized by a duration T 90 ; an echo train comprising a first 180° RF pulse  110 , a first echo  130 , and X−1 additional 180° RF pulses  110   a  and X−1 additional echoes  130   a , X≧1; and a navigator RF pulse  120 ; wherein said method comprises: (a) applying a residual magnetization (RM) pulse  300  prior to said 90° RF pulse, said RM pulse having amplitude G RM   pe  along a phase axis and either positive or negative sign relative to an origin along said phase axis; (b) applying a shim gradient pulse  200  of amplitude at least sufficient to cancel any net effect on said gradient-dependent residual magnetization B g  produced by said RM pulse  300 ; (c) applying, prior to said first 180° RF pulse, a single preparation gradient pulse  310  characterized by amplitude G shift   pe ≦G RM   pe , whereby for a gradient pulse duration T, k shift   pe =G shift   pe T along said phase axis; (d) applying, for each 180° pulse i (1≦i≦X) in said echo train: (i) a first encoding gradient pulse  320  applied subsequent to 180° pulse i and prior to echo i, said first encoding gradient pulse characterized by amplitude G ai   pe  such that k ai   pe =G ai   pe T along said phase axis; and (ii) a second encoding gradient pulse  330  applied subsequent to said echo i and prior to 180° pulse i+1, said second encoding gradient pulse characterized by amplitude G bi   pe  such that k bi   pe =G bi   pe T along said phase axis, said second encoding gradient G bi   pe  having an amplitude of identical sign to the sign of the amplitude of said RM pulse; and, (e) applying, subsequent to said navigator pulse, a final gradient pulse  340 , said final gradient pulse having an amplitude of sign identical to the sign of said RM pulse. 
         [0010]    It is a further object of this invention to disclose such a method, wherein said preparation gradient pulse  310  is characterized by k shift   pe ≧k R   pe , where 
         [0000]    
       
         
           
             
               
                 k 
                 R 
                 pe 
               
               = 
               
                 
                   
                     k 
                     max 
                     pe 
                   
                   2 
                 
                 + 
                 α 
               
             
             , 
             
               
                 k 
                 max 
                 pe 
               
               = 
               
                 1 
                 
                   dr 
                   pe 
                 
               
             
             , 
           
         
       
     
         [0000]    dr pe  is a spatial resolution along the phase axis, and α is an asymmetric k shift, α≧0. 
         [0011]    It is a further object of this invention to disclose such a method as defined in any of the above, wherein for 1≦i≦X, k ai   pe =G ai   pe T=k shift   pe +k i   pe . 
         [0012]    It is a further object of this invention to disclose such a method as defined in any of the above, wherein for 1≦i≦X, k bi   pe =G bi   pe T=k shift   pe −k i   pe . 
         [0013]    It is a further object of this invention to disclose such a method as defined in any of the above, wherein said final gradient pulse  340  is characterized by k=k shift   pe . 
         [0014]    It is a further object of this invention to disclose such a method as defined in any of the above, wherein said FSE sequence is a 3D FSE sequence comprising an embedded 2D FSE sequence and an encoding axis k pe2  along said slice axis, N pe2  increments along said slice axis, j increments of k pe2 , 1≦j≦N pe2 , the j th  increment of k pe2  (k j   pe2 ) being restricted to values in the range of 
         [0000]    
       
         
           
             
               
                 
                   - 
                   
                     
                       k 
                       max 
                       
                         pe 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     2 
                   
                 
                 + 
                 β 
               
               ≤ 
               
                 k 
                 j 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               ≤ 
               
                 
                   
                     k 
                     max 
                     
                       pe 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   2 
                 
                 + 
                 β 
               
             
             , 
           
         
       
     
         [0000]    where 
         [0000]    
       
         
           
             
               
                 k 
                 max 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               = 
               
                 1 
                 
                   dr 
                   s 
                 
               
             
             , 
           
         
       
     
         [0000]    dr s  is a spatial resolution along the slice axis, and β is an asymmetric k pe2  shift; and further wherein said method additionally comprises: (a) applying a slice RM pulse  850  prior to said 90° RF pulse, said slice RM pulse characterized by amplitude G RM   s  and a positive or negative sign along a slice axis, wherein G RM   s  has a constant amplitude throughout said FSE sequence; (b) applying a slice shim gradient pulse  700  of amplitude at least sufficient to cancel any net effect on said gradient-dependent residual magnetization B g  produced by said slice RM pulse  850 ; (c) applying slice gradient pulses  890  of amplitude G s  along said slice axis, substantially simultaneously with each of said 90° and 180° RF pulses in said FSE pulse sequence; (d) applying, prior to the first 180° pulse, a preparation encoding gradient  810  having amplitude G 0   pe2 ≦G RM   s , thereby providing k 0   pe2 =G 0   pe2 T along said slice axis; (e) for each 180° pulse i (1≦i≦X) in said echo train: (i) applying, subsequent to said 180° pulse i and prior to echo i, a first encoding gradient pulse  820  of amplitude G aj   pe2 , thereby providing k aj   pe2 =G aj   pe2 T along said slice axis; and (ii) applying a second encoding gradient pulse  830  of amplitude G bj   pe2  subsequent to said echo i, thereby providing k bj   pe2 =G bj   pe2  T along said slice axis; and, (f) applying, subsequent to said navigator pulse, a final gradient pulse  840 ; further wherein the amplitude of each of said gradient pulses  810 - 840  has a sign identical to, and an amplitude smaller than, the amplitude of said slice RM pulse. 
         [0015]    It is a further object of this invention to disclose such a method for reducing artifacts produced during a 3D FSE sequence, wherein 
         [0000]    
       
         
           
             
               
                 k 
                 0 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               = 
               
                 
                   
                     k 
                     shift 
                     
                       pe 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   - 
                   
                     
                       
                         G 
                         s 
                       
                        
                       
                         T 
                         90 
                       
                     
                     2 
                   
                 
                 ≥ 
                 0 
               
             
             , 
             
               
                 k 
                 shift 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               = 
               
                 
                   
                     G 
                     shift 
                     
                       pe 
                        
                       
                           
                       
                        
                       2 
                     
                   
                    
                   T 
                 
                 ≥ 
                 
                   k 
                   0 
                   
                     pe 
                      
                     
                         
                     
                      
                     2 
                   
                 
               
             
             , 
             
               
 
             
              
             
               
                 G 
                 shift 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               ≤ 
               
                 G 
                 RM 
                 s 
               
             
             , 
             
               
                 k 
                 R 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               = 
               
                 
                   
                     k 
                     max 
                     
                       pe 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   2 
                 
                 + 
                 β 
               
             
             , 
           
         
       
     
       and G s ≦G RM   s . 
       [0016]    It is a further object of this invention to disclose such a method for reducing artifacts produced during a 3D FSE sequence as defined in any of the above, wherein k aj   pe2 =G aj   pe2 T=k shift   pe2 =k j   pe2 . 
         [0017]    It is a further object of this invention to disclose such a method for reducing artifacts produced during a 3D FSE sequence as defined in any of the above, wherein k bj   pe2 =G bj   pe2  T=k shift   pe2 =k j   pe2 . 
         [0018]    It is a further object of this invention to disclose such a method for reducing artifacts produced during a 3D FSE sequence as defined in any of the above, wherein said final slice gradient pulse  840  is characterized by providing k=k shift   pe2 . 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]    The invention will now be described with reference to the drawings, wherein 
           [0020]      FIG. 1  shows the relevant encoding axis of a conventional FSE pulse sequence of a type known in the art; 
           [0021]      FIG. 2  shows the relevant encoding axis of an FSE pulse sequence according to one embodiment of the present invention; 
           [0022]      FIG. 3  shows the relevant encoding axes of a conventional 3D FSE pulse sequence of a type known in the art; and, 
           [0023]      FIG. 4  shows the relevant encoding axes of a 3D FSE pulse sequence according to one embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0024]    In the following description, various aspects of the invention will be described. For the purposes of explanation, specific details are set forth in order to provide understanding of the invention. It will be apparent to one skilled in the art that there are other embodiments of the invention that differ in details without affecting the essential nature thereof. Therefore the invention is not limited by that which is illustrated in the figure and described in the specification, but only as indicated in the accompanying claims, with the proper scope determined only by the broadest interpretation of said claims. 
         [0025]    The term “unipolar FSE” is used herein to describe an FSE sequence in which all encoding gradient pulses are of the same sign. 
         [0026]    The expression “RM” is used herein to represent the term “residual magnetization.” 
         [0027]    For the sake of simplicity we assume that the gradient is constant such that k=GT. During a 2D FSE sequence comprising X iterations, k i   pe  is incremented through the change in the gradient strength such that k i   pe =iΔG pe T, 1≦i≦X. Note that k i   pe  is restricted to the range 
         [0000]    
       
         
           
             
               
                 - 
                 
                   
                     k 
                     max 
                     pe 
                   
                   2 
                 
               
               + 
               α 
             
             ≤ 
             
               k 
               i 
               pe 
             
             ≤ 
             
               
                 
                   k 
                   max 
                   pe 
                 
                 2 
               
               + 
               α 
             
           
         
       
     
         [0000]    where k max   pe  is defined by the desired resolution along the phase axis, 
         [0000]    
       
         
           
             
               
                 dr 
                 pe 
               
               = 
               
                 1 
                 
                   k 
                   max 
                   pe 
                 
               
             
             , 
           
         
       
     
         [0000]    dr pe  is the resolution of a pixel along the phase axis, and α is an asymmetric k shift. We define 
         [0000]    
       
         
           
             
               k 
               L 
               pe 
             
             = 
             
               
                 
                   - 
                   
                     
                       k 
                       max 
                       pe 
                     
                     2 
                   
                 
                 + 
                 
                   α 
                    
                   
                       
                   
                    
                   and 
                    
                   
                       
                   
                    
                   
                     k 
                     R 
                     pe 
                   
                 
               
               = 
               
                 
                   - 
                   
                     
                       k 
                       max 
                       pe 
                     
                     2 
                   
                 
                 + 
                 
                   α 
                   . 
                 
               
             
           
         
       
     
         [0000]    The asymmetric k shift is assumed herein to be nonnegative, hence |k L   pe |≦|k R   pe |. 
         [0028]    Reference is now made to  FIG. 2 , which illustrates the pulse sequence of the present invention. The pulse sequence comprises a 90° RF pulse ( 100 ) followed by an echo train of length X, comprising X 180° RF pulses ( 110 ), and a final 180° navigator pulse ( 120 ). The symbol τ represents the time delay between the 90° RF pulse and the initial 180° RF pulse; the time delay between successive 180° RF pulses in the echo train will thus be 2τ, and the time between a given 180° RF pulse and the consequent echo will necessarily be τ as well. One exemplary 180° RF pulse  110  in the echo train is illustrated in the figure; the parentheses indicate that pulse  110  in the echo train can be repeated an arbitrary number (i.e. X) of times. Also shown in  FIG. 2  are the gradient pulses that are part of the pulse sequence disclosed in the present invention, with their amplitudes along the phase axis: at time  400  prior to the 90° RF pulse, a gradient pulse  300  of amplitude G RM   pe  for producing a dominant residual magnetization (henceforth referred to as the “RM pulse”); a preparation (“k shift”) gradient pulse ( 310 ) prior to the first 180° RF pulse; pairs of encoding gradient pulses ( 320  and  330 ), prior to and following each of the echoes ( 130 ), of amplitudes G ai   pe  and G bi   pe  respectively, where i is the index of the echo (1≦i≦X), and a final gradient pulse  340  between the navigator pulse and the navigator echo. In preferred embodiments of the invention, gradient pulses  310  and  330  both have values of k shift   pe . The parasitic inherent RM gradient  210  is constant during the pulse sequence, as explained below. 
         [0029]    The figure illustrates a central innovation of the present invention, namely, that the sequence all of the encoding gradient pulses are of the same sign as that of the RM pulse (unipolar FSE). That is, the method does not involve any inverted or reversed gradient pulses. This innovation leads to two important consequences. First, the RM gradient is now dominated by the largest gradient in the sequence along the phase axis, and does not change during the sequence. This gradient, having amplitude G RM   pe  and produced before time  400 , will therefore define the RM along the phase axis. A shim gradient  200  of opposite polarity is applied so that the net effect of the RM gradient will be zero. Second, the lack of a gradient of opposite sign guarantees accurate performance of the gradient amplifier. 
         [0030]    In order to achieve the same encoding pattern within the constraint that −k L   pe ≦k i   pe ≦k R   pe , the following two relations must be maintained: 
         [0000]        k   ai   pe   =k   shift   pe   +k   i   pe  and 
         [0000]    
       
      
       k 
       bi 
       pe 
       =k 
       shift 
       pe 
       −k 
       i 
       pe  
      
     
         [0031]    Note that the 180° RF pulse inverts the sign of k shift   pe , so in preferred embodiments of the invention, k ai   pe , k bi   pe ≧0 (k shift   pe ≧k R   pe2 ≧|k L   pe2 |). The phase at time  410  in  FIG. 2  is φ 410   pe =−k shift   pe ·r pe . At the echo (time  420  in  FIG. 2 ), the phase is φ 420   pe =(−k shift   pe +k ai   pe )·r pe . Substitution of the expression for k ai   pe  given above yields φ 420   pe =k i   pe ·r pe , i.e. the desired phase at the echo. The phase at time  430  is φ 430   pe =(k i   pe +k bi   pe )·r pe . Substitution of the expression for k bi   pe  given above into the expression for φ 430   pe  yields φ 430   pe =k shift   pe ·r pe . Thus, the gradient pattern disclosed herein maintains the desired FSE phase conditions; at each echo, the phase goes as k i   pe ·r pe , and between each pair of 180° pulses, a constant phase is repeated, regardless of the value of k i   pe . 
         [0032]    With respect to the navigator pulse, the phase at time  440  in the sequence shown in  FIG. 2  is given by φ 440   pe =−k shift   pe ·r pe . With an additional gradient characterized by k shift   pe , the overall phase during the navigator pulse will be zero, as is necessary for monitoring the field drift. 
         [0033]    As noted above, the gradient-dependent RM B g  depends on the characteristics of the particular magnet, and is typically on the order of 0.1% of the gradient strength. Thus, in order to be able to calculate the minimum amplitude necessary for the shim gradient pulse  200 , it is necessary to know B g  prior to application of the method disclosed herein. In general, B g  is measured once for the specific NMR/MRI instrument of interest, using any appropriate method known in the art, and its value recorded for future reference. 
         [0034]    The method for reducing artifacts disclosed herein as applied to 3D FSE is also contemplated by the inventors as being within the scope of the invention. The 3D FSE sequence comprises an embedded 2D FSE sequence; in 3D FSE, the slice axis serves as an additional phase encoding axis, k pe2 . For a number of increments N pe2  along the slice axis and 1≦j≦N pe2 , k j   pe2  is incremented by changing the slice gradient in a manner analogous to that described i above for 2D FSE, with the analogous constraint that 
         [0000]    
       
         
           
             
               
                 
                   - 
                   
                     
                       k 
                       max 
                       
                         pe 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     2 
                   
                 
                 + 
                 β 
               
               ≤ 
               
                 k 
                 j 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               ≤ 
               
                 
                   
                     k 
                     max 
                     
                       pe 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   2 
                 
                 + 
                 β 
               
             
             , 
           
         
       
     
         [0000]    where k max   pe2  is defined by the desired resolution along the slice axis, 
         [0000]    
       
         
           
             
               
                 k 
                 max 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               = 
               
                 1 
                 
                   dr 
                   s 
                 
               
             
             , 
           
         
       
     
         [0000]    dr s  is the spatial resolution along the slice axis, and β is an asymmetric k pe2  shift. Note that the index j is incremented after each iteration through i (i.e. k j   pe2  is incremented after each run through k i   pe ). Analogously to the 2D case, was adopt the convention that β≧0 and define 
         [0000]    
       
         
           
             
               
                 k 
                 L 
                 
                   pe 
                    
                   
                       
                   
                    
                   2 
                 
               
               = 
               
                 
                   
                     - 
                     
                       
                         k 
                         max 
                         
                           pe 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       2 
                     
                   
                   + 
                   
                     β 
                      
                     
                         
                     
                      
                     and 
                      
                     
                         
                     
                      
                     
                       k 
                       R 
                       
                         pe 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                 
                 = 
                 
                   
                     
                       k 
                       max 
                       
                         pe 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     2 
                   
                   + 
                   β 
                 
               
             
             , 
           
         
       
     
         [0000]    hence |k L   pe |≦|k R   pe |. 
         [0035]    Reference is now made to  FIG. 3 , which depicts a 3D FSE pulse sequence of a type known in the art. The slice select gradient inverts its sign several times during the pulse sequence. At time a, after the excitation slice select pulse, a refocusing slice select gradient is required that will have a reversed gradient sign with 
         [0000]    
       
         
           
             
               k 
               = 
               
                 
                   
                     - 
                     
                       G 
                       s 
                     
                   
                    
                   
                     T 
                     p 
                   
                 
                 2 
               
             
             , 
           
         
       
     
         [0000]    where T p  is the duration of the excitation pulse. The slice select gradient is active during the 180° pulse. At time b following the 180° RF pulse, an encoding gradient, G j   pe2 , provides k j   pe2 . At time c following the echo, a gradient pulse of opposite sign is applied in order to maintain the necessary conditions that the k should have a value of k j   pe2  during the echo and that the overall phase should remain constant between the 180° pulses. 3D FSE techniques known in the art suffer from the same difficulties and problems discussed above for 2D FSE, in particular, the creation of artifacts as a result of non-constant RM and non-ideal gradient amplifier performance. 
         [0036]    Reference is now made to  FIG. 4 , which depicts a 3D FSE sequence according to one embodiment of the current invention. As with the 2D FSE sequence illustrated in  FIG. 2 , the 3D FSE pulse sequence comprises a 90° RF pulse ( 100 ) followed by an echo train of length X, comprising X 180° RF pulses ( 110 ), and a final 180° navigator pulse ( 120 ). As was shown in  FIG. 2 , only one exemplary 180° RF pulse in the echo train ( 110 ) is illustrated in the figure; the parentheses indicate that it can be repeated an arbitrary (i.e. X) number of times. Also shown in  FIG. 4  are the gradient pulses that are part of the pulse sequence disclosed in the present invention, with their amplitudes along the slice axis and phase axis, respectively: at time  900  prior to the 90° RF pulse, RM pulse  300  (amplitude G RM   pe  along the phase axis) and slice RM pulse  800  (amplitude G RM   s  along the slice axis) are provide. As in the case of 2D FSE, a preparation (“k shift”) phase gradient provides k shift   pe  ( 310 ), and pairs of encoding gradient pulses, G ai   pe  and G bi   pe  ( 320  and  330 ), prior to and following each of the echoes ( 130 ), provide k ai   pe  and k bi   pe  respectively, where i is the index of the echo within the train (1≦i≦X), and a final gradient pulse  340  between the navigator pulse  120  and the navigator echo  140  are applied along the phase axis. In preferred embodiments of the invention, both gradient pulses, at  310  and at  330  provide the value k shift   pe . Along the slice axis, slice gradient pulses  890  of amplitude G s  are applied substantially simultaneously with the 90° and 180° RF pulses  100 ,  110 , and  120 . A preparation slice gradient pulse  810  is applied prior the first 180° RF pulse to give 
         [0000]    
       
         
           
             
               k 
               0 
               
                 pe 
                  
                 
                     
                 
                  
                 2 
               
             
             = 
             
               
                 k 
                 shift 
                 pe 
               
               - 
               
                 
                   
                     
                       G 
                       s 
                     
                      
                     
                       T 
                       90 
                     
                   
                   2 
                 
                 . 
               
             
           
         
       
     
         [0000]    Pairs of encoding gradients,  820  and  830 , having amplitudes G aj   pe2  and G bj   pe2 , respectively, are applied along the slice axis prior to ( 820 ) and following ( 830 ) each of the echoes in the echo train ( 130 ), thereby providing k aj   pe  and k bj   pe2 . A slice navigator gradient pulse  840  is applied along the slice axis between the navigator pulse  120  and its echo  140 . In preferred embodiments of the invention, the amplitude of pulse  840  provides k shift   pe2 . The amplitude G s  of the refocusing pulse can be subtracted either at time  910  or it can be added after 180° RF pulse  110  (i.e. at time  920 ). Incrementation of the pulses is performed in an analogous manner to that described above for the case of 2D FSE. 
         [0037]    As with the 2D FSE sequence presented above, a central innovative aspect of unipolar 3D FSE is that all of the gradient pulses have the same sign. The elimination of the need to invert the sign of the gradient pulses provides the same benefits in 3D FSE that it does in 2D FSE, namely, the elimination of artifacts due to RM and the non-ideal nature of the gradient amplifier. The combination of k shift   pe2 , k aj   pe2 , and the 180° RF pulse provides the required increment in k j   pe2 . The conditions for k a   pe2  and k bj   pe2 , analogous to the conditions for k ai   pe  and k bi   pe  given above for 2D FSE, are 
         [0000]        k   aj   pe2   =k   shift   pe2   +k   j   pe2  and 
         [0000]    
       
      
       k 
       bj 
       pe2 
       =k 
       shift 
       pe2 
       −k 
       j 
       pe2  
      
     
         [0038]    In unipolar 3D FSE, as with unipolar 2D FSE, a strong constant gradient pulse is applied along the slice axis prior to 90° RF pulse  100  in order to produce constant RM throughout the run. The RM is canceled by implementing a slice shim gradient  700  along the slice axis in addition to the shim gradient  200  applied along the phase axis.