Patent Application: US-201113695159-A

Abstract:
a grase - type propeller sequence called steer - prop is disclosed . this sequence exploits a serious of steer blips together with rewinding gradient pulse to traverse k - space . steer - prop improves the scan time by a factor of 3 or higher compared to fse - propeller , provides improved robustness to off - resonance effects compared to epi - propeller , and addresses a long - standing phase correction problem inherent to grase based sequences . steer - prop also enables intra - blade , inter - blade , and inter - shot phase errors to be separately determined and independently corrected .

Description:
the embodiments disclosed herein by way of example provide example techniques applicable in an mri system . an mri system typically comprises hardware components including a plurality of gradient coils positioned about a bore of a magnet , an rf transceiver system , and an rf switch controlled by a pulse module to transmit rf signals to and receive rf signals from an rf coil assembly . the received rf signals are also known as magnetic resonance ( mr ) signal data . an mri system also includes a computer programmed to cause the system to apply to an object in the system various rf signals , magnetic fields , and field gradients for inducing spin excitations and spatial encoding in an object , to acquire mr signal data from the object , to process the mr signal data , and to construct an mr image of the object from the processed mr signal data . the computer may include one or more general or special purpose processors , one or more forms of memory , and one or more hardware and / or software interfaces for interacting with and / or controling other hardward components of the mri system . mr signal data detected from an object are typically described in mathematical terms as “ k - space ” data . k - space is the fourier inverse of image space . an image in actual space is produced by a fourier transform of the k - space data . mr signal data are acquired by traversing k - space over the course of applying to the object the various rf pulses and magnetic field gradients . in practice , techniques for acquiring mr signal data from an object are closely related to techniques for applying the various rf pulses and magnetic field gradients to the object . the example embodiments disclosed herein relate to configuring rf pulses and magnetic field gradients so as to enable and / or cause k - space traversal for data acquisition in a particularly advantageous manner . further , the example embodiments can be implemented in the form of one or more computer programs or applications that , when executed by the computer ( e . g ., one or more of the processors ), cause the mri system to apply the various rf pulses and magnetic field gradients , traverse k - space in the prescribed , advantageous manner , and acquire the corresponding mr signal data . more particularly , the example embodiments offer specific advantages over k - space traversal techniques that employ strategies based on the propeller method . initially implemented in a multi - shot fast spin echo ( fse ) pulse sequence , the propeller method ( 1 ) traverses k - space using a series of rectangular strips rotated about the k - space origin . each spin echo in the fse echo train is used to acquire one line of k - space data , and thus the entire echo train produces a blade or strip consisting of n parallel k - space lines where n equals the echo train length ( etl ). the subsequent repetitions ( or “ trs ”) involve the rotation of frequency and phase encoding gradients about the slice - selection axis , producing additional blades in k - space , each rotated with an incremental angle to cover a complete circular area of k - space . the central k - space region is sampled by every blade , allowing self - navigation to compensate for motion . in - plane motion correction can be performed by reconstructing a series of low - resolution phase maps , one for each blade , based on the data in the central overlapping region . the motion - induced phase errors for a given blade are evaluated by comparing the phase against the phase of a reference blade , and subsequently removed during image reconstruction . although propeller offers robustness against motion , in certain applications , such as human brain diffusion studies , the time required for high - resolution imaging can become impractically long . gradient and spin echo ( grase ) is a hybrid of fse and epi that can be applied to propeller that yields reduced scan time . one such technique , referred to “ turboprop ” ( 9 ), increases the blade width , improving immunity to motion correction because a large amount of redundant data at the k - space central region can be used for evaluating data consistency . each turboprop scan consists of multiple , parallel blades that are combined into a single wider blade . however , inter - blade phase errors are complicated and not easy to be untangled . more particularly , phase inconsistency can exist among the spin - echo signals if the carr - purcell - meiboom - gill ( cpmg ) condition is not satisfied ( 10 ). additionally phase errors can also exist among the gradient echoes , primarily due to the polarity change of the readout gradient . by traversing k - space of a grase sequence in a manner to produce multiple , mutually oblique blades that intersect and overlap near the origin ( center ) of k - space , the inter - blade phase errors advantageously can be separated and corrected independently . in order to achieve such obliquely intersecting blades in a single repetition time ( tr ) of a grase sequence , k - space traversal needs to be “ steered ” from one blade to another within each shot of a sequence ( i . e ., each tr ). this can be achieved by devising specific gradient - echo pulse trains within each of multiple spin - echoes of a grase sequence . as disclosed herein , this technique is referred to as “ steer - prop ” and the corresponding sequence is referred to as “ gradient and spin echo propeller ( grasp ).” beyond the advantageous phase error correction made possible , steer - prop also further significantly reduces the time to sample k - space data when compared to the original propeller technique ( 1 ). steer - prop uses n rf refocusing pulses after each excitation rf pulse to produce a cpmg spin echo train . each spin echo was further split into m gradient echoes by a bipolar readout gradient . by way of example , n could be in a range of 4 - 64 , and m could be in the range of 3 - 7 , although other values of m and / or n could be used . steer - prop employs a series of blip gradient pulses to distribute the m gradient echoes to m different blades . in doing so , m blades are sampled within each shot of a sequence ( i . e ., each tr ). an example embodiment of a method of steer - prop is illustrated in fig1 . by way of example , the example method can be a computer - implemented method in an mri system such as the one described above . as illustrated in fig1 , at step 102 , following an excitation radio frequency ( rf ) pulse , a first rf pulse is applied to an object in the mri system , and after a first fast spin echo ( fse ) inter - echo time interval , as second rf pulse is applied to the object . at step 104 , in the first fse inter - echo time interval between the first and second rf pulses , a first magnetic field gradient ( g x ) pulse train is applied to the object along a first direction . the first g x pulse train includes an integer number m adjacent g x pulses , and consecutive pairs of g x pulses of the first g x pulse train are separated by a g x steering pulse . the last g x pulse of the first g x pulse train is followed by a first g x rewinding pulse . at step 106 , a first magnetic field gradient ( g y ) pulse train is applied to the object along a second direction . the first g y pulse train includes m adjacent g y pulses , and consecutive pairs of g y pulses of the first g y pulse train are separated by a g y steering pulse . the last g y pulse of the first g y pulse train is followed by a first g y rewinding pulse . each g y pulse of the first g y pulse train forms a respective first - train g x - g y pulse pair with a simultaneous corresponding g x pulse of the first g x pulse train . further , each g y steering pulse forms a respective first - train g x - g y steering - pulse pair with a simultaneous corresponding g x steering pulse of the first g x pulse train , and the first g y rewinding pulse forms a first simultaneous g x - g y rewinding - pulse pair with the first g x rewinding pulse of the first g x pulse train . finally , at step 108 , k - space data are acquired along a first set of m mutually oblique lines intersecting in a central region of k - space , wherein each of the m mutually oblique lines of the first set corresponds to a different respective first - train g x - g y pulse pair . in accordance with the example embodiment , the first direction , along which g x is applied , and the second direction , along which g y is applied are orthogonal to one another . in accordance with the example embodiment , applying each first - train g x - g y steering - pulse pair repositions a starting point for k - space traversal from one of the m mutually oblique lines of the first set to another . in addition , applying the first simultaneous g x - g y rewinding - pulse pair repositions a starting point for k - space traversal to a reference location of k - space . by way of example , m could be in a range of 3 - 7 , although values outside of this range could be used as well . in further accordance with the example embodiment , the first and second rf pulses are an rf refocusing pulse , the first resulting in a spin - echo . each of the magnetic field gradient pulses g x and g y results in a gradient echo . taking m = 3 , as an example , three gradient echoes would be generated within the first spin echo interval between the first and second rf refocusing pulses . the second refocusing pulse would result in a second spin echo . it will be appreciated that steer - prop could also be embodied as a non - transitory computer - readable medium , such as magnetic disk , cd - rom , or the like , having non - transitory computer - readable medium having stored thereon computer - executable instructions that , if executed a processor or processors of the mri system , cause the mri system to perform functions of the example method as described above . it will also be appreciated that the method steps described above could be modified or rearranged , and that additional steps could be added , without changing the scope or spirit of the example embodiment or other steer - prop embodiments . for example , g x and g y pulses that are described above as being paired ( including steering and rewinding pulses ) may not need to be applied strictly simultaneously . in some embodiments , the temporal relation prescribed by the design of the g x and g y pulse trains could be such that paired pulses are approximately rather than strictly simultaneous . fig2 a illustrates g x and g y pulse trains with m = 3 , and fig2 b shows the resulting k - space traversal along three blades . the three gradient lobes , shown as trapezoids , correspond to acquisition k - space data for each of the three blades . note that the apparent absence of a first g y pulse actually corresponds to a pulse amplitude of zero . the steering pulses are shown as triangles ( although other shapes of gradient pulses can also be used ), and are referred to as steer blips . they are used to steer the k - space trajectory to the desired blade . the triangular gradient pulses at the end of the gradient echo train rewind the phase in order to satisfy the cpmg condition . typically , k - space is described in a rectangular coordinate system with orthogonal axes k x and k y . in such a description , g x is applied along the k x - axis and g y is applied along the k y - axis . it will be appreciated that other coordinate systems , such as a radial coordinate system could be used to describe k - space . the traversal of k - space resulting from the pulse trains is illustrated in fig2 b . the line b 1 is first traversed . since the amplitude of g y is zero for the first gradient echo , as noted above , the k y - component of the line b 1 is zero , and the b 1 is thus horizontal . the first pair of steering blips then steers to the next ( second ) starting point on line b 2 . the second pair of steering blips then steers to the next ( third ) starting point on line b 3 . finally , the rewind pulse pair returns to the initial point in k - space . a single spin echo interval containing a g x - g y gradient echo pulse train , such as the one shown in fig2 a is referred to herein a “ segment .” by repeating segments within a pulse sequence while varying the phase - encoding gradient g pe ( see fig2 a ) in each segment , lines parallel but offset from b 1 , b 2 , b 3 result in filling out three blades , as indicated . each repeat segment results in different set of m lines distributed among m blades . a sequence of three spin echoes , each having gradient pulse trains ( g x and g y trains ), is illustrated in fig3 . for a segment repeated n times n lines will fill out each of the m blades . with this scheme , each excitation ( or tr ) acquires a total of m × n k - space lines that are evenly distributed among the m blades , improving the data acquisition speed by a factor of m as compared to fse - propeller with the same spin echo train length . for a desired matrix size l , the minimum number of excitations p to cover k - space fully can be calculated by the area , instead of the amplitude alone , of the steep blips controls how the k - space traversal is accomplished . in order to achieve the k - space traversal shown in fig2 b , the areas of individual steer blip pulses are calculated , as shown in fig4 . these steer blip pulse areas depend on the phase encoding amplitude of the spin - echo under consideration and the rotation angle between two successive blades , θ . the area under a particular phase encoding gradient lobe ( a y ) and the area corresponding to the largest phase encoding step ( a y max ) are given by equations 2 and 3 respectively , as : a y = e - 0 . 5 fov × γ ( 2 ) a y ma ⁢ ⁢ x = e - 0 . 5 fov × γ ( 3 ) where fov is the field of view in units of cm , γ is the gyromagnetic ratio ( 42 . 58 × mhz / t for proton spins ), e is in the range − e + 1 ≦ e ≦ e and corresponds to a given phase - encoding step within the blade , and e corresponds to the largest positive phase encoding step , and is related to the echo train length ( m ) by the area a y has a positive or negative sign depending upon the location of the phase - encoding step . steering between blades is based on the gradient areas given by equations 2 and 3 and converting them into the corresponding components along the readout and phase - encoding directions of the subsequent blades using the blade rotation angle θ . to compute the area required for the steering blip pulses , k - space distance between the end of the current blade and the beginning of the subsequent blade is needed . for example , in the case of k - space distance corresponding to g y θ ( fig4 b ) the traversal comprises moving from point e b1 to the top of blade b 2 . the gradient area required for this step is given by equation 4 . the area a x θ required for the gradient blip g x θ is computed as shown in equation 5 . a similar strategy is applied to obtain the traversal between blades b 2 and b 3 with the areas a y 2θ ( for g y 2θ ) and a x 2θ ( for g x 2θ ) given by equations 6 and 7 . a y θ =( a y max − a y )+( a y max + a y ) cos θ ) ( 4 ) a y 2θ =( a y max − a y ) cos θ −( a y max + a y ) cos 2θ ( 6 ) a x 2θ =( a y max − a y ) sin θ +( a y max + a y ) sin 2θ ( 7 ) it can be observed from fig4 b and 4 c that gradients g x θ and g y 2θ have negative polarity as required by their traversal direction . it is noted that the gradient waveforms shown in fig2 a and 3 are incomplete . for example , the pre - phasing gradient along the g x direction is not shown because this gradient pulse is typically applied between an excitation rf pulse and a refocusing rf pulse . additionally , the slice - selection gradient is also omitted because slice - selection gradient is not involved in the steer process . it is worth noting that the last gradient pulse in the segment for either g x or g y pulse train is important as it returns the k - space trajectory to a consistent position . between each refocusing pulse , the spin - echo amplitude decays according to t 2 relaxation . as a result , the snr is lower for lines acquired near the end of the echo train compared to the lines acquired earlier . assigning the spin echoes in linear format can cause large signal amplitude discontinuities between blades which then lead to severe ghosting artifacts . in the case of diffusion imaging , application of the diffusion gradients causes deviations from the cpmg condition , leading to phase and magnitude instability in the odd - numbered spin echoes . in order to compensate for these effects the following described view ordering scheme can be used ( as shown in fig5 ). the even echoes are assigned across the center of the blade , so that the signal at the center of k - space is stable . odd echoes are split between the blade edges , assigned so that the t 2 decay profile across the blade does not have any sharp discontinuities . the steer - prop technique faces three kinds of phase errors that need to be accounted for in order to obtain images of acceptable quality . 1 . inter - shot : phase inconsistency ( errors ) in between tr &# 39 ; s caused primarily by motion ; 2 . inter - blade : phase inconsistency ( errors ) between the different gradient echoes that are distributed across different blades ; 3 . intra - blade : phase inconsistency ( errors ) across the different k - space lines within a given blade . one of the advantages of steer - prop is the ability to separately determine and independently correct for the three type of phase error described above . further detail is provided below . to obtain the intra - blade phase errors , two single - shot orthogonal reference scans ( ors ) are acquired during pre - scan using grasp pulse sequences with a zero blade angle ( i . e ., θ = 0 ). in the first reference scan , the readout gradient is applied along the x - axis , and all gradient activity along the y - axis is disabled . in the second reference scan , the gradient waveforms are swapped between the x - and y - axes . for each reference scan , the gradient echoes of all spin echoes are fourier transformed to obtain complex projections of the object . from these projections , spatially constant ( α ) and linear ( β ) phase errors are calculated using the method proposed by ahn and cho ( 11 ): reference scan 1 : α 1mn , β 1mn for m = 1 , . . . , m blades , and n = 1 , . . . , n lines , reference scan 2 : α 2mn , β 2mn for m = 1 , . . . , m blades , and n = 1 , . . . , n lines , where the first subscript represents the reference scan number , m and n denote the gradient echo and spin echo indices , respectively . for a given blade m with an orientation angle φ m , the constant ( ξ ) and linear ( ψ ) phase errors among the k - space lines are obtained as follow : ξ mn = α 1mn cos φ m + α 2mn sin φ m ( 8 ) ψ mn = β 1mn cos 2 φ m + β 2mn sin 2 φ m . ( 9 ) with known phase errors , intra - blade phase correction will proceed using the established phase correction method for each blade by adjusting the receiver frequency and a tweaking gradient area ( 12 ). with the removal of the intra - blade phase error , the inter - blade phase errors within a shot can be corrected using two approaches . first , phase inconsistencies among the m gradient echoes acquired from the ors described above can be used . the central gradient echo of the first spin echo can be selected as a reference and the phase errors for all other gradient echoes are estimated with respect to the reference . both constant and linear phase errors are removed during reconstruction using an established method developed for epi ( 13 ). second , the inter - blade phase errors within a shot can be estimated by comparing the phase among the blades in the same shot using redundant data in the central k - space region traversed by all blades . the phase inconsistency can then by removed during image reconstruction . this method is similar to the one originally proposed by pipe ( 1 ), except that only m blades , one corresponding to each gradient echo within the same shot , are used to perform phase correction , instead of using all propeller blades . the motion - induced inter - shot phase errors are corrected by comparing the phase between different excitation groups based on data consistency in the central overlapping region of k - space . the algorithm originally proposed by pipe ( 1 ) for fse - propeller can be used to remove the inter - shot phase errors in grasp , except that a comparison is made between the phase of different groups of blades acquired from different shots , instead of on a blade by blade basis . both in - plane and through plane motion are corrected in this manner . an example embodiment of a method of phase error correction based on steer - prop traversal of k - space is illustrated in fig6 . by way of example , the example method could be a computer - implemented method in an mri system such as the one described above . as shown in fig6 , at step 602 a first grasp sequence is applied to an object in the mri system . in accordance with the example embodiment , the first grasp sequence could comprise a first radio frequency ( rf ) sequence of periodic rf pulses , an accompanying first magnetic field gradient ( g x ) sequence of periodic g x pulse trains along a first direction , and an accompanying corresponding first magnetic field gradient ( g y ) sequence of periodic g y pulse trains along a second direction . by designing the first rf , g x and g y sequences in accordance with the steering technique describe above , they can be configured to cause traversal in k - space along a first plurality of parallel line groupings , where each parallel line grouping of the first plurality forms a respective first grasp blade , and each respective first grasp blade is oblique to the other respective first grasp blades and intersects the other respective first grasp blades in a central region of k - space . at step 604 , first grasp k - space data are acquired from along the parallel line groupings of the first plurality during a first repetition time interval corresponding to a duration of the first grasp pulse sequence ( e . g ., the first shot ). at step 606 , a second grasp sequence is applied to the object in the mri system . in accordance with the example embodiment , the second grasp sequence comprises a second radio frequency ( rf ) sequence of periodic rf pulses , an accompanying second magnetic field gradient ( g x ) sequence of periodic g x pulse trains along a second direction , and an accompanying corresponding second magnetic field gradient ( g y ) sequence of periodic g y pulse trains along a second direction . by designing the second rf , g x and g y sequences in accordance with the steering technique describe above , they can be configured to cause traversal in k - space along a second plurality of parallel line groupings , where each parallel line grouping of the second plurality forms a respective second grasp blade , and each respective second grasp blade is oblique to the other respective second grasp blades and intersects the other respective second grasp blades in the central region of k - space . at step 608 , second grasp k - space data are acquired from along the parallel line groupings of the second plurality during a second repetition time interval corresponding to a duration of the second grasp pulse sequence ( e . g ., the second shot ). finally , at step 610 , phase errors are separately determined and independently corrected for : ( i ) intra - blade k - space data in the first grasp k - space data , ( ii ) inter - blade k - space data in the first grasp k - space data , ( iii ) intra - blade k - space data in the second grasp k - space data , ( iv ) inter - blade k - space data in the second grasp k - space data , and ( v ) inter - shot k - space data between the first and second shots . it will be appreciated that phase error correction using the steer - prop technique or grasp sequence can also be embodied as a non - transitory computer - readable medium , such as magnetic disk , cd - rom , or the like , having non - transitory computer - readable medium having stored thereon computer - executable instructions that , if executed a processor or processors of the mri system , cause the mri system to perform functions of the example method as described above . it will also be appreciated that the method steps described above could be modified or rearranged , and that additional steps could be added , without changing the scope or spirit of the example embodiment or other embodiment of phase error correction using steer - prop . for example , g x and g y pulses that are described above as being paired ( including steering and rewinding pulses ) may not need to be applied strictly simultaneously . in some embodiments , the temporal relation prescribed by the design of the g x and g y pulse trains could be such that paired pulses are approximately rather than strictly simultaneous . the steer - prop sequence was first implemented and tested on a 3 . 0 t ge signa hdx scanner ( ge healthcare , waukesha , wis ., usa ). an fse pulse sequence was modified to implement the steer - prop pulse sequence , as explained in above . this pulse sequence was initially tested on the cylindrical ge dqa phantom , using the quadrature head coil , supplied by the scanner manufacturer . t 2 - weighted steer - prop images were acquired in the axial plane with the following imaging parameters : tr = 4 s and te = 72 ms . for the purpose of comparison , a similar image was obtained using a conventional fse - based propeller sequence with the same imaging parameters . following this verification , several experiments were performed on a healthy female volunteer ( age : 29 years ) to evaluate the steer - prop sequence . all experiments were carried out using the quadrature head coil . in the first volunteer experiment , axial t2 and diffusion weighted images were obtained in the brain , using the following imaging parameters : tr = 4000 ms , te = 128 ms , etl = 8 , matrix size = 256 , fov = 26 cm , slice thickness = 5 mm , b = 500 s / mm 2 , nex = 2 , and scan time = 2 min 13 sec . for comparison , corresponding images were also obtained using the fse - propeller sequence . as diffusion - weighting images are commonly acquired using single - shot spin - echo epi , a dw - epi acquisition was performed with matching imaging parameters . to assess the robustness of the steer - prop sequence to subject motion , the volunteer was trained to move her head with low to moderate frequency at regular intervals during the acquisition . axial steer - prop and fse - propeller images were acquired with the same imaging parameters given above , at a slice location similar to the previous acquisition . both acquisition strategies were compared against a standard multi - shot t2 - weighted cartesian fse acquisition . subject motion was comparable over all three scans . dielectric resonance effects are usually more pronounced at higher field strengths , and result in a significant brightening of the center of the image . as this effect may complicate the assessment of steer - prop images at 3 . 0 t , the pulse sequence was also implemented on a 1 . 5 t ge signa hdx scanner . with this pulse sequence , axial steer - prop images were acquired at 1 . 5 t with the quadrature transmit - receive head coil using the following imaging parameters : tr = 4 s , te = 72 ms , etl = 8 , fov = 24 cm , slice thickness = 5 mm , bw = 125 khz , matrix size = 256 × 256 and nex = 2 . to demonstrate the robustness of steer - prop , diffusion weighted images were further acquired on axial and non - axial ( i . e ., sagittal , coronal and oblique ) planes on the volunteer using the following imaging parameters : tr = 4 s , te = 72 ms , etl = 8 , fov = 24 cm , slice thickness = 5 mm , bw = 125 khz , matrix size = 256 × 256 and nex = 2 , b = 500 s / mm 2 . the oblique plane was chosen parallel to the cerebellar tentorium , ˜ 40 ° from the axial plane on the volunteer . single - shot epi images were acquired at the same locations with similar imaging parameters . fig7 shows the t 2 - weighted images of the phantom scans acquired at 3 t . the steer - prop image ( fig7 b ) is visually comparable to the fse - propeller image ( fig7 a ). snr measurements revealed about a 30 % reduction for the steer - prop compared to fse - prop images , but the imaging speed was improved 3 - fold . t 2 - and diffusion - weighted images obtained with a b = 500 s / mm 2 on a human subject using epi , fse - propeller and steer - prop are shown in fig8 . the image quality for steer - prop ( fig8 c , f ) was comparable to that of fse - prop ( fig8 b , e ). the severe distortion seen on epi images ( fig8 a , d ) primarily due to off - resonance effects such as magnetic susceptibility was appreciably improved on the steer - prop images . shading was observed in the steer - prop images on the posterior side of the brain due to dielectric resonance at 3 t . images comparing performance on motion induced scans using conventional fse , fse - propeller and steer - prop sequences are shown in fig9 . while the fse images ( fig9 a ) showed severing motion related ghosting , both fse - propeller ( fig9 b ) and steer - prop ( fig9 c ) performed comparably in eliminating the motion artifacts . fig1 shows the comparison results of t 2 - and diffusion - weighted images with b = 750 s / mm 2 acquired at 1 . 5 t field strength . the steer - prop images ( fig1 b , d ) once again displayed comparable image quality to that of the fse - prop images ( fig1 a , c ) although with a slight difference in contrast . the steer - prop images have a combined t 2 and t 2 * weighting . the t 2 * effect produced the contrast difference observed . the run time for the steer - prop sequence was ˜ 2 min compared to ˜ 6 min for the corresponding fse - prop . it can also be noted that the steer - prop images do not show any dielectric shading at this field strength . finally the results of the steer - prop sequence on non - axial diffusion - weighted scan of a human subject are shown in fig1 , in comparison with the conventional single - shot epi . the axial images ( fig1 a , e ) showed the smallest discrepancies , as expected , because of the small magnetic susceptibility differences in the specific imaging plane and the relatively small contributions from the concomitant gradient . for images acquired in sagittal plane , the ss - epi images ( fig1 f ) exhibited substantial gross distortion largely due to concomitant gradient fields as well as localized distortion arising from the magnetic susceptibility differences in the frontal lobe . both types of distortion were virtually eliminated in the corresponding steer - prop image ( fig1 b ). similar improvements were also observed in coronal ( fig1 c ) and oblique ( fig1 d ) planes . an exemplary embodiment of the present invention has been described above . those skilled in the art will understand , however , that changes and modifications may be made to this embodiment without departing from the true scope and spirit of the invention , which is defined by the claims . 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