MAGNETIC RESONANCE IN MEDICINE 3, 823-833 (1986)
`
`RARE Imaging: A Fast Imaging Method for Clinical MR
`
`J. HENNIG,*A. NAUERTH,? AND H. FRIEDBURG*
`
`*Department of Diagnostic Radiology, University Hospital, University of Freiburg, Hugstetter Strasse 55,
`West Germany, and TBruker Medizintechnik GmbH, POB 67, 7512 Rheinstetten-4/West Germany
`
`Received May 6, 1985; revised April 14, 1986
`
`Based on the principles of echo imaging, we present a method to acquire sufficient data
`for a 256 X 256 image in from 2 to 40 s. The image contrast is dominated by the transverse
`relaxation time T2. Sampling all projections for 2D FT image reconstruction in one (or a
`few) echo trains leads to image artifacts due to the different T2 weighting ofthe echo. These
`artifacts cannot be described by a simple smearing out of the image in the phase direction.
`Proper distribution of the phase-encoding steps on the echoes can be used to minimize
`artifacts and even lead to resolution enhancement. In spite of the short data acquisition
`times, the signal amplitudes of structures with long T2 are nearly the same as those in a
`conventional 2D FT experiment. Our method, therefore, is an ideal screening technique
`for lesions with long T2. 0 1986 Academic h ~ , Inc.
`
`Conventional imaging techniques used in MRI take several minutes for a multislice
`and/or multiecho 256 X 256 image. The use of these time-consuming methods causes
`several problems in routine clinical work. These well known problems include patient
`discomfort and positioning-especially when one is looking for small lesions and
`image artifacts due to patient movement.
`It would therefore be of great importance to have an imaging method that allows
`a more rapid data acquisition. Although one is willing to pay some price in image
`quality for such a faster image, the image has to fulfill several conditions to be of any
`help in the problems mentioned above. The resolution should not be worse than that
`of a normal image, the image contrast should be variable and good enough to distinguish
`normal tissue from lesions, and of course the signal-to-noise ratio should be good
`enough to deliver an acceptable image quality. Above that, the imaging method should
`use only rffield strength, gradient field strength, and rising times which lay well within
`the limits given by the national health organizations ( I ) .
`There are several methods that lead to faster imaging. The standard menu of most
`of today's clinical MRI systems allows the fast acquisition of a low-resolution (128
`X 256) image by simply reducing the repetition time of a single-slice single-echo ex-
`periment. Since in such an experiment practically all the magnetization is very heavily
`saturated, the resulting image has very low S/N and contrast. Better results can be
`achieved by performing the experiment using excitation pulses with smaller flip angle
`(2-4). Although this leads to much better SIN and contrast, these methods still lack
`sensitivity for structures With long relaxation times, which are the ones most sought
`after in clinical MRI, especially in head investigations.
`The method we pursued is based on the principle of echo imaging, first introduced
`
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`0740-3194/86 $3.00
`Copyright 0 1986 by Academic Press, Inc.
`All rights of reproduction in any form resewed.
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`HENNIG, NAUERTH, AND FRIEDBURG
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`to MRI by Mansfield (5-7). Long echo trains are generated whereby each echo is
`encoded differently for spatial coordinates (Fig. 1). Applied to 2D FT, where one axis
`of the imaged plane is represented by the phase information of the echoes, this means,
`that all other sources affecting the phase of the echoes have to be dealt with adequately.
`Disastrous phase errors can be introduced by H I , Ho, and switched gradient field
`inhomogeneities. Sampling data very fast minimizes magnetic field effects, as has been
`shown by Mansfield (5-7). Although a MR-real-time movie could be demonstrated
`with this method, its routine application is restricted since the gradient field strength
`necessary lies outside the possibilities of routine MRI systems.
`Several methods to overcome inhomogeneities by self-compensating spin-echo se-
`quences have been proposed (8-Z0), but, due to the fact that only some inhomogeneities
`were accounted for, only a modest approximation to a clinical fast imaging sequence
`could be achieved (10, ZZ). The problem can be solved by respecting the CPMG
`conditions regarding the phase of the magnetization not only in respect to the phase
`of the transmitter signals but to the switched gradient fields as well (12). This means,
`all gradient effects are compensated within one echo cycle, so that no accumulative
`effects can arise. There are different ways this principle can be incorporated into a
`working pulse program (13, Z8). This enables the data acquisition with only a few-
`in the limiting case one-excitations of the spin system.
`
`IMAGE QUALITY
`The data flow in the 2D FT image reconstruction algorithm can be characterized
`by
`
`F T
`FT
`E + F - E l - S.
`
`1
`
`FIG. 1. Principle of echoimaging. (a-d) show 4 echo trains of a conventional 2D FI experiment. Each
`echotrain carries different phase encoding cp. In the echo imaging experiment only one echo train is sampled,
`the phase encoding is different for each echo.
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`Echoes E are sampled in the time domain, their Fourier transforms Fare rearranged
`to give the “echoes” E’, which yield the shape function S after the second FT. In a
`conventional 2D FT experiment all projections necessary for image reconstruction
`are read out at the same time after excitation. Contrary to that, each projection in an
`echoimaging experiment is read out at a different time and therefore experiences a
`different attenuation due to T2 relaxation. To evaluate the quality of the image mea-
`sured by this method one has to know how this affects the image contrast.
`An easy approach to this problem is to consider first a conventional 2D FT exper-
`iment performed on a point-like object located at the center of the gradient system.
`Due to its location this object experiences no influence due to gradients whatsoever
`and all echoes E are characterized by frequency zero and an amplitude that is pro-
`portional to the product of the spin density with the value of the T2 relaxation function
`at the echo readout time. The Fourier transform yields identical delta functions at the
`origin. Rearrangement of the data matrix according to the 2D FT algorithm yields
`“echoes” E‘, all of which are zero except one, which again is characterized by frequency
`zero. The second Fourier transform yields the set of shape functions S, all of which
`are zero except the one at the center, which again is given by a delta function. The
`resulting image shows intensity only in the voxel at the center.
`If an echoimaging experiment is performed on this trivial case, all echoes are again
`characterized by frequency zero. The amplitude, however, is now different in all pro-
`jections due to T2 relaxation. This means, that after the first Fourier transform one
`gets a set of delta functions with different amplitudes. The result after rearrangement
`and second Fourier transform strongly depends on the pattern of the data sampling.
`If the dephasing steps are distributed stochastically on the echoes of the echotrain, the
`result is a noise-like pattern for the “echo” E‘, the corresponding image consists of a
`point in the center due to the fact, that all values of E‘ are greater zero, plus many
`artifacts randomly distributed along the central line of the image.
`A more rational approach would be a sequential distribution of the phase-encoding
`steps on the echo train. In this case the “echo” E’ looks like a discrete representation
`of the T2 relaxation function of the object. The time interval between two sampling
`points is given by the echo spacing 2*7,. The resulting shape function consists of a
`Lorentzian line, whose width is determined by the relaxation time T2. The image
`appears to be smeared out in the phase direction, the smearing being more severe for
`short T2 and/or long echo spacing 2*7,.
`If an echo imaging experiment is performed that delivers coherent echoes in the
`manner described in the previous chapter, then the outcome of the experiment is not
`altered by the addition of gradients. This means, that independent of its location, a
`point-like object always yields an image, which is smeared out somewhat in the phase
`direction (14).
`The complementary case is that of an image with infinite extension. Here E’ is
`given by a delta function whose amplitude is solely defined by the amplitude of the
`projection with zero dephasing, since this is the only one with nonzero intensity. The
`resulting image is a grey plane with homogeneous intensity, the intensity value is given
`by the product of the spin density with the value of the relaxation function at the
`readout time of that particular echo. In general, objects with short relaxation times
`will appear darker than those with long relaxation times at equal spin density.
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`HENNIG, NAUERTH, AND FRIEDBURG
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`0
`
`90'
`
`-90'
`
`0
`
`c 'f
`
`t
`-180'
`
`-90'
`
`180'
`=-180°
`FIG. 2. The "echo" E' as yielded after the first half of the 2D FT algorithm. The horizontal scale gives
`the relative phaseshift of neighboring voxels due to phase encoding. For clarity two cycles of E' are shown.
`In an echo imaging experiment E' is multiplied by the relaxation function. Three possibilities differing in
`the sequence of phase-encoding steps are represented by (a-c).
`
`A somewhat more realistic situation arises if one looks at objects with finite extension
`inside the image frame and characterized by one relaxation function. The result of an
`echo imaging experiment for such a case is shown qualitatively in Figs. 2 and 3. Figure
`2 shows the "echo" E' as a result of the first Fourier transform and rearrangement of
`the data matrix in a conventional 2D FT experiment. E' is cyclic in the sense that a
`phase difference of - 180" between neighboring points yields the same result as a phase
`difference of 180" according to the aliasing principle in discreet Fourier transformation.
`For the sake of the following argument, two cycles of E' are shown. As described
`above, this "echo" has to be multiplied by the discreet representation of the relaxation
`
`FIG. 3. The result of experiments 2a-c. The resolution of the final shape functions S (right) strongly
`depend on the way of phase encoding. S can appear even to be resolution enhanced as compared to the
`result of a conventional 2D FT (d). The effects are exaggerated in these purely qualitative drawings.
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`function, if an echo imaging experiment is performed, where the phase-encoding steps
`are distributed sequentially. The outcome of this experiment depends not only on the
`fact that the phase-encoding steps are distributed sequentially on the echoes, but also
`on which phase is attributed to the first echo, that is, where the experiment starts in
`the phase cycle. Three cases are shown in Figs. 2a-c. Figure 3 shows the final result
`after the second Fourier-transform. Figure 3d shows the shape function as yielded in
`a conventional 2D FT experiment. Figures 3a-c show the strong dependence of the
`result on the exact manner of distributing the phase-encoding steps. It is particularly
`interesting to note, that the shape can appear to be sharpened (Fig. 3a), contrary to
`what one would expect by a simplistic generalization of the argument for point-like
`objects.
`This sharpening can be rationalized if E' is separated into an ascending part and a
`descending part. Multiplying the ascending part with the monotonous descending
`relaxation function leads to a flatter slope and therefore to a sharpening after Fourier
`transformation. Multiplication of the descending part (shown in dotted line in Figs.
`3a-c) yields an even steeper slope and broadening after Fourier transformation. The
`shape function S is the sum of both parts.
`According to the basic properties of Fourier transformation the center (= zero fre-
`quency) amplitude of the shape function is given by the integral of E' after multipli-
`cation with the discreet representation of the relaxation function. It is therefore de-
`pendent on T2 and 2*7, as well as on the exact shape of the object and the manner
`of phase encoding.
`The slope of the discreet representation of the relaxation function depends not only
`on T2, but also on the echo spacing 2*7,. Shorter echo spacing leads to a more gradual
`slope and therefore to a less pronounced effect on the amplitude of the shape function
`as well as its distortion.
`Due to technical restrictions, 2*7, cannot be made arbitrarily small in a multiecho
`experiment. An artificial shortening of the sampling steps for the relaxation function
`can be achieved if the experiment is performed with n excitations instead of one and
`the phase-encoding steps are interleaved (15). Discontinuities arising from the fact
`that by simple repetition of the multiecho experiment under variation of the phase-
`encoding groups of n projections are sampled at identical readout times, can be removed
`by one of the following methods:
`(1) Prolongation of the times between 90" and the first 180" pulse by 7Jn in con-
`secutive echo trains.
`(2) Substitution of the 90" pulse by a 90"-~,/n-180" pulse sequence.
`(3) Substitution of the 90" pulse by a 90" pulse followed by an orthogonal spin-
`locking pulse of duration 7Jn.
`For an explicit calculation for a realistic case, the image representing spin density has
`first to be separated into regions with identical T2. E' has to be calculated for all those
`shape functions by inverse Fourier transformation and the multiplication according
`to the phase-encoding scheme carried out using the appropriate discreet representation
`of the respective relaxation functions. Fourier transformation and addition of the
`results for all different T2's leads to the echo image.
`Of course such a calculation is impracticable for a clinical case. Some insight can
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`HENNIG, NAUERTH, AND FREDBURG
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`however be gained by looking at the result of the explicit calculation for objects with
`Lorentzian spindensity distribution along the phase direction, which is given in the
`Appendix. Figures 4a-d show the influence of T2 and the width of a structure on the
`signal intensity for a singleexcitation echo image and one that used 16 excitations in
`the manner described above. It is clear, that the relaxation constant is the main de-
`tennining parameter for the intensity attenuation (Figs. 4a, b). We therefore call this
`method RARE imaging for Rapid Acquisition with Relaxation Enhancement.
`Figure 4b shows that the T2 contrast is much less pronounced if one samples the
`data in 16 echotrains with 16 echoes each, leading to a good presentation of even
`short T2 structures. The influence of the width of the structure is shown in Figs.
`4c-d. Sharp structures are more attenuated than structures with medium width. Not
`shown in the graphs is the sharp decline of the signal intensity for very broad structures
`especially when the dephasing zero point is put into late echoes.
`A very interesting point to note is given by the second vertical scale in Figs. 3 and
`4. It gives the signal sampled per unit of time as compared to a conventional 2D
`experiment and therefore can be used as a measure of the efficiency of the imaging
`method. For structures with long T2, this figure of merit can be as high as 100, clearly
`contradicting the common misconception, that faster imaging for a given resolution
`is only attainable at the cost of low signal to noise.
`
`Fu
`50
`
`25
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`c
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`LE1
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`a
`32
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`d
`
`1000
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`2000 als-’)
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`FIG. 4. Calculated relative intensities for Lorentzian shapes in a 256 X 256 RARE image. The intensity
`units Id are scaled to I equal to the spin density. Fwre of merit F,,, is given as the quotient of S i
`sampled per unit of time for RARE image divided by the same number for a conventional 2D FT image
`with same resolution. (a) I vs T2 for a singleshot imase; (b) I vs T2 for a 16cxcitation image; (c) I vs u for
`a singleshot image; (d) I vs u for 16-excitation image where u is the linewidth of the Lorentzian shape in
`Hz for a total image size of 25 kHz. y ~ o gives the acho number with dephasing gradient 0.
`
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`RESULTS
`The validity of the arguments presented in the previous chapter is demonstrated
`by the graphs shown in Fig. 5, where the relative signal intensity is plotted vs the
`relaxation time for a human patient head slice. Although an attempt to attribute the
`size of structures has not been made quantitatively, it is obvious, that the sharper
`structures of the skin are more attenuated than more extended structures inside the
`head for equal T2. The images, from which the figures are taken, are shown in Figs.
`6a-c. T2 values were calculated from 12 echoes in a conventional multiecho 2D fl
`sequence.
`A comparison of the single acquisition image (Fig. 5b) with a RARE image taken
`with 16 acquisitions (Fig. 5c) shows, that the T2 contrast is much stronger in the single
`acquisition image. It is obvious as well, that the single acquisition image has sufficient
`resolution to be a valuable tool for patient positioning. More than that, due to its T2
`character it is especially suited to detect lesions with long T2.
`From a clinical point of view it is most important to note that the RARE sequence
`delivers images which are practically free from artifacts if an appropriate phase-encoding
`scheme is chosen. This is markedly different from the situation one encounters when
`echo imaging is applied to a back-projection imaging scheme (16).
`
`DISCUSSION
`Since its implementation in October 1984, we have examined about 1 100 patients
`with RARE imaging in our department. We have found, that it is an indispensable
`tool for exact patient positioning. Above that, more than 90% of lesions in the head,
`which were lesions with long T2, were clearly shown in the RARE imaging alone.
`Multiple sclerosis plaques are shown clearly in the RARE image. Combined with
`multislice techniques, a head scan with 8 slices can be performed in less than 2 min,
`leading to very short overall investigation times per patient. Due to the fact that the
`RARE sequence, which has proven to be most useful in head investigations and which
`is represented by Fig. 6c, gives only low T2 contrast between medium T2 values (200
`ms and more), fat around the spinal chord is not always clearly distinguishable from
`tumors and therefore different sequences giving sharper contrast have to be tailored
`
`I ':"
`
`5
`5
`1 0
`FIG. 5. Rel. intensities I=, and figures of merit FM vs T2 for RARE images shown in FIG. 6. (a) Single-
`shot experiment; (b) 16-excitation experiment. Open circles correspond to sharp structures.
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`HENNIG, NAUERTH, AND FRIEDBURG
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`FIG. 6. Conventional 2D FT image (a) compared to a single-shot RARE image (b) and a 16-excitation
`RARE image (c) of a patient with recurrent pituitary adenoma with infiltration of the brain tissue. Imaging
`parameters for the conventional image were 1800 ms for the repetition time, echo readout time 33 ms.
`
`for these applications. The single acquisition experiment (Fig. 6b) promises to be most
`useful in these cases (18).
`In the abdomen, where the prediction of relaxation times is most difficult and short
`T2 are not uncommon, the choice of the appropriate RARE sequence is often difficult-
`as is the choice of the appropriate conventional 2D FT experiment. RARE can be
`used here as a fast means to check for the T2 sensitivity of a suspected lesion. According
`to the contrast of the RARE image one can choose the 2D FT sequence most likely
`to yield a good presentation of the lesion with more confidence, so that the overall
`efficiency and speed of an examination is increased even if the RARE image gives
`only poor lesion contrast.
`The high signal sampling efficiency of RARE promises to make it a good method
`for 3D FT. Apart from that, it can be used to acquire images with very high SIN in
`reasonable time by averaging. Both possibilities are studied at the moment in our
`department.
`
`EXPERIMENTAL
`
`All our experiments were performed on a 0.23-T system Bruker BNT 1 100. Patients
`were investigated using a 60-cm body coil, a 50-cm body coil, 28 and 22 cm head
`coils, and various surface coils for special cases. No special setup procedures were
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`FIG. 6-Continued.
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`HENNIG, NAUERTH, AND FRIEDBURG
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`necessary for imaging with our method, allowing us to apply it as part of our routine
`measurement menu.
`Slice width was 8 mm standard some investigations were performed with down to
`2 mm width. 2D FT and RARE imaging were taken without patient dislocation to
`allow the direct comparison of images.
`
`APPENDIX
`
`Explicit Evaluation of the Shape Function of a Lorentzian
`Image with RARE Imaging
`
`A structure with Lorentzian spin-density distribution oriented along the phase-
`encoding gradient and symmetrical around the gradient field zero point yields in a
`2D FT imaging sequence an echo for the second Fourier transformation which can
`be described as
`
`E = Moexp(a - cp)
`E = Moexp(-a - cp)
`
`for
`
`for
`
`cp < 0
`
`cp > 0
`
`where cp, the time coordinate in a normal 1D F'T experiment, is given by the dephasing
`gradient as described by Ernst (1 7). Fourier transformation yields the well-known
`function
`
`where w is the spatial coordinate in frequency units. To calculate the lineshape according
`to a RARE imaging experiment, one has to multiply the echo function E with the
`relaxation function. The zero point of both functions needs not to be identical.
`The time variable of the relaxation function has to be transformed into the time
`domain of the phase-encoding gradient. This can be done easily if one takes into
`account that the dwell time of the phase-encoding gradient steps has to be identified
`with the echo spacing 27,. Due to the symmetry of the 2D lT algorithm, the dwell
`time of the phase encoding can be set equal to the dwell time dw of the data sampling
`relaxation by a factor 27,/dW for a single shot experiment or 27,/(n - dw) if one samples
`for a geometrically square image. This leads to a compression of the timescale for the
`data in n acquisitions in the interleaving manner described above. This yields
`
`E' = Moexp - 27e
`
`)exp(a(cp -
`
`( n.dw.T2
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`Fourier transformation gives
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`-
`a -
`
`exp(- a - p0).
`- iu
`
`MO
`27,
`n-dw+ T2
`(po represents the dephasing zero point, that is, the center of the “echo” E’.
`Neglecting the first-order phase distortion factor exp(-iw(po) this can be described
`as the sum of three functions. The real part of the first term gives a Lorentzian line
`sharpened by 27J(n-dw* T2) compared to (I) and the real part of the second term
`gives a Lorentzian line broadened by the same term. The amplitude of both functions
`is attenuated by exp((-2r,cpo/(n-dw* T2)). The third term gives the loss of the signal
`due to the cutoff of the echo at cp = 0. If (po = 0 the first and third terms cancel and
`one gets the familiar solution of the Fourier transform of an FID. For sharp structures,
`where a < 27&
`dw T2) the amplitude of the signal is directly proportional to MO T2,
`giving an image identical in appearance to the product of a spin-density image with
`a T2 image as calculated from a multiecho sequence.
`
`REFERENCES
`1. T. F. BUDmGER, IEEE Trans. Nwl. Ski. 26,2812 (1979).
`J. C. WATERTON, H. G. LOVE, X. P. ZHU, 1. ISHERWOOD, AND D. RoWUNDS, Br.
`2. J. P. R. JENKINS,
`Heart J. 53,91 (1985).
`3. P. VAN DUK, Roceedings Fourth Annual Meeting of the Society for Magnetic Resonance in Medicine,
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`4. A. WE, J. FRAIM, D. MATTHAEI, W. HAEMCKE, AND K. D. MERDOLDT, Ro~xdqs, Fourth
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`7. P. MANSFIELD, Br. Med. Bull. 40, 187 (1984).
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`10. E. M. HAACKE, F. H. BEARDEN, AND J. R. CLAYTON, Proceedings Fourth Annual Meeting of the
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`11. C. M. J. VAN UUEN, Magn. Reson. Med. 18,268 ( 1984).
`12. S. M E ~ M
`AND D. GILL, Rev. Ski. Instrum. 29,688 (1958).
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`14. A. MEHLKOPF, P. VAN DER MEULEN, AND J. SMIDT, Mugn. Reson. Med. 1,295 (1984).
`15. 1. R. YOUNG AND M. BURL, UK Patent Awl. GB 2056078 A.
`16. L. D. HALL AND S. SUKUMAR, Magn. Reson. Med. 18, 179 (1984).
`17. A. KUMAR, D. WELTI, AND R. ERNST, J. Magn. Reson. 1669 (1975).
`18. J. HENNIG, H. FRIEDBURG, AND B. STROEBEL, J. Compul. Assist. Tomw. 10,375 (1986).
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