Method and device for determination of a magnetic resonance control sequence

Abstract

A magnetic resonance control sequence with a pulse arrangement that acts selectively in at least two spatial directions in order to excite a limited rotationally symmetrical excitation profile within an examination subject has an RF excitation pulse formed as a sequence of multiple partial RF pulses, and gradient pulses in the two spatial directions that are coordinated with the partial RF pulses so that the RF energy introduction of different partial RF pulses in transmission k-space occurs on circular k-space transmission trajectories that are concentric to one another. The amplitude of the RF envelope of the partial RF pulses is constant during the duration of a traversal of each circular k-space trajectory. The control sequence can also be used in a calibration of a magnetic resonance system.

Claims

1. A method for operating a magnetic resonance apparatus, said method comprising: in a computerized processor, determining a magnetic resonance control sequence as a radio-frequency (RF) excitation pulse, comprised of a sequence of multiple, partial RF pulses, coordinated with gradient pulses in two spatial directions placed in parallel with said sequence of multiple, partial RF pulses so as to cause said RF excitation pulse to selectively excite nuclear spins in at least two spatial directions to produce a limited, rotationally symmetrical excitation profile within an examination subject; in said computerized processor, determining said sequence of multiple, partial RF pulses in order to cause an RF energy introduction of different partial RF pulses, among said sequence of multiple, partial RF pulses, in transmission k-space to respectively occur on circular k-space transmission trajectories that are concentric to each other; in said computerized processor, determining an amplitude of an RF envelope of said partial RF pulses to be respectively constant during a duration of traversal of each circular k-space trajectory; and in said computerized processor, generating control signals corresponding to the determined magnetic resonance control sequence, with the determined sequence of multiple, partial RF pulses and with the determined RF envelope of said partial RF pulses, and emitting said control signals to said magnetic resonance apparatus in order to acquire magnetic resonance data from a subject.

2. A method as claimed in claim 1 comprising, in said computerized processor, setting the duration of the traversal of the respective circular k-space trajectories to be the same duration for respectively different partial RF pulses among said sequence of multiple, partial RF pulses.

3. A method as claimed in claim 1 comprising, in said computerized processor, determining the duration of the traversal of the respective circular k-space trajectories individually for different partial RF pulses in said sequence of multiple, partial RF pulses.

4. A method as claimed in claim 1 comprising, in said computerized processor, setting the duration of traversal of the respective circular k-space trajectories to be a maximum that causes said gradient pulses not to exceed a predetermined maximum gradient slew rate.

5. A method as claimed in claim 1 comprising, in said computerized processor, determining said gradient pulses in order to cause two of said concentric circular k-space trajectories, respectively associated with temporally adjacent partial RF pulses in said sequence of multiple, partial RF pulses, to be traversed in opposite directions in transmission k-space.

6. A method as claimed in claim 1 comprising, in said computerized processor, determining said gradient pulses in order to cause said circular k-space trajectories to form equidistant rings in transmission k-space.

7. A method as claimed in claim 1 comprising, in said computerized processor, determining said gradient pulses in order to cause said concentric circular k-space trajectory used to form rings having a radial spacing relative to each other that becomes smaller in a direction of the common center of said concentric circular k-space trajectories.

8. A method as claimed in claim 1 comprising, in said computerized processor, selecting a number of said concentric circular k-space trajectories depending on a ratio of a spacing between a first side lobe of the excitation profile to a diameter of said excitation profile.

9. A method as claimed in claim 1 wherein said excitation profile is a cylindrical excitation profile, and comprising, in said computerized processor, determining the amplitude of the envelope of the partial RF pulses in order to cause a target flip angle, produced by said partial RF pulses in said cylindrical excitation profile, to be substantially constant.

10. A method to calibrate a magnetic resonance apparatus, comprising: in a computerized processor, determining a magnetic resonance control sequence as a radio-frequency (RF) excitation pulse, comprised of a sequence of multiple, partial RF pulses, coordinated with gradient pulses in two spatial directions placed in parallel with said sequence of multiple, partial RF pulses so as to cause said RF excitation pulse to selectively excite nuclear spins in at least two spatial directions to produce a limited, rotationally symmetrical excitation profile within an examination subject; in said computerized processor, determining said sequence of multiple, partial RF pulses in order to cause an RF energy introduction of different partial RF pulses, among said sequence of multiple, partial RF pulses, in transmission k-space to respectively occur on circular k-space transmission trajectories that are concentric to each other; in said computerized processor, determining an amplitude of an RF envelope of said partial RF pulses to be respectively constant during a duration of traversal of each circular k-space trajectory; in said computerized processor, generating control signals corresponding to the determined magnetic resonance control sequence, with the determined sequence of multiple, partial RF pulses and with the determined RF envelope of said partial RF pulses, and emitting said control signals to said magnetic resonance apparatus in order to repeatedly operate said magnetic resonance apparatus, in a plurality of repetitions, according to said determined magnetic resonance control sequence so as to acquire magnetic resonance image data in each repetition; and with said control signals in respective repetitions, changing, from repetition-to-repetition, a gradient delay time associated with said gradient pulses until a gradient delay time is achieved that causes a predetermined quality criterion of said image data to be satisfied.

11. A magnetic resonance apparatus comprising: a magnetic resonance data acquisition unit comprising an RF transmission system and a gradient system; a computerized processor configured to determine a magnetic resonance control sequence as a radio-frequency (RF) excitation pulse, comprised of a sequence of multiple, partial RF pulses, coordinated with gradient pulses in two spatial directions placed in parallel with said sequence of multiple, partial RF pulses so as to cause said RF excitation pulse to selectively excite nuclear spins in at least two spatial directions to produce a limited, rotationally symmetrical excitation profile within an examination subject; said computerized processor being configured to determine said sequence of multiple, partial RF pulses in order to cause an RF energy introduction of different partial RF pulses, among said sequence of multiple, partial RF pulses, in transmission k-space to respectively occur on circular k-space transmission trajectories that are concentric to each other; said computerized processor being configured to determine an amplitude of an RF envelope of said partial RF pulses to be respectively constant during a duration of traversal of each circular k-space trajectory; and said computerized processor being configured to generate control signals corresponding to the determined magnetic resonance control sequence, with the determined sequence of multiple, partial RF pulses and with the determined RF envelope of said partial RF pulses, and to emit said control signals to said magnetic resonance data acquisition unit in order to operate said RF transmission system and said gradient system so as to acquire magnetic resonance data.

12. A non-transitory, computer-readable data storage medium encoded with programming instructions, said storage medium being loaded into a computerized control and evaluation system of a magnetic resonance apparatus, and said programming instructions causing said computerized control and evaluation unit to: determine a magnetic resonance control sequence as a radio-frequency (RF) excitation pulse, comprised of a sequence of multiple, partial RF pulses, coordinated with gradient pulses in two spatial directions placed in parallel with said sequence of multiple, partial RF pulses so as to cause said RF excitation pulse to selectively excite nuclear spins in at least two spatial directions to produce a limited, rotationally symmetrical excitation profile within an examination subject; determine said sequence of multiple, partial RF pulses in order to cause an RE energy introduction of different partial RF pulses, among said sequence of multiple, partial RF pulses, in transmission k-space to respectively occur on circular k-space transmission trajectories that are concentric to each other; determine an amplitude of an RF envelope of said partial RE pulses to be respectively constant during a duration of traversal of each circular k-space trajectory; and generate control signals corresponding to the determined magnetic resonance control sequence, with the determined sequence of multiple, partial RF pulses and with the determined RE envelope of said partial RF pulses, and emit said control signals to said magnetic resonance apparatus in order to operate said magnetic resonance apparatus so as to acquire magnetic resonance data from a subject.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic depiction of an exemplary embodiment of a magnetic resonance system according to the invention.

(2) FIG. 2 is a schematic depiction of equidistant, concentric ring trajectories in an x/y plane in k-space according to a first exemplary embodiment of the invention.

(3) FIG. 3 shows a magnetic resonance slice image of a cylindrically symmetrical excitation profile and the 1st lateral excitation within a phantom in positional space.

(4) FIG. 4 is a simplified depiction of a pulse diagram for explanation of the design of an individual partial RF pulses.

(5) FIG. 5 is a schematic, enlarged depiction of equidistant, concentric ring trajectories in the I-th quadrant of an x/y plane in k-space to explain the density of the trajectories.

(6) FIG. 6 is a simplified depiction of a pulse diagram of an RF excitation pulse according to a first exemplary embodiment of the method according to the invention.

(7) FIG. 7 is a simplified depiction of a pulse diagram of an RF excitation pulse according to a second exemplary embodiment of the method according to the invention.

(8) FIG. 8 is a simplified depiction of a pulse diagram of an RF excitation pulse according to a third exemplary embodiment of the method according to the invention.

(9) FIG. 9 is an enlarged depiction of portions of the pulse diagram according to FIG. 8.

(10) FIG. 10 is a schematic depiction of concentric ring trajectories in an x/y plane in k-space according to a second exemplary embodiment of the invention.

(11) FIG. 11 is a schematic depiction of a trajectory with a spiral-shaped trajectory in the outer region and concentric ring trajectories in the inner region in an x/y plane in k-space, according to a third exemplary embodiment of the invention.

(12) FIGS. 12 through 14 show different slice image exposures of excitations of different excitation profiles given different gradient delay times for comparison, respectively above by means of an EPI excitation and below with a variant of a method according to the invention.

(13) FIG. 15 is an adjustment diagram (flowchart) for an embodiment of a method to calibrate a magnetic resonance system according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(14) A magnetic resonance (MR) system 1 according to the invention is schematically depicted in FIG. 1. The system includes the actual magnetic resonance scanner 2 with an examination space 8 or patient tunnel located therein. A bed 7 can be driven into this patient tunnel 8, such that a patient O or test subject lying on the bed 7 can be supported at a defined position within the magnetic resonance scanner 2 (relative to the magnet system and radio-frequency system arranged therein) during an examination. The patient O or test subject on the bed 7 also can be moved between different positions during a measurement (data acquisition).

(15) Among the components of the magnetic resonance scanner 2 are a basic field magnet 3, a gradient system 4 with magnetic field gradient coils to generate magnetic field gradients in the x-, y- and z-direction, and a whole-body radio-frequency (RF) coil 5. The magnetic field gradient coils in the x-, y- and z-direction are controllable independently of one another so thatby a predetermined combinationgradients can be applied in arbitrary spatial directions (for example in a slice selection direction, in a phase coding direction, or in a readout direction) that are not necessarily situated parallel to the axes of the spatial coordinate system. The acquisition of magnetic resonance signals produced in the examination subject O takes place using the whole-body coil 5 with which the radio-frequency signals for creation of the magnetic resonance signals are also normally emitted. However, these signals are typically received with a local coil arrangement 6 with local coils (of which only one is shown) placed on or below the patient O, for example. All of these components are known in principle to those skilled in the art, and therefore are only roughly schematically depicted in FIG. 1.

(16) The components of the magnetic resonance scanner 2 are controllable from a control device 10. This can thereby be a control computer that can also include a number of individual computers (which possibly are spatially separated and connected among one another via suitable cables or the like). This control device 10 is connected via a terminal interface 17 with a terminal 20 through which an operator can control the entire system 1. In the present case, this terminal 20 has a computer 21 with keyboard, one or more monitors and additional input devices (for example mouse or the like). The computer 21 may be designated such that a graphical user interface is provided to the operator.

(17) Among other things, the control device 10 has a gradient control unit 11 that can include multiple sub-components. The individual gradient coils can be fed with control signals according to a gradient pulse sequence GS via this gradient control unit 11. As described above, these are gradient pulses that are set at precisely provided temporal positions and with a precisely predetermined time curve during a measurement.

(18) Moreover, the control device 10 has a radio-frequency transmission unit 12 in order to feed respective radio-frequency pulses into the whole-body radio-frequency coil 5 according to a predetermined radio-frequency pulse sequence RFS of the control sequence AS. The radio-frequency pulse sequence RFS includes the aforementioned selective excitation pulses. The receipt of the magnetic resonance signals then occurs with the aid of the local coil arrangement 6, and the raw data RD acquired by this are read out and processed by an RF reception unit 13. The magnetic resonance signals in digital form are passed as raw data RD to a reconstruction unit 14, which reconstructs the image data BD from these and stores them in a memory 16 and/or passes them via the interface 17 to the terminal 20 so that the operator can view them. The image data BD can also be stored and/or displayed and evaluated at other locations via a network NW. Alternatively, a radio-frequency pulse sequence can be emitted via the local coil arrangement and/or the magnetic resonance signals can be received by the whole-body radio-frequency coil (not shown).

(19) Through an additional interface 18, control commands are transmitted to other components of the magnetic resonance scanner 2 (for example the bed 7 or the basic field magnet 3) or measurement values and other information are received.

(20) The gradient control unit 11, the RF transmission unit 12 and the RF reception unit 13 are controlled in coordination by a measurement control unit 15. Through appropriate commands, this ensures that the desired gradient pulse sequence GS and radio-frequency pulse sequence RFS of the pulse sequence are emitted. Moreover, it must be ensured that the magnetic resonance signals at the local coils of the local coil arrangement 6 are read out by the RF reception unit 13 at the matching point in time and are processed further, meaning that readout windows must be set in that the ADCs of the RF reception unit 13 are switched to receive, for example. The measurement control unit 15 likewise controls the interface 18.

(21) The basic workflow of such a magnetic resonance measurement and the cited components for control are known to those skilled in the art, and thus need not be discussed in further detail herein. Moreover, such a magnetic resonance scanner 2 and the associated control device can have additional components, which here are likewise not explained in detail herein. The magnetic resonance scanner 2 can also be designed differently, for example with a laterally open patient space, or as a smaller scanner in which only one body part can be positioned.

(22) In order to start a measurement, via the terminal 20 an operator typically selects a control protocol P provided for this measurement from a memory 16, in which control protocols P for respectively different measurements are stored. This control protocol P includes, among other things, various control parameter values SP for the respective measurement. Among these control parameter values SP are, for example, the sequence type, the target magnetizations for the individual radio-frequency pulses, echo times, repetition times, the various selection directions etc. Slice thicknesses, resolution, number of slices and, in the case of a 3D excitation, the slab thickness or additional dimensions of an arbitrary excitation profile (i.e. excitation profile data), can likewise be provided in the protocol P. Furthermore, the control parameter values SP can include information as to whether the respective measurement is a measurement with navigator and, if so, the excitation profile data for the excitation profile EP, which is necessary for this navigator application. For the application schematically depicted in FIG. 1, this excitation profile EP can be the aforementioned pencil beam that extends cylindrically symmetrically in the z-direction in the body of the patient O, and proceeds through the diaphragm 9 of the patient O.

(23) All of these control parameter values SP are provided via (among other things) an input interface 24 of a control sequence determination device 22 so that this determines a matching control sequence AS. The control parameter values SP can initially be offered to the operator for adoption upon retrieval of this protocol, and the operator can arbitrarily vary the values with the use of the user interface and adapt them to the current examination task. In particular, the operator can establish the excitation profile data (for example a diameter d, the precise position of the axis of symmetry, etc. of the rotationally symmetrical excitation profile EP) via the computer 21 of the terminal 20 with the associated graphical user interface, or can modify excitation profile data that are already defined in the protocol P via the control parameter values SP. This is indicated by the interface arrangement 23 in FIG. 1.

(24) Moreover, the user can also retrieve control protocols via a network NW (instead of from the memory 16), for example from a manufacturer of the magnetic resonance system, with corresponding control parameter values SP, and then use these as described in the following.

(25) Based on the control parameter values SP (including the excitation profile data), a control sequence AS is then determined according to which the control of the remaining components via the measurement control unit 15 ultimately takes place. This control sequence then includes (among other things) the pulse arrangement in order to selectively excite the chosen excitation profile EP. As mentioned, the control sequence AS is calculated in a control sequence determination device 22 that is depicted as part of the terminal 20, and is passed to the control device 10 of the magnetic resonance scanner 2 via a control sequence output interface 25. Among other things (the additional components are not depicted in FIG. 1 for the sake of better clarity), the control sequence determination device 22 comprises a pulse arrangement determination unit 26 which determines the aforesaid pulse arrangement for selective excitation of the excitation profile EP. For example, the entire control sequence determination device 22 and its components can be realized in the form of software on one or more suitable processors. The precise functionality of the control sequence determination device 22 and its individual components is explained further in the following, wherein the pencil beam excitation explained above is merely assumed as an example without, however, limiting the invention to this example.

(26) To design a two-dimensional RF pulse in order to excite an x/y plane situated orthogonal to the axis of symmetry s in positional space of a cylindrically symmetrical excitation profile EP, in addition to the excitation profile in this plane a two-dimensional k-space transmission trajectory must in general initially be chosen within the associated x/y plane in k-space (with the time-dependent coordinates (k.sub.x(t), k.sub.y(t)) in k-space, also abbreviated in the following as (k.sub.x, k.sub.y)). The excitation profile is determined by the function P(x,y) at the location with the coordinate values x and y. The function P(x,y) indicates the desired magnitude of the transversal magnetization relative to the magnitude of the steady state magnetization, thus has no unit. The k-space coverage (extent) of this trajectory determines the spatial resolution with which the desired selection profile can be realized. The sampling density of the trajectory in k-space determines the spacing of the first lateral band of the excitation in positional space, also called FOV (field of view). Such lateral bands are unavoidable due to the discrete sampling.

(27) With the selected k-space trajectory (k.sub.x, k.sub.y), the two-dimensional gradient field (g.sub.x(t), g.sub.y(t)) during the radio-frequency radiation is linked via

(28) $\begin{array}{cc}\left(k_x\left(t\right),k_y\left(t\right)\right)=-\frac{}{2}{}_t^T\left(g_x\left(\right),g_y\left(\right)\right)d\mathrm{and}& \left(1\right)\\ \left(g_x\left(t\right),g_y\left(t\right)\right)=\frac{2}{}\left(\frac{d{k}_x\left(t\right)}{dt},\frac{d{k}_y\left(t\right)}{dt}\right)& \left(2\right)\end{array}$

(29) The minus sign in Formula (1) is a consequence of the convention of starting the integration at the end of the RF pulse (t=T). The time t thus indicates the remaining time until the end of the RF pulse.

(30) The associated pulse shape b.sub.1(t) of the RF pulses b.sub.1(t) is the time-dependent amplitude that results from the weighted two-dimensional Fourier transformation of the desired spatial excitation profile P(x,y) by the desired excitation profile P(x,y):

(31) $\begin{array}{cc}{b}_1\left(t\right)\frac{.Math.\left(g_x\left(t\right),g_y\left(t\right)\right).Math.}{\left(k_x\left(t\right),k_y\left(t\right)\right)}{}_{-}^{}{}_{-}^{}P\left(x,y\right)e^{2i\left(k_{x}x+k_{y}y\right)}dxdy& \left(3\right)\end{array}$

(32) This formula can be derived from the Bloch equation (in the limit of the small angle excitation); see for example J. Pauly et al. A k-Space Analysis of Small-Tip-Angle Excitation in Journal of Magn. Res. 81, Pages 43 to 56, 1989, and C. J. Hardy et al. Correcting for Nonuniform k-Space Sampling in Two-Dimensional NMR Selective Excitation in Journal of Magn. Res. 87, Pages 639 to 645, 1990.

(33) In Formula (3), the first weighting factor
|(g.sub.x(t),g.sub.y(t))|={square root over (g.sub.x.sup.2(t)+g.sub.y.sup.2(t))}(4)
is the transverse velocity in k-space.

(34) The second factor weights the density of k-space sampling at the position (k.sub.x, k.sub.y) in k-space:

(35) $\begin{array}{cc}\left(k_x,k_y\right)=\frac{l\left(k_x,k_y\right)}{A\left(k_x,k_y\right)}& \left(5\right)\end{array}$

(36) In Formula (5), A(k.sub.x, k.sub.y) is a small area of k-space in the environment of the k-space point (k.sub.x, k.sub.y), and l(k.sub.x, k.sub.y) is the length of the trajectory that is enclosed by the area. The factors according to Formulas (4) and (5) clearly indicate that the RF amplitude is to be reduced where k-space is scanned slowly or, respectively, with high density, and vice versa.

(37) In the method according to the invention, a k-space trajectory with at least two concentric ring trajectories should be chosen for selective excitation of the excitation profile. Such a k-space trajectory, with eight concentric ring trajectories TR.sub.1, TR.sub.2, . . . , TR.sub.8 in total that respectively proceed at an equidistant radial distance kr relative to one another, point-symmetrically around the center point of k-space S.sub.k, is shown as an example in FIG. 2.

(38) A concentric ring trajectory is achievable in that the two selection gradients (i.e. the gradient pulses emitted during the selective RF pulse and serving for selection) are modulated by a sine or, respectively, cosine function during the RF radiation:

(39) $\begin{array}{cc}{g}_{x,n}\left(t\right)=A_n\sin \left(2\frac{t}{T_n}\right)g_{y,n}\left(t\right)=A_n\cos \left(2\frac{t}{T_n}\right)& \left(6\right)\end{array}$
wherein n is the excitation index (i.e., the index of the ring trajectory) that assumes a value between 1 and N, wherein N is the number of rings of the chosen trajectory (in the example according to FIG. 2, N=8 thus applies). A.sub.n is the magnitude of the gradient amplitude during the n-th excitation, and T.sub.n is the duration of the n-th excitation (i.e. the RF radiation at the n-th ring). One possible common phase factor is omitted in Formulas (6)without limiting the generalityin order to keep the formulas as simple as possible.

(40) The first weighting factor in Formula (3)the k-space transverse velocityis therefore constant during the traversal of a ring trajectory:
|(g.sub.x,n(t),g.sub.y,n(t))|={square root over (g.sub.x,n.sup.2(t)+g.sub.y,n.sup.2(t))}=A.sub.n(4)

(41) The second weighting factorthe density compensation factor

(42) $\begin{array}{cc}{}_n\left(k_x,k_y\right)=\frac{l_n\left(k_x,k_y\right)}{A_n\left(k_x,k_y\right)}& \left(5^{}\right)\end{array}$
can be estimated for equidistant ring trajectories via the reciprocal value of the radial spacing kr between adjacent rings in k-space. This is explained in detail below with the use of FIG. 5. The density compensation factor is only significant in the case of a variable density allocation of k-space with ring trajectories, namely non-equidistant spacing of the ring trajectories. For specific ring trajectories, n (with 1<n<N) can then be used as a density compensation factor (for example 1) due to the average radial spacing from the two nearest neighbor rings.
According to the invention, the desired excitation profile P(x,y) is rotationally symmetrical and thus depends (insofar as it is specified in polar coordinates) only on the radial spacing r={square root over (x.sup.2+y.sup.2)}, and not on the polar or azimuthal angle .sub.r, meaning that P(x,y)=P(r) applies.

(43) Via a coordinate transformation of the Fourier transformation in Formula (3) of Cartesian to polar coordinates,

(44) $\begin{array}{cc}\underset{-}{\overset{}{}}\underset{-}{\overset{}{}}P\left(x,y\right)e^{2i\left(k_x\left(t\right)x+k_y\left(t\right)y\right)}d\mathrm{xd}y=\underset{r=0}{\overset{}{}}\underset{{}_r=-}{\overset{}{}}P\left(r\right)e^{2i\mathrm{kr}\cos \left({}_r-{}_k\right)}rdrd{}_r=\underset{r=0}{\overset{}{}}\underset{{}_r=-}{\overset{}{}}P\left(r\right)\left(\underset{m=-}{\overset{}{.Math.}}{i}^m{J}_m\left(\mathrm{kr}\right)e^{\mathrm{im}\left({}_r-{}_k\right)}\right)rdrd{}_r& \left(3^{}\right)\end{array}$
.sub.r is the azimuthal angle of the spatial vector (x,y)=(r, .sub.r), and .sub.k is the azimuthal angle of the wave vector (k.sub.x, k.sub.y)=(k, .sub.k), and J.sub.m is the m-th order Bessel function. Under the assumption that the desired excitation profile is rotationally symmetrical, the integration over the spatial azimuthal angle can be incorporated into the sum, and only the 0th-order term remains. Formula (3) can therefore be simplified as:

(45) $\begin{array}{cc}{b}_1\left(t\right)2\frac{\left|\left(g_x\left(t\right),g_y\left(t\right)\right)\right|}{\left(k_x\left(t\right),k_y\left(t\right)\right)}\underset{0}{\overset{}{}}P\left(r\right)J_0\left(k\left(t\right)r\right)rdr& \left(7\right)\end{array}$

(46) Since the magnitude of the wave vector k(t)=k is constant on an orbit, it directly follows from this depiction that the integral on the right side is also constant for a defined orbit (excitation), and therefore the b.sub.1 amplitude during a single ring trajectory as well. As explained above, switching delays of the gradient coils thus are no longer of consequence.

(47) A two-dimensional RF pulse according to the invention can be constructed as a composite RF pulse with multiple such partial pulses, wherein each partial pulse comprises a rectangular pulse with constant amplitude b.sub.1 (n) of duration T.sub.n, and the gradients oscillate sinusoidally or, respectively, cosinusoidally with period T.sub.n during the radiation duration T.sub.n, such that an orbit (namely the associated n-th ring trajectory) in associated excitation k-space is traversed.

(48) In practice, the ring trajectories must initially be established more precisely for excitation of a defined volume or excitation profile before the design of the individual partial pulses. In the following, a cylindrical rod volume with a diameter d (which, for example, can be used in the navigator technique) is assumed again as an example.

(49) The parameters that are relevant to the user (and therefore specified by him) are the diameter d of the rod and the spacing S.sub.SL of the first lateral excitation SL (side lobe). Side lobes are unavoidable due to the discrete sample of k-space. The user will choose the spacing S.sub.SL of the first side lobe SL to be so large that it specifically lies outside of the examination subject and no tissue is excited with it. If the examination subject is an adult, typical values are d25 mm for the diameter of the excitation and S.sub.SL400 mm for the spacing of the first side lobe given the aforementioned navigator application.

(50) From Formula (7) it is clear that the complex-valued b.sub.1 field and the desired excitation profile P(r) form a Fourier transformation pair.

(51) From the property P(r)=0 for r>S.sub.SL and the Nyquist theorem, the minimum spacing of the sampling in k-space follows according to

(52) $\begin{array}{cc}\mathrm{kr}\frac{1}{2.Math.S_{\mathrm{SL}}}& \left(8\right)\end{array}$

(53) The specified diameter d of the excitation over the diameter 2.Math.kr.sub.max=2.Math.N.Math.kr of scanned k-space determines the number N of ring trajectories:

(54) $\begin{array}{cc}\frac{d}{2}=\frac{1}{2.Math.{\mathrm{kr}}_{\max }}.fwdarw.d=\frac{1}{N.Math.\mathrm{kr}}& \left(9\right)\end{array}$

(55) Since the Fourier transformation of the desired excitation profile for kr>kr.sub.max is zero, its frequency spectrum is limited. The Nyquist theorem is therefore applicable, and the relation (9) is a direct consequence of this.

(56) The minimum number N of ring trajectories is obtained from Formulas (8) and (9) as a function of the specified parameters d (diameter of the excitation profile) and S.sub.SL (spacing of the first side lobe):

(57) 0$\begin{array}{cc}N=2.Math.\frac{S_{\mathrm{SL}}}{d}& \left(10\right)\end{array}$

(58) As an example, for explanation, FIG. 3 shows a positional space image of a slice (thus a cross section) through a rod-shaped excitation profile EP with diameter d and with a side lobe SL at a distance S.sub.SL. The positional space image is an image of a spherical phantom with a diameter of 240 mm. In a FLASH sequence, the conventional excitation profile was replaced by a two-dimensional selective RF pulse with an excitation trajectory according to the invention, with concentric ring trajectories. The number of rings was set at N=8, and the spacing of the first lateral ring was set equal to 64 mm. This corresponds to the trajectory shown in FIG. 2, meaning that FIGS. 2 and 3 also illustrate the correlation of the excitation in the two Fourier domains (excitation profile in positional space in FIG. 3 and associated excitation k-space S.sub.k in FIG. 2). According to Formula (10), a diameter of the central excitation profile of d=2.Math.64/8 mm=16 mm would be expected with this. The dimensions determined in the measurement according to FIG. 3 agree well with this calculation. The second lateral band would have a radius of 128 and a diameter of 256 mm, and therefore is already located outside of the sphere. In the acquisition, a quadratic matrix was used with 256 pixels in the readout direction and phase coding direction respectively. The remaining sequence parameters in the creation of the image in FIG. 3 were TR=50 ms, TE=6.3 ms and flip angle 30, resonance frequency=123 MHz.

(59) If the number N of ring trajectories and the radii kr.sub.n=n.Math.kr of the ring trajectories n=1 to N are established on the basis of the diameter d of the excitation profile and the side lobe spacing S.sub.SL, with the use of Formulas (1) and (2) the maximum gradient amplitude A.sub.n and the pulse duration T.sub.n are established for each of the ring trajectories. By integration of Formula (6) over a quarter period, the following relation is obtained between the radius kr.sub.n=n.Math.kr and the magnitude of the gradient amplitude A.sub.n as well as the duration T.sub.n of the n-th ring trajectory:

(60) $\begin{array}{cc}{A}_n=\frac{2}{\left(\text{/}2\right)}\frac{n.Math.\mathrm{kr}}{T_n}& \left(11\right)\end{array}$

(61) In order to minimize the duration of the excitation pulse, T.sub.n in Formula (11) is chosen so short that (for example) a specified maximum gradient amplitude G.sub.max and a specified maximum permissible gradient slew rate S.sub.max are specifically not exceeded. While the maximum permissible gradient amplitude G.sub.max is normally established by the capability of the gradient system, the capability of the gradient system and possible nerve stimulation of the examined person are advantageously considered in the specification of the maximum permissible gradient slew rate S.sub.max.

(62) FIG. 4 shows an example of a design of a partial RF pulse RF.sub.n of a single ring trajectory. The depiction here takes place in the form of a small excerpt from a sequence diagram (pulse diagram). In this pulse diagram, the radio-frequency pulses are shown in a typical manner on an upper time axis, and the gradient pulses to be switched in coordination with said radio-frequency pulses are shown on various time axes lying below this, over time t. Here only the gradient pulses (amplitude A.sub.n of the gradient curves) GP.sub.x,n, GP.sub.y,n in the x-direction and y-direction that are relevant to the selective excitation within the slice are shown. Shown beneath each of the gradients is the respective accumulated 0th moment (the magnitude of the area under the respective gradient pulse) F.sub.1, F.sub.2with different polarity depending on the active directionacting on the spins due to the appertaining gradient curve.

(63) The zero point of the time axis coincides with the middle of the partial RF pulse RF.sub.n; corresponding to Formula (6), the x gradient pulse GP.sub.x,n has a sinusoidal curve, the y-gradient pulse GP.sub.y,n has a cosinusoidal curve, each with a period duration T.sub.n (i.e. the time length of the ring trajectory). This selection can take place arbitrarily without limitation of generality. A respective prephasing pulse VP.sub.x, VP.sub.y is shown in both gradient directions before the use of the radio-frequency pulse at the point in time t=T.sub.n/2. After the radio-frequency pulse RF.sub.n is interrupted at the point in time t=T.sub.n/2, a respective rephasing pulse RP.sub.x, RP.sub.y is switched.

(64) Therefore, the prephasing pulse VP.sub.y in the y-direction is reasonable since the gradient field cannot be ramped up instantaneously from zero to A.sub.n at the point in time t=T.sub.n/2. It thus serves to ramp up the current through the gradient coil. The rephasing gradient RP.sub.y in the y-direction accordingly serves to ramp down the gradient current. The total moment of the two gradient pulses VP.sub.y, RP.sub.y is zero (F.sub.2+F.sub.2=0) for each partial RF pulse, i.e. for each ring trajectory. It is thereby achieved that (static) spins that were excited in the transverse plane by an earlier partial pulse such as a prephasing gradient or a rephasing gradient, acquire no phase as a consequence of these gradients. In the special embodiment shown in FIG. 4, a triangular (or trapezoidal) curve was chosen for the prephasing or, respectively, rephasing gradient VP.sub.y, RP.sub.y because the duration of the gradient can therefore be minimized for given maximum amplitude G.sub.max and slew rate S.sub.max. However, there is a great deal of freedom here. For example, the gradient noise could be reduced with a three-quarters sine wave. Furthermore, a gradient curve could be chosen from three loops for which the first moment also disappears in order to also leave spins flowing in the y-direction unaffected.

(65) The prephasing pulse VP.sub.x in the x-direction serves to center the k-space trajectory. Its 0th moment F.sub.1 is identical to the 0th moment F.sub.1 under a quarter period of the sinusoidal gradient pulses GP.sub.x,n during the RF excitation. The rephasing gradient RP.sub.x in the x-direction has the same absolute area F.sub.1 and opposite polarity. This brings the k-space trajectory back to the origin. The total moment of the gradient in the x-direction (with and without RF radiation) is zero. Therefore, (static) spins that were already excited by an earlier partial pulse remain unaffected. In the embodiment shown in FIG. 4, a triangular curve was selected again to minimize the required time. For example, a trapezoidal curve or a half-sine wave are also alternatively possible here. For example, if the two-dimensional selective RF pulse is used as an excitation pulse in a spoiled gradient echo sequence in which all spins are located before the excitation in the longitudinal direction, the prephasing gradient VP.sub.x can thus be omitted in the x-direction for the first partial pulse of the excitation, for example, since gradients have no influence on spins with longitudinal alignment.

(66) As explained above, the b.sub.1 amplitude is constant in each of the individual partial pulses. The calculation of the values b.sub.11, b.sub.12, . . . , b.sub.1N of the N partial pulses takes place with the use of Formula (7) given a predetermined desired, rotationally symmetrical excitation profile P(r). This Formula (7) specifies only the relative b.sub.1 amplitude of each partial pulse or the proportionality, but this is sufficient. The physical value of the b.sub.1 amplitude (for example in T) can therefore be determined as follows.

(67) The magnetization of spins, whose resonance frequency lies within the bandwidth of a (partial) RF pulse, will be flipped out of the steady state by the flip angle

(68) $\begin{array}{cc}=\underset{t_0}{\overset{t_0+T}{}}{b}_1\left(t\right)dt& \left(13\right)\end{array}$
at the end of the pulse, wherein t.sub.0 is the activation time of the partial pulse, and the gyromagnetic ratio is a physical constant that depends on the excited nucleus. For protons, their value =2.Math.42.57 MHz/T.

(69) Since the b.sub.1 amplitude is constant during a partial pulse, for the flip angle contribution of the n-th partial pulse it directly follows from Formula (13) that:
.sub.n=b.sub.1nT.sub.n(13b)
wherein b.sub.1n is the value for the n-th partial pulse that is calculated with the aid of Formula (7) (with equals sign instead of the proportionality sign), and b.sub.1n=c.Math.b.sub.1n is the initially unknown physical b.sub.1 amplitude of the n-th partial pulse. Under the assumption that the total duration of the RF pulse is short relative to the relaxation times (thus the spins do not relax again to a relevant extent during the RF radiation), it is then the case that the flip angle of the composite pulse is equal to the sum of the flip angle contributions .sub.n of the n-th partial pulses:

(70) $\begin{array}{cc}=\underset{i=1}{\overset{N}{.Math.}}{}_i=\underset{i=1}{\overset{N}{.Math.}}{b}_{1i}^{}{T}_i& \left(14\right)\end{array}$
wherein i is hereby only an additional running variable across all partial pulses; N is again the total number of partial pulses.

(71) From Formula (14), the flip angle contribution .sub.n of the n-th partial pulse is obtained according to:

(72) $\begin{array}{cc}{}_n=\frac{{}_n}{}\stackrel{14}{=}\frac{{}_n}{\underset{i=1}{\overset{N}{.Math.}}{}_i}=\frac{.Math..Math.b_{1n}^{}{T}_n}{\underset{i=1}{\overset{N}{.Math.}}.Math.b_{1i}^{}{T}_i}=\frac{.Math..Math.c.Math.b_{1n}{T}_n}{\underset{i=1}{\overset{N}{.Math.}}.Math.c.Math.b_{1i}{T}_i}=\frac{.Math..Math.c.Math.b_{1n}{T}_n}{.Math.c.Math.\underset{i=1}{\overset{N}{.Math.}}{b}_{1i}{T}_i}=\frac{.Math.b_{1n}{T}_n}{\underset{i=1}{\overset{N}{.Math.}}{b}_{1i}{T}_i}& \left(15\right)\end{array}$
The last equals sign applies because the proportionality constant c between b.sub.1n and b.sub.1n (b.sub.1n=c.Math.b.sub.1n) is independent of the partial pulse n. The constant c can thus be pulled into the denominator before summation and be shortened.

(73) The calculation of all terms on the right side of Formula (15) has previously been shown. With the use of Formula (13b), the sought physical value of the b.sub.1 amplitude of the n-th partial pulse can then be calculated from the flip angle .sub.n:

(74) $\begin{array}{cc}{b}_{1n}^{}=\frac{{}_n}{T_n}.& \left(16\right)\end{array}$

(75) As discussed above, the b.sub.1 amplitude of a partial pulse is the one-dimensional Fourier transformation of the desired radial profile, weighted with two factors (namely the k-space transversal velocity and the density compensation factor). The integral in Formula (7) can be calculated analytically or numerically depending on the desired excitation profile. In the realized embodiment, a Gaussian excitation profile

(76) $\begin{array}{cc}P\left(r\right)=\frac{a^2}{}{e}^{-a^2{r}^2}& \left(17\right)\end{array}$
was chosen, wherein the variable a was established across the desired diameter d such that 90% of the total area lies under the Gaussian function within the diameter d.

(77) The first weighting factorthe k-space transversal velocityis equal to the magnitude A.sub.n of the gradient amplitude:
|(g.sub.x,n(t),g.sub.y,n(t))|={square root over (g.sub.x,n.sup.2(t)+g.sub.y,n.sup.2(t))}=A.sub.n.(18)

(78) The magnitude A.sub.n of the gradient amplitude is constant during the entire ring trajectory and is specifiedvia Formulas (8) to (11)as a function of the predetermined parameters d, S.sub.SL.

(79) The calculation of the second weighting factorthe density compensation factoris explained in the following as an example of a concentric ring trajectory with equidistant ring spacing.

(80) According to Formula (5), the density compensation factor can be approximated by the quotient from the area A(k.sub.x, k.sub.y) and the length l(k.sub.x, k.sub.y) of the trajectory that is enclosed by this area A, which area and length are associated with a k-space sample point (k.sub.x, k.sub.y). The RF amplitude is digitized in every practical realization. M.sub.n is the number of RF sample points (samples) of the n-th partial pulse. The length l.sub.n of the n-th trajectory that is associated with each sample point is then the diameter of the n-th ring trajectory, divided by the number of sample points:

(81) $\begin{array}{cc}{l}_n=\frac{2.Math.{\mathrm{kr}}_n}{M_n}=\frac{2.Math.n.Math.\mathrm{kr}}{M_n}& \left(19\right)\end{array}$

(82) As can be seen in FIG. 5 (shaded area), the area A that is linked with the single sample is simply this length l.sub.n multiplied by the spacing kr between two adjacent ring trajectories:
A.sub.n=l.sub.nkr(20)

(83) The density compensation factor .sub.n for the n-th ring trajectory is thus

(84) $\begin{array}{cc}{}_n=\frac{l_n}{A_n}=\frac{l}{\mathrm{kr}}& \left(21\right)\end{array}$

(85) In the examples (equidistant ring spacing) shown in FIGS. (2) and (5), the density compensation factor is thus identical for all partial pulses. Given non-equidistant ring spacing (see for example FIG. 10), for a ring trajectory the radial ring spacing kr in Formulas (20) and (21) can be approximately replaced by the mean spacing from the two neighboring ring trajectories.

(86) The center of the rotationally symmetrical excitation profile can be displaced by a distance (x, y) away from the isocenter of the gradient system in that the b.sub.1 field is modulated with a phase factor that is linearly proportional to the current gradient moment:
b.sub.1n,complex(t,x,y)=b.sub.1ne.sup.2i(k.sup.x,n.sup.(t)x+k.sup.y,n.sup.(t)y)(22)
wherein b.sub.1n is the time-independent b.sub.1 amplitude of the n-th partial pulse for the excitation in the isocenter, and (k.sub.x,n(t), k.sub.y,n(t)) is the wave vector at the point in time t upon traversal of the n-th ring. The RF pulse herein does not differ from known, two-dimensional selective RF pulses in the prior art.

(87) There are various possibilities for the embodiment of a pulse arrangement according to the invention, wherein a two-dimensional selective RF pulse is created by a composition of such partial pulses explained above.

(88) In the simplest embodiment, the partial pulses are simply executed in chronological order. The time interval between the individual pulses can thereby be freely selected in principle. Due to the unavoidable T.sub.1 and T.sub.2 relaxation of the spins that are affected by an earlier partial pulse, and due to the dephasing of the signal of already excited spins (for example as a result of B.sub.0 inhomogeneities during the execution of the later partial pulses), an optimally short duration of the total pulse is preferred in most cases. It is preferably sought to minimize the time periods in which no RF radiation takes place.

(89) FIG. 6 shows a pulse diagram of the pulse arrangement PA of a simulation of the two-dimensional selective RF pulse RFE according to the invention, which was used to acquire the image in FIG. 3 (see also in this regard the ring trajectories in FIG. 2), together with the associated gradient pulses GP.sub.x, GP.sub.y in the x-direction and y-direction (similar to as in FIG. 4, but now the complete two-dimensional selective RF pulse RFE). The b.sub.1 amplitude of the partial RF pulses is shown on the upper axis in arbitrary units ([a.u.]). Shown on the axes located below these are the gradient amplitudes, likewise in arbitrary units. The units of the time axes are respectively s. The selective RF pulse can be subdivided into eight partial pulses RF.sub.1, RF.sub.2, RF.sub.3, . . . , RF.sub.8. The duration T of the first partial pulse RF.sub.1 with maximum k-space radius kr.sub.max is chosen to be as short as is possible for given maximum allowable gradient amplitude G.sub.max and given maximum allowable gradient slew rate S.sub.max. The duration T of the additional partial pulses RF.sub.2, RF.sub.3, . . . , RF.sub.8 is not gradient-limited. Rather, the duration T for traversal of all ring trajectories TR.sub.1, TR.sub.2, TR.sub.3, . . . , TR.sub.8 (and therefore the duration T of the respective rectangular RF pulses RF.sub.1, RF.sub.2, RF.sub.3, . . . , RF.sub.8) is chosen the same for all partial pulses. According to the nomenclature given two-dimensional selective spiral pulses, this can be considered as an execution with constant angular velocity (constant angular rate).

(90) The (constant) amplitudes b.sub.1 of the individual rectangular partial pulses RF.sub.1, RF.sub.2, RF.sub.3, . . . , RF.sub.8 were calculated as explained above.

(91) FIG. 7 shows a corresponding (simulated) pulse diagram of a pulse arrangement (PA) with another embodiment variant of a two-dimensional selective RF pulse RFE according to the invention, together with the associated gradient pulses GP.sub.x, GP.sub.y in the x-direction and y-direction. The significant difference relative to the variant according to FIG. 6 is that here the duration T.sub.1, T.sub.2, T.sub.3, . . . , T.sub.8 of each individual pulse RF.sub.1, RF.sub.2, RF.sub.3, . . . , RF.sub.8 was calculated individually, and in fact such that the given maximum allowable gradient amplitude G.sub.max and maximum allowable gradient slew rate S.sub.max are specifically not exceeded for a given k-space radius kr.sub.n=(Nn+1)kr of the respective n-th ring trajectory TR.sub.1, TR.sub.2, TR.sub.3, . . . , TR.sub.8. Again in accordance with the nomenclature given two-dimensional selective spiral pulses, this could be designated as an embodiment with constant (gradient) slew rate.

(92) In the two embodiments presented in FIGS. 6 and 7, the rephasing gradients of the n-th partial pulse are respectively merged with the prephasing gradients of the n+1-th partial pulse. Such a combination of two gradients means that, instead of executing the two gradients in chronological order, only one gradient (gradient pulse) is switched whose 0th moment is equal to the sum of the 0th moments of the individual gradients. The goal of the combination is primarily a time savings. An additional advantage of the combination of adjacent gradient pulses is that the gradient noise, eddy currents and the heating of gradient coils and gradient amplifiers can hereby be reduced.

(93) In the embodiment according to FIG. 7, the time intervals T.sub.1, T.sub.2, T.sub.3, . . . , T.sub.8 in which the RF radiation takes place are optimal. Any additional shortening would lead to exceeding the maximum allowable gradient slew rate S.sub.max or maximum allowable gradient amplitude G.sub.max. An additional shortening of the total duration of the two-dimensional selective RF pulse RFE or, respectively, the total pulse arrangement PA is thus possible only via a shortening of the times without RF radiation during which the rephasing gradients and prephasing gradients are executed.

(94) In this regard, FIG. 8 shows a corresponding (simulated) pulse diagram of a pulse arrangement PA with an embodiment variant of a two-dimensional selective RF pulse RFE according to the invention, together with the associated gradient pulses GP.sub.x, GP.sub.y in the x-direction and y-direction, in which the time between the intervals with RF radiation is again reduced. This is achieved in that adjacent ring trajectories in k-space are traversed with different rotation direction. For example, the rotation direction of the partial pulses with odd index is counter-clockwise, and opposite the clockwise rotation direction of the partial pulses with even index.

(95) The advantage of this variant is explained using FIG. 9, which shows an enlarged section of two adjacent partial RF pulses RF.sub.n, RF.sub.n+1 and the associated segment of the gradient pulse GP.sub.y in the y-direction (for example, the partial RF pulses RF.sub.n, RF.sub.n+1 that are concretely depicted in FIG. 9 can correspond to the pulses RF.sub.3, RF.sub.4 in FIG. 8 which lie in the segment characterized by two lines, but the principle applies just as much to all other chronologically successive partial pulses RF.sub.n, RF.sub.n+1).

(96) As is apparent in FIG. 9, the y-gradient is composed of two triangular gradients between the time interval T.sub.n and the time interval T.sub.n+1. The first gradient has an amplitude A.sub.n and a ramp duration RT.sub.n; the second gradient has an amplitude A.sub.n+1 and ramp duration RT.sub.n+1. The following applies:
A.sub.nRT.sub.n+A.sub.n1RT.sub.n+1=0(23)

(97) The magnitude of the area (i.e. the magnitude of the 0th gradient moment) of the two triangular gradients is thus the same. With this, (static) spins that are located after the n-th excitation pulse in the transversal plane acquire no phase as a consequence of these gradients. The original conditionthat the moment of the n-th y-rephasing gradients and of the n+t1-th y-prephasing gradients is respectively zerocan be replaced (given adjacent ring trajectories respectively traveling in opposite directions due to the different polarity of the amplitudes A.sub.n and A.sub.n+1) by the weaker condition that the total moment of the composite gradient (see Equation (23)) disappears. This is the cause of the additional time gain in this method variant.

(98) An additional exemplary embodiment of a transmission trajectory in k-space S.sub.k (similar to as in FIG. 2) is shown in FIG. 10. The total transmission trajectory is hereby likewise comprised of concentric ring trajectories around the k-space center. However, the individual ring trajectories TR.sub.1, TR.sub.2, TR.sub.3, . . . no longer have uniform radial spacings as in the exemplary embodiment according to FIG. 1. Instead of this, the ring spacing kr.sub.1, kr.sub.2, kr.sub.3, . . . is reduced bit by bit towards the k-space center. In particular, the k-space center can be oversampled, meaning that the ring spacing is chosen to be smaller near the center than the value given by the right side of Formula (8). With a denser scanning of the k-space center, it is to be expected that unwanted excitations are reduced outside of the desired excitation profile P(r). In order to avoid an extension of the total pulse due to the denser scanning of the k-space center, the k-space periphery can be undersampled, meaning that the ring spacing kr.sub.1, kr.sub.2, kr.sub.3, . . . will be chosen to be greater than required by Formula (8).

(99) An exemplary embodiment of a transmission trajectory in k-space S.sub.k (similar to as in FIG. 2) that is constructed according to the invention is shown in FIG. 11, wherein only in an inner region of k-space S.sub.k (for example in a radius region kr, up to half of the maximum radius kr.sub.max) is the transmission trajectory formed from concentric ring trajectories around the k-space center. Instead of this, a spiral trajectory TR.sub.S is used in the peripheral radius region kr.sub.a of k-space S.sub.k. As already presented above and as verified again using tests, the advantage of the concentric ring trajectories relative to conventional spiral trajectories is the greater robustness, in particular with regard to gradient delays. However, one advantage of the spiral trajectory is their quickness. In order to utilize both advantages, in this variant the peripheral regions of excitation k-space are therefore initially traversed with a partial pulse with an (incomplete) spiral trajectory, and subsequently the central regions of k-space are traversed with partial pulses that respectively realize a concentric ring trajectory.

(100) In principle, naturally a reverse arrangement would also be possible, meaning that concentric ring trajectories are to be used outward and a spiral trajectory is to be used inward. However, the variant shown in FIG. 11 is inasmuch advantageous since the information in the peripheral k-space region is less relevant than the information from the k-space center. This is also the reason why the k-space center is always covered last in the other shown variants (see FIGS. 2 and 10).

(101) As shown above, the b.sub.1 amplitude of each partial pulse which is radiated on a ring trajectory is constant, which is different than is the case given the known two-dimensional selective RF pulses with EPI or spiral trajectories. An unwanted delay between radiated RF energy and actual applied gradient field therefore leads only to errors right at the beginning of the partial pulse and right at the end of the partial pulse. This leads to an extraordinary robustness of the selection profile given the existence of gradient delay units.

(102) FIGS. 12 through 14 shows an experimental verification of this robustness. For this, in a two-dimensional selective FLASH sequence the excitation pulse is replaced by a two-dimensional selective RF pulse. In the upper row of all three FIGS. 12 through 14, this two-dimensional selective RF pulse is respectively a conventional pulse with EPI trajectory; in the lower row, it is a composite RF pulse with concentric ring trajectories according to the invention.

(103) In all figures, the images in the middle and right column respectively differ from the associated images in the left column in that the radiated RF field has additionally been artificially delayed by 15 s or 45 s is relative to the applied gradient field (the delay time is respectively designated with Del). The phantom used in the measurements is a sphere filled with phantom fluid. The clearance of the first lateral band is 128 mm in all cases, and therefore is outside of the phantom.

(104) In all excitations with EPI trajectories the desired excitation profile is a quadratic rod, and given all excitations with concentric ring trajectories the desired excitation profile is respectively a cylinder, in order to respectively adapt the shape of the excitation profile to the basic geometric structure of the trajectories and thus ensure a comparability. The number N of ring trajectories is 8 in the excitation according to the invention, and the diameter of the cylinder is accordingly approximately 32 mm. The parameters of the EPI pulse have been chosen so that the edge length of the quadratic rod is (at least theoretically) likewise 32 mm.

(105) The readout field of view is in all cases respectively 256 mm and oriented orthogonal to the rod axis or, respectively, cylinder axis. The images have been acquired in a Siemens 3T MAGNETOM Verio.

(106) In FIG. 12, the phantom is located in the isocenter of the MR system. In FIGS. 13 and 14, the phantom and the desired location of the excitation have been displaced by 50 mm in the x-direction or, respectively, y-direction. The rod axis or, respectively, cylinder axis in all cases respectively points in the z-direction of the magnet (thus in the direction of the B.sub.0 field).

(107) In all three experiments, it is apparent that the profile of the EPI trajectory is significantly disrupted given 15 s delay time and totally disrupted given 45 s, while the profile of the concentric ring trajectories is largely maintained. A slight smearing is only apparent at 45 s.

(108) Given the off-center excitations (FIGS. 13 and 14), the delay time produces a slight displacement of the excitation relative to the desired location (which lies in the middle of the readout field of view). However, this error is harmless in many applications, in particular in a navigator application, since here for example the rod-shaped volume to be excited does not necessarily need to be localized to the dome of the liver (for example) in order to correctly detect the breathing movement.

(109) Furthermore, this property of the method can also advantageously be used to adjust and/or calibrate the delay times. For example, for this an artificially inserted additional delay time could be varied until the measured excitation profile is located precisely at the desired location, and thus the system-inherent (initially unknown) delay time is compensated exactly. Whether this calibration must take place once or in vivo depends on the cause of the delay times.

(110) A simplified flowchart for such a method is schematically presented in FIG. 15. In a step I, a two-dimensional selective excitation of a precisely defined excitation profile initially takes place with the aid of the method according to the invention. In step II, image data reconstructed on the basis of this measurement implemented in step I are subsequently presented to an operator. This operator can then decide whether the excitation profile is located precisely at the desired point. If this is not the case, in step III he artificially modifies the gradient delay time. The gradients can thereby be varied in different spatial directions. In step I, a new measurement is subsequently implemented with identical excitation profile, and the images that are thereby obtained are displayed again in step II. If the operator is satisfied with the result in step II, the magnetic resonance system is adjusted (or, respectively, a calibration has taken place after corresponding protocoling of the values) and the actual measurement can then take place in step IV. Instead of a visual monitoring by an operator, an automatic analysis of the image data can also take place in a more comfortable variant. For example, the position of the excitation profile in the image data can be established with the aid of an image recognition software, and then an adjustment of the gradient delay times can take place automatically based on this in step III etc., until ultimately the delay times are compensated according to the image data.

(111) The method and devices that are described detail herein are exemplary embodiments, and the basic principle can be varied by those skilled in the art without departing from the scope of the invention. For example, instead of being realized at the terminal the control sequence determination device 22 can also be part of the control device 10 itself, in particular can also be components of the measurement control unit 15. The control sequence determination device could likewise also be realized at a separate computer system which, for example, is connected with the magnetic resonance system 1 via the network NW. The terms unit and module do not preclude these items from being formed by multiple components that can also be spatially distributed.