MAGNETIC RESONANCE WITH TIME SEQUENTIAL SPIN EXCITATION
DESCRIPTION
The present application relates to the magnetic resonance arts. It particularly relates to reducing spatial non-uniformity in magnetic resonance applications due to coil Bi non-uniformity at ultra high field due to dielectric and conductivity effects by a subject, and is described with particular reference thereto. The following relates more generally to reducing spatial non-uniformity in magnetic resonance applications generally, such as due to coil loading, equipment imperfections, static (Bo) magnetic field non-uniformity, dielectric or eddy current effects, or so forth.
Radio frequency coils for use in magnetic resonance scanners are typically configured to produce a substantially uniform Bi field within an examination region in the unloaded condition. That is, the radio frequency coil produces a substantially uniform Bi field without a subject arranged in the examination region. Ideally, a subject placed in the examination region will therefore experience a substantially spatially uniform Bi field that defines a substantially spatially uniform tip angle distribution of the spins throughout the subject, which is conducive to accurate magnetic resonance imaging and/or spectroscopy.
However, the insertion of an object, such as a human imaging subject, into the examination region can distort the B| field, especially at Bo fields of 3T or higher. Such distortions are typically due to dielectric and/or conductivity effects, and are related to the RF wavelength in the object becoming comparable to the size of the object. Subject-induced Bj field distortion and loading, becomes increasingly problematic as the asymmetry of the imaging subject increases (e.g., in the case of a "broad-shouldered" or otherwise asymmetric human imaging subject) and as the strength of the static (i.e., Bo) magnetic field increases. Hence, coil loading has become increasingly problematic as commercial magnetic resonance scanners have progressed from low-field (e.g., 0.23 Tesla, 1.5 Tesla) to progressively higher static magnetic fields (e.g., 3 Tesla, 7 Tesla, or so forth). Loading the coil can also be more problematic for large coils that couple to a large examination region, both because of the larger subject size and the larger area over which a substantially uniform B| field is to be maintained. For large- volume imaging of human subjects, a quadrature body coil is sometimes used. Quadrature body coils provide efficient radio frequency coupling with a large region of interest such as a torso, legs, or
other portion of a human imaging subject. A quadrature body coil is generally cylindrical in shape, and has radial symmetry. Examples include a quadrature birdcage body coil and a quadrature transverse-electromagnetic (TEM) body coil. The quadrature body coil includes I and Q channel input ports that are driven by radio frequency energy at a 9Oo phase difference to produce a rotating Bs field for exciting magnetic resonance. B] non-uniformity has been addressed in various ways. In a post-acquisition processing approach, the acquired magnetic resonance data is corrected after acquisition to account for distortion of the Bi field. While a correction for the receive coil sensitivity pattern can be made the excitation still has a distribution of tip angles that affects the MR experiment. The range of excited tip angles can be reduced by using adiabatic RF pulses but this approach is time and RF exposure expensive as well a limiting RF sequences.
In another approach, multiple independent radio frequency amplifiers arc used to generate a custom Bi field. For example, in the case of a quadrature body coil, each of the I and Q ports may be driven by a different amplifier. The amplitude and phase of each amplifier are selected to tailor the Bi field distribution. This approach works well, except that the extent of Bi field distribution tailoring is limited to four degrees of freedom, namely the amplitude and phase of each of the two amplifiers. To provide additional degrees of freedom, the radio frequency coil can be reconfigured to include additional ports that are connected with additional radio frequency amplifiers. For example, a TEM coil can be configured to have each rung, or each selected group of rungs, independently driven by a different radio frequency amplifier. For an eight clement TEM coil, for example, up to eight amplifiers can be used providing sixteen degrees of freedom for tailoring the Bj field. The substantial flexibility in tailoring the Bi field to compensate for coil loading using these approaches comes, however, at the cost of substantial increase in system complexity and cost. Radio frequency amplifiers are costly components. Each separately driven port requires its own waveform generation control, amplifier, and dedicated radio frequency cabling, trapping, and so forth. The additional radio frequency connections occupy valuable bore space and introduces opportunities for detrimental radio frequency cross -coupling.
In accordance with one aspect, a magnetic resonance scanner is disclosed. A main magnet generates a static magnetic field at least in an examination region. A magnetic resonance excitation system includes at least one radio frequency coil arranged to inject radio frequency energy into the examination region and at least two radio frequency amplifiers coupled with different input ports of the at least one radio frequency coil. A controller controls the magnetic resonance excitation system to produce a time-varying spatial B i field distribution in a subject in the examination region that time-integrates to define a spatial tip angle distribution in the subject having reduced spatial non-uniformity. In accordance with another aspect, a magnetic resonance excitation method is disclosed. A B[ non-uniformity imposed on at least one radio frequency coil by a subject coupled with the at least one radio frequency coil is determined. A time-varying spatial Bi field distribution is generated in the subject using the at least one radio frequency coil. The time- varying spatial B] field distribution time-integrates to define a spatial tip angle distribution in the subject that is more spatially uniform than the time-varying spatial Bi field distribution.
In accordance with another aspect, a magnetic resonance excitation apparatus is disclosed. Means are provided for determining a B[ non-uniformity imposed on at least one radio frequency coil by a subject coupled with the at least one radio frequency coil. Means including the at least one radio frequency coil are provided for generating a time-varying spatial B1 field distribution in the subject. The time-varying spatial Bi field distribution time-integrates to define a spatial tip angle distribution in the subject having reduced spatial non-uniformity.
One advantage resides in providing flexible and effective compensation for B] field non-uniformity.
Another advantage resides in providing compensation for different types of patterns of Bs non-uniformity without using different compensation coils or other loading-specific hardware.
Another advantage resides in acquisition of more accurate magnetic resonance data with reduced effects of Bi non-uniformity.
Another advantage resides in improved reconstructed image quality. Another advantage resides in improved magnetic resonance spectra.
Still further advantages of the present invention will be appreciated to those of ordinary skill in the art upon reading and understand the following detailed description.
The invention may take form in various components and arrangements of components, and in various steps and arrangements of steps. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention.
FIGURE 1 diagrammatically shows a magnetic resonance scanner including a quadrature body coil, two independent radio frequency amplifiers separately driving the I and Q input ports of the quadrature body coil, and a two channel scanner controller with temporal sequencer for exciting a time-varying spatial B| field distribution.
FIGURE 2 diagrammatically shows the magnetic resonance excitation system of the magnetic resonance scanner of FIGURE 1 in greater detail.
FIGURE 3 show spatial Bi field distributions for modeling of an elliptical cardiac phantom placed in a quadrature body coil in a 3 Tesla magnetic field, for four different excitation conditions.
FIGURES 4 and 5 show spatial tip angle distributions produced by two different time-invariant Bi field distributions.
FIGURE 6 shows a spatial tip angle distribution for a time-integrated combination of the time-invariant Bi field distributions of FIGURES 4 and 5.
FIGURE 7 diagrammatically shows another magnetic resonance scanner employing a plurality of local coils in place of the quadrature body coil of FIGURE 1.
FIGURE 8 diagrammatically shows the magnetic resonance excitation system of the magnetic resonance scanner of FIGURE 7 in greater detail.
With reference to FIGURE 1, a magnetic resonance scanner 10 includes a scanner housing 12 in which a patient 16 or other subject is at least partially disposed. A protective insulating bore liner 18 of the scanner housing 12 optionally lines a generally cylindrical bore or opening of the scanner housing 12 inside of which the subject 16 is disposed. A main magnet 20 disposed in the scanner housing 12 is controlled by a main magnet controller 22 to generate a static (Bo) magnetic field in at least a scanning region
including at least a portion of the subject 16. Typically, the main magnet 20 is a persistent superconducting magnet surrounded by cryoshrouding 24. In some embodiments, the main magnet 20 generates a main magnetic field of at least about 0.2 Tesla, such as 0.23 Tesla, 1.5 Tesla, 3 Tesla, 7 Tesla, or so forth. Magnetic field gradient coils 28 are arranged in or on the housing 12 to superimpose selected magnetic field gradients on the main magnetic field in at least the scanning region. Typically, the magnetic field gradient coils include coils for producing three orthogonal magnetic field gradients, such as x-gradient, y-gradient, and z-gradient.
A generally cylindrical quadrature body coil 30 is mounted substantially coaxially with the bore of the magnetic resonance scanner 10. In some embodiments, the quadrature body coil 30 is a permanent fixture mounted inside the scanner housing 12. In some embodiments, the quadrature body coil 30 is mounted on a dielectric former or other holder that can be slidably inserted into and removed from the bore of the magnetic resonance scanner 10, or slidably inserted into and removed from an annular receptacle of the scanner housing 12. In other embodiments, the quadrature coil 30 can be a local quadrature coil, such as a head quadrature coil or a knee quadrature coil. In some embodiments the quadrature body coil 30 is a quadrature birdcage coil including a plurality of rungs arranged generally parallel with the axis of the bore and operatively interconnected by two or more endrings, endcaps, or other terminating structures disposed at or near the opposite ends of the rungs. In some embodiments the quadrature body coil 30 is a quadrature transverse-electromagnetic (TEM) coil including a plurality of rods arranged generally parallel with the axis of the bore and operatively interconnected by a generally annular radio frequency shield or screen substantially surrounding the rods. The quadrature body coil 30 optionally includes capacitances, inductances, resistances, chokes, transistors, relays, or other components for providing radio frequency tuning, decoupling, current blocking or trapping, or other functionality.
In some embodiments, the quadrature body coil 30 performs both transmit and receive functions. That is, the quadrature body coil 30 is externally energized to excite magnetic resonance in the subject 16, and is also used to receive magnetic resonance signals generated by the excitation. In some embodiments, the quadrature body coil 30 performs the transmit function, and a separate receive coil 34 receives magnetic resonance signals generated by the excitation. The optional separate receive coil 34 can be a surface
coil as illustrated, or a surface coils array, or an arm coil, leg coil, or other local coil. In some embodiments, the scanner 10 is configurable so that in some imaging applications the quadrature body coil 30 performs both transmit and receive functions while in other imaging applications the quadrature body coil 30 performs the transmit function and a separate receive coil performs the receive function. The optional separate receive coil 34 typically includes detuning circuitry that detunes the receive coil during the transmit phase to avoid overloading the receive coil.
With continuing reference to FIGURE 1 and with further reference to
FIGURE 2 which shows a magnetic resonance excitation system 36 of the magnetic resonance scanner of FIGURE 1 in greater detail, an I-channel radio frequency amplifier
38 generates an I-channel radio frequency drive signal having an amplitude Ai and a phase φι at the magnetic resonance frequency, while a Q-channel radio frequency amplifier 40 generates a Q-channel radio frequency drive signal having an amplitude AQ and a phase ΦQ at the same magnetic resonance frequency. The I-channel and Q-channel radio frequency drive signals are independent in that they may have different amplitudes Ai, AQ (within the limits imposed by the dynamic ranges of the amplifiers 38, 40) and different relative phases φi, ΦQ. The I-channel drive signal output by the I-channcl radio frequency amplifier
38 is fed into an I-channcl input port 42 of the quadrature body coil 30. The Q-channel drive signal output by the Q-channel radio frequency amplifier 40 is fed into a Q-channel input port 44 of the quadrature body coil 30.
If the I-channel and Q-channel radio frequency drive signals are of equal amplitude (AI=AQ) with a 90° phase difference between the I- and Q-channel radio frequency drive signals (ΦQ-ΦI=90°), then the quadrature body coil 30 is operated in the usual quadrature mode that produces a B] field vector that rotates at the magnetic resonance frequency. However, if two separate RF waveform generators and two independent amplifiers 38, 40 are provided, there is in general no restriction on the I- and Q-channel radio frequency drive signal amplitudes Aj, AQ and the phase difference ΦQ-ΦI therebetween.
With reference to FIGURE 1, optionally a magnetic field gradients controller 54 operates the magnetic field gradient coils 28 to spatially localize the magnetic resonance excitation to a slab or other localized region. Optionally, the magnetic field
gradient controller 54 operates the magnetic field gradient coils 28 to apply one or more spatial encoding magnetic field gradient pulses.
In the embodiment of FIGURE 1, a radio frequency receiver 56 is operatively connected with the illustrated local coil 34 to read magnetic resonance signals during a readout phase of the magnetic resonance sequence. Alternatively, in some embodiments the radio frequency receiver 56 is operatively coupled with the I and Q channel input ports 42, 44 of the quadrature body coil 30 during the readout phase, with suitably radio frequency circuitry being provided to switch between operative connection of the quadrature body coil 30 with the radio frequency amplifiers 38, 40 during the transmit phase and operative connection with the radio frequency receiver 56 during the readout phase. Optionally, the magnetic field gradient controller 54 operates the magnetic field gradient coils 28 during the readout phase to provide additional spatial encoding (i.e., readout encoding) of the magnetic resonance signals.
The magnetic resonance samples acquired during the readout are stored in a data buffer 58. A magnetic resonance data processor 60 performs processing of the acquired magnetic resonance data to extract useful information. In imaging applications, the data processor 60 suitably performs image reconstruction using a Fast Fourier transform or other image reconstruction algorithms comporting with the selected spatial encoding applied during generation of the magnetic resonance data. In spectroscopic applications, the processing performed by the data processor 60 may include, for example, performing spectral fast Fourier transform operations to recover chemical shift and J-coupling data. The resulting processed data (e.g., images, spectra, or so forth) are suitably stored in a data/images memory 62, displayed on a user interface 64, printed, communicated over the Internet or a local area network, stored on a non-volatile storage medium, or otherwise used. In the example configuration illustrated in FIGURE 1, the user interface 64 also interfaces a radiologist or other operator with the scanner controller 66 to control the magnetic resonance scanner 10. In other embodiments, a separate scanner control interface may be provided.
With reference to FIGURES 1 and 2, the magnetic resonance excitation system 36 is configured to allow time-averaging of a Bλ (r) field so as to compensate for Bi spatial non-uniformity. In this notation, r denotes spatial position, so that B1 (T)
denotes the spatial B| field distribution. Applying a time-invariant B] (F) field for a time τ produces a spatial tip angle distribution θ (F) given by:
where γ is the gyromagnetic ratio and B
x (F) is the component of the B
x (r) vector that
contributes to magnetic resonance excitation. For the time-invariant B1(F) field the component B1 +(F) is independent of time, and Equation (1) simplifies to:
θ(F) = γ|<(r)| -τ (2), where τ is the duration of application of the constant |B| "] field.
The magnetic resonance scanner 10 includes the capability of generating a time-varying spatial Bx (F) field distribution that varies in spatial shape, by independently controlling the 1 and Q channel radio frequency amplifiers 38, 40. Denoting the time-varying spatial 2J1 (F) field distribution as Bx (F J) where t denotes time, Equation (1 ) becomes:
If only a single radio frequency amplifier was used in conjunction with a hybrid circuit to produce the 1 and Q components, then the time- varying spatial B
x (Fj) field distribution could only be varied in amplitude or phase - that is, the spatial shape of the spatial B
x (F, t) field distribution could not be varied. This is the case with a typical MR system. In contrast, in the scanner 10 the time-varying spatial B
x (Fj) field distribution can have varying shape.
FIGURE 3 shows spatial B
x (F, t) field distributions for modeling of an elliptical cardiac phantom (aspect ratio = 19cm/35cm = 0.54, length = 34cm, conductivity = 0.5 S/m, and relative permittivity = 78) placed in a quadrature body coil in a 3 Tesla static (B
0) magnetic field. FIGURE 3 shows the spatial B
x (FJ) field distributions for four conditions: Ai=I, A
Q=O (i.e., driving only the I channel using the I-channel amplifier 38); A
1=O, A
Q=I (i.e., driving only the Q channel using the Q-channel amplifier 40); ApI,
(i.e., driving the quadrature body coil 30 in quadrature mode using both amplifiers 38, 40); and ApI, A
Q= I , φp90°, Φ
Q=O° (i.e., driving the quadrature body coil 30 in anti-quadrature mode using both amplifiers 38, 40). In the |B|
H|-field maps of FIGURE 3 (as well as those of FIGURES 4-6), regions of about average [B]
H |-field intensity are shown with whiter grayscale values; whereas, regions of low or high JBi
+ - field intensity are shown with darker grayscale values. That is, relatively uniform regions arc whiter, while regions substantially contributing to non-uniformity are darker. Substantial spatial non-uniformities are seen for each of the coil operational modes, principally due to dielectric and eddy current effects in the cardiac phantom.
By suitably combining different spatial Zf1 (F, t) field distributions in time, a time-varying spatial Bi field distribution can be produced in a subject that time-integrates to define a spatial tip angle distribution in the subject having reduced spatial non-uniformity. The combination can be continuous, e.g. by applying Equation (3), or can involve combining two or more time-invariant spatial Bi field distributions each held constant over selected time interval τ. For example, the amplifiers 38, 40 can be controlled by the controller 66 to produce a first time-invariant spatial Bi field distribution Bi (r
( D over a time τ^ and a second time-invariant spatial Bs field distribution B^ (r) over a
(2) time τ2, the first and second time-invariant spatial Bi field distributions being different due to different RF excitation conditions. The combined tip angle Q (F) is given by a linear combination of Equation (2):
B[F) ^ y B{{r) t -X 1 +y B:{ή (4).
(I ) (2)
If a third time-invariant spatial Bi field distribution 5,+ (r) is applied
(3) over a time τ3, where the first, second, and third time-invariant spatial B| field distributions are different, then the resulting tip angle θ (F) is given by: θ (r) = γ |z?,+ (rj| -τ ι + γ *,f (r)|(2) -T2 + Y^(F) (5).
(3)
More generally still, if N different time-invariant spatial Bi field distributions 5,+ (r)
OO are applied each for a selected time τn, where n=l ...N indexes the applied time-invariant spatial field distributions, then the resulting tip angle θ (F) is given by:
FIGURES 4-6 show an application of Equation (4). FIGURE 4 shows a spatial tip angle distribution B1 (V) produced by a time-invariant B^ (r) field
(i) distribution in which ApI , AQ=O.1 , φρθ°, ΦQ=40° applied for a time interval τj. FIGURE 5 shows a spatial tip angle distribution G2(F) produced by a time-invariant
5,+ (r) field distribution in which Ap0.4, Ao=0.9, φ,=120°, φQ=0° applied for a time
interval τ2. In the spatial tip angle distribution θt (F) of FIGURE 4, the central region represents a large tip angle of about 90-120°, while in the spatial tip angle distribution Θ2 (r) of FIGURE 5, the central region represents a small tip angle of about 0-40°.
FIGURE 6 shows a spatial tip angle distribution Θ(F) for the time-integrated combination of the time-invariant p/ (r) and
(i) /V (F) field
(2) distributions of FIGURES 4 and 5 combined in accordance with Equation (4) with Ti=T2. The field spatial tip angle distribution θ (F) of FIGURE 6 has a tip angle of 90°±9.25°, with a 67% decrease in standard deviation versus operation of the coil 30 in quadrature. While FIGURE 6 shows a combination of two different time-invariant Bi field distributions B^ (F) and B1 (/-) , it is anticipated that by selectively combining three
W (2) different time-invariant Bi field distributions in accordance with Equation (5), or four or more different time-invariant Bi field distributions in accordance with Equation (6), can provide still further reduced spatial nonuniformity in the spatial tip angle distribution θ (F) . In general, it can be expected that it will usually be possible to combine two selected different time-invariant Bi field distributions so as to produce a spatial tip angle distribution B (F) that is more spatially uniform than either constituent time- invariant spatial Bi field distribution. Similarly, it can be expected that a time- varying spatial Bi
field distribution can be chosen to produce a spatial tip angle distribution that is more spatially uniform than the time- varying spatial B, field distribution.
With reference to FIGURES 1 and 2, the time-invariant spatial Bi field distribution used to create a more uniform spatial tip angle distribution can be either continuously varying (analyzed using Equation (3)) or discretely varying (analyzed using Equations (4)-(6)). In the continuously varying approach, the controller 66 controls the radio frequency amplifiers 38, 40 to generate output radio frequency signals with amplitudes A](t), AQ(t) and phases φ[(t), φQ(t) that are functions of time to produce a time-varying field distribution Bf (r,t) that time-integrates in accordance with Equation (3) to produce a spatial tip angle distribution θ (r) having reduced spatial non-uniformity. In the discretely varying approach, the controller 66 controls the radio frequency amplifiers 38, 40 to generate a temporal sequence of time-invariant output radio frequency signals each having amplitudes At(,,), AQ^J and phases φi(,,), ΦQ(,,) that produce time-invariant field distributions B] (r) that sum in accordance with Equation (6) to produce a spatial tip
angle distribution θ (r ) having reduced spatial non-uniformity. A temporal sequencer 70 determines suitable continuous functions As(t), AQ(t), φj(t), φo(t) or discrete values A](n), AQ(H), φ](n), ΦQ(,,) that provide the spatial tip angle distribution θ (r) having reduced spatial non-uniformity based on a determination of the coil loading imposed on the radio frequency coil 30 by a subject in the examination region. The determination of B| non-uniformity can be done in various ways. In some embodiments, a pre-scan is performed and an image of the subject reconstructed, and the B] non-uniformity estimated from the reconstructed image. In other embodiments, the B1 non-uniformity may be estimated based on measurements of the dimensions of the subject. For example, the shoulder width and chest diameter of a human subject may be measured to estimate the amount of Bi non-uniformity the human subject will impose upon the coil. In some embodiments, the temporal sequencer 70 includes a look-up table of continuous functions A|(t), AQ(I), φi(t), ΦQ(O or discrete values Aφ,), AQ(Π), φi(,,), ΦQ(Λ) that provide substantial uniformity for the spatial tip angle distribution Θ (F) . The look-up table values arc suitably pre-determined by finite element analysis simulations, or by experimental measurements on phantoms or human objects with different aspect ratios, or
so forth. In other embodiments, the temporal sequencer 70 may include a finite element analysis electromagnetic simulator or other calculator for estimating suitable values of the continuous functions A[(t), AQ(I), φi(t), ΦQ(1) or discrete values A[(n), AQ^), φi(n), ΦQOU that provide substantial uniformity for the spatial tip angle distribution θ (F) . That is, in the discrete embodiment a composite Bi pulse or pulse packet is applied by the amplifiers 38, 40 which includes a series of two (Equation (4)), three (Equation (5)), or N (Equation (6)) sub-pulses which cumulatively produce the selected spatial tip angle distribution. Each sub-pulse has a selectable amplitude, phase, and/or duration to provide numerous degrees of freedom in tailoring the overall Bi pulse or pulse packet. In some embodiments, a sensor, sensor array or analyzer detects or measures the Bi field distribution to provide feedback 72 of the actual applied Bi field at the region of interest. In these embodiments, a series of pilot B| pulses are suitably applied and the detected or measured Bi field distribution is used by the temporal sequencer 70 to dynamically or iteratively adjust the Bj sub-pulses or Bj pulse shape to achieve the desired spatial tip angle distribution. For these embodiments, a dedicated sensor, sensor array or analyzer can be used, or the receive coil 34 can be used as the sensor, along with suitable processing performed by the data processor 60 or another processor, to produce the feedback 72 for dynamically or iteratively tailoring the Bi sub-pulses or Bi pulse shapes.
With reference to FIGURES 7 and 8, the technique of using a time-varying field distribution By {r,t) that time-integrates (for example, using a suitable one of
Equations (3)-(6)) to define a spatial tip angle distribution in the subject that is more spatially uniform than the time-varying spatial B] field distribution can be applied to other magnetic resonance excitation systems. A magnetic resonance scanner 10' includes a different magnetic resonance excitation system 36' in which the quadrature body coil 30 is replaced by an array of local coils 301, 302, 303. While three local surface coils 301, 302, 303 are shown, other types and/or numbers of local coils can be used. The I-channel and Q-channel radio frequency amplifiers 38, 40 are replaced by a set of three radio frequency amplifiers 40' that are independently controlled by the scanner controller 66. More generally, each local coil 301, 302, 303 has an input port that is coupled to its own independent amplifier - accordingly, the local coil 301 can be operated at amplitude Ai(t) and phase φi(t), the local coil 302 can be operated at amplitude A
2(t) and phase φ
2(t), and
the local coil 303 can be operated at amplitude A
3(t) and phase φ
3(t). In the embodiment of FIGURE 7, the local coils 301, 302, 303 operate as transmit/receive CTVR
x) coils that are selectively coupled with either the radio frequency amplifiers 40' or the radio frequency receiver 56 by a suitable switch 80. The time-varying Bi field distribution β,
+ (r,f) is generated by the combination of local coils 301, 302, 303 based on the time-varying amplitudes Ai(t), A
2(t), A
3(t) and time-varying phases φs(t), φ
2(t), φ
3(t). As in the quadrature body coil embodiment, the time integration can be either continuous (where Aι(t), A
2(t), A
3(t), φi(t), φ
2(t), φ
3(t) are in general continuous functions of time) or discrete (where the amplitudes and phases are varied discretely, e.g. A|
(tl), A
2(H), A
3(nj, φi
(11), φ2
ftl), φ
3(n> where n=l ...N denotes the number of discrete time-invariant B] field distributions 5,
+ that are combined in accordance with Equation (6).
The example magnetic resonance excitation systems 36, 36' are not exhaustive. As another example of a suitable magnetic resonance excitation system, a degenerate birdcage or TEM coil can be used, with individual rungs or rods driven by separate radio frequency amplifiers in accordance with the techniques disclosed herein.
It is to be appreciated that less than all of the coil parameters may be varied. For example, referencing back to the embodiment of FIGURES 1 and 2, in some instances it may be sufficient to keep As and φi constant (that is, the output of amplifier 38 is held constant) and to vary AQ and ΦQ continuously or discretely to effectuate the time-varying Bi field distribution B\ (r,t) . Indeed, it may be sufficient to vary only AQ or only ΦQ
continuously or discretely to effectuate the time-varying B; field distribution 5s + (r,f) .
The invention has been described with reference to the preferred embodiments. Modifications and alterations may occur to others upon reading and understanding the preceding detailed description. It is intended that the invention be constructed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.