Parallel Excitation With an Array of Transmit Coils

Transcription

1 Parallel Excitation With an Array of Transmit Coils Yudong Zhu* Magnetic Resonance in Medicine 51: (2004) Theoretical and experimental results are presented that establish the value of parallel excitation with a transmit coil array in accelerating excitation and managing RF power deposition. While a 2D or 3D excitation pulse can be used to induce a multidimensional transverse magnetization pattern for a variety of applications (e.g., a 2D localized pattern for accelerating spatial encoding during signal acquisition), it often involves the use of prolonged RF and gradient pulses. Given a parallel system that is composed of multiple transmit coils with corresponding RF pulse synthesizers and amplifiers, the results suggest that by exploiting the localization characteristics of the coils, an orchestrated play of shorter RF pulses can achieve desired excitation profiles faster without adding strains to gradients. A closed-form design for accelerated multidimensional excitations is described for the small-tip-angle regime, and its suppression of interfering aliasing lobes from coarse excitation k-space sampling is interpreted based on an analogy to sensitivity encoding (SESE). With or without acceleration, the results also suggest that by taking advantage of the extra degrees of freedom inherent in a parallel system, parallel excitation provides better management of RF power deposition while facilitating the faithful production of desired excitation profiles. Sample accelerated and specific absorption rate (SAR)-reduced excitation pulses were designed in this study, and evaluated in experiments. Magn Reson Med 51: , Wiley-Liss, Inc. Key words: parallel transmission; parallel excitation; RF coil array; multidimensional RF pulse; multidimensional excitation; B 1 field inhomogeneity; SAR reduction; fast imaging Spatially selective excitation is widely used in MRI to induce transverse magnetization while limiting the size of the signal-contributing volume. Slice-selective excitation, the most commonly used form, confines the signal-contributing volume to a thin slice, simplifying spatial encoding during signal acquisition to a speedier 2D task. Multidimensional excitation (1 3), that produces localization along more than one dimension, has been used to further this speed advantage. Its applications include localized spectroscopy (4,5), reduced-fov scan of a region of interest (ROI) (6,7), imaging of uniquely-shaped anatomy (8 10), and EPI with a shortened echo train length (11). In addition to localized excitation, profile (flip, phase, and frequency) control across a sizeable volume with selective excitation has been exploited to improve excitation profile fidelity in the presence of B 0 inhomogeneity (12) or gradient nonlinearity (13), and to reduce susceptibility artifacts (14,15). GE Corporate R&D Center, iskayuna, ew York. *Correspondence to: Yudong Zhu, Ph.D., GE Corporate R&D Center, K1- MR129, One Research Circle, iskayuna, Y zhu@crd.ge.com Received 4 August 2003; revised 10 ovember 2003; accepted 11 ovember DOI /mrm Published online in Wiley InterScience ( Wiley-Liss, Inc. 775 Selective excitation is commonly implemented on a volume transmit coil that produces a relatively uniform B 1 field, e.g. a birdcage coil with quadrature drive (16,17). Highly efficient algorithms exist for designing excitation pulses that suit such a configuration. Technical difficulties remain, however. For example, problems with excitation pulse duration, excitation profile accuracy, RF power, and specific absorption rate (SAR) represent some of the outstanding challenges in a variety of applications. Compared to 1D excitation, flexible profile control along multiple dimensions with 2D or 3D excitation entails intensified pulsing activity and often requires powerful gradients to keep the pulse duration in check. This limitation hinders applications of multidimensional excitation on scanners with general-purpose gradients. The substantial subjectdependency of the B 1 field, which results from increased wave behavior and source subject interaction at high frequencies (17 19), may also contribute to the difficulty of maintaining excitation profile control. An elevated rate of RF power deposition at high frequencies represents yet another factor that has a significant impact on the design and application of RF transmit modules and/or excitation pulses. The use of adiabatic pulses (20,21) represents a pulse design approach that addresses the difficulty of excitation profile control associated with B 1 inhomogeneity. This approach applies only to certain profiles, however, and tends to involve high RF power. A B 1 -field optimization approach that aims at maximizing global B 1 homogeneity addresses the control issue through transmit module improvements. Adaptations of the transmit coil geometry or the driving mechanism (19,22 25) have been shown to reduce B 1 inhomogeneity. At high frequencies, however, the capability of a field optimization approach is limited. Even with calibration-guided adjustments of driving-port weights (19), the degree to which the spatial variation of the composite B 1 field approaches the desired pattern is highly dependent on the characteristics of component B 1 fields, and results tend to be subject to considerable residual inhomogeneity. To accelerate the multidimensional excitation pulses, two recent studies (27,28) proposed the use of a parallel excitation architecture multiple transmit elements driven by independent drivers. The principle underlying both acceleration methods may be considered as the excitation counterpart to sensitivity encoding (SESE) (29) or simultaneous acquisition of spatial harmonics (SMASH) (30). Individual B 1 field patterns are employed (27,28) to suppress aliasing lobes arising from sampling density reduction in the excitation k-space, while, in comparison, spatial information encoded with the individual sensitivity patterns is used by SESE or SMASH to resolve ambiguity (aliasing) due to sampling density reduction in the acquisition k-space.

2 776 Zhu In this study we extend the work described in Ref. 28. We explore both multidimensional excitation acceleration and SAR control by exploiting the distributed nature and the orchestrated driving of multiple transmit coils. The proposed parallel excitation approach emphasizes the coordination of multiple transmit elements to effect appropriate B 1 spatiotemporal variations, as opposed to the traditional practice of arranging B 1 temporal variations only. This is shown to provide better management of multidimensional pulse length or RF power deposition while facilitating the faithful production of desired excitation profiles. The design of the parallel excitation pulses is approached from the perspective of spatial and spatialfrequency domain weighting. In the following sections, the theoretical results underlying the design methods are presented, examples of accelerated or SAR-reduced excitation pulse designs are described, and experimental evaluations of parallel excitation principles are reported. MATERIALS AD METHODS Parallel Excitation With a Transmit Coil Array The transverse magnetization resulting from a small-tipangle excitation with a single transmit coil may be analyzed by Fourier-transforming the k-space trajectory that is traversed and weighted during the excitation (1): M x j M 0 x b x k W k S k e j2 k x dk, [1] where S(k) represents a spatial-frequency sampling trajectory controlled by the switching gradients, W(k) is the spatial-frequency weighting induced by the driving RF source, and b(x) is the spatial weighting induced by the coil s B 1 field pattern. When several sets of pulse synthesizer and amplifier form parallel the RF sources that simultaneously drive the corresponding coils in a transmit coil array during excitation, multiple spatial and spatial-frequency weighting influence the creation of the transverse magnetization. Within the limits of the small-tip-angle approximation, the k-space perspective expressed by Eq. [1] can be extended to analyze the parallel excitation system based on the property of linearity: M x j M 0 x n 1 b n c n,l W l k S k e x k j2 k x dk. [2] where denotes the total number of transmit coils, n and l are coil indices, c n,l s are the coefficients that characterizes the mutual coupling between the coils, W l (k) s represent the spatial-frequency weighting induced by the independently controlled RF sources, and b n (x) s are the spatial weighting induced by the coils B 1 field patterns. Let g(x) denote the term in Eq. [2] that defines the excitation profile. With rearrangement of the order of evaluations, g(x) may be expressed as g x c n,l b n W l k S k e n 1 x k j2 k x dk bˆ W l k S k e j2 k x dk, [3] l x k which indicates that when one analyzes the parallel transmit system, one may use bˆ l(x) n 1 c n,l b n (x), the effective spatial weighting, to account for coupling-induced intercoil correlations. As an example, consider a 2D excitation setup that involves the use of an echo-planar (k x,k y ) trajectory, with k x being the slow direction and kx being the sampling period. Let {(x,y) x min x x max, y min y y max } specify the field of view (FOV) that contains the subject. The k-space weighting and sampling gives rise to a 2D excitation profile, which, as entailed by Eq. [3], is a weighted superposition of periodic functions: g x, y bˆ l x, y u l x m, y. [4] m In deriving Eq. [4], we used the notation u l (x) and to represent, respectively, W l (k)e j2 k x dk and 1/ kx, and suppressed z-dependence for simplicity. Equation [4] explicitly shows that the discrete nature along k x necessarily implies aliasing lobes along x. Of significance, Eq. [4] also hints at design improvement opportunities that are offered by the multiple weighting in the spatial (bˆ l(x)) and spatial-frequency (W l (k)) domains. This can be compared to the case of excitation with a body coil (volume coil with b(x) 1), where a typical pulse design has the side lobes pushed outside the subject by limiting sampling period kx to be no greater than 1/D (D x max x min ). Excitation Profile Creation via Orchestrated Driving In the small-tip-angle regime, one can generally approach the design of gradient and RF pulses given a desired excitation profile by solving an inverse problem defined by Eq. [3]. For simplicity and insights, the illustrations of the design principles in this work focus on the 2D excitation case described above. To achieve a 2D excitation profile given by g(x,y), we consider solutions of type u l (x,y) h l (x,y)g(x,y). Eq. [4] then becomes g x, y m g x m, y h l x m, y bˆ l x, y, which in general requires, for all (x,y) inside the FOV, h l x m, y bˆ l x, y 1, m 0 0, otherwise.

3 Parallel Excitation With Transmit Coil Array 777 By sorting the equations (e.g., through a change of variables), it can be shown that {h l (x,y), l 1,...,} is typically constrained, at each (x,y), by K linear equations (K is defined as the smallest integer that is D/ ): where C x,y C x,y h x,y e 1 [5] bˆ 1 x, y bˆ 2 x, y bˆ x, y, bˆ 1 x m, y bˆ 2 x m, y bˆ x m, y h x,y h 1 x, y h 2 x, y h x, y T, e T, and {x,...,x m (m 0),...} represents the set of x coordinates within the FOV that are evenly spaced and interassociated due to aliasing. When a design employs a sampling period kx that is greater than 1/D, all but the first equation in Eq. [5] represent the suppression of aliasing side lobes located within the FOV. Solving Eq. [5] repeatedly for locations throughout the FOV yields h l (x,y) s, which then allow the calculation of k-space weighting according to W l k x h l x g x e j2 k x dx. [6] Equation [6] suggests that the k-space weighting, and the RF pulse waveform associated with the lth coil, can be calculated with the Fourier transform of a spatiallyweighted version of the desired excitation profile, where the spatial weighting is derived from the B 1 field maps and the k-space traversing trajectory. The quality of the B 1 maps has a direct impact on excitation profile accuracy. The maps may be experimentally calibrated one at a time. With this approach, each calibration may involve an imaging experiment that uses a single element of the transmit array for transmission (with zero inputs to other elements) and the body coil for reception. A division of the result by a reference image to remove the modulation of subject contrast, and additional processing to suppress the effects of noise, in a way similar to that detailed in Ref. 29, then provides an estimate of the effective B 1 map associated with the transmit element. Alternatively, one may infer the B 1 maps from sensitivity maps based on the principle of reciprocity. This represents a more efficient scheme, as multiple sensitivity maps can be calibrated in parallel. However, the opposite phase (17) and possible changes in coil coupling characteristics between transmit and receive, if not accounted for, may compromise the accuracy of the estimated effective B 1 maps. In the degenerate case in which a single coil is used for transmission, Eqs. [5] and [6] lead to W(k) b 1 j2 k x (x)g(x)e dx, which is recognized as the same design described in Ref. 1, except for an extra b 1 (x) term that attends to the effect of B 1 inhomogeneity. Pulse Design for Excitation Acceleration The redundancy of a parallel excitation system relative to a single-channel excitation system manifests itself in the extra degrees of freedom in solving Eq. [5] or the more general inverse problem defined by Eq. [3]. Comparing the use of the two types of systems in the 2D excitation case, we note that given the same excitation profile, the redundancy of the parallel system offers the capacity for a possible excitation acceleration of up to -fold over a singlechannel body-coil system. Formally, this is revealed by the fact that Eq. [5] admits at least one solution if D/, or equivalently, kx /D, which is in contrast to the more stringent requirement of kx 1/D in the case of body-coil transmission. Intuitively, one can best appreciate the capacity for acceleration or reduction in excitation k-space sampling density by recognizing that while a reduction in excitation k-space sampling density causes aliasing lobes to locate inside the subject, an appropriate design of the spatial-frequency domain weighting (W l (k)) can combine with the spatial domain weighting (bˆ l(x)) and the aliasing pattern (as determined by the sampling) to cause incoherent addition, resulting in the reduction or annihilation of the aliasing lobes net amplitudes. For an acceleration factor that is smaller than, or, equivalently, a sampling period that is smaller than /D, Eq. [5] typically admits a family of solutions of dimensionality -K. This results in choices of excitation pulse designs that are all capable of producing a main lobe that matches the desired excitation profile, and, when applicable, of simultaneously suppressing the aliasing lobes. The specific design that uses h l (x,y) s calculated by solving Eq. [5] in the minimum norm sense is notable because it tends to lessen the sensitivity of the excitation profile to perturbations, or reduce the power requirement on the RF amplifiers. The duality between the parallel excitation approach and the SESE-based parallel acquisition approach can be explored. The results from another study (31) and its extension suggest that the de-aliasing in the Cartesian-trajectory SESE reconstruction is equivalent to evaluating a spatially-weighted superposition of periodic functions (aliased images), with the sensitivity matrix being a key input for the determination of the spatial weighing functions. With the parallel excitation approach, suppression of aliasing is also via a spatially-weighted superposition of periodic functions (main and aliased lobes), except that in this case, the superposition results from the spin system s linear response to multiple RF sources (in the small-tipangle regime), the periodic patterns are induced by the designed pulses, and the spatial weighting originates from the B 1 field patterns (Eqs. [3] and [4]). Management of RF Power Deposition A parallel excitation system composed of multiple transmit coils and supporting driving sources offers opportunities for SAR management. Compared to uniform coverage of a subject volume with a single transmit coil, focused

4 778 Zhu excitation of only the ROI with an array of distributed local transmit coils may primarily employ the coils in close proximity, thus preventing substantial RF power deposition beyond the region. In addition, taking advantage of the extra degrees of freedom in the parallel system may lead to further SAR reduction. Conceptually, this may be accomplished by choosing, among the many ways of orchestrating the sources to produce a desired excitation profile, the one that induces an E field with as small as possible an ensuing RF power deposition. The integration of SAR management into the design of parallel RF pulses is described in this work with a focus on the minimization of SAR averaged over the subject volume and the excitation period, which is defined by SAR ave 1 P 1 1 P V x 2 x E x, p t 2 dv. [7] p 0 where denotes tissue conductivity, is density, V is the size of the irradiated subject volume, and P is the total number of time points used to quantify the temporal average. Consider, for example, a case involving multiple loop coils placed facing the surface of a large slab of conducting material (26). At low frequencies, the fields inside the slab tend to be dominated by the incident fields, which are produced by the currents in the coils. Following a quasistatic approach in analyzing electric and magnetic nearfields, one can characterize the fields with a vector potential A: A I l 4 C l ds x x, where the line integrals over the currents in the coils are based on filament approximation of the coil conductors, and the fields are related to A by B A and E da/dt. In this case, the E(x,p t) 2 term in Eq. [7] may be evaluated as E x, p t 2 j A x, p t 2 I l p t j 4 C l ds x x 2 2 I l p t l x, [8] which is a quadratic form in [I 1 (p t) I 2 (p t)...i (p t)], a vector with values of the current waveforms at time p t. Sorting out the volume integral and temporal summation, one may express SAR ave as a quadratic function in the samples of the current waveforms: SAR ave s H Fs, [9] vector s collects in a corresponding order a total of P samples of the current waveforms. Provided that the electric field scales linearly with applied source functions, a quadratic relationship in the form of Eq. [9] between average SAR and source function samples generally holds. However, in the presence of biological objects, or at high frequencies, it is difficult to solve Maxwell s equations, and one may need to rely on calibration results or direct E field measurements to construct the F matrix. Pulse Design for SAR Reduction Given the dependencies of the absorption rate and transverse magnetization on the applied source functions, the determination of a set of coordinated source functions that produces the desired excitation profile while inducing minimum SAR is possible in theory. In the small-tip angleregime or its extension (1,2), where a linear treatment of the Bloch equations is appropriate, we show that a closedform solution exists for multidimensional excitation design, which obviates the need to search a vast design space. Consider the 2D excitation example described above. Equations of the form of Eq. [5], which stem from the requirement of creating the desired main lobe in the subject while avoiding aliasing lobes, collectively constrain the spatial patterns of h l (x) s. Pooling these equations together thus gives the design constraints, which, in a matrix form, may be expressed as: C all h all e all. [10] In Eq. [10], C all is a block-diagonal matrix with C (x,y) s on the diagonal and zeros everywhere else, and h all and e all are vectors representing, respectively, concatenated h (x,y) s and e 1 s. If the moving sample (1) of the weighting functions is carried out at a constant rate, the W l (k(t)) s are proportional to the current waveforms. The Fourier transform relationship between the W l (k) s and the h l (x) s (Eq. [6]) then allows one to rewrite Eq. [9] in terms of h all : SAR ave h H all Vh all. [11] The quadratic form remains, as the Fourier transform defines a linear mapping from h l (x) to W l (k). A variable sample rate (33) would only modify entries of matrix V to match gradient amplitude changes. For the case discussed here, the design therefore boils down to minimizing a quadratic function subject to a linear constraint: minimize h H all Vh all subject to C all h all e all, [12] where superscript H denotes conjugate transpose, matrix F carries entries evaluated based on Eqs. [7] and [8], and which, in practice, can be solved using well-known numerical techniques (34,35).

5 Parallel Excitation With Transmit Coil Array 779 FIG. 1. Transmit array facing a thin 40-cm-wide slab object located 3 cm below the array surface. The array is comprised of nine identical 19.8 cm 6.4 cm rectangular loop coils that were placed on a flat form and lined up along x with a uniform center-to-center spacing of 4 cm. Experiments The design principles for the small-tip-angle parallel excitation pulses were evaluated in simulation and phantom experiments. To evaluate the design principle for accelerated multidimensional excitation, we first examined parallel excitation with a transmit coil array in a simulation study. The transmit array was comprised of nine identical 19.8 cm 6.4 cm loop coils that were placed on a flat form and lined up along x (Fig. 1). This array faced a thin slab object below the array surface. 2D excitation with a desired excitation profile across the object in the form of g(x) g x (x) g z (z) was approached with parallel excitation pulses. In this case, the use of an echo-planar k x -k z trajectory consisting of k x constant lines evenly spaced by kx, the negligible y- and z-direction B 1 variation in the localized volume, and the separability of g(x) yielded solutions to Eq. [6] of the form W l (k) U kx,l (k x ) U kz (k z ), where U kx,l k x x U kz k z z h l x g x x e j2 xkx dx g z z e j2 zkz dz. The simple setting of this first experiment allows one to concentrate on understanding and designing excitation k-space weighting as functions of k x while leaving the treatment of k z direction weighting to the classical approach described in Ref. 1. Equations of form Eq. [5] were constructed, and weightings over k x -k z were determined. The RF pulse waveforms were then calculated based on Eq. [6]. As a reference, body-coil excitation pulses aimed at the same 2D localization were designed following the approach of Ref. 1. The design principle for accelerated excitation was further evaluated in a phantom study, which was carried out on a 1.5 Tesla MRI scanner (CVi; GE Medical Systems, Milwaukee, WI) with a setup very similar to that used in the simulation study described above. The transmit coil array of interest was of the same geometry and was placed 3 cm above a water-filled brick phantom ( cm 3 ). Since the scanner only supported single-channel RF pulse transmission, we examined parallel excitation indirectly, by mimicking simultaneous driving of the nine array elements through a series of nine single-channel experiments. The validity of the approach is ensured by the property of linearity in the small-tip-angle regime, which allows one to predict the result of a parallel excitation experiment from the superposition of transverse magnetization distributions observed from single-channel excitation experiments. Specifically, a single transmit/receive loop coil (19.8 cm 6.4 cm) was attached to the scanner s RF interface. During the nine experiments, the coil was placed and driven one configuration at a time, each with a position and RF pulse corresponding to one of the nine elements on the virtual coil array we desired to simulate. After each transmission was completed, the coil was immediately switched to the receive function, whereas throughout the experiments the scanner s body coil was kept detuned. 2D excitation and acquisition were carried out with the use of a gradient-echo sequence. From one experiment to another, the excitation k-space traversing was kept the same (i.e., echo-planar k x -k z trajectory, with k x being the slow direction) but the weighting (RF pulse) was changed according to the excitation pulse design. The 2D acquisition produced images that mapped out the water phantom along x and z (and projected along y, the normal direction of the 1-cm slab). We quantified the 2D transverse magnetization distributions by removing the coils sensitivity profiles from the images. The distributions were then superimposed to provide an estimate of the distribution resulting from the corresponding parallel excitation experiment. By the design of the study, coil coupling is not a factor. B 1 maps that were estimated based on Biot-Savart s law were used in both the RF-pulse calculations and the sensitivity-profile removal. In another study on excitation acceleration, an allaround array geometry (Fig. 6) was examined. The array consisted of seven transmit elements that were distributed azimuthally on a wraparound form inside a scanner s patient bore. Computer simulations evaluated 2D excitation designs that localized along both the x- and y-dimensions. Coupling between elements was not negligible and was taken into account (Eq. [3]), with a coupling matrix determined from mutual inductance calculations (26). The designs used the original Eqs. [5] and [6]. A simpler separable treatment of k x and k y, similar to that used in the first simulation study, is not suitable for this geometry. Finally, the effectiveness of the SAR management scheme, as integrated in the parallel pulse design, was evaluated. The evaluation was carried out in the same fashion as the first simulation study, except for the application of parallel excitation pulses of design-type Eq. [12] instead of Eq. [5]. With the calculated h l (x,z) s, Eq. [6] gave the weighting over k x -k z, which in turn determined the RF pulse waveforms. The resulting excitation profile and average SAR were compared to those in the first simulation study. RESULTS The focused excitation of a5cm 5 cm region centered at x 8cmandz 0 inside the slab object was investigated in the first simulation study. Based on a body transmit coil and the method described in Ref. 1, the reference design employed pulses that traversed 57 k x constant lines at

6 780 Zhu FIG. 2. Summary of the results of the first simulation study: (a) magnitude of localization profiles along x due to the individual coils in the array; (b and c) U kx,4 (m kx ) and U kx,7 (m kx ), the k x -direction weighting contributed by the coils positioned at x 4cm and x 8 cm, respectively; and (d) comparison of results between the accelerated parallel excitation and the conventional bodycoil excitation. kx 1/31.6 cycles/cm. The x-direction localization that resulted from this reference design is shown in Fig. 2d. A parallel excitation design accomplished the 2D localization task with the transmit coil array. Representing a fourfold acceleration, the design employed pulses that traversed 14 k x constant lines at kx 1/7 cycles/cm. U kx,4 (m kx ) and U kx,7 (m kx ), the k x -direction weighting contributed by the coils positioned at x 4 cm and x 8 cm, respectively, are illustrated in Fig. 2b and c. Localization along x due to each of the nine coils is shown in Fig. 2a (magnitude). ote that while the first aliasing side lobes were 4.5 times closer to the target (center-to-center spacing 7 cm) as a result of the sampling density reduction, the net amplitudes of these as well as other aliasing lobes located inside the 40-cm FOV were negligible due to incoherent addition (Fig. 2d). Compared to the results of the body-coil approach, the localization of the parallel excitation was as well refocused (the imaginary component (not shown) was negligible) and of comparable spatial resolution (Fig. 2d). In the phantom study, the effects of incoherent addition on aliasing side lobes were the focus of investigation. To this end, 2D excitation pulses were designed to target a region in the water phantom directly below the center element. To facilitate the investigation, the pulse calculations further assumed an extended linear array instead of the nine-element one. The designed pulses were 5.7 ms in length. For the center element experiment, Fig. 3a shows the applied RF pulse (magnitude and phase) as well as G x and G z, the gradient pulses identically executed in all the experiments of the series. Removing the coil s sensitivity profile from the resulting image provided an estimate of the 2D transverse magnetization distribution induced by the element, as shown in Fig. 3b (magnitude). Figure 3c illustrates the B 1 /sensitivity maps used. As a reference, Fig. 3d shows the transverse magnetization distribution from a nonselective excitation in a body-coil transmitreceive experiment. oticeable in Fig. 3b is a noise amplification effect due to the division operation employed for sensitivity profile removal, which tends to increase in severity farther away from the sensitive region. To prevent excessive noise amplification from obscuring the investigation, the division operation was suppressed in distant regions. The results from all nine experiments are summarized in Fig. 4, which displays in rows 1 9 the mapped transverse magnetization corresponding to each of the experiments (magnitude shown; left: Fig. 3b-type maps, but with cropped extent along z; right: maps at z 0). The bottom row presents the result of superimposing the individual maps, intended as a prediction of the result of a corresponding parallel excitation. Again, a substantial reduction of aliasing side lobes due to incoherent addition was observed. With the setup, contributions from the elements in the establishment of the main lobe and the suppression of the aliasing lobes were readily appreciated. The results from the center element alone and from the middle five and middle nine elements, as shown in Fig. 5, suggested that local excitation profile control was mainly achieved through nearby coils. The use of the extended array assumption in the pulse calculations accounted for much of the residual aliasing (incomplete annihilation) toward the nine-element array s boundary. Augmenting the array with elements beyond the nine can rectify this effect, as Fig. 5 suggests. Designing pulses for the nine-element array in the first place, as one normally would (e.g., the first simulation study), can also eliminate this effect, in which case the boundary coils weighting would experience the greatest changes. 2D parallel excitation pulses for the wraparound array were designed and evaluated. The simulations concentrated on the task of selectively exciting an arbitrarily positioned local volume within a 40 cm 23 cm axial FOV (Fig. 6). Equation [5] was solved repeatedly based on the effective B 1 field patterns and an EPI trajectory consisting of 14 k x constant lines at kx 1/6.9 cycles/cm. For the lth coil, l 1,2,...,7, the product of the desired 2D localization profile with the calculated h l (x,y) was then Fourier-transformed to derive the coil s k-space weighting and RF pulse waveform. Figure 6 shows the 2D localiza-

7 Parallel Excitation With Transmit Coil Array 781 FIG. 3. (a) Applied gradient (G x and G z ) and RF (RHO and THETA) pulses used in the center element experiment, (b) resulting 2D transverse magnetization distribution (magnitude shown) as estimated by removing coil sensitivity weighting from the acquired image, (c) B 1 maps (magnitude shown) used in the pulse design, and (d) transverse magnetization distribution from a nonselective excitation in a reference body-coil transmitreceive experiment. tion patterns due to each of the seven coils (magnitude). Figure 7 shows the net localization profile induced by the parallel excitation. The net result is virtually free of aliasing side lobes and represents an excellent match to that of a reference excitation, which involved body-coil transmission of a fourfold-longer conventional RF pulse (1). The design of the last simulation study resulted in parallel excitation pulses that differed in shape from the pulses in the first simulation study. Figure 8 presents the outcome, with a format identical to that of Fig. 2. While the pulses maintained the same level of localization accuracy and spatial resolution (Fig. 8d) as that of the pulses in the FIG. 4. Results from all nine experiments. Rows 1 9: The mapped transverse magnetization corresponding to each of the experiments (magnitude shown; left: Fig. 3b-type maps, but with cropped extent along z; right: maps at z 0). Bottom row: the result of superimposing the individual maps.

8 782 Zhu FIG. 5. Results from the center coils: (a) one coil, (b) five coils, and (c) nine coils. first simulation study, the design changes led to a 38% reduction in average SAR (Eq. [7]), confirming the substantial impact of the integrated SAR management scheme. DISCUSSIO AD COCLUSIOS With the proposed parallel excitation approach, designed RF pulses are synthesized, amplified, and fed to corresponding transmit elements in parallel to induce both spatial and temporal variations of the composite B 1 field, which, accompanied by appropriate gradient changes played out in synchrony, create a desired excitation profile upon completion of excitation. This is in contrast to a conventional approach, where the design of coil geometry and the offsets of driving-port phase/magnitude target B 1 - field spatial homogeneity, and an RF pulse played during excitation is limited to manipulate B 1 -field temporal variation only. The new concept of inducing appropriate B 1 spatiotemporal variations for excitation has significant ramifications for RF excitation performance. Given a desired excitation profile, the parallel excitation approach exploits the extra degrees of freedom inherent in the system, and accommodates excitation acceleration and/or SAR control to the extent that the underlying inverse problem (e.g., Eqs. [5] and [10]) remains non-overdetermined. To the same end, the conventional approach only has gradient amplitude scaling as a generally applicable means. With the further proposed pulse design methods, the driving RF pulse waveforms are calculated via Fourier transform of spatially weighted versions of the desired excitation profile. The pulses enable one to accelerate multidimensional excitation by reducing excitation k-space sampling density, and to minimize RF power deposition by tailoring the E field. However, for the full potential of the parallel excitation approach to be realized, the applicability of the design methods must be further extended beyond the small-tip-angle regime. The main challenge, then, is expected to be the nonlinearity of the Bloch equation, which may call for the use of iterative-pulse design methods. It is clear that the conditioning (35) of the parallelexcitation s B 1 matrix or the parallel-acquisition s sensitivity matrix determine a corresponding case s sensitivity to perturbations. For a parallel acquisition, the received data is noisy. Even if there is no noise or error in the FIG. 6. Selective excitation of an arbitrarily positioned local volume within a 40 cm 23 cm axial FOV: the 2D localization patterns (magnitude) due to each of the seven elements on the transmit coil array. [Color figure can be viewed in the online issue, which is available at wiley.com.]

9 Parallel Excitation With Transmit Coil Array 783 FIG. 7. Selective excitation of an arbitrarily positioned local volume within a 40 cm 23 cm axial FOV: the net localization profile (real component shown, imaginary component negligible) induced by the parallel excitation. sensitivity matrix, the noise in the data propagates to the final image as determined by the sensitivity matrix (gfactor (29)). On the other hand, for a parallel excitation, the effect of noise is more benign. Because of the very high signal-to-noise ratio (SR; contributions to B 1 from the driving RF sources vs. the thermal noise) typical of RF transmission, the use of parallel excitation introduces minimum randomness in the excitation profile, and hence there is a negligible effect on image SR. The duality between the parallel excitation approach and a SESE-based parallel acquisition approach in fact extends beyond a symmetry in form. Consider a SESE acquisition with RF fields and sampling periods matching that of the 2D excitation case (an example scenario of operating a transmit-receive array). The sensitivity matrix T can be shown to be C (x,y). This structural symmetry implies identical conditioning of the two cases. In general, the various connections between parallel excitation and parallel acquisition allow one to employ some of the same techniques used to enhance robustness for example, one can solve Eq. [5] with regularization (32) if desired. From an application perspective, fast imaging is an area where the present parallel excitation approach may have a significant impact. For example, under circumstances in which the anatomy of interest is contained in a local region, the use of a multidimensional excitation that spotlights the region can accelerate imaging by alleviating the burden of spatial encoding inflicted on signal acquisition. Representing improvements over conventional excitations, multifold shorter parallel excitations promise to realize imaging volume definition/steering while breaking the time-cost barrier that hindered the practical use of multidimensional pulses in the past. Compared to the use of a parallel acquisition approach (e.g., Refs. 29 and 30), focused imaging based on the parallel excitation approach is not subject to the unique SR degradation described by the g-factor. Its volume coverage, however, is smaller. It is possible to combine the two approaches, which yields an even greater capacity for scan time reduction. While the experiments reported here focused on 2D localization, the parallel excitation approach applies to the creation and acceleration of general 2D excitation profiles, with utilities including correction for field imperfection-induced effects (12 15) and non-fourier spatial encoding (36). The applicability of the approach can certainly be further extended to more dimensions. In high-field imaging, the transmit system and driving means described in this work may represent more than just an appealing alternative to the conventional approach. With the latter, complex electromagnetic effects may pose considerable challenges to profile (uniformity) control, and RF heating in the subject s body may present a major concern in scan safety. The new approach embodies an integrated treatment of excitation pulses and transmit coils, and thus promises to provide a better excitation profile control than one that relies solely on resonance module improvement. Transmission with a distributed parallel system, acceleration of excitation, and manage- FIG. 8. Summary of the results of the third simulation study: (a) magnitude of localization profiles along x due to the individual coils in the array; (b and c) U kx,4 (m kx ) and U kx,7 (m kx ), the k x -direction weighting contributed by the coils positioned at x 4cm and x 8 cm, respectively; and (d) result of the accelerated and SAR-minimized parallel excitation vs. that of the conventional bodycoil excitation.

10 784 Zhu ment of SAR further imply a viable solution to the challenging issues of power deposition at high-field strength. The required field calibration contributes an overhead, which, while likely a necessity for quality and safe imaging at high B 0 strength, should be checked and possibly minimized. From a system perspective, multiple driving sources represent a new requirement. Building a multielement transmit array and integrating it into an MRI system call for innovative solutions to address further issues that may include efficiency, coupling, and calibration. The impact of array design on the performance of accelerated or SARmanaged excitation remains an important subject to be studied. The criteria for a good design should include 1) sufficient robustness of the excitation profile creation against perturbation, and 2) low RF power deposition accompanying the excitation profile creation. Meeting criterion 1 implies graceful rather than catastrophic profile deterioration in the presence of such factors as calibration errors and noise. Fundamentally, the individual B 1 maps and the excitation k-space traversing trajectory dictate how sensitive main lobe creation and aliasing lobe suppression are to perturbations, in which regard an appropriate measure could be the condition number of the C (x,y) matrix (Eq. [5]). Criterion 2 gauges the efficiency and safety of a transmit array, a suitable measure of which could be the largest eigenvalue of the F matrix (Eq. [9]). Certainly, complex electromagnetic interactions between the resonance module and the subject at high-field strength imply that a high-frequency array design may possibly be optimized only in an average sense. ACKOWLEDGMETS The author thanks Dr. John Pauly and Dr. orbert Pelc for valuable discussions, and Dr. W. Thomas Dixon for proofreading the manuscript. REFERECES 1. Pauly J, ishimura D, Macovski A. 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