Method for multi-mode, multi-load, and multi-domain optimization of a multi-channel near-field RF transmitter

Abstract

The invention relates to a method for optimization of a performance of a multi-channel transmitter including several transmit elements, particularly in a magnetic resonance imaging device. The method includes: (a) Exciting the transmit elements of the multi-channel transmitter by electric excitation signals comprising a specific power, with the power of the excitation signals partially reflected by the transmit elements of the multichannel transmitter, (b) Determining a reflected power which is reflected by the multi-channel transmitter during excitation of the transmit elements, (c) Determining reflection coefficients S.sub.xx of the multi-channel transmitter, (d) Determining reflection coefficients S.sub.xy of the multi-channel transmitter, (e) Calculating a performance criterion representing the performance of the multi-channel transmitter, with the performance criterion based on the reflected power, the reflection coefficients S.sub.xx and the reflection coefficients S.sub.xy, and (f) Tuning the multi-channel transmitter so that the performance criterion is optimized.

Claims

1. Method for optimization of a performance of a multi-channel transmitter comprising several transmit elements, wherein the method comprises: a) exciting the transmit elements of the multi-channel transmitter by electric excitation signals comprising a specific power, wherein the power of the excitation signals is partially reflected by the transmit elements of the multi-channel transmitter; b) determining a reflected power which is reflected by the multi-channel transmitter during excitation of the transmit elements; c) determining reflection coefficients S.sub.xx of the multi-channel transmitter, wherein said reflection coefficients S.sub.xx represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the x-th transmit element of the multi-channel-transmitter; d) determining reflection coefficients S.sub.xy of the multi-channel transmitter, wherein said reflection coefficients S.sub.xy represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the y-th transmit element of the multi-channel-transmitter; e) calculating a performance criterion representing the performance of the multi-channel transmitter, wherein the performance criterion is based on e1) the reflected power, e2) the reflection coefficients S.sub.xx, and e3) the reflection coefficients S.sub.xy; and f) tuning the multi-channel transmitter so that the performance criterion is optimized, wherein an optimization criterion is calculated according to the following formula and the multi-channel transmitter is tuned so that the optimization criterion is minimized: $EF = \underset{\underset{elements}{all transmitter}}{.Math.} w_{xx_i} \times {.Math. S_{xx_i} - S_{xx, Target} .Math.}^{p} + \underset{\underset{pairs of transmitter elements}{all decoupled}}{.Math.} w_{xy_i} \times {.Math. S_{xy_i} - S_{xy, Target} .Math.}^{p} + w_{refl} \times {.Math. P_{Re fl_transitter} .Math.}^{p}$ with: EF: Optimization criterion w.sub.xx.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xx.sub._.sub.i for the individual transmit element “i”, w.sub.xy.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xy.sub._.sub.i for the “i” decoupled pair of transmit elements S.sub.xx,Target: Predetermined target value for each element reflection coefficient S.sub.xx.sub._.sub.i S.sub.xy,Target: Predetermined target value for each reflection coefficient S.sub.xy.sub._.sub.i w.sub.refl: Weighting factor for reflected power of the entire multi-channel transmitter P.sub.Refl.sub._.sub.transmitter: reflected power of the entire multi-channel transmitter p: is a selected number.

2. Method according to claim 1, wherein the reflected power is measured for the entire multi-channel transmitter.

3. Method according to claim 1, wherein a) the excitation signals are radio frequency signals, and b) the excitation signals all have a fixed amplitude and a fixed phase.

4. Method according to claim 1, wherein a) the multi-channel transmitter is, after optimization, used at a certain operating frequency, and b) at least one of the reflection coefficients S.sub.xx and S.sub.xy and the reflected power are determined at the operating frequency of the multi-channel transmitter.

5. Method according to claim 1, wherein the reflection coefficients and the reflected power is numerically simulated so that the optimization criterion is numerically simulated without any transmitter measurements.

6. Method according to claim 1, wherein the multi-channel transmitter is a single-row transmitter comprising a single row of transmit elements.

7. Method according to claim 1, wherein the reflected power is measured for each of the transmitter elements separately.

8. Method according to claim 1, wherein the reflected power is measured for each row of multi-channel multi-row transmitter separately.

9. Method according to claim 1, wherein the reflection coefficients and the reflected power is measured so that the optimization criterion is calculated based on transmitter measurements.

10. Method according to claim 1, wherein the multi-channel transmitter is a multi-row transmitter including multiple rows of transmit elements.

11. Method according to claim 1, wherein the method is performed in a magnetic resonance imaging device.

12. Method according to claim 1, wherein the method is performed for at least one excitation mode and only one load of the multi-channel transmitter.

13. Method for optimization of a performance of a multi-channel transmitter comprising several transmit elements, wherein the method comprises: a) exciting the transmit elements of the multi-channel transmitter by electric excitation signals comprising a specific power, wherein the power of the excitation signals is partially reflected by the transmit elements of the multi-channel transmitter; b) determining a reflected power which is reflected by the multi-channel transmitter during excitation of the transmit elements; c) determining reflection coefficients S.sub.xx of the multi-channel transmitter, wherein said reflection coefficients S.sub.xx represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the x-th transmit element of the multi-channel-transmitter; d) determining reflection coefficients S.sub.xy of the multi-channel transmitter, wherein said reflection coefficients S.sub.xy represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the y-th transmit element of the multi-channel-transmitter; e) calculating a performance criterion representing the performance of the multi-channel transmitter, wherein the performance criterion is based on e1) the reflected power, e2) the reflection coefficients S.sub.xx, and e3) the reflection coefficients S.sub.xy; and f) tuning the multi-channel transmitter so that the performance criterion is optimized, wherein an optimization criterion is calculated according to the following formula and the multi-channel transmitter is tuned so that the optimization criterion is minimized: $EF = \underset{\underset{elements}{all transmitter}}{.Math.} w_{xx_i} \times {.Math. S_{xx_i} - S_{xx, Target} .Math.}^{p} + \underset{\underset{pairs of transmitter elements}{all decoupled}}{.Math.} w_{xy_i} \times {.Math. S_{xy_i} - S_{xy, Target} .Math.}^{p} + \underset{all modes}{.Math.} w_{m_i} \times {.Math. P_{Re fl_transitter} .Math.}^{p}$ with: EF: Optimization criterion w.sub.xx.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xx.sub._.sub.i for the individual transmit element “i” w.sub.xy.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xy.sub._.sub.i for the “i” decoupled pair of transmit elements S.sub.xx,Target: Predetermined target value for each element reflection coefficient S.sub.xx.sub._.sub.i S.sub.xy,Target: Predetermined target value for each reflection coefficient S.sub.xy.sub._.sub.i w.sub.m.sub._.sub.i: Weighting factor for reflected power of the entire multi-channel transmitter for given transmit mode “i” P.sub.Refl.sub._.sub.transmitter.sub._.sub.i: reflected power of the entire multi-channel transmitter for given transmit mode “i” p: is a selected number.

14. Method according to claim 13, wherein the method is performed for at least two excitation modes and only one load of the multi-channel transmitter.

15. Method for optimization of a performance of a multi-channel transmitter comprising several transit elements, wherein the method comprises: a) exciting the transmit elements of the multi-channel transmitter by electric excitation signals comprising a specific power, wherein the power of the excitation signals is partially reflected by the transmit elements of the multi-channel transmitter; b) determining a reflected power which is reflected by the multi-channel transmitter during excitation of the transmit elements; c) determining reflection coefficients S.sub.xx of the multi-channel transmitter, wherein said reflection coefficients S.sub.xx represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the x-th transmit element of the multi-channel-transmitter; d) determining reflection coefficients S.sub.xy of the multi-channel transmitter, wherein said reflection coefficients S.sub.xy represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the y-th transmit element of the multi-channel-transmitter; e) calculating a performance criterion representing the performance of the multi-channel transmitter, wherein the performance criterion is based on e1) the reflected power, e2) the reflection coefficients S.sub.xx, and e3) the reflection coefficients S.sub.xy; and f) tuning the multi-channel transmitter so that the performance criterion is optimized, wherein an optimization criterion is calculated according to the following formula and the multi-channel transmitter is tuned so that the optimization criterion is minimized: $EF = \underset{all loads}{.Math.} [\begin{matrix} \underset{\underset{elements}{all transmitter}}{.Math.} w_{xx_i} \times {.Math. S_{xx_i} - S_{xx, Target} .Math.}^{p} + \\ \underset{\underset{pairs of transmitter elements}{all decoupled}}{.Math.} w_{xy_i} \times {.Math. S_{xy_i} - S_{xy, Target} .Math.}^{p} + \\ \underset{all modes}{.Math.} w_{m_i} \times {.Math. P_{Re fl_transmitter_i} .Math.}^{p} \end{matrix}]$ with: EF: Optimization criterion w.sub.xx.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xx.sub._.sub.i for the individual transmit element “i” w.sub.xy.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xy.sub._.sub.i for the “i” decoupled pair of transmit elements S.sub.xx,Target: Predetermined target value for each element reflection coefficient S.sub.xx.sub._.sub.i S.sub.xy,Target: Predetermined target value for each reflection coefficient S.sub.xy.sub._.sub.i w.sub.m.sub._.sub.i: Weighting factor for reflected power of the entire multi-channel transmitter for given transmit mode “i” P.sub.Refl.sub._.sub.transmitter.sub._.sub.i: reflected power of the entire multi-channel transmitter for given transmit mode “i” p: is a selected number.

16. Method according to claim 15, wherein the method is performed for at least two excitation modes and at least two loads of the multi-channel transmitter.

17. Method for optimization of a performance of a multi-channel transmitter comprising several transit elements, wherein the method comprises: a) exciting the transmit elements of the multi-channel transmitter by electric excitation signals comprising a specific power, wherein the power of the excitation signals is partially reflected by the transmit elements of the multi-channel transmitter; b) determining a reflected power which is reflected by the multi-channel transmitter during excitation of the transmit elements; c) determining reflection coefficients S.sub.xx of the multi-channel transmitter, wherein said reflection coefficients S.sub.xx represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the x-th transmit element of the multi-channel-transmitter; d) determining reflection coefficients S.sub.xy of the multi-channel transmitter, wherein said reflection coefficients S.sub.xy represent a signal ratio between an incident wave applied to the x-th transmit element of the multi-channel transmitter and a resulting wave reflected from the y-th transmit element of the multi-channel-transmitter; e) calculating a performance criterion representing the performance of the multi-channel transmitter, wherein the performance criterion is based on e1) the reflected power, e2) the reflection coefficients S.sub.xx, and e3) the reflection coefficients S.sub.xy; and f) tuning the multi-channel transmitter so that the performance criterion is optimized, wherein there is an interlaved excitation of the individual transmit elements of the multi-channel transmitter, an optimization criterion is calculated according to the following formula and the multi-channel transmitter is tuned so that the optimization criterion is minimized: $EF = \underset{\underset{elements}{all transmitter}}{.Math.} w_{xx_i} \times {.Math. S_{xx_i} - S_{xx, Target} .Math.}^{p} \underset{\underset{pairs of transmitter elements}{all decoupled}}{.Math.} w_{xy_i} \times {.Math. S_{xy_i} - S_{xy, Target} .Math.}^{p} + w_{refl} \times {.Math. P_{Re fl_transitter} .Math.}^{p} + \underset{N_{is}}{.Math.} w_{t_i} \times {.Math. P_{Re fl_transmitter_is_i} - \frac{P_{Transmit}}{N_{is}} .Math.}^{p}$ with: EF: Optimization criterion w.sub.xx.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xx.sub._.sub.i for the individual transmit element “i” w.sub.xy.sub._.sub.i: Weighting factor for the reflection coefficient S.sub.xy.sub._.sub.i for the “i” decoupled pair of transmit elements S.sub.xx,Target: Predetermined target value for each element reflection coefficient S.sub.xx.sub._.sub.i S.sub.xy,Target: Predetermined target value for each reflection coefficient S.sub.xy.sub._.sub.i w.sub.t.sub._.sub.i: Weighting factor for reflected power of the entire multi-channel transmitter for given transmit mode “i” P.sub.Refl.sub._.sub.transmitter.sub._.sub.i: Reflected power of the multi-channel transmitter for given interleave stage “i” P.sub.Transmit: Power transmitted by the multi-channel transmitter N.sub.is: Number of interleave stages p: is a selected number.

18. Method according to claim 17, wherein the method is performed for at least one excitation mode and at least one load of the multi-channel transmitter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIGS. 1A and 1b show a flowchart illustrating an optimization method according to the invention.

(2) FIG. 2A shows the frequency dependence of the reflection coefficient S.sub.xx for a frequency domain optimization,

(3) FIG. 2B shows the frequency dependence of the reflection coefficient S.sub.xy for a frequency domain optimization,

(4) FIG. 2C shows the frequency dependence of the reflection coefficient S.sub.xx for a dual domain optimization both in the frequency domain and in the time domain.

(5) FIG. 2D shows the frequency dependence of the reflection coefficient S.sub.xy for a dual domain optimization both in the frequency domain and in the time domain.

(6) FIG. 3A shows a Monte Carlo histogram of the ratio P.sub.refl.sub._.sub.transmitter/P.sub.transmit in percent for the CP1 mode and a frequency domain optimization.

(7) FIG. 3B shows a Monte Carlo histogram of the ratio P.sub.refl.sub._.sub.transmitter/P.sub.transmit in percent for the CP2 mode and a frequency domain optimization.

(8) FIG. 3C shows a Monte Carlo histogram of the ratio P.sub.refl.sub._.sub.transmitter/P.sub.transmit in percent for the CP1 mode and a dual domain optimization.

(9) FIG. 3D shows a Monte Carlo histogram of the ratio P.sub.refl.sub._.sub.transmitter/P.sub.transmit in percent for the CP2 mode and a dual domain optimization.

(10) FIG. 4 shows the investigated single row transmitter comprised of 8 channels with identical rectangular loops of length 120 mm and the angular size 40 degrees, mounted on a cylindrical acrylic former with diameter of 280 mm.

(11) FIG. 5 shows the investigated triple-row transmitter, each non-overlapped row is comprised by 8 identical rectangular loops of length 70 mm and the angular size 40 degrees, mounted on a cylindrical acrylic former with diameter of 280 mm.

DETAILED DESCRIPTION OF THE DRAWINGS

(12) In the following, the flowcharts shown in FIGS. 1A and 1B are described.

(13) In a first step S1, excitation modes are defined for excitation of the multi-channel transmitter. Further, loads (subjects) of the multi-channel transmitter are defined and circuit level optimization criteria are determined.

(14) In a second step S2, a decision is made whether the optimization is performed in numerical domain or using measurements of a real multi-channel transmitter.

(15) In the following, steps S3-S6 are explained which refer to the optimization using measurement data of a real multi-channel transmitter.

(16) In step S3, the coil elements of the multi-channel transmitter are manufactured.

(17) Then, in step S4, the other components (e.g. trim capacitors, decoupling networks, etc.) of the multi-channel transmitter are soldered.

(18) In step S5, the reflection coefficients S.sub.xx of all transmitter elements and the reflection coefficients S.sub.xy of all decoupled pairs of transmitter elements are measured for given loads. The reflection coefficients S.sub.xx represent a signal ratio between an incident wave applied to the x-th coil element of the multi-channel transmitter and a resulting wave reflected from the x-th coil element of the multi-channel transmitter.

(19) The reflection coefficients S.sub.xy represent a signal ratio between an incident wave applied to the x-th coil element of the multi-channel transmitter and a resulting wave reflected from the y-th coil element of the multi-channel transmitter.

(20) In step S6, the power P.sub.Refl.sub._.sub.transmitter reflected by the entire transmitter, or by each transmitter row is measured or calculated using S parameter data for given loads (subjects) and excitation modes.

(21) In the following, the corresponding steps S7-S10 are explained which relate to the calculation of the afore-mentioned data in numerical domain.

(22) In step S7, three-dimensional electro-magnetic simulations of the multi-channel transmitter are calculated with given loads (subjects).

(23) Then, in step S8, RF circuit simulations of the multi-channel transmitter with given loads are calculated.

(24) In step S9, the element reflection coefficients S.sub.xx and the reflection coefficients S.sub.xy of all decoupled pairs of transmitter elements are extracted for given loads.

(25) Further, in step S10, the reflected power is calculated for given loads (subjects) and excitation modes.

(26) In step S11, an error function EF is calculated wherein the error function EF is an optimization criterion. The error function is calculated on the basis of the reflected power P.sub.Refl.sub._.sub.transmitter, the reflection coefficients S.sub.xx and the reflection coefficients S.sub.xy according to the following formula:

(27) $EF = \underset{all loads}{.Math.} [\begin{matrix} \underset{\underset{elements}{all transmitter}}{.Math.} w_{xx_i} \times {.Math. S_{xx_i} - S_{xx, Target} .Math.}^{p} + \\ \underset{\underset{pairs of transmitter elements}{all decoupled}}{.Math.} w_{xy_i} \times {.Math. S_{xy_i} - S_{xy, Target} .Math.}^{p} + \\ \underset{all modes}{.Math.} w_{m_i} \times {.Math. P_{Re fl_transmitter_i} .Math.}^{p} \end{matrix}]$

(28) Then, in step S12, the value of the error function EF is compared with a predetermined target value EF.sub.Target.

(29) If the actual value of the error function EF is smaller than the predetermined target value EF.sub.Target, then it is determined in step S16 that the multi-channel transmitter is ready for use.

(30) Otherwise, step S13 estimates the adjustment direction for variable components (e.g. trim capacitors) of the multi-channel transmitter.

(31) In step S14, the variable components (e.g. trim capacitors) are adjusted to new values.

(32) In step S15, it is determined whether a recalculation is made in the numerical domain or not, if so, the method continuous with step S8 in FIG. 1A. Otherwise, the method continuous with step S4 in FIG. 1A.

Example Data

(33) The geometry of the single and multi-row loop-based transmitters that we investigated is described in [M. Kozlov, R. Turner: “Analysis of RF transmit performance for a multi-row multi-channel MRI loop array at 300 and 400 MHz”, Proceedings of the Asia-Pacific Microwave Conference 2011, Melbourne, Australia, p. 1190-1193, December 2011; M. Kozlov, R. Turner, “Influence of loop array geometry on near field transmit properties at 300 MHz”, Proceedings of 2011 IEEE International Symposium on Antennas and Propagation, Spokane, USA, p. 1715-1718, July 2011]. For example: a) the investigated single row transmitter is comprised of 8 channels with identical rectangular loops of length 120 mm and the angular size 40 degrees, mounted on a cylindrical acrylic former with diameter of 280 mm (cf. FIG. 4); b) the investigated triple-row transmitter, each non-overlapped row is comprised by 8 identical rectangular loops of length 70 mm and the angular size 40 degrees, mounted on a cylindrical acrylic former with diameter of 280 mm (cf. FIG. 5). The realistic 3-D EM model of the transmitters included all construction details for the resonance elements, simulated with precise dimensions and material electrical properties. The loads utilized were the multi-tissue Ansoft human body models, cut in the middle of the torso, with different scaling factors: a medium-size head #1 with scaling X=0.9, Y=0.9, Z=0.9, a large-size (almost fully occupying the transmitter volume when the diameter was 250 mm) head #2 with scaling X=0.95, Y=0.975, Z=0.9, and a small-size head #3 with scaling X=0.85, Y=0.85, Z=0.9. To investigate transmitter transmit performance sensitivity to load position, the latter was varied.

(34) The RF circuit simulator was Agilent ADS 2011.10, and Ansoft HFSS 14 was chosen as the 3-D EM tool.

(35) For the single row 8-element transmitter, or for the triple row transmitter, where each non-overlapped row is correspondingly comprised of 8 identical rectangular loops, components to be optimized are: the matching capacitor for each element matching network, the tuning capacitor for each element tuning network, the decoupling capacitor or mutual inductance between decoupling inductors for each decoupling network. This results in 24 or 120 optimization variables for the single row transmitter, or the triple row transmitter respectively.

(36) Initial guesses are made (based on numeral simulation, experience, or experimentally derived knowledge) for the values of adjustable lumped elements, as well as the range over which adjustable elements can be varied.

(37) For the single row transmitters, each optimization can be performed in two steps: 3000 random tries, followed by “Quasi-Newton” optimization until no further improvement was possible. This ensures that the global minimum condition has been found. It takes less than 1 minute to compute the values of all variable components for a given set of individually weighted criteria. All weight factors can be equal to 1 for the first optimization trial. If P.sub.refl.sub._.sub.transmitter in one mode was still more than 5% of P.sub.transmit the weight factor of the criterion for P.sub.refl.sub._.sub.transmitter was step by step increased by 1.0 until the worst case value of P.sub.refl.sub._.sub.transmitter was less than 5% of P.sub.transmit for all excitation modes.

(38) For double and triple row transmitters, the optimization approach described above could be insufficient to provide global optimization, because the number of independent optimization variables is too high for the entire optimization space to be covered by 3000 random tries. Simply increasing the number of random tries does not help, because the required number of tries becomes so large that the optimization time becomes unacceptably long. To keep optimization time at a reasonable level (a few minutes), a two stage optimization approach is implemented for transmitters with cylindrical (or close to cylindrical symmetry). Despite the asymmetry of the human head model, the cylindrical symmetry of the elements in each transmitter row ensures that the value of adjustable elements of the tuning and decoupling networks are relatively similar, within the same row.

(39) Thus the preliminary values of optimization variables are obtained by performing the first stage optimization with independent variables grouped for each row and each type of network. This approach reduces the number of independent optimization variables from 120 to 15 for the triple row transmitter. As a result, the use of 3000 random tries becomes reasonable for approaching the preliminary values of optimization variables.

(40) At the second stage, using the “Quasi-Newton” method, optimized values for all ungrouped independent variables are obtained when the optimizer reports that no further improvement is possible. To ensure (to some extent) that the two stage optimization approaches global minimum condition, a multi-start strategy should be used. This consists of re-running both stages of the optimization several (e.g. five) times with different initial conditions. If the data spread is small (less than 5% peak to peak variation of both optimization variables and quantitative results) then the multi-start is considered to be sufficient for obtaining optimized values of independent variables with about 5% uncertainty. If the data spread is not small, the multi-start procedure is performed 5 times more. When the best optimization of both multi-start tries reaches similar final error values, and the peak-to-peak variation in their optimization variables and results is less than 5%, the optimization procedure is stopped, and values from the best optimization try are considered as the final result. Each dual stage optimization takes about 2 minutes: thus, in most cases, the entire multi-row transmitter circuit optimization require about 10 minutes, much faster than the approximately one day required for 3D-EM simulation of a multi-row transmitter using an up-to-date Dell Precision T7500 Workstation with 96 GB RAM and 12 cores.

(41) The time-domain only optimization, guided by EF defined in (5), resulted in P.sub.refl.sub._.sub.transmitter=0, and the best performance for optimization of the excitation mode. In other modes P.sub.refl.sub._.sub.transmitter could approach 40% of P.sub.transmit and performance was sub-optimal.

(42) In the CP1 mode, optimization in the frequency domain resulted in relatively small P.sub.refl.sub._.sub.transmitter (less than 10% of P.sub.transmit), thus ensuring almost the best performance. This was guided by EF defined in (1) with only adjacent elements included in the decoupled element pair list, S.sub.xx,Target=−30 dB, S.sub.xy,Target=−20 dB and all weighting factors equal to 1. However, in the CP2 mode, P.sub.refl.sub._.sub.transmitter was significantly larger (mostly more than 25% of P.sub.transmit). Consequently the transmit performance in the CP2 mode was significantly reduced. For a given mode B.sub.1+ homogeneity was similar after both optimizations.

(43) Extension of the decoupled element pair list by including also all second-neighbour pairs did not essentially improve CP2 mode transmit performance, compared with the original frequency domain optimization.

(44) Dual-domain optimization resulted in negligible P.sub.refl.sub._.sub.transmitter (less than 3% of P.sub.transmit) for both CP1 and CP2 modes, provided that coupling to the second-neighbour elements was less than −9 dB after frequency domain optimization. In this condition, the coupling between the second-neighbour elements decreased by 4 to 8 dB, but the single resonance element matching became relatively poorer (in the range −10 dB to −15 dB), and adjacent element coupling increased by 3 to 5 dB. Thus, despite giving the best transmit performance in the desired excitation modes, both the frequency dependence of S.sub.xx (i.e. element matching) and S.sub.xy (i.e. the coupling between adjacent elements) resemble the corresponding frequency dependence of a sub-optimal, badly tuned transmitter (FIG. 2A-2D).

(45) To mimic a sub-optimally tuned transmitter, obtained after in the frequency domain optimization, S.sub.xy,Target and S.sub.xy,Target were changed to be −10 dB and −12 dB respectively. Starting the optimization from several different initial conditions, a set of optimization results was obtained for several transmitter geometries. Despite the very similar visual appearance of the frequency dependence of element matching and coupling between adjacent elements for all tuning parameters (plotted in dB scale), the transmit performance showed highly significant variation, from very sub-optimal (P.sub.refl.sub._.sub.transmitter about 30% of P.sub.transmit) to nearly the best (P.sub.refl.sub._.sub.transmitter˜0). This finding has a rational explanation: from (4) P.sub.refl.sub._.sub.transmitter depends on all the interactions within the transmitter (not only the subset of interactions described by element matching and coupling between adjacent elements), and also on the phases of coupling between adjacent elements, which are rarely analysed.

(46) It is becoming increasingly important to be able to generate not only several fundamental excitation modes, but also to have ability to adjust amplitude and phase of excitation signals for given fundamental excitation mode (to apply so-called static RF shimming), in order to obtain better homogeneity in a given VOI or part of VOI.

(47) FIGS. 3A-3D show Monte Carlo histograms of a ratio P.sub.refl.sub._.sub.transmitter/P.sub.transmit in percent.

(48) FIGS. 3A and 3C refer to the first circular polarization (CP1) mode, while FIGS. 3B and 3D refer to the second circular polarization (CP2) mode. Further, FIG. 3A and 3B illustrate a frequency domain optimization, while FIGS. 3C and 3D illustrate a dual domain optimization.

(49) By Monte Carlo analysis, using 4000 trials with uniform +/−30% variation of phase for each excitation signal for CP1 and CP2 modes, the influence of dual-domain optimization on transmitter performance after static RF shimming was investigated. These results allow us to conclude that dual-domain optimization improves not only performance in fundamental CP1 and CP2 modes, but also the performance after static RF shimming has been performed for these fundamental modes (FIGS. 3A-3D).

(50) Similar to single row transmitter, the dual-domain optimization of dual and triple row transmitters resulted in: a) significant reduction of P.sub.refl.sub._.sub.transmitter for all modes, provided that coupling to the second-neighbour elements in all direction was less than −9 dB after frequency domain optimization, b) S parameter matrix looked like a “badly” tuned transmitter, and c) improved performance after static RF shimming around given fundamental modes. However, the larger the number of transmitter elements, the larger is the worst case value of P.sub.refl.sub._.sub.transmitter. For example, for a triple row transmitter, P.sub.refl.sub._.sub.transmitter could not be reduced to below 5% of P.sub.transmit in some excitation modes.

(51) This novel optimization procedure has no practical effect on safety excitation efficiency, defined as B.sub.1+v/√SAR.sub.10g, or the peak location of the specific absorption rate averaged over 10 gram (SAR.sub.10g). From the MRI perspective, it is the level of safe excitation efficiency that defines MRI scanner performance, not the peak SAR.sub.10g, which increases when the new optimization procedure is used, simultaneously with an increase of B.sub.1+v.

(52) Although the invention has been described with reference to the particular arrangement of parts, features and the like, these are not intended to exhaust all possible arrangements of features, and indeed many other modifications and variations will be ascertainable to those of skill in the art.

Method for multi-mode, multi-load, and multi-domain optimization of a multi-channel near-field RF transmitter

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