Active Phased Array Techiques for High-Field MRI Pedram Yazdabakhsh 1, Klaus Solbach Uiversity Duisburg-Esse, Hochfrequeztechik, Bismarckstr.81, D-4784, Duisburg, Germay 1 pedram.yazdabakhsh@ui-due.de Abstract This paper describes recet developmets i high field Magetic Resoace Imagig (MRI) cocerig the applicatio of active phased array techiques. The pulse amplitudes ad phases of currets i Atea (Coil) arrays are adjusted i order to improve the homogeeity of the magetic flux desity distributio iside the ihomogeeous patiet s body. This ca be realized either by usig the atea elemets combied with a Butler matrix which is excited by phase/amplitude steered power amplifiers or by coectig the atea elemets directly to the power amplifiers. A improved system icludes a variable power combiig stage for maximum utilizatio of istalled trasmit power. I. INTRODUCTION MRI is a imagig techique widely used to produce high quality images of the iside of the huma body. The maget system is used to produce a itese ad homogeeous field i the regio to be imaged to obtai images of good quality. I high-field MRI, RF power pulses of 1 kw peak per atea elemet (coil) are commo ad the sigal frequecy is, e.g. 297 MHz for a 7 Tesla (bias) static ad homogeeous magetic flux desity B. Atea (coil) elemets arrayed i a circle aroud the patiet are employed for the geeratio of RF magetic flux B 1 iside the patiet s body with circular polarizatio w.r.t the logitudial axis of the MRI tube. The ihomogeeity of the patiet s body at this high frequecy creates strog variatios i the magetic flux desity produced by the atea array, if we employ uiform curret excitatio. Therefore, adjustmets of the phase ad amplitude of the elemets of a circular atea (coil) arrays are required i order to improve the RF field homogeeity (called B 1 or RF shimmig), [1]. II. METHODS FOR AMPLITUDE / PHASE CONTROL We itroduce two cocepts borrowed from the phased array techology to cotrol the phase ad amplitude of atea elemet (coil) arrays i a MRI system ad after that a major improvemet over both cocepts will be itroduced. A. Butler Matrix Multi-Mode Feed Network The first cocept is the use of a Butler matrix [2], which is coected to the atea elemets o the output side ad to the liear pulse power amplifiers (LPPAs) at the iput side. Due to the iheret phase progressio of the Butler matrix etwork the iput sigals from the amplifiers create phase modes (istead of beams i atea arrays) of magetic flux with circular polarizatio at the array elemets which ca be superimposed to couter the effects of the ihomogeeous patiet s body [3]. We ca cotrol the superpositio by adjustig the iput sigal phase to the power amplifiers ad coect each amplifier to oe iput port of the Butler matrix. This results i oe of the power amplifiers to create the CP +1 - mode which exhibits 36 phase rotatio of elemet curret aroud the circular array while the ext amplifier supplies its power to the CP +2 mode which exhibits 72 of phase shift, ad so o. The cocept is depicted i Fig. 1. Fig.1 Cocept of phase mode creatio by Butler matrix; atea (coil) elemets coected to the Butler matrix output 1) Iheret limitatios of this cocept Oly half of the iput ports create the right haded circular polarizatio, the other half is opposite haded ad less useful for trasmissio. The umber of atea elemets (coils) must be equal to the umber of power amplifiers. Give the umber of LPPAs, which are the expesive compoets i the system, the resolutio of the created field distributio is limited. Trasmittig oly through the right haded circular polarizatio ports of the matrix, this relatio ca be improved to allow twice as may atea elemets as there are trasmitters. For optimum superpositio, it may be ecessary to adjust the amplitude of the various modes. However, whe equal power amplifiers are employed, most amplifiers will operate below maximum, i.e., the istalled power i geeral will be uderutilized ad the MRI image sigal-to-oise ratio degraded. I particular, the first circular polarized phased mode CP +1 ca be cosidered the fudametal mode which should trasmit most of the available power this is ot possible i the basic cocept sice all iput ports of the Butler Matrix receive the same maximum power of a sigle LPPA.
2) Butler Matrix Realizatio The realizatio of Butler matrix requires a combiatio of 9 hybrid couplers (3dB) ad fixed phase shifters. Lie crossovers of covetioal Butler matrix desigs are oe of the mai drawbacks, sice they may add several udesired effects. To overcome this problem, a ew layout of a 8 8 Butler matrix was desiged as Fig. 2 which uses ports at the edges as well as at the ceter of the matrix. Fig. 3 Realized Brach-Lie coupler for 297 MHz Fig. 4 Realized 8 8 Butler matrix i microstrip techology (split boards of RO43) for 297 MHz Fig. 2 Plaar 8 8 Butler matrix without ay crossig ad additioal output phase shifters For the 9 hybrid couplers, Brach-Lie (BL) couplers were used because of their high power ad high voltage hadlig capability. Our realizatio was based o microstrip techology ad has bee desiged iitially o RO43 substrate with permittivity of 3.38, loss taget of.27 ad a thickess of h=1.524 mm. This results i a brach lie legth of 13.59 cm, a series lie legth of 13.21 cm, ad a total size of 14.7cm 16.2 cm for the BL coupler. To realize a 8 8 Butler matrix at 297 MHz, costructed from twelve BL couplers, the size of each coupler eeded to be reduced. Therefore, a compact size BL coupler has bee desiged usig chamfered beds to fold the braches ad reduce the total size of the coupler, see Fig. 3. Usig this method, the size of the BL coupler was reduced to 1.7cm 9cm. This coupler has bee implemeted i the layout eviromet of the Agilet ADS software suite ad has bee optimized, realized, ad tested. The full Butler matrix etwork as show i Fig. 2 could be realized i just oe board, but the physical dimesios of the Butler matrix would be 6cm 65cm, which is difficult to maufacture ad to accommodate i the bore of the MRI system. To reduce the total size of the maufactured Butler matrix, it was split ito 6 substrates with cable coectios. The output phase shifters ad related BL couplers were realized o four separate substrates, with two substrates each stacked above ad below the two mai substrates (each mai substrate icludes four BL couplers), as show i Fig. 4. The size of this Butler matrix was reduced to 28(legth) 22(width) 18 (height) cm 3 [4]. B. Vector Modulator for Full Phase / Amplitude Cotrol The secod cocept is borrowed from techology of the fully active phased array: We coect each LPPA to oe atea elemet ad we fully cotrol the amplitude ad phase of each amplifier usig a Vector Modulator at the iput (low power). The complete system, cosistig of a log chai of Power Splitter, Vector Modulator, Power Amplifiers, Power combier, Switches, Trasmit Atea Level Sesors (TALES), log Coaxial Cables ad eight atea elemets (Coils), is sketched i Fig. 5. The eight trasmit chaels are cotrolled i phase ad amplitude by the vector modulator; switches allow the trasmit power to be optioally combied ito oe sigle chael ad fed ito a special sigle port atea (e.g., bird cage coil) [5]. 1) Limitatios of this cocept The optimum excitatio of the atea elemets may demad a large variatio of the output power of the idividual LPPAs. Sice the amplifiers are limited i power, most amplifiers have to be backed off from their maximum power such that their istalled power is uderutilized. The umber of amplifiers must be exactly equal to the umber of atea elemets which teds to seriously limit the resolutio of the B 1 field cotrol.
Fig. 5 Block diagram of our active phased array for MRI ad details of our vector modulator 2) Vector Modulator Realizatio Eight silico RFIC quadrature modulators AD8345 ad eight quad chael digital potetiometers AD843 were employed i our desig. Surface-mout high frequecy relays were used as safety overrides ad to switch the vector modulator i ad out of the RF path. Relays ad potetiometers are cotrolled by a PIC18F455 Microcotroller. This I-Q type vector modulator yields 256 256 possible sigal combiatios, with each symbol represetig 16 bits. Circuit boards used i the vector modulator are show i Fig. 6. Usig a GUI program writte i MATLAB, the PIC18F455 Microcotroller receives cotrol data via a USB port, ad the appropriate sigals are set to the potetiometers. Fially, the potetiometers produce cotrollig voltages for I ad Q of the vector modulator. All of the circuits for eight chaels have bee fabricated ad itegrated ito oe 19 chassis, see Fig. 7. C. Improved Active Phased Array System for MRI A major improvemet over both cocepts allows the flexible combiatio of power from several LPPAs to feed sigle phase modes of a Butler matrix. The ovel feed etwork cocept allows adjustmet of all modes i phase ad amplitude as required for B 1 shimmig ad at the same the (close to) full utilizatio of istalled power of the LPPAs. This cocept uses a first Butler matrix as a variable power combier[6] ad a secod Butler matrix for the creatio of phase modes at the coil array. The iput sigals to the power amplifiers are amplitude / phase cotrolled by a vector modulator ad the output power sigals are fed ito the first Butler matrix. Depedig o the settig of the vector modulators, this Butler matrix combies the iput power ito the output ports at prescribed amplitude ad phase relatios. The combied power the is fed to a secod Butler matrix which produces the phase modes at the coil array. I this way, e.g., the first ad most importat CP +1 - mode ca be fed the majority of power while other modes receive less power while all power amplifiers ca utilize their full istalled power. We realized this cocept i our 7 Tesla MRI system [7] usig a 8-chael amplifier bak, two 8x8 Butler matrices ad a 8-elemet coil array, Fig. 8. Fig. 6 Circuit boards ad system schematic to cotrol the amplitude ad phase Fig. 8 Variable Power Combier Active Phased Coil Array system 1) Abstract of Cocept Theory The sigals at the N N Butler matrix ca be described by N N scatterig matrix (S-matrix) which relates the outgoig wave amplitudes to the icidet wave amplitudes. Sice we deal with a ideally matched Butler matrix, for the purpose of describig the wave combiatio, we ca eglect most of the S-matrix elemets ad relate just the outgoig waves B to the icidet waves A i a trasmissio partial scatterig matrix S T as: B = k S A (1) T Fig. 7 Fabricated vector modulator I a lossless ad ideally matched Butler matrix the elemets of this matrix are of magitude 1 ad preset phase-oly terms. The power splittig property of the N N Butler matrix is represeted by the factor k. We ca apply the scatterig matrix to show that the output sigal at the j-th port is a summatio (superpositio) of cotributios from all iput sigals weighted by the correspodig coefficiets:
(db) B j = k ( S A + S A +... + S A = k S A (2) Tj1 1 Tj2 2 TjN N ) N i= 1 I the case that all amplitudes A i are chose cojugate complex (egative phase ad uit amplitude) of the correspodig coefficiet, the summatio gives N. This meas that all iput power is codesed ito the output power at port j. I this way we have defied a characteristic vector of iput sigals which provide full sigal combiatio ito the j-th output port: * A j) = S (3) i ( Tji All characteristic vectors combied ito oe matrix ca be see to be the traspose cojugate complex of our partial scatterig matrix: A1 (1) L A1 ( N) A( i, j) = M M M (4) AN (1) L AN ( N) We realize that each colum represets the excitatio (iput) sigal vector A(j) for complete sigal combiatio ito oe output port. Due to the liearity of the superpositio of wave sigals withi the etwork we may combie iput sigal vectors i order to superimpose output sigals such that a required power distributio is realized. Usig the trasmissio partial scatterig-matrix S T to relate the outgoig waves B of the 8 8 Butler matrix to the icidet waves A, the required iput sigal phases were calculated based o the superpositio of the characteristic iput vectors usig a geetic algorithm optimizer [8]. For a proof-ofcocept demostratio, power levels of 5%, 25%, 12.5% ad 12.5% for the first four output ports were arbitrarily chose, ad the phase weightigs were calculated. III. RESULTS A. Brach Lie Coupler ad Butler Matrix To examie the performace of realized BL coupler (Fig. 3) ad Butler matrix (Fig. 4), measuremets were carried out at 297 MHz usig a Automatic Vector Network Aalyzer (ANA). The measuremet result for BL coupler is preseted i Fig. 9. -5 measured S-parameters for BL coupler fabricated o RO43 substrate S11 S21-3 S41 S31 1 15 2 25 3 35 4 45 5 Frequecy (MHz) (a) Phase (Degree) 2 15 1 5-5 Tji Phase differece betwee the outputs (S21-S41) X: 297 Y: -269.6-3 1 15 2 25 3 35 4 45 5 Frequecy (MHz) Fig. 9 (a) Measured S-parameters (b) Phase differece betwee the output ports of hybrid coupler (b) i This coupler, fabricated o RO43, has a atteuatio loss of.15 db ad the isolatio of -33 db. The phase error of.41 has bee foud for this coupler. Fig. 1 shows the isertio loss values of the 8 8 Butler matrix whe port 1 of Butler Matrix is fed. The 8-chael Butler matrix fabricated o RO43 had a effective overall mode error of 1.91 at a overall atteuatio loss of.72 db. These results demostrate the good performace i terms of accuracy ad loss of the realized Butler matrix; cosiderable improvemets i phase ad amplitude accuracy ad i atteuatio loss are possible if cables are avoided ad the matrix realized i oe board. For operatio of the Butler Matrix with 1 kw power level at the ports, we ca use SMA coectors but for combied power from 8 amplifiers (8 kw) to drive, e.g. a multi coil array i birdcage mode, Type-N coectors for higher voltage hadlig are madatory. (db) Fig. 1 measured trasmissio S-parameters for Butler matrix fabricated o RO43-5 S12 S13 S14-3 S15 S16 S17 S18 S19-4 1 15 2 25 3 35 4 45 5 Frequecy (MHz) Trasmissio measuremets of the 8 8 Butler matrix B. Vector modulator The vector modulator iterally uses a poly-phase 9 phase shift filter for the creatio of a i-phase (I) sigal ad a quadrature (Q) sigal. The quadrature phase error was foud to be just above 1 at 297 MHz. Both I- ad Q-sigals are cotrolled i amplitude by the differetial d.c. voltages applied. The level rage that ca be cotrolled was foud to be more tha 3 db at 297 MHz without extra zeroadjustmet. Usig the 8-bit potetiometers for the geeratio of the cotrol voltages, the vector modulator produces 128 equal amplitude steps betwee the maximum ad the miimum output sigal for positive ad 128 steps for egative sig. The size of these steps was verified i measuremets for high to medium levels which meas that the amplitude accuracy of the vector modulator is about.1; however, at the low levels aroud -3 db, a residual sigal (feed-through) degrades the level cotrol. The recombiatio of level cotrolled I- ad Q-sigals produces the ultimate output sigals of the vector modulator, such that the resolutio is of the order.1 i amplitude ad from.5 to 5 i agle for amplitudes i the to db rage. Note that the vector modulator electroic IC exhibits oliear characteristics whe the iput sigal exceeds the compressio poit; therefore, a atteuator was placed at the iput, see Fig 5. Usig this vector modulator i our system, the fial images from MRI were produced as i Fig. 11. Results show that the system is capable of full modulatio.
C. Variable Power Combier First laboratory measuremets of the variable power combier (Fig. 8) with a ANA have bee doe by first splittig the excitatio sigal (TX) from the ANA ito 8 equal parts ad feedig these ito the iput ports of our matrix. The phase shift was realized usig coaxial cables iserted ito the coectio paths. However, the cable legths could ot be realized precisely, so that a average phase error of 8 was achieved; see Fig. 12. The output sigals from the matrix were measured by the ANA as S 12 trasmissio coefficiets. Compariso of desig levels ad measured levels as plotted i Fig. 13 prove the cocept although some amplitude error remais at the output ports. Fially, Fig. 14 shows the profiles of the modes produced by this variable power combier Active Phased Coil Array system i MRI. (a) Fig. 11 Images obtaied with flexible 8-ch body array. (a) Phase shifts of chaels adjusted to yield good image quality throughout the whole image. (b) Amplitude ad phase shift adjusted for optimized B 1 + homogeeity i right body regio Fig. 12 Fig. 13 Isertio Phase Output Power(dB) 4 35 3 25 2 15 1 5 Required phase shift Realized phase shift (b) 1 2 3 4 5 6 7 8 Iput Port Required (ideal) ad realized phase shift of iput sigals -3-4 Required output power Realized output power -45 1 2 3 4 5 6 7 8 Output Port Relative output power at the port of the 8 8 Butler matrix Fig. 14 Profiles of the four CP + modes produced by the variable power combier i combiatio with a Butler matrix drive 8-chael head coil with prescribed power levels (left); combiatio of the four CP + modes (right) IV. CONCLUSIONS I this paper we have described our recet work o high field MRI cocerig the applicatio of active phased array techiques, i particular, the use of the well-kow Butler matrix feed system ad the full amplitude / phase cotrol of all chaels. A major improvemet was itroduced by the use of the ovel variable power combier based o a Butler matrix ad vector modulator cotrol of sigals. I this way, we ca produce the fudametal ad higher-order circularly polarized modes with prescribed power ratios. I geeral, arbitrary amplitude ad phase shift for the created phase modes at the coil array ca be prescribed ad the cotrol vectors ca be geerated by a geetic optimizatio routie which chooses amplitude ad phase weights i such a way as to maximize the utilizatio of istalled power for ay combiatio of modes. Preset work cocers the desig of power combiers ad 8x8 ad 16x16 Butler matrices usig our Microstrip Matrix Techology with the aim to realize isertio loss dow to about.5 db at 297 MHz for a 8x8 matrix usig higherpermittivity dielectric substrate which also yields a smaller form factor. ACKNOWLEDGMENT The authors wish to thak M. E. Ladd, A. Bitz, S. Orzada (Erwi L. Hah Istitute for Magetic Resoace Imagig, Esse, Germay), M. Vester (Siemes Medical Solutios, Erlage, Germay) ad R. Oppelt (Siemes Corporate Techology, Erlage, Germay) for cotributios to this paper. REFERENCES [1] Collis, et al., Combiatio of optimized trasmit arrays ad some receive array recostructio methods ca yield homogeeous images at very high frequecies, Mag.Reso.Med. 25, o.54, pp. 1327-1332. [2] J. Butler et al., Beamformig matrix simplifies desig of electroically scaed ateas, Electroic Desig, vol.9, pp 17-173, Apr 1963. [3] J.Nistler et al., Usig a Mode Cocept to reduce hardware eeds for multi chael trasmit arrays, ISMRM. [4] P. Yazdabakhsh, K. Solbach, et al. Plaar Butler Matrix Techology for 7 Tesla MRI, ISMRM 29, submitted for publicatio. [5] P. Yazdabakhsh, S. Held, K. Solbach, et al. 16-Bit Vector Modulator for B 1 Shimmig i 7T MRI, ISMRM 29, submitted for publicatio. [6] Germa Patet Applicatio DE 1 26 28 69 A1, Verstaerkereirichtug fuer eie Modeatee, filed 22 Jue 25. [7] P. Yazdabakhsh, K. Solbach, et al. Variable Power Combier for a 7T Butler Matrix Coil Array, ISMRM 29, submitted for publicatio. [8] D.E. Goldberg, Geetic Algorithms i Search, Optimizatio, ad Machie Learig, Addiso-Wesley. Publishig Compay, Ic., 1989