A Safe Transmission Line for MRI

Magnetic resonance imaging (MRI) has been established as a reliable and safe imaging method for the human body. However, electric conductors, such as cables situated near or in the human body, should be avoided because induced currents in the cables
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  1094 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 6, JUNE 2005 A Safe Transmission Line for MRI Peter Vernickel*, Volkmar Schulz, Steffen Weiss, and Bernhard Gleich  Abstract— Magnetic resonance imaging (MRI) has been estab-lished as a reliable and safe imaging method for the human body.However,electricconductors,suchascablessituatednearorinthehumanbody,shouldbeavoidedbecauseinducedcurrentsintheca-bles can cause hazardous heating in the surrounding tissue. In thispaper,anewprincipleforthedesignofatransmissionlineisintro-duced and demonstrated, which is capable of avoiding dangerousheating of cables. The principle is based on transformers placedalongtheline,splittingthelonglineintoseveralshortnotresonantand thus safe sections. A transformer design is introduced alongwiththetheoreticalaspectsforboththeavoidanceoftheundesiredinduced currents and the reduction of signal attenuation. Further-more, the design fulfills the geometrical requirements of the sidelumen of a standard catheter. Matching networks, whose elementsare determined by power matching, are used to reduce signal at-tenuation by the transformers. A prototype was built to validateboth theory and the simulations. As demonstrated in this work, itis possible to build safe transmission lines for MRI, making appli-cations such as active catheter tracking possible. We expect thateven new applications, such as safe intravascular imaging will bepossible in a safe manner in the future.  Index Terms— Catheter, heating, magnetic resonance imaging(MRI), safety, specific absorption rate (SAR), transmission line. I. I NTRODUCTION I NTHE LASTYEARS,thenumberofminimalinvasivepro-cedures vastly increased [1]. Many vascular diseases likecongenital heart disease are now treated at lower risk for thepatient and at lower costs. Currently, transluminal proceduresare mostly performed under X-ray fluoroscopy. However, X-rayimaging exposes the patient and medical staff to ionizing radi-ation and does not provide soft tissue contrast. The use of realtime magnetic resonance imaging (MRI) overcomes these dis-advantages and is indicated especially in pediatry [2] and inlong-lastingexaminationslikeelectro-physiologicalprocedures[3].One major problem in MRI systems is the hazard of tissueheating. First, heating results from currents flowing in resis-tive metallic loops induced by gradient or RF—fields [4]. Thesecond heating effect is caused by eddy currents, excited byRF—transmission in the conducting tissue of the human body. Manuscript received August 4, 2004; revised October 31, 2004.  Asterisk in-dicates corresponding author. *P. Vernickel was with the Department of Technical Systems, Philips Re-search Laboratories, Hamburg, Germany. He is now with the Department of Technical Systems, Philips Research Laboratories, Hamburg 22335, Germany(e-mail: Schulz was with the Department of Technical Systems, Philips Re-search Laboratories, Hamburg, Germany. He is now with the PhilipsResearch Laboratories, Department of Solid State Lighting, Aachen, Germany(e-mail: Weiss and B. Gleich are with the Department of TechnicalSystems, Philips Research Laboratories, Hamburg 22335, Germany(e-mail:; Object Identifier 10.1109/TBME.2005.846713 For intravascular guide wires and cables, as examined in thispaper,theheatingiscausedbyfromRF-electro-magneticwavesin the tissue guided by the conductor structure [5]–[7]. The free space common mode resonant frequency of these waveson the metallic structures is reduced, because of the dielectricproperties of the human body surrounding the metallic structureor wire. By inserting the conductor in the body, the commonmode resonant frequency is shifted continuously from its freespaceresonantfrequencydowntothelowestpossiblefrequencyfor the maximum introduced length. Additionally, permittivityvaries with the tissue type making the common mode resonantfrequency hard to predict. A match between the Larmor fre-quency and common mode resonant frequency causes serioustissue heating, especially near the tip of the conductor structure[8].Recently, the integration of parallel resonant circuits formedby coaxial chokes or traps into the cable has been proposedto prevent tissue heating [9], [10]. If the resonant frequency of  those circuits is matched to the frequency of the unwanted cur-rents, the circuits form high impedances and limit the commonmode currents. However, this self-resonance can cause localenergy dissipation and tissue heating [10] and can be excitednot only by cable coupling, but also by local excitation of theresonator.This paper proposes to suppress the resonance effects forcommon mode currents by dividing the long metallic structureinto short off-resonant sections. Thus, the common moderesonant frequency of the sections is shifted to higher frequen-cies, depending on the number of divisions. Consequently, thehazardous matching between the Larmor frequency and thecommon mode resonant frequency is avoided. This approachsuppresses the undesired currents without using any resonanceeffects. The disadvantage of local energy deposition is avoidedentirely. By using transformers at the connection points of thesection, the signal (differential mode current) is transmitted viainductive coupling. Matching networks are introduced betweenthe transformers and the transmission line sections to increasethe signal transmission. Unfortunately, the stray capacitanceof each transformer leads to some capacitive common modecoupling between the short conductor sections. This couplingmust be limited by an appropriate design of the transformer, sothat the shift of the resonant frequency is kept high enough.Furthermore, other constraints exist on the transformer de-vice. No ferromagnetic parts can be used in the circuitry inorder to warrant MR-compatibility. The cross section of thetransformer of choice must be in the order of 1 mm to ful-fill the space requirements of catheters. Additionally, all linesections have to be flexible enough to follow the intravascularpathways. To meet all of the constraints of the transformerdesign, the geometry represented in Fig. 1 was used. Suchtransformers can be manufactured by using printed circuit 0018-9294/$20.00 © 2005 IEEE  VERNICKEL  et al. : A SAFE TRANSMISSION LINE FOR MRI 1095 Fig. 1. Micro strip transformer with primary and secondary coil on a PCB,each with one winding. Solder joints are for easy use in experiments and wereabscised for prototype experiments. board (PCB) technology. In this work, various geometricaldimensions were examined to find an optimal parameter set.II. T HEORY For this section the common mode and the differential modeare considered in separate subsections.  A. Avoidance of Common Mode Resonance Commonly, transmission lines consist of coaxial cables orpair lines. Currents induced by external alternating fields flowon the outer conductor of coaxial cables. Thus, the electromag-neticRF-fieldscausedbyjacket current-and chargedistributionare the same for a coax cable and a coated wire with equal ra-dialdimensions.Fora two-strip line,theconductorsare situatedvery close to each other, and common mode current is flowingin phase in both strips. Thus, at some distance, the net commonmode fields are also similar to those of a single wire. The reso-nant frequency of such a single wire structure can be derived by(1)where is the frequency, the speed of light ( in vacuum),the wavelength and and the effective relative permit-tivity and permeability. The effective material parameters resultfrom the relation of the wire diameter, the coating thickness andthe properties of the wire coating and the tissue. In general, theeffective relative permeability of the material used for MR ex-aminations is . Resonance occurs, if the length of thewire meets(2)and the first resonant frequency can be calculated by(3)Theoveralllength isdefinedbytheapplication,andtheef-fective relative permittivity can be decreased only by increasingthe ratio between the thickness of the coating and the conductordiameter [13], which is limited by the allowed outer diameter of the catheter. It is known from antenna theory that the first res-onant frequency is shifted to higher frequencies by introducingcapacitorsalonganantenna[14].Thissuggeststhatthecommonmode resonant frequency can be shifted to beyond the Larmorfrequency to avoid tissue heating and image artifacts. Fig. 2. (a) Two-port chain model of the safe transmission line. The secondmatching network at port T2 results by exchanging the ports of matchingnetwork 1. This section is repeated several times according to the requiredcommon mode suppression. (b) Matching network to match transformerimpedance to the transmission line impedance. The temperature increase of lossy tissue such as blood ismainly caused by dissipation in the surrounding tissue and notby resistive heating of the conductor. Therefore, the electro-magnetic field distribution in the surrounding material has tobe calculated to properly estimate tissue heating. Typically, thespecific absorption rate (SAR) is used as a measure for tissueheating [12], [15] and is defined as (4)where is the electric conductivity, the mass density andthe magnitude of the net electric field. The local SAR has to beexamined,becausetheelectricfieldismaximalintheimmediatevicinity of the transmission line.  B. MR Signal Transmission in Differential Mode In the differential mode, the new transmission line is treatedas a chain of two-ports elements. The maximum power shouldbe transmitted at the basic frequency, so power-maximizedmatching has to be accomplished [16]. This means that theinput impedances at any interface in the chain have to be com-plex conjugated. The input impedance of the transmission lineis expected to be real (i.e., 50 for coax cables), and theinput impedance of the transformer is complex in general.So, an additional two-port is required to fulfill the condition of the power matching.To find an appropriate network, first the input impedanceof the transformer has to be known [Fig. 2(a)](5)The impedance matrix of a two-port network in general is(6)and can be written for the symmetric transformer as [11](7)where are the complex voltages and the complex cur-rents at the ports with all currents pointing into the ports. Theelectricaltransformerparametersare theprimary andsecondaryinductance , the mutual inductance and the ohmic winding  1096 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 6, JUNE 2005 resistance . The angular frequency is denoted as . As men-tioned above, the transformer has to be terminated with its com-plex conjugate input impedance , so(8)The complex conjugate termination fulfills the resonance con-dition for the transformer at the terminated port. The imaginarypart of the sum impedance at the interface between transformerand termination is zero. Dividing the first line of (6) by andthe second line by and considering (5) and (8) yields(9)By eliminating , the following expression is obtained:(10)with as the unknown imaginary part of the inputimpedance. Equation (10) can be separated into a real part andan imaginary part, so the input impedance of the transformercan be determined.After calculating the input impedance, the matching network can be designed. Different nonresistive T-, - or L-networkscan be used to match the transformer to the line. An L-network [Fig. 2(b)] was chosen, as it consists of only two capacitiveelements and , which are easy to realize even in aminiaturized design. At port M1, the first matching network should have the input impedance of the transmission line(for real input impedances reflection minimization and powertransmission maximization are the same), and at port M2, thecomplex conjugate input impedance of the transformer. Thesetwo conditions can be formulated as (11) and (12)(11)(12)The matching network is fully determined by these conditions,since an L- network has two degrees of freedom ( , ). Thematching network element can be distributed equally overthe nodes 1 and 2 to form a symmetric signal path for avoid-anceofmodecrosstalkbetweencommonanddifferentialmode.The second matching network at port T2 is determined by ex-changing ports M1 and M2. The number of network elementsmay be reduced further, to comply with space requirements orto simplify manufacturing. By predefining(13)for (11) and (12), one element is omitted. However, one degreeof freedom is lost in these cases, and a transformer with specialparameters is required.III. M ETHODS The measurements and simulations are described separatelyfor thecommon modeand thedifferential mode.In thefirst sub-section, a common mode simulation model was defined, andbasic system requirements were stated. Next, a transformer de-sign was determined, which fulfills the specified requirements.The local SAR in the surrounding tissue was calculated to testthe suppression of the common mode currents. The shift of thecommon mode resonant frequencies was measured in a trans-mission line prototype to verify the simulation results.The required matching network parameters for signal trans-mission were determined, and the network elements were im-plemented in the transmission line. The scattering parametersand were acquired in simulations and measurements,to evaluate the signal transmission properties. All simulationsand measurements were performed for a 1.5T MR-system, witha Larmor frequency of MHz.  A. Common Mode1) Determining Basic Requirements of the Trans- formers:  The required stray capacitance and the necessarynumber of the transformers are the basic attributes of thetransmission line design and were examined using the fol-lowing model. It was designed to simulate a transmission linefully imbedded in the high medium. The 3-D MoM ToolFEKO [17] was used to calculate the dependencies betweenthe common mode currents and the stray capacitance and thenumber of the transformers. The model consisted of a layer of lossy dielectric material with the thickness , repre-senting human tissue. The lossy dielectric layer was centeredbetween perfect electric conductor (PEC) layers of distancerepresenting the RF screen. The properties of saltwater ( , , )were chosen for the simulation, as a simplified model of thephysical properties of human tissue. One conducting andproperly driven rod was added next to each PEC layer for RFexcitation. The coated wire, modeling the transmission line,was placed off center to avoid the vanishing of the electric fieldat the center of the model. The wire had a radius mand a length , the coating thickness ( ,) was mm. These parameters approximate a 12 Fmm catheter. All electric and geometric parameterswere chosen to obtain a resonant frequency below , what isabsolutely possible in practice. The transformers were modeledin the form of their stray capacitances as lumped capacitors andplaced along the wire. The impressed current was calculatedby using FEKO. The resonant frequency of the common modecurrent was calculated for different capacitances and capacitornumbers, to determine the required stray capacitance and thenumber of the transformers necessary for a sufficient resonantshift. Initially, one capacitor was placed in the middle of theline, and its capacitance was modified. Subsequently, up to fourcapacitors with equal capacitances were added equidistantly tothe transmission line. 2) TestofVariousTransformerDesigns:  Havingdeterminedthe basic requirements of the transformer, a proper design couldbe found. The appropriate capacitance of the transformerwas determined via simulations utilizing the MoM. The trans-formers were represented by a wire segment structure. The wirediameter was chosen to be m. In contrast to thecommon mode model, the wires were situated in free space  VERNICKEL  et al. : A SAFE TRANSMISSION LINE FOR MRI 1097 to limit the calculation time. The geometric parameters of thetransformer, , and were modified to calculate the ca-pacitance . Therefore, two of these parameters were keptconstant, whereas the third parameter was changed within apractical range. Additionally, the winding inductance, , andthe coupling factor, , were simulated, as theyare also influenced by geometry and will be utilized in later de-sign steps. was found by connecting the two loops with avoltage source. As all conductor elements were short comparedwith the wavelength, was calculated from the imaginarypart of the input impedance seen by the source. The inductanceandthecouplingfactorwereconfirmedbyperformingtwoinputimpedance calculations at one transformer port, while the otherport was open- or short-circuited. 3) SAR Simulation:  After the stray capacitances for a suffi-cient frequency shift were known, the influence of the shift onthe SAR had to be examined. The impressed current and theelectromagnetic field in the surrounding medium were calcu-lated for by using the common mode model and the MoM.The SAR was derived from the known electrical fields as shownin(4).TheclinicalthresholdofthelocalSARis definedfor 10gcontiguous tissue [12]. Therefore, a cubic volume containing10 g of tissue was chosen to determine the SAR. The transmis-sion line coating was not considered for local SAR calculationsbecause of its low losses. Consequently, a hollow cylinder withthe diameter of the outer transmission line was excluded fromthecube,leadingtoarequirededgelengthof mm for10 g of tissue . The electric field in this cube was calculatedona3-Dgridwith1mmspacing.Thecubewasshiftedalongthetransmission line to find the maximum local SAR. The gain of theSAR, , duetothepresenceofthetransmissionlinewasusedasameasureindependentofthespatialvariationsoftheex-citation field [18]. For this case, the SAR with the wire model,, is related to the SAR without the wire as follows:(14)This method was repeated for several transformer positions tofind the optimal transformer distribution along the transmissionline with the lowest maximum . 4) Prototype Assembly and Measurements:  Two trans-mission lines were built for experiments, one with and onewithout transformers. The standard line and the transformerline consisted of coaxial cable (SML50, Axon Kabel GmbH,, mm of the length and were coated with a heat shrink tube(BPVDF 1/16, BIT Bierther Isolationsprodukte GmbH). Thetransformer line was interrupted by three matched equidistanttransformers (Fig. 3). The winding distance of the trans-formers was defined by the minimum substrate (RT/Duroid5870, Rogers Corp., Chandler, AZ) thickness of m. The overlapping length was chosen to bemm and the strip distance m. The wind-ings were realized as copper strips m m .Both samples were placed in a water bath (0.08% ,0.2% NaCl) to examine the resonant frequency shift effect. The Fig. 3. Transmission line with three matched transformers includedinto standard coaxial cable (1.1 mm in diameter). The total length of thetransmission line is 1.5 m. scattering parameter was recorded for the frequency rangeof interesting by using a network analyzer and a RF pickup coilto excite a current on the structure. Therefore, the pickup coilwas weakly coupled at sensitive points to evoke the first reso-nance mode.  B. Differential Mode1) Simulation of Signal Transmission:  The signal transmis-sion properties of the transformer line were assessed by sim-ulating the scattering parameters and . The reflectioncoefficient , describes the matching between the input im-pedances at the interface of two devices. The transmission co-efficient , describes the relation between the signal strengthfed to the input and the signal strength available at a loadmatched to the output of a line. The transmission line wasmodeled by four equidistant nonradiating lossless transmissionlinesconnectedviathetransformersandthematchingnetworks.The same transformer model was used as for the determinationof the transformer design. By considering the skin effect (skindepth m at ) for the input impedance calcula-tion, the ohmic winding resistance was obtained. Based onthe parameters , and , the matching network elementsfor a line impedance of 50 were calculated. andwere derived directly by using the S-parameter calculation inFEKO. The scattering parameters and were acquiredbetween 45 MHz and 100 MHz. 2) Measurements of Signal Transmission:  The prototypetransformer line described in the section on the common modeexperiments was also used to measure the signal transmissionproperties. The matching network elements were obtained byusing the same methods used in simulations. To measureand , the transmission line was connected to the input portsof a network analyzer.To evaluate the transmission parameter for differentmedia, the measurement was performed with and withoutimmersion of the transformer line in the salt-water solution.  1098 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 6, JUNE 2005 Fig. 4. Simulation of the resonant frequency of the common mode model(a) for one transformer with variable    and (b) for n transformers with   . Additionally, in (a), the resonant frequency of the modelwithout of the model without any transformer along the line is indicated. IV. R ESULTS AND  D ISCUSSION  A. Common Mode1) Determining Basic Requirements of the Trans- formers:  By using the common mode model, a resonantfrequency of MHz was determined for the coatedwire without transformers. The maximum resonant frequencyshift was examined, as the relative permittivity of human tissueis , and the wire was completely immersed in the highmaterial. The common mode resonant frequency was shiftedto higher frequencies by adding one capacitor in the center of the wire, as shown in Fig. 4(a). As expected, the shift increasedby decreasing the capacitance . Further increases incapacitance led to the decrease of the resonant frequency tothat of the transmission line model without transformers. It canbe concluded that the transformers should preferably have alow stray capacitance in the order of a few pF. In Fig. 4(b), theresonant frequency is shown for the transmission line modelwith 1–4 transformers, each with , and placedequidistantly along the line. The resonant frequency is alsoshifted to higher frequencies by this measure. If the straycapacitance of a single transformer is too high for the required Fig. 5. Variation of the geometrical parameters of the transformer in Fig. 3.Resulting from simulation, the electrical parameters    ,    and    areshown for (a)        and        m, (b)        and       m, and (c)        m and        m. shift, increasing the number of transformers can be used toreach a higher resonant frequency. However, each transformerintroduces signal losses and a trade off has to be found betweenan optimal common mode suppression and an acceptablesignal attenuation by limiting the number of the transformers.
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