Analysis of Conservative and Magnetically Induced Electric Fields in a Low-Frequency Birdcage Coil *

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1 Journal of letromagnet Analyss and Applatons, 2013, 5, Publshed Onlne July 2013 ( 271 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col * Bu S. Park 1#, Sunder S. Rajan 1, Chrstopher M. Collns 2, Leonardo M. Angelone 1 1 Dvson of Physs, Center for Deves and Radologal Health, Offe of Medal Produts and Tobao, Food and Drug Admnstraton, Slver Sprng, USA; 2 Department of Radology, New York Unversty, New York, USA. mal: # bu.park@fda.hhs.gov Reeved May 16 th, 2013; revsed June 17 th, 2013; aepted June 25 th, 2013 Copyrght 2013 Bu S. Park et al. Ths s an open aess artle dstrbuted under the Creatve Commons Attrbuton Lense, whh permts unrestrted use, dstrbuton, and reproduton n any medum, provded the orgnal work s properly ted. ABSTRACT Numeral methods are used to evaluate varatons of the eletromagnet felds generated by a head-szed brdage ol as a funton of load ( loadng effet ). The loadng effet was analyzed for the ases of a ol loaded wth a ondutve ylndral sample, a deletr ylndral sample, and an anatomally prese head model. Maxwell equatons were solved by means of fnte dfferene tme doman (FDTD) method onduted at 12.8, 64, and 128 MHz. Smulaton results ndate that at 12.8 MHz the onservatve eletr feld aused by the salar eletr potentals between the ol and the load or wthn the load was sgnfantly hgher than the magnetally-ndued eletr feld and was the major omponent of the eletr feld. The ampltudes of and are seen to be lower wthn a sample than at a orrespondng loaton n an empty ol, but approxmately 65% hgher n the spae between ol and sample than at a orrespondng loaton n an empty ol. Ths s due to polarzaton effets generatng an addtonal salar potental parallel to the orgnal feld. The nreased eletr feld between ol and sample may ause nreased power deposton at the surfae of the sample and may affet the RF-ndued urrents n external leads used for physologal reordng,.e. CG, durng MRI sannng. Keywords: MRI; FDTD; Loadng ffet; Conservatve letr Feld; Brdage Col 1. Introduton In magnet resonane magng (MRI), the sgnal to nose rato (SNR) and the spef energy absorpton rate (SAR), the dosmetr parameter used to establsh safety lmts for human subjets by the Internatonal letrotehnal Commsson (IC) [1] and the US Food and Drug Admnstraton [2], depend upon the eletr feld. The an be deomposed nto a onservatve and magnetally-ndued eletr felds (felds) [3] and a dstnton s often needed between the two omponents. Conservatve -felds aused by the salar eletral potental on ondutors gve rse to a porton of sample loss also referred to as deletr loss [4]. Magnetally-ndued -felds are reated by the tme-varyng magnet felds [5], and gve rse to a * Dslamer: The menton of ommeral produts, ther soures, or ther use n onneton wth materal reported heren s not to be onstrued as ether an atual or mpled endorsement of suh produts by the Department of Health and Human Serves. # Correspondng author. porton of sample loss also referred to as ndutve loss [4]. In some ases t s possble to redue the losses due to wthout hangng the urrent dstrbuton or magnet feld dstrbuton usng a so alled -sheld [6], and thus mantanng the desred senstvty and feld of vew (FOV) whle redung SAR n the sample and/or the nose reeved from the sample [6-9]. A prevous study [6] showed that ths method ould be appled to a solenod ol. Ths study evaluated whether the method of -sheld ould be also extended to a brdage ol, the most ommon type of ol used n human MRI. One of the motvatons of ths study to understand the mehansm of thermal njury to skn s urrently the most ommon type of adverse event reported for MRI sans [10]. Another reason for ths study s to fnd the effet of a ondutve or a deletr sample related to the safety assurane n a regon of nterest (ROI), partularly between the RF ol and the sample. Prevous researh [9,11] showed that the eletr feld nsde a ol would be dereased wth addton of a loadng sample. Copyrght 2013 SRes.

2 272 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col Conversely, the hypothess drvng the proposed study was that the eletr feld dereases only wthn the loadng sample, but t s the same or hgher n the spae between ol and sample. Changes n eletr feld between ol and sample may ause nreased power deposton n the subjet skn, wth possble related thermal njury [10]. Moreover, hanges n eletr feld may also affet the RF-ndued urrents n external leads used for physologal reordng durng MRI (e.g.cg or G leads). Addtonally, there have been some suggestons that may play a sgnfant role n the sample loss, although t s generally beleved that almost all of the sample loss s magnetally-ndued [12]. The study was onduted by means of numeral smulatons ondutng a systemat analyss of the eletromagnet feld, nludng and generated by the brdage ol wthn and surroundng the load. The study took advantage of a reently developed method based on quas-stat approxmaton that allows separatng numerally-alulated -feld dstrbutons nto onservatve and magnetally-ndued portons [3]. We performed numeral eletromagnet feld smulatons wthn and surroundng a hgh pass (HP) brdage ol ombned wth a ylndral ondutve phantom and a human head model at dfferent frequenes. Addtonally, the volume harge densty (ρ υ ) dstrbuton generatng the salar eletr potental and was alulated to support the explanaton of eletromagnet feld varatons. Results were analyzed to evaluate the ontrbuton of and RF magnet feld B 1 to the eletromagnet feld dstrbuton. Conservatve and Magnetally-Indued letr Feld The power loss (P) an be alulated as [8]: 1 2 P d 2 v (1) vol where σ s the ondutvty (S/m) and s the ampltude of the eletr feld (V/m), whh an be separated as two omponents: A (2) t where A s the vetor magnet potental (Wb/m) and s the salar eletr potental (V), respetvely. In order to redue the power absorbed by the sample, the should be mnmzed, whh means mnmzng the omponents and/or. 2. Materals and Methods 2.1. Brdage Head Col A hgh-pass (HP) brdage head ol was modeled usng 12 rods of 300 mm of length, dsposed rularly wth an nner dameter (ID) of 290 mm. To aurately smulate the feld dstrbuton generated by an deal hgh-pass brdage ol, 12 snusodal voltage soures of 1 V ampltude n seres wth a 50 Ω resstor were plaed n both the top and bottom rngs, n the mddle of eah of the segments between the rods of the ol (Fgure 1). ah soure was assgned a phase-shft equal to the azmuthal poston of the segment (.e., 30 C) between voltages n adjaent end rng segments, and wth soures n opposte end rngs havng opposte orentaton. The followng frequenes were modeled: 12.8, 64, and 128 MHz, orrespondng to 0.3, 1.5 and 3.0 T for water proton MRI Load: Phantom and Head Model The brdage head ol was loaded wth a ylndral sample havng ID of 200 mm and length of 300 mm wth a 5 mm resoluton. Three dfferent eletral propertes for the phantom were smulated, namely: a) ondutve sample (σ = 0.2 S/m, ε r = 1), b) deletr sample (σ = 0 S/m, ε r = 78), and weak salne (σ = 0.2 S/m, ε r = 78) [6]. Smulatons were also performed wth an anatomally-prese human head model (Fgure 1). The human head model was reated by segmentng the dgtal photograph data of the Natonal Lbrary of Medne s Vsble Human Projet [13, 14], and then transformng these segmented mages nto a 3D grd of Yee ell ubes [15]. The human head model had a mm 3 sotrop resoluton and ontaned 20 tssue types [16,17] havng dfferent ondutvty (σ) and relatve permttvty (ε r ) values Numeral Smulatons and Data Proessng All smulatons were performed usng ommerally avalable software (xfdtd, Remom, In, State College, PA) and analyss of results was performed n Matlab (The MathWorks, In., Natk, MA). Smulaton results of eletromagnet felds were normalzed so that B 1 4T at the ol enter orrespondng to a 1.5 ms (a) Fgure 1. Geometry of hgh pass (HP) brdage ol (yellow), sample (green, (a)) and head model (b) used for numeral smulatons. (b) Copyrght 2013 SRes.

3 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col pulse [14]. 56 vs. 76 V/m) n the average and 70% nrease The parameters used for the FDTD smulatons to en- (.e., 231 vs. 134 V/m) n the maxmum wthn the sure onvergene of the smulatons were: 500,000 num- whole sample when the ol was loaded wth the onduber of tme steps, 30 db onvergene threshold, and tve, deletr, or weak salne phantom ompared to the and separaton method was empty ol perods. The appled only at the 12.8 MHz beause the methods assumes quas-stat approxmaton. Calulaton proedures for the method were developed and explaned n [3] and are reported n the appendx for the reader s onvenene. 3. Results Fgure 2 shows the normalzed x-, y- and z-omponent of and B 1 wthn the empty ol n a sngle plane (YZ-plane) passng through the so-enter at 12.8 MHz. Values for were lose to zero (.e., less than 0.04 V/m) along the axs of the RF ol, nreasng wth dstane from the enter lne followng Faraday s Law. Table 1 reports the results of the smulatons wth the ol loaded wth the ondutve, deletr, or weak salne phantom. There was approxmately 25% reduton (.e., Conversely, when omparng the results of the ol loaded wth the head model vs. the empty ol, there was a 30% reduton (.e., 53 vs. 76 V/m) n the average and a 430% nrease (.e., 716 vs. 134 V/m) for the maxmum, respetvely (Table 1). Addtonally, there was approxmately a 20% reduton for average (.e., 63 vs. 53 V/m) and maxmum (.e., 100 vs. 81 V/m) when omparng the empty ol vs. the ol loaded wth the sample. Fnally, when lookng at the, there was a destrutve nterferene between and throughout the ylndral sample or throughout the head, leadng to an overall reduton of (.e., 40 V/m n the empty ol vs. 20 V/m wth the weak salne or 16 V/m n the Head). Fgure 3 and Table 2 show the normalzed y-omponent of the, and at 12.8 MHz along the entral sagttal plane (YZ-plane) wth the ol empty, Fgure 2. Magntudes of x-, y-, and z-omponents of onservatve -feld, magnetally-ndued -feld, -feld, and magnet flux densty B 1 n the empty brdage ol at 12.8 MHz. The ol was drven by a voltage soure wth a 50 Ω resstor and results were normalzed to B1 4 T at the ol enter. Copyrght 2013 SRes.

4 274 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col Table 1. Normalzed eletromagnet feld propertes wthn the whole sample when loaded wth ondutve (thrd row), deletr (fourth row), weak salne (ffth row), and human head model (sxth row) usng a hgh pass (HP) brdage ol at 12.8 MHz. All values were normalzed so that B 1 4 T at the ol enter MHz B 1 Mean [μt] std [10 7 ] Mean [V/m] Max [V/m] Mean [V/m] Max [V/m] Mean [V/m] Max [V/m] Ar Condutve (σ = 0.2, ε r = 1) Deletr (σ = 0, ε r = 78) Weak Salne (σ = 0.2, ε r = 78) Head Model Table 2. Normalzed magntude of 2D (YZ-plane) rotatng RF magnet feld B 1 and y-omponent of onservatve -feld ( Y, ), magnetally ndued -feld ( Y, ) and -feld ( Y ) between the ol and the sample n Fgure 3. All values were normalzed so that B 1 4 T at the ol enter MHz B 1 Y, Y, Y Mean [μt] std [10 7 ] Mean [V/m] Max [V/m] Mean [V/m] Max [V/m] Mean [V/m] Max [V/m] Ar Condutve (σ = 0.2, ε r = 1) Deletr (σ = 0, ε r = 78) Weak Salne (σ = 0.2, ε r = 78) Fgure 3. Calulated magntude y-omponent of -feld ( Y, frst olumn), magnetally ndued -feld ( Y,, seond olumn) and onservatve -feld ( Y,, thrd olumn) at 12.8 MHz when loaded wth ar (frst row), ondutve (σ = 0.2 S/m, ε r = 1, seond row), deletr sample (σ = 0 S/m, ε r = 78, thrd row) and human head model (fourth row). The z-dretonal sze of a head mage (fourth row) s longer than others to nlude nek and shoulder regon. The weak salne mages, smlar to ondutve or deletr ones, are not shown n ths fgure. Copyrght 2013 SRes.

5 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col loaded wth the ondutve, the deletr phantom, and the head model. The hange of eletr feld near the endrng wth and wthout the head model an be observed (red arrows n the fourth row). The eletr feld dstrbu- 275 ton for the ondutve sample, the deletr sample, and the weak salne (not shown) was very smlar (see also Table 3). Fgure 4 and Table 3 show the normalzed z-ompo- Fgure 4. Calulated magntude of -feld z-omponent at 12.8 MHz. Other parameters are same as Fgure 3. Note that the magntude of onservatve -feld (Z,, thrd olumn) s nreased when loaded wth a ondutve or a deletr sample whereas no dfferene n magnetally-ndued -feld (Z,, seond olumn). Whte retangular dotted lnes n a frst olumn ndate the regon of a sample. The eletr feld dstrbuton for the ondutve sample, the deletr sample, and the weak salne (not shown) was almost the same. Copyrght 2013 SRes.

6 276 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col Table 3. Normalzed magntude of 2D (YZ-plane) rotatng RF magnet feld B 1 and z-omponent of onservatve -feld ( Z, ), magnetally ndued -feld ( Z, ) and -feld ( Z ) wthn the sample n Fgure 4. Other parameters are same as Table MHz B 1 Z, Z, Z Mean [μt] std [10 7 ] Mean [V/m] Max [V/m] Mean [V/m] Max [V/m] Mean [V/m] Max [V/m] Ar Condutve (σ = 0.2, ε r = 1) Deletr (σ = 0, ε r = 78) Weak Salne (σ = 0.2, ε r = 78) nent of, and at 12.8 MHz along the entral sagttal plane (YZ-plane). The z-omponent of wthn the sample was nreased of about 10% n average and 55% n maxmum (Table 3) wth addton of a ondutve sample, a deletr sample or a weak salne (not shown), whereas no hanges were observed n the z-omponent of. Fgure 5 shows the magntude of, and and rotatng RF magnet feld ( B 1, fourth row) after normalzaton for the ol empty (frst olumn), loaded wth ondutve ylnder (seond olumn), deletr ylnder (thrd olumn) and human head model (fourth olumn). For the ol loaded wth ondutve sample, deletr sample, and weak salne (not shown), the and dereased wthn the sample, but nreased n the spae between sample and ol. Fgure 6 and Table 4 show the eletromagnet feld as a funton of frequeny (12.8 MHz, 64 MHz, and 128 MHz) for the empty ol (frst row), and the ol loaded wth a weak-salne ylndral sample (seond row) and a head model (thrd row). As frequeny nreased from 12.8 MHz to 128 MHz, the average magntude of eletr feld wthn the weak salne sample (.e., mean sample ) nreased of about 390% (.e., 20 vs. 98 V/m ). The felds for the ol loaded wth a ondutve or deletr sample (not shown) were smlar to the ones of the ol loaded wth weak salne. Fgure 7 shows the alulated volume harge densty ( D,where D s the eletr flux densty) at the frequenes of 12.8 (frst olumn), 64 (seond olumn), and 128 MHz (thrd olumn) wth dfferent loadng ondtons. The harge densty was hghly onentrated on the surfae of the sample or the head model regardless of the operatng frequenes. 4. Dsusson For the empty ol, the z-omponent of the manly aused by the urrents flowng along the rungs-s domnant beause s perpendular to the magnet flux densty B followng Faraday s Law (Fgure 2). On the sagttal plane (YZ-plane) the x-omponent of manly aused by the end-rng urrents-was hgher than the y-omponent; the omparson was reversed on the oronal planes. The value of at the enter was zero (Fgures 2-5), as expeted gven the spef eletral onfguraton of the ol and an be explaned by means of the magnet vetor potental A, proportonal to the urrent densty J (quaton (3)). Beause opposte sdes of a brdage ol n deal mode 1 resonane have equal J flowng n the opposte dreton and generatng an opposng A, the two A havng same ampltude and opposte dreton anel eah other out at the enter. In these results, the value of eletr feld n the so-enter of the ol was very lose to zero but not exatly zero (.e., 0.04 V/m, less than 0.2% of average eletr feld wthn the whole sample). The was sgnfantly dfferent when the ol was loaded wth a ondutve, a deletr, a weak-salne sample, or a human head model, wth approxmately a 25% - 30% hange n the average and up to 430% hange n maxmum wthn the whole sample (Table 1). Ths was due to the addtonal salar potental (ϕ) wthn and surroundng the sample, as shown n Fgure 3. When a ondutve, deletr, or weak-salne sample s loated wthn the eletr feld generated by the RF ol, harged partles wthn the sample are moved to the boundares of the sample, resultng n a polarzaton feld whh ether has same or opposte dreton of the orgnal feld dependng on the spef regon onsdered and on the omponents of the ol. Beause of suh polarzaton effets, the z-omponent of ( Z, ) wthn the sample nreased (Fgure 4 and Table 3); however, beause the addtonal salar eletr potental had opposte dreton of the orgnal one, the y-omponent of ( Y, ) dereased wthn the sample. Moreover, beause Y, was the domnant omponent of the, ths resulted n an overall reduton n the and an nrease of magnet feld homogenety wthn the sample (Fgure 3, Tables 1 and 2). These results are n lne wth publshed lterature [8,9,11]. However, the Y, between a ol and Copyrght 2013 SRes.

7 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col 277 Fgure 5. Total magntude of onservatve -feld (, frst row), magnetally-ndued -feld (, seond row), -feld (, thrd row) and rotatng RF magnet feld ( B 1, fourth row) after normalzaton when loaded wth ar (frst olumn), ondutve sample (seond olumn), deletr sample (thrd olumn) and human head model (fourth olumn). The z-dretonal sze of a head mage (fourth olumn) s longer than others to nlude nek and shoulder regon. The eletr feld dstrbuton for the ondutve sample, the deletr sample, and the weak salne (not shown) was almost the same. Table 4. Results of the 3D eletromagnet smulatons wthn the sample at the dfferent frequenes evaluated n ths study. Mean and standard devaton (std) of rularly polarzed RF magnet feld B 1 and eletr feld ( ) when loaded wth ar, weak salne and human head model at three dfferent frequenes of 12.8, 64, and 128 MHz. B 1 Sample Mean [μt] std [10 7 ] Mean Sample [V/m] Ar (12.8 MHz) Weak Salne (12.8 MHz) Head (12.8 MHz) Ar (64 MHz) Weak Salne (64 MHz) Head (64 MHz) Ar (128 MHz) Weak Salne (128 MHz) Head (128 MHz) a sample was nreased beause the addtonal salar eletr potental-due to the presene of the sample-had the same dreton of the orgnal one. Ths result extends prevous publshed lterature showng that the eletr feld would derease wthn the sample when the ol s loaded wth a ondutve or a deletr sample (as shown n (9,11)) (Table 1) and addtonally demonstrateng that the eletr feld nreases between ol and the sample (Table 2). Ths result may have onsequenes on subjet safety. For example, the aumulaton of harge Copyrght 2013 SRes.

8 278 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col Fgure 6. Calulated magntude of -feld ( ) at three dfferent frequenes of 12.8 (frst olumn), 64 (seond olumn), and 128 MHz (thrd olumn) for the empty ol (ar frst row), and the ol loaded wth a weak salne phantom (seond row) and a human head model (thrd row). The z-dretonal sze of a head mage (thrd row) s longer than others to nlude nek and shoulder regon. on the boundary regon of the sample may nrease loal and 10 g-average SAR. Moreover, when external ondutve leads for physologal montorng (e.g.cg, G) are present, the nrease n eletr feld between ol and sample may result n nreasng ndued urrents along the montorng leads, wth possble nrease of loal SAR at the nterfae between leads and patent skn. Beause of dffultes of SAR and temperature alulaton n free spae, dret omparsons of losses and heatng n the objets were not studed. The eletr feld varaton of the x-omponent wth addton of the samples was not shown n the fgures beause of the small absolute ampltude (less than 15% ompared to the y- and z-omponent for the sagttal vew) and beause no dfferene was noted among all the loadng samples onsdered. Addtonally, the results wth a weak salne sample were smlar to the results obtaned wth a ondutve or a deletr sample (Tables 2 and 3). The hange for the magnetally ndued -feld wth addton of the sample was muh less when ompared to (.e., about 13% - 18% hange n the average and up to 22% hange n the maxmum ) (Table 1 and Fgures 3-5). The reason that the value of wthn and surroundng the sample appears to be relatvely ndependent of sample propertes at 12.8 MHz an be explaned usng Faraday s law. s ndued by a tme varyng vetor magnet potental (quaton (2)) whh s manly aused by the onduton urrent flowng n the RF ol. Beause the RF ol used n ths ase s very small (300 mm n length and 290 mm ID) ompared to the eletral wavelength (free spae wavelength at12.8 MHz equal to 23.4 m), the presene of the sample does not sgnfantly affet the dstrbuton of ol urrents (no wavelength effet) and spefally (Fgure 5). However, as the frequeny nreased from 12.8 MHz to 128 MHz (free spae wavelength equal to 2.34m) and both proportonal to the frequeny (quaton (2)) also nreased and the was muh hgher, (.e., about 644% nrease n average Copyrght 2013 SRes.

9 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col 279 Fgure 7. Calulated volume harge densty D at the three frequenes of 12.8 (frst olumn), 64 (seond olumn), v and 128 MHz (thrd olumn) wth the empty ol (frst row), and the ol loaded wth weak-salne (seond row) and head model (thrd row). The harge densty dstrbuton for the ondutve sample (not shown), the deletr sample (not shown), and the weak salne was almost the same. wthn the head model ompared to 12.8 MHz) (Fgure 6 and Table 4). The alulated volume harge densty n Fgure 7 was hghly onentrated on the boundary regon of the sample and the head model, mathng well wth the nreased onservatve eletr feld between the ol and the loadng. A prevous study [6] showed that n a solenod ol the -sheld an be used effetvely to redue wth- out hangng B 1 beause the dreton of -sheld n the solenod ol s orthogonal to the dreton of urrent n the ol wres [6,8,9]. However, the results of ths study show that the dfferene n urrent dretons along the struture between a brdage and a solenod ol s sgnfant enough to do not allow usng the same - sheld approah wth a brdage ol. 5. Conluson Ths study presents the varatons of eletromagnet feld nsde a brdage ol when loaded wth a ondutve ylndral sample, a deletr ylndral sample, a weak-salne ylndral sample, or a head model. The results were presented usng a desgned and separaton method at the frequeny of 12.8 MHz. The addtonal salar potental aused by the polarzaton effets wthn the load aused an nrease of the y-omponent of between ol and sample, and a derease wthn the sample at 12.8 MHz resultng n hgher poss- blty of nreased power deposton n the subjet skn and ndued RF urrents n external leads used for physologal reordng,.e. CG. The proposed and separaton method an be appled as long as the urrent densty n the RF ol s muh greater than that n the sample and no sgnfant wavelength effets are present for the aurate alulaton of magnet vetor potental A. As the frequeny nreased from 12.8 MHz to 128 MHz, the -feld wthn and surroundng the sample nreased sgnfantly. Results ndate that the -sheld approah, prevously proposed for a solenod ol to redue sample heatng, annot be used wth a brdage ol. RFRNCS [1] Internatonal letrotehnal Commsson (IC), Internatonal Standard, Medal qupment Part 2: Partular Requrements for the Safety of Magnet Resonane qupment for Medal Dagnoss, 3rd dton, Internatonal letrotehnal Commsson, Geneva, Vol. 601, 2010, pp [2] Gudane for Industry and FDA Staff: Crtera for Sgnfant Rsk Investgatons of Magnet Resonane Dagnost Deves, dgudane/gudanedouments/um htm [3] B. S. Park, A. G. Webb and C. M. Collns, A Method to Separate Conservatve and Magnetally-Indued letr Felds n Calulatons for MRI and MRS n letrally-small Samples, Journal of Magnet Resonane, Copyrght 2013 SRes.

10 280 Analyss of Conservatve and Magnetally Indued letr Felds n a Low-Frequeny Brdage Col Vol. 199, No. 2, 2009, pp do: /j.jmr [4] D. I. Hoult and P. C. Lauterbur, The Senstvty of the Zeugmatograph xperment Involvng Human Samples, Journal of Magnet Resonane, Vol. 34, No. 2, 1979, pp [5] W. Mao, B. A. Chronk, R.. Feldman, M. B. Smth and C. M. Collns, Consderaton of Magnetally-Indued and Conservatve letr Felds wthn a Loaded Gradent Col, Magnet Resonane n Medne, Vol. 55, No. 6, 2006, pp do: /mrm [6] B. S. Park, T. Neuberger, A. G. Webb, D. C. Bgler and C. M. Collns, Faraday Shelds wthn a Solenodal Col to Redue Sample Heatng: Numeral Comparson of Desgns and xpermental Verfaton, Journal of Magnet Resonane, Vol. 202, No. 1, 2010, pp do: /j.jmr [7] D. G. Gadan and F. N. H. Robnson, Radofrequeny Losses on NMR xperments on letrally Condutng Samples, Journal of Magnet Resonane, Vol. 34, No. 2, 1979, pp [8] A. Krahn, U. Prller, L. msley and F. ngelke, Resonator wth Redued Sample Heatng and Inreased Homogenety for Sold-State NMR, Journal of Magnet Resonane, Vol. 191 No. 1, 2008, pp do: /j.jmr [9] F. D. Doty, J. Kulkarn, C. Turner, G. ntzmnger and A. Belek, Usng a Cross-Col to Redue RF Heatng by an Order of Magntude n Trple-Resonane Multnulear MAS at Hgh Felds, Journal of Magnet Resonane, Vol. 128 No. 2, 2006, pp do: /j.jmr [10] P. T. Hardy Jr. and K. M. Wel, A Revew of Thermal MR Injures, Radolog Tehnology, Vol. 81, No. 6, 2010, pp [11] Q. X. Yang, A Method of Utlzaton of Hgh Deletr Constant (HDC) Materals for Redung SAR and nhanng SNR n MRI, US Patent No. 20,110,152,670, [12] K. R. Mnard and R. A. Wnd, Solenodal Mrool desgn-part II: Optmzng Wndng Parameters for Maxmum Sgnal-to-Nose Performane, Nulear Magnet Resonane, Vol. 13 No. 3, 2001, pp do: /mr.1008 [13] C. M. Collns and M. B. Smth, Calulatons of B 1 Dstrbuton, SNR and SAR for a Surfae Col Adjaent to an Anatomally-Aurate Human Body Model, Magnet Resonane n Medne, Vol. 45, No. 4, 2001, pp do: /mrm.1092 [14] C. M. Collns and M. B. Smth, Sgnal-to-Nose Rato and Absorbed Power as Funtons of Man Magnet Feld Strength, and Defnton of 90 RF Pulse for the Head n the Brdage Col, Magnet Resonane n Medne, Vol. 45, No. 4, 2001, pp do: /mrm.1091 [15] K. Yee, Numeral Soluton of Intal Boundary Value Problems Involvng Maxwell s quatons n Isotrop meda, I Transatons on Antennas and Propagaton, Vol. 14, No. 3, 1966, pp do: /tap [16] C. Gabrel, T. Y. A. Chan and. H. Grant, Admttane Models for Open nded Coaxal Probes and Ther Plae n Deletr Spetrosopy, Physs n Medne and Bology, Vol. 39, No. 12, 1994, pp do: / /39/12/004 [17] Federal Communaton Commsson (FCC), Body Tssue Deletr Parameters, Copyrght 2013 SRes.