A New FDTD Method for the Study of MRI Pulsed Field Gradient- Induced Fields in the Human Body

Transcription

1 A New FDTD Method for the Study of MRI Pulsed Field Gradiet- Iduced Fields i the Huma Body Stuart Crozier, Huawei Zhao ad Liu Feg Cetre For Magetic Resoace, The Uiversity of Queeslad, St. Lucia, Qld 4072, Australia I moder MRI, patiets are exposed to strog, rapidly switched magetic field gradiets that may be able to elicit erve stimulatio (-4. This paper provides the umerical results of a ivestigatio ito iduced curret spatial distributios iside huma tissue whe exposed to these pulsed magetic field gradiets. Covetioal FDTD methods are uable to model these effects as the effective frequecies of the iput source are less tha 00kHz or so, relatively low for FDTD calculatios. A ew High Defiitio FDTD variat was developed to operate over this badwidth ad a umber of body ad gradiet models are aalysed usig the ew method. Itroductio Whe patiets udergo a Magetic Resoace Imagig (MRI sca, they are subject to both strog static ad temporal magetic fields as well as radio-frequecy fields. MRI is iteded to be a o-ivasive modality ad ay iteractio betwee these fields ad the patiets must be well cotrolled ad withi safe limits. As MRI istrumetatio moves towards the use of higher field stregths ad faster scaig, the potetial for field/patiet iteractio icreases. There are a rage of tissues that comprise the huma body ad each has a differet frequecy-depedet coductivity ad permittivity; it is these properties that effect the iteractio with electromagetic fields. If the extet of the field/patiet iteractios could be better uderstood by experimetally validated theoretical models of the pheomea, the the equipmet ca be re-egieered with these limitatios i mid. The resultat scaers would have both improved performace ad better patiet safety. The temporal magetic fields i a MR system are desiged to vary at each poit i the regio beig imaged. This is achieved by the use of gradiet coils. However, whe the gradiet coils are switched very rapidly, the strog, timevaryig magetic fields produced ca be resposible for stimulatig erves i the peripheral regios of the body (PNS. It is a major goal of this project to devise ew methods for accurately modellig the effects of switched gradiets o the huma body ad to further desig ew, cliically useful, gradiet coils that miimize the risk of such stimulatio. Methods Covetioal FDTD methods proceed by repeatedly solvig for a fiite differece aalogue of Maxwells equatios withi each cell of a defied lattice. They accomplish this by attemptig to arrive at steady state behaviour for the E ad B fields withi each cell as a result of the trackig of a icidet wave ad its iteractios with the medium. I a typical FDTD simulatio, computatioal times o the order of a few periods of the source are required, limitig the method to high frequecy aalyses. For low frequecy problems, it is ot feasible to ru the covetioal FDTD techique for a full period. For example, with a 00 Hz source icidet o a biological model of isotropic resolutio 0 mm, covetioal FDTD stability criteria would result i a computatio time of about 00 years! To obtai the solutio withi a fractio of the source period, a ew timefrequecy coversio method has bee developed. Usig the proposed ew HD-FDTD techique, oly a fiite umber of solutios are eeded i the time domai, ad the a iverse approach ca be used to calculate A i ad B i.if the source electromagetic field is represeted i Time-Harmoic form, each of the harmoics may be calculated usig FDTD i a relatively straightforward fashio. Assumig that the source field cosists of siusoidal compoets of frequecies M, /0$ IEEE

2 Report Documetatio Page Report Date 25 Oct 200 Report Type N/A Dates Covered (from... to - Title ad Subtitle A New FDTD Method for the Study of MRI Pulsed Field Gradiet-Iduced Fields i the Huma Body Cotract Number Grat Number Program Elemet Number Author(s Project Number Task Number Work Uit Number Performig Orgaizatio Name(s ad Address(es Cetre For Magetic Resoace The Uiversity of Queeslad St. Lucia, Qld 4072, Australia Sposorig/Moitorig Agecy Name(s ad Address(es US Army Research, Developmet & Stadardizatio Group (UK PSC 802 Box 5 FPO AE Performig Orgaizatio Report Number Sposor/Moitor s Acroym(s Sposor/Moitor s Report Number(s Distributio/Availability Statemet Approved for public release, distributio ulimited Supplemetary Notes Papers from 23rd Aual Iteratioal Coferece of the IEEE Egieerig i Medicie ad Biology Society, October 25-26, 200 held i Istabul, Turkey. See also ADM0035 for etire coferece o cd-rom., The origial documet cotais color images. Abstract Subject Terms Report Classificatio Classificatio of Abstract Classificatio of this page Limitatio of Abstract UU Number of Pages 4

3 2 M,, 2 M, the the field (magetic or electric ca be represeted at each temporal poit as f(, r t = A(si( r M t+ B ( r i i i I order to obtai the solutio i a very small fractio of the period of the source, a ew timefrequecy coversio techique has to be adopted. The amplitude ad phase terms are the ukows to be foud. Assumig that the trasiet respose will die out after L p loops, ad the correspodig iteratio umber is Lp L. Whe Nit Lp L, the time depedet solutios s, s 2,, s m will be recorded at the times t, t 2,, t m. I geeral, m 2, ad the complete system may be represeted as: s = Ai( sibicos( Mit + cosbisi( Mit s2 = Ai( sibicos( Mit2 + cosbisi( Mit2, sm = Ai( sibicos( Mitm + cosbisi( Mitm I our proposed method, oly a fiite umber of solutios are eeded i time domai, ad the a iverse approach is used to calculate A i ad Bi at each frequecy. To verify the model, HD- FDTD calculatios based a oe-dimesioal plae wave icidet o a sigle, lossy (coductive dielectric material were made ad compared with aalytical solutios (see figure. trasmitted wave. A = 80 ad I = 0.5 were used for the material. The space was broke ito cm elemets. Accordig to the stability criterio, for oe completed loop (oe forward ad backward path, 635 iteratios are required. Two source frequecies, 50 Hz ad 00 khz, were tested. The results of the covergece history are give i figure 2, where figure 2 (a ad (b preset field amplitude ad phase solutios for f = 00 khz. The solutio for f = 50 Hz showed slightly better correlatio. The solutios are calculated for loop, 5 loops, 0 loops ad 30 loops, i which the iteratio umber are 635, 375, 6350 ad 9050 respectively. The accuracy of the solutios obtaied after 30 loops idicates that the algorithm is very accurate at low frequecy ad that both absorbig boudaries performed efficietly. The computatioal time o a sigle processor Su Eterprise 450 was < secod for this simple problem. Amplitude aalytical loops 5 loops 0 loops 30 loops Z(m e s 0 a h P aalytical loops 5 loops 0 loops 30 loops Fig. The test problem I order to test the absorbig boudary coditios, Mur s first order absorbig boudary is used to absorb the reflected wave ad Bereger s PML is used to absorb the Z(m

4 3 Fig.2 The magetic field amplitude (top ad phase (bottom results for the test problem. Note the excellet covergece after 30 loops. Results Huma Body Simulatio The huma body model (Fig. 3 was positioed cetrally i a maget system with a Maxwell-coil pair z-gradiet coil. A complete huma body model with frequecy depedet electrical parameters (ε,σ,µ, was used. The ier surface of maget was treated as perfect coductor wall. A PML absorbig boudary, which trucates computatioal domai, is used to surroud the huma body. A 2.5 khz curret source Ji = J0 si(2 F f t was used to drive a Maxwell-coil pair gradiet set. I this system, isotropic cm resolutio was used, represetig a large mesh. After the HD-FDTD algorithm was ru for 40,000 iteratios, the eddy curret desity was obtaied from the E-field solutio. The solutios required approximately 5 hours of parallel processig o a 4-processor Su Eterprise 450. A represetatio of the eddy curret desity i X-Y cross-sectios coverig the model is show i figure 4. (3 T.S. Ibrahim et. al. Abstracts of the 8 th ISMRM, p49, (2000. (4 S.Crozier et. al. Cocepts i Mag. Reso.. 9, 95-20, (997. (5 L. Forbes ad S. Crozier Phys. Med. Biol. 42(2, (200. (6 S. Crozier ad D.M. Doddrell J. Mag. Reso., 03, (993. (7 S. Crozier, L. Forbes ad D.M. Doddrell J. Mag. Reso., 07,26-28 (994. (8 S.Crozier et. al.. J. Mag. Reso. 39, 8-89, (999. (9 K. S. Yee, IEEE Tras. Ateas Propagat., 4, , (966. (0 K. Umashakar ad A. Taflove, IEEE Tras. Electromagetc Compatibility, 24, , (982. ( W. L. Ko ad R. Mittra, Electromagetics, 5: , (995. (2 R. Hollad, IEEE Tras. Electromagetic Compatibility, 36,, 32-39, (994. (3 C. M. Furse ad O. P. Gadhi Bioelectromagetics, 9, , (998. (4 J. D. Moerloose, T. W. Dawso, ad M. A. Stuchly Radio Sciece, 32(2,329-34,(997. Figure 3 The body positio Coclusio The comprehesive prelimiary results show above for the calculatio of iduced fields show cosiderable promise as a aid to better uderstadig of the iteractio betwee the pulsed gradiet fields geerated i a MR scaer ad the huma body. E8 Refereces ( J. Ji et. al., Phys. Med. Biol. 4, , (996. (2 C.Collis et. al. Abstracts of the 8 th ISMRM, p48, (2000.

5 4 Figure 4 The iduced curret (A/m2 i various parts of the body model, resultig from a siusoidal gradiet of peak amplitude 40 mt/m. Y X Z