Nonlinear Split-ring Metamaterial Slabs for Magnetic Resonance Imaging

Nonlinear split-ring metamaterial slabs for magnetic resonance imaging Marcos A. Lopez,1Manuel J. Freire,1,a兲Jose M. Algarin,1Volker C. Behr,2Peter M. Jakob,2 and Ricardo Marqués1 1Department of Electronics and Electromagnetism, Faculty of Physics, University of Seville, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain 2Department of Experimental Physics 5 (Biophysics), Institute of Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany 共Received 20 February 2011; accepted 17 March 2011; published online 1 April 2011兲 This work analyzes the ability of split-ring metamaterial slabs with zero/high permeability to reject/confine the radiofrequency magnetic field in magnetic resonance imaging systems. Split-ring slabs are designed and fabricated to work in a 1.5 T system. Nonlinear elements consisting of pairs of crossed diodes are inserted in the split-rings, so that the slab permeability can be switched between a value close to unity when interacting with the strong field of the transmitting coil, and zero or high values when interacting with the weak field produced by protons in tissue. Experiments are shown where these slabs locally increase the signal-to-noise-ratio. © 2011 American Institute of Physics.关doi:10.1063/1.3574916兴 Application of metamaterials in magnetic resonance imaging 共MRI兲has been previously explored in several works making use of devices based on swiss-rolls,1–5wires,6and capacitively-loaded split rings.7–9Most of these works have explored the subwavelength imaging ability of metamaterials with negative permeability 共 ␮ 兲. In previous works of the authors, metamaterials slabs with ␮ =−1 have been fabricated and tested in MRI systems to show the ability of these slabs to increase the sensitivity of surface coils7,8and to improve the field localization of these coils, a fact that may find applications in parallel MRI.9Although metamaterials can be engineered to tailor whatever value of ␮ at the desired frequency, little attention has been paid to values of ␮ different from negative ones. In the present work, it is explored the application in MRI of capacitively-loaded split-ring metamaterials which show zero permeability 共 ␮ =0兲or high permeability 共 ␮ →⬁兲at the operating frequency. ␮ =0 and ␮ →⬁ slabs can reject and confine, respectively, the radiofrequency 共rf兲magnetic field, as sketched in Fig. 1. These properties can help to locally increase the signal-to-noise-ratio 共SNR兲 of surface coils in certain configurations which have been experimentally investigated in this work. Typical MRI acquisition consists of the excitation of tissue with a strong and uniform rf field generated by a transmitting body coil, and then the detection of the weak field generated by hydrogen nuclei in tissue by means of surface coils. The split-ring device previously reported by the authors consisted of a ␮ =−1 slab,7–9which does not distort the uniform excitation field. However, ␮ =0 and ␮ →⬁slabs can actually distort this field. Therefore, it is necessary to implement these slabs as nonlinear slabs which can be automatically switched to show ␮ ⯝1 under the strong field of excitation and ␮ =0 and ␮ →⬁under the weak field coming from tissue. This can be accomplished in the practical implementation of the slabs by inserting nonlinear elements in the split-rings that allow to switch between different responses under strong or weak fields. In particular, a pair of crossed diodes inserted in each split-ring can help to switch off them under the strong excitation field. Following the homogenization procedure previously reported by some of the authors,10 two split-ring slabs of 6⫻6⫻1 unit cells with a periodicity of 15 mm were designed to exhibit ␮ =0 and ␮ →⬁at the frequency of 63.6 MHz. This frequency corresponds to the Larmor frequency of the 1.5 T Siemens Avanto MRI system sited in the Department of Experimental Physics 5 共Biophysics兲of the University of Würzburg 共Germany兲, where the experiments reported in this work were done. The fabricated split-rings have 12 mm in diameter and 1.87 mm of strip width for the ␮ =0 slab, 11.8 mm in diameter, and 1.7 mm of strip width for the ␮ →⬁slab. Each split-ring in the array contains a 470⫾1% pF nonmagnetic capacitor 共American Technical Ceramics Corp., NY, USA兲for resonance at a specific frequency below 63.6 MHz, and a pair of crossed diodes 共Microsemi Corp., CA, USA兲in parallel with the capacitor 共see Fig. 2兲in order to switch off the slab in transmission. Under the strong excitation field, the high electromotive force induced in the rings makes the diodes to drive and then the capacitors are short-circuited, so that the split-rings behave like simple closed metallic rings. Following the mentioned homogenization procedure,10 the calculated permeability for this system of simple metallic loops is ␮ =0.85, a value which is closed to the value of the permeability of air. Once the sample is excited, the tissue reradiates a weak field which is unable to drive the diodes, so that the rings behave like resonant circuits. The frequency of resonance has been chosen so that from the homogenization model10 the system has ␮ =0 and ␮ =⬁at the working frequency of 63.6 MHz. Since the capacitance of each split-ring is fixed, the frequency of resonance was fitted by adjusting the dimensions a兲Electronic mail: [email protected]. FIG. 1. Sketch of the magnetic field lines for 共a兲a single coil, 共b兲a ␮ =0 slab perpendicular to the coil, and 共c兲a ␮ →⬁slab placed parallel to the coil. APPLIED PHYSICS LETTERS 98, 133508 共2011兲 0003-6951/2011/98共13兲/133508/3/$30.00 © 2011 American Institute of Physics98, 133508-1 09 June 2025 13:14:43 of the rings. A small correction to the value predicted by the homogenization model was necessary due to the parasitic reactance of the diodes. For the experiments, a 90 mm in length receive-only loop coil was used and a 12⫻12⫻18 cm3phantom, filled with a hydroxyethyl cellulose solution doped with 1.5 g/l CuSO4, was used as a load for the experiments. The loop was tuned to 63.63 MHz and matched to 50 ⍀in the presence of the slabs and the phantom. It was actively decoupled by a tuned trap circuit including a PIN diode in transmission. The active decoupling for the loop was ⫺25 dB with and without the metamaterial slabs. All the experiments were performed in the 1.5 T system mentioned above. In the ␮ =0 experiment, the metamaterial slab is perpendicular to the loop and it is positioned at one side of the phantom 关see Fig. 3共a兲兴, so that the magnetic flux is rejected by the slab and then confined inside the phantom. This will increase the signal coming from this region of the phantom. In the ␮ =⬁experiment, the metamaterial slab is placed parallel to the loop in the opposite side of the phantom 关see Fig. 4共a兲兴in order to guide the flux lines through the phantom. SNR maps were calculated from a series of phantom measurements11 for both the ␮ =0 and the ␮ =⬁slabs and compared with the situation where the slabs were removed. In Fig. 3共a兲, the calculated SNR maps are shown for both the presence and the absence of the ␮ =0 slab, and profiles along the white dashed line are compared in Fig. 3共b兲. The comparison between these profiles show that the signal increases up to 64% in the side of the phantom where the ␮ =0 slab is placed. The calculated SNR maps for the ␮ =⬁slab are shown in Fig. 4共a兲, and the corresponding profiles in Fig. 4共b兲. The signal presents an increment of up to 200% with the presence of the slab. In the experiments, an artifact appeared in the phantom’s surface due to the discrete nature of the split-ring structure but it was easily removed by taking the slab 1 cm far from the surface of the phantom. This work demonstrates how split-ring metamaterial slabs designed with specific permeability values can increase FIG. 3. 共Color online兲共a兲SNR map for the experiment with the ␮ =0 slab in an axial plane. 共b兲Profile of the SNR along the white line in the map. The SNR is given in arbitrary units. FIG. 4. 共Color online兲共a兲SNR map of the experiment with the ␮ →⬁slab in an axial plane. 共b兲Profile of the SNR along the white line in the map. The SNR is given in arbitrary units. FIG. 2. 共Color online兲Sketch of the constituent element and photographs of the slabs. The slabs are 6⫻6⫻1 unit cells and the periodicity is 15 mm. The ␮ =0 slab has been fabricated with rings of 12 mm in diameter and 1.87 mm of strip width, and the ␮ →⬁slab has been fabricated with 11.8 mm in diameter and 1.7 mm of strip width. For both cases, 470 pF capacitors were used to tune the loops. A pair of crossed diodes in parallel with the capacitors provides the nonlinear response which is different for strong or weak fields. 133508-2 Lopez et al. Appl. Phys. Lett. 98, 133508 共2011兲 09 June 2025 13:14:43 the SNR in different configurations. The SNR gain can be improved with a smart design of the configuration, making a suitable choice of the size of both the coil and the sample. ␮ =0 slabs surrounding the sample could improve the SNR in the borders of the sample and thus the SNR will be homogenized in the field of view of the coil. In the ␮ =⬁experiment, although the SNR gain could not be comparable to that provided by another coil positioned in the same position as the slab, the metamaterial slab could be useful in limited channel systems or as complement of an array. This work was supported by the Spanish Ministerio de Ciencia e Innovacion under project Consolider under Grant No. CSD2008-00066. The authors want to thank the company NORAS MRI Products for the advice. 1M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291,849共2001兲. 2V. C. Behr, A. Haase, and P. M. Jakob, Concepts Magn. Reson., Part B 23B,44共2004兲. 3M. C. K. Wiltshire, Phys. Status Solidi B 244,1227共2007兲. 4M. Allard, M. C. K. Wiltshire, J. V. Hajnal, and R. M. Henkelman, Proceedings of the 13th International Society for Magnetic Resonance and Medicine, Miami, FL, 7-13 May 2005 共unpublished兲,p.871. 5M. Allard and R. M. Henkelman, J. Magn. Reson. 182, 200 共2006兲. 6X. Radu, D. Garray, and C. 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