0 μ Magnetic Polarizer for 1.5-T MRI

One of substantial challenge for imaging of objects and bodies with non-invasive techniques is well tackled by MRI systems, which plays an important role to characterize symptoms and diagnosis of the nature of illness in human body [1,2]. These systems offer different signal strengths of transient transverse magnetic field (B1) and static magnetic field (B0) for different imaging requirements to identify the biological structures. Scientists adopted different techniques to surpass MRI system efficiency by maintaining B1 without increasing B0 to avoid the risk of tissue heating and specific absorption ratio (SAR) due to absorbed power in human tissue at greater B0 [3-15]. They concluded that greater B0 of MRI system was harmful for human body which caused nausea and giddiness [16]. The homogeneity of magnetic field (B-field) and SNR at region of interest, ROI depended upon B1 which was mainly governed by transmit/receive MR coils of MRI system. B1 perturb ROI’s protons from equilibrium which yielded in image acquisition at receiver MR coil [17-19].


Introduction
One of substantial challenge for imaging of objects and bodies with non-invasive techniques is well tackled by MRI systems, which plays an important role to characterize symptoms and diagnosis of the nature of illness in human body [1,2]. These systems offer different signal strengths of transient transverse magnetic field (B 1 ) and static magnetic field (B 0 ) for different imaging requirements to identify the biological structures. Scientists adopted different techniques to surpass MRI system efficiency by maintaining B 1 without increasing B 0 to avoid the risk of tissue heating and specific absorption ratio (SAR) due to absorbed power in human tissue at greater B 0 [3][4][5][6][7][8][9][10][11][12][13][14][15]. They concluded that greater B 0 of MRI system was harmful for human body which caused nausea and giddiness [16]. The homogeneity of magnetic field (B-field) and SNR at region of interest, ROI depended upon B 1 which was mainly governed by transmit/receive MR coils of MRI system. B 1 perturb ROI's protons from equilibrium which yielded in image acquisition at receiver MR coil [17][18][19].
In the present work, we explored the significance of 0 μ SRRs magnetic polarizer, when used with MRI system; distort, reject and redistributed the RF field efficiently towards ROI and could locally enhanced B 1 field at ROI without increasing B 0 . This property was absent in previous work of negative permeability -μ metamaterial lenses [26]. Polarizer with compact thickness of only 5 mm and novel combination of parametric elements (capacitors, inductors), exhibited resonance at very low working frequency of 63.85 MHz, which was the frequency of operation for 1.5-T MRI systems. Use of parametric elements in design yielded in reduction of propagation losses which improved SNR at ROI and finally improved B field in that region. We presented analysis for 0 μ polarizer when used with MRI test bed setup that showed superior B field and SNR at ROI inside phantom in comparison to the equivalent setup, where the polarizer was absent. In addition, we proposed optimized placement of the MR coil and polarizer in accordance with ROI, which could reduce the SAR and enhanced B field at ROI.
The paper was organized as follows; section 2; Geometrical study of B 0 at MR coil and B 1 at ROI due to 0 μ magnetic polarizer; section 3; Relative permeability {μ r } parameters retrieval method and plot analysis; section 4; Design configuration and circuit model calculations; section 5; B-Field and SNR comparison; Experimental Test bed Setup Analysis; The paper was concluded in section 6.
Geometrical Study of B 0 at MR Coil and B 1 at ROI due to 0 μ Magnetic Polarizer Figure 1a depicted magnetic resonance (MR) coil facing Z-plane and carrying current I due to E (applied electric field). The electromotive force (emf) produced by MR coil as Lorentz magnetic force generated static magnetic field B 0 around MR loop coil [31,32]. Magnetic dipole D as magnetically susceptible material was placed at the distance x from MR coil. Geometry of MR coil as torus had diameter d M {d M =2(r M r' M )} with outer radius r M and inner radius r' M respectively. Thickness of MR coil was taken as t M =2 r' M . By the help of Biot-Savart's Law [32], we studied static magnetic field B 0 .
Where area A=πr 2 of the circular MR coil. We further attributed IA=D m . Now we consider 0 μ magnetic polarizer as shown in Figure  1b, where inductive power transfer was strictly contingent upon strong Abstract Study of human pathologies and acquisition of anatomical images without any surgical intervention inside human body is possible because of magnetic resonance imaging (MRI). This work exploits the notable properties of zero permeability (0 μ) split ring resonators (SRR) metamaterial (MM) magnetic polarizer which could distort, control and reject uniform RF (radio frequency) magnetic field for 1.5-T MRI systems. Unique polarizer was proposed to etch on PCB (printed circuit board) slabs for compact thickness of 5 mm only. In addition, polarizer was loaded with novel combination of parametric elements (capacitors, inductors) which could made the structure tunable to achieve resonance at different working frequencies. We achieved the value of relative permeability, μ r =0.02+j0.1 for 1.5-T MRI systems at 63.85 MHz. Furthermore polarizer, when used with MRI scanner at optimized position, uniformly redistributed and enhanced the magnetic field while lowered specific absorption ratio (SAR), induced electric field, power dissipation, and locally improved SNR (signal to noise ratio) at the scanned region of phantom {real case was human body}. The polarizer minimized the damaging effects of RF energy absorption in human tissue and prevented them from heating. coupling of evanescent waves between polarizer's medium due to applied static magnetic field B 0 created by transmitting loop MR coil ( Figure 1).  [33]. Figure 1b gave geometrical study of 0 μ magnetic polarizer whose thickness was t L and the design facing X-axis transmitted TM component of evanescent wave k z with angle ϕ 1 to k ' z with angle ϕ 2 . Furthermore, 0 μ magnetic polarizer rejected and controlled TE component of evanescent wave with its magnitudes of wave vectors k z with their angles ϕ 1 to magnitudes of vectors k '' z with their angles ϕ 3 , finally yielded in restoration of B 0 to B 1 at D. The incidence of TE plane wave evanescent in X-axis as magnitudes of vectors k '' z with their angles ϕ 3 in the sense of transient transverse magnetic field B 1 was calculated [34].
Eind was induced electric field at D, k x z 0 and k x z 0 were normal components of wave vectors k x along Z-axis and k z along X-axis, respectively.
'' z z z k k x k z + = was magnitudes of wave vectors with their phase angles ϕ 3 at D from the direction of polarizer.
, where μ r was the relative permeability of our design and ω was angular frequency of incident evanescent wave. 0 inc E was an incident electric field applied to MR coil. Then we calculated transfer function incidence of TE plane wave vectors k '' z [33].
λ Was wavelength of the incident wave and 3 1 ∅ = ∅ . The expression for µ r was calculated.
ω 0 and ω m were resonant angular frequency (restoring force) and magnetic plasma frequency (switching force) respectively. γ was damping factor. It has been noticed that

Relative Permeability {μ r } Parameters Retrieval Method and Plot Analysis
Magnetic dipoles of magnetically susceptible materials aligned themselves in the direction of externally applied B-field which depended upon strength of B-field. In result, those materials were resonant at particular frequencies. For 0 µ magnetic polarizer, we retrieved relevant values from S-parameter measurements through transmission and reflection coefficients [35]. By using boundary conditions as unit cell in CST Microwave studio for our design in frequency domain solver, we analyzed wave vectors k z , k '' z with their phase angles φ 1 , φ 3 of incident wave and finally measured relative permittivity Where η was the wave impedance of magnetic polarizer. For the targeted frequency of 1.5-T MRI system, we then calculated S 21 and S 11 in the frequency range from 30 to 80 MHz for nit cell geometry as described in section 4, for magnetic polarizer. Relative permeability, μ r =0.02+j0.1 was then calculated and plotted as a function of frequency and depicted in Figure 2a. It was observed and shown in inset of Figure  2b, that real part of magnetic permeability µ r became nearly zero and resonant in the frequency range from 63.85 MHz to 64.1 MHz.

Design Layout and Circuit Model Computation
A regular array of split ring resonator unit cell arranged in square lattice exhibited strong coupling among themselves due to strong mutual induction and finally reduced propagation losses [36,37]. SRR unit cell was schematically depicted in Figure 3a where three copper rings P 1 , P 2 and P 3 were restacked in a way to make 3D symmetry of cubic structure. Figure 3b depicted one side of square SRR copper ring with thickness and width of t c =0.070 mm and W=0.3 mm respectively. SRR ring was etched on nonmagnetic PCB and loaded with lumped elements e.g., capacitor element c e =0.13nF and inductor element l e =37.2nH. The PCB with its material properties had relative permittivity ε r =2.33, relative permeability µ r =1, and a thickness t s =0.381 mm. The side length of the SRR square was S=4.4 mm. Complete design was composed of 3-D array of SRR unit cells having a periodicity a=5 mm, which was then also the lens thickness t L . It was observed that nonlinear significance of lumped elements enhanced the importance of design to make it resonant at different working frequencies. Lumped elements maintained uniformity of induced currents i p , in each SRR ring and minimized losses in wave propagation. This mechanism reconstructed the amplitude of incoming signal [29][30][31][32][33][34][35][36][37][38]. Specifically inductor supported B field concentration into SRR circuit array by re-linking the field to arrays and finally made uniform formation of induced currents. This uniform formation of induced currents among SRR arrays provided strong mutual induction among them due to strong coupling between arrays [39].
Equivalent Circuit model of Figure 3a, was explained in Figure 4, where unit cell composed of three periodically arranged 0 μ polarizer SRR magnetically coupled rings loaded with lumped inductor l e and lumped capacitor c e , finally making RLC circuit. The SRR rings of unit cell were named as P 1 , P 2 and P 3 . The generation of magnetic flux created by the MR coil across SRR rings P 1 , P 2 and P 3 depended upon induced currents i P among P 1 , P 2 and P 3 [34]. Figure 4 demonstrated C P {self capacitance}, L P {self inductance}, R P {self resistance} and M LP {mutual inductance between SRR rings P 1 , P 2 and P 3 } of the unit cell ( Figures  3 and 4).
Total flux through each ring was calculated as the sum of external source B flux and flux across SRR rings in the result of induced currents i P and mutual inductance M LP between SRR rings P 1 , P 2 and P 3 of unit cell [40].
∆ 1 =Flux through single SRR, say; P 1 , B=Externally produced flux because of MR coil, M (LP) =Mutual inductance among P 1 P 2 and P 1 P 3 in a unit cell respectively, 1 P i =Induced current i P created by external field B at SRR P 1 . Flux through single unit cell was derived as: , ' P =Total SRR rings in unit cell (P 1 , P 2 , P 3 ), ∆'=Magnetic flux generated at single unit cell because of external applied field and ' We applied the Kirchhoff 's voltage law (KVL) on the equivalent circuit model of single unit cell, yielded [40]; ' P V =External voltage applied to polarizer's unit cell, ' P R =overall self-resistance, ' P L =overall self-inductance, ' P C =overall self-capacitance of polarizer's SRR of single unit cell, ' LP M =overall mutual inductance among SRR rings, say; P1, P2 and P3. No external voltage was applied to polarizer's structure as input and induced currents i P were resulted in SRR rings, ' P , because of externally applied magnetic field created by MR loop coil. In consequence, we took V P ' = 0 volts for polarizer's SRR rings. Self-resistance R, was calculated by considering skin depth δ for polarizer's SRR rings [41].
δ=Skin depth for copper material, µ r1 =1 {relative permeability of copper}, f=resonance frequency for SRR, µ 0 =free space relative permeability, σ=copper's conductivity. At 63.85 MHz, δwas calculated as 0.0083 mm for copper SRR ring. The SRR's thickness t c in our design was 0.070 mm and clearly resulted as t c >δ. For this purpose, we needed to adopt two certain rules for calculations of self-resistance R P [42].

( )
t s =PCB thickness, ε 0 =Permittivity of free space, ε r =PCB's Relative permittivity. Finally we calculated M LP12 among two SRR rings. We used mutual inductance algorithm in our calculations [46].
It was deduced from equivalent circuit model in Figure 4 that each polarizer's ring was making RLC series circuit with its elements, (c e , l e ) and RLC parallel circuit with other rings. Furthermore mutual inductance among SRR rings of unit cell resulted in RLC series circuit. Then total mutual inductance M' LP between the rings was calculated.
Table 1 resulted in stronger overall mutual inductance M ' LP among SRR rings, say; (P 1 , P 2 and P 3 ) for single unit cell in comparison with individual self-inductance L P and overall self-inductance L P ' . These results provided a strong case of coupling of one SRR ring with its neighbors and yielded in surpassed magnetic field in presence of magnetic polarizer. By exploiting eqns. (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22), we finally calculated overall magnetic flux ' ∆ / unit cell of magnetic polarizer in the consequence of applied magnetic field.

B-Field and SNR comparison; Experimental Test Bed Setup Analysis
Experimental setup for MRI test bed was adopted using commercial COMSOL Multi-physics software as depicted in Figure 5. Magnetic field, B and SNR were measured at magnetically susceptible dipole D, which was positioned at distance x from MR loop coil and located inside phantom. It was studied in the light of Reciprocity theorem that received transient transverse magnetic field B 1 from dipole D was proportional to static magnetic field B 0 /unit induced current at that dipole D [47][48]. Noise in the signal was related to SNR and it was observed that due to intrinsically thermally generated noise currents produced noise resistance at dipole D, which resulted in creation of noise in the signal. This noise creation was in direct proportion with square root of generated noise resistance [49][50][51][52]. It concluded that induced current density at dipole D resulted in better and enhanced B 1 . However, this induced current density became the cause of more power dissipation at dipole D, which yielded in generation of more noise resistance and finally decayed SNR. That's why optimized position of MR coil in accordance with distance of dipole D was recommended for better results in both received SNR and B 1 . Further, we calculated power dissipation as; Where Iind was induced current at dipole D because of constant current intensity I generated by MR coil. R noise was noise resistance due to intrinsically thermally generated noise currents because of power dissipation at D. E ind was reflected induced electric field because of was induced current density at dipole D due to I. J ind is induced current density which was proportional to I ind ( Figure 5).
Finally SNR was derived at dipole D for the given experimental setup depicted in Figure 5, with or without the presence of 0 μ magnetic polarizer in the setup. Polarizer facing X-axis and composed of 6 PCB sheets with dimensions 120 × 120 × 5 mm 3 , contained 24 × 24 cubic unit cells  loaded with l e , c e . Those cubic unit cells had repetition of 5 mm with overall 3456 SRR's. The phantom with its directions in Z-axis and with dimensions 120 × 120 × 150 mm 3 , with phantom's relative permittivity ε r =90-j197 [51]. Magnetic dipoles D 1 , D 2 and D 3 were facing Z-axis with same dimensions 2 × 2 × 16 mm 3 and at optimized distances x =10 mm for D 1 , x=20 mm for D 2 and x=30 mm for D 3 from MR coil, respectively with same relative permittivity as phantom. MR coil was placed at the distance x=10 mm from phantom surface which was same as the distance of D 1 from MR coil. Throughout in the simulations for polarizer, we used μ r =0.02+j0.1, as explained in section 3. Configuration of magnetic resonance coil was already mentioned in section 2, where r M =22 mm at t M =2 mm with r' M = mm was used.
Astute inspection of Figures 6a-6i showed that B-field was rejected, controlled and enhanced in the presence of 5 mm thick 0 μ polarizer. It was observed in Figure 6a for dipole D 1 that initially B-field was higher even without using polarizer. It was obvious that D 1 was much exposed {near} to the MR coil in comparison with D 2 and D 3 and that's why intensity of B-field at D 1 due to enhanced power dissipation, and induced current resulted in high values at D 1 even when polarizer was not used (Figure 6b). It meant that for the dipoles positioned like D 1 , initially, polarizer was not effective to enhance B-field up to certain distance. However it was observed for D 1 , that B-field started increasing at distance x=9-15 mm in the presence of polarizer (Figure 6a). This fact could be understandable in Figure 6c. We know that enhanced power dissipation yielded in heating and resulted in more thermally noise generation around the dipole which was near the MR coil due to intrinsically thermally generated noise currents, which resulted in increased noise resistance and decayed SNR. We observed that polarizer locally surpassed SNR at D 1 , Figure 6c which immediately enhanced B-field at D 1 at the distance x=9-15 mm in the presence of polarizer, Figure 6a, where field intensity due to MR coil started weakening. At D 2 and D 3 , we observed that B-field surpassed its values in presence of polarizer in comparison to its absence, (Figures 6d-6g) even power dissipation was higher due to field intensity of MR coil in the absence of polarizer (Figures 6e-6h). But due to weakening of field intensity of MR coil at D 2 and D 3 , polarizer in its presence, locally enhanced SNR at D 2 and D 3 , and reduced noise resistance which was the cause of creating intrinsically thermally generated noise currents because of high power dissipation (Figure 6f-6i). This significance not only yielded in reduced power dissipation (Figures 6e-6h) and heating effect at D 2 and D 3 , but also improved B-field at those positions and reduced SAR (Figures 6d-6g).
Safety aspects depended on the absorption of the electromagnetic (EM) energy and power dissipation which could be attributed as SAR (specific absorption ratio) at the scanned region inside the human body  during their MRI scanning [52]. The large SAR value yielded to heat the human tissue due to radio frequency (RF) pulses generated by MR coil and could be harmful for the biological structure of tissue. SAR was proportional to the square of electric field applied to MR coil [53] ( Figure 6).
We observed that applied electric E field was concentrated at the edges of the MR coil loop antenna and it had the lowest values at middle of MR coil, which meant that electric field did not encountered the magnetic field in the middle of the loop as the transversal Eigen modes for electric field were disappeared in that area and in result SAR was reduced in that region, say; middle area of the loop . This aspect provided the possibility to redistribute RF field and reduce SAR in the region of interest which in resulted not only locally enhanced the magnetic field in that region but also improved SNR. Furthermore the technique removed electric field, substantially decreased the power dissipation and EM energy absorption at ROI which could the best optimized technique to avoid the damages caused from human tissue heating inside human body. This effect could be clearly seen at dipole D 2 positioned in the middle of the MR coil shown in Figure 5, and analyzed in Figures 6e-6f. We observed substantial decrease in power dissipation and locally increase in SNR at D 2 , which was positioned at x=20 mm from MR coil loop antenna. We also observed that polarizer enhanced the magnetic field at D 2 while substantially keeping power dissipation low and high SNR in comparison to the results in its absence. We concluded that the efficiency of polarizer could be increased by choosing the optimized position of MR coil, in the way to exactly position ROI at the center of the coil. That yielded in reducing SAR, power dissipation, increasing B-field and SNR at ROI (Figure 7). Figure 7 depicted noise resistance analysis at magnetic dipoles D 1 , D 2 and D 3 in the presence of polarizer. As we have mentioned above, that noise resistance deeply impacted SNR and this effect could also be deduced from eqn. (24). We observed more noise generation at dipoles positioned near to MR coil. So dipoles experienced more noise resistance in comparison to the dipoles positioned at farther distances from MR coil in the setup of Figure 5. It was due to intrinsically thermally generated noise currents which limited SNR at ROI which were near to MR coil. This effect could be clearly seen in Figure 6, that larger power dissipation quickly decreased SNR at the dipoles. At the optimized position of MR coil with respect to D 2 , in the presence of polarizer, we observed an ample decrease of noise resistance, power dissipation, and enhanced SNR (Figure 7, Figures 6e and 6f).

Conclusion
We designed a novel and compact 0 μ magnetic polarizer SRR metamaterial fully operational at 63.85 MHz. The design more specifically reduced specific absorption ratio (SAR) effects as well as improved image quality for 1.5 T MRI systems. Polarizer was the combination of SRR copper loops and loaded with lumped capacitor c e and inductor l e with compact thickness of only 5 mm. It could efficiently distort, reject, control and redistributed the RF field inside phantom {real case was human body} and could locally enhanced magnetic field by increasing SNR and reducing noise resistance at ROI without increasing the static magnetic field of external MR coil of MRI system. This unique combination of lumped elements with copper loops has not been used before for such applications. Polarizer exploited nonlinear characteristics of the lumped elements especially inductor element which exhibited minimized propagation losses, strong mutual inductance and uniformity of currents between SRR rings. In result, amplitude of the incoming decaying signal was reconstructed due to polarizer's material's property at frequency of resonance. Furthermore, polarizer allowed an opportunity for the construction of tunable magneto-inductive SRR metamaterial at very low working frequencies.
In addition we highlighted the significance of polarizer in the optimized MRI test bed setup as it improved magnetic field and removed induced electric field at different dipole positions inside phantom (real case human body) in the setup which reduced the power dissipation at that dipole positions finally resulted in improved SNR and reduced SAR at dipoles. The design improved the safety aspects to avoid human tissue heating due to large power dissipation because of radio frequency RF pulses generated by MR coil which could be harmful for the biological structure of tissue.
Future prospect of our designed magnetic polarizer SRR metamaterial can be the fabrication of smart clothes for patients using MRI scanning, which will enhance image resolution inside human body.