modeling analysis of inductive coupling for biomedical applications

8/12/2019 Modeling Analysis of Inductive Coupling for Biomedical Applications

1/14

UMN

Modeling Analysis of Inductive

Coupling for Biomedical ApplicationsFinal Report

AB

Spring 2012


2/14

1

Table of Contents

Introduction .................................................................................................................................................. 2

Coupling Analysis ....................................................................................................................................... 3

Design for Coil Decoupling ....................................................................................................................... 6

Wedge Implementation for Rod Conductors...................................................................................... 7

Wedge Implementation for Strip Conductors..................................................................................... 9

Conclusion ................................................................................................................................................. 11

References ................................................................................................................................................ 12

Appendix A ................................................................................................................................................ 13


3/14

2

Introduction

Magnetic resonance imaging (MRI) techniques exploit the excitation of nuclei intocoherent precession using a controlled magnetic field. This requires coupling between the nuclei(specimen) and a source of RF power in the form of external circuitry. These devices are called

RF coils and are designed to operate in the general band of the Larmor frequency as specifiedby equation 1 [1].

= 02 172(1)

= 42.58 /: gyromagnetic ratio of hydrogen 0 = 4: uniform magnetic field produced by the main magnet

Although many different RF coil configurations are in existence, the particular type that is ofinterest is known as a TEM head coil as shown in figure 1. Head coils are geometricallydesigned for a human head to fit in the imaging area with minimal excess space.

Figure 1: TEM Head Coil [2]

The structure is comprised of N = 4 to 16 uniformly spaced RF coils, implemented with copperrods or strips in a cylindrical configuration. Beneath the coils lies a teflon or air substrateseparating the conductors from the cylindrical ground plane located on the outer radius. Figure1 shows the case for 16 RF coils implemented with copper rods using an air substrate.

Because of the close coil-to-coil proximity in the cylindrical structure, RF coils couple toone another with the most substantial case being for N = 16. To facilitate new potential imagingapplications, it is desired to isolate and individually control each coil requiring a level ofdecoupling between conductors. To achieve such a design, an analysis of the coil-to-coilcoupling must first be analyzed per the number of coils in the structure followed by the modelingof a proposed modification to decrease the current coupling levels.


4/14

3

Coupling Analysis

The head coil to be analyzed has an outer radius of 15 cm at the surface of the groundplane followed by a 2 cm thick substrate making the inner radius 13 cm. Since the inner radiusof the cylindrical structure is fixed, the coil-to-coil spacing is determined by the number of coils N

in the structure since any number of coils must be uniformly spaced. The upper part of figure 2illustrates these dimensions with 8 coils comprised of 1 cm diameter copper rods. Usingelementary trigonometry, the center-to-center coil spacing is computed using equation 2.

() = 2 sin(2)

= 12.5 : MRI cylinder center to coil center spacing = 2 16: Number of uniformly spaced coils

Figure 2: RF Coil Model Approximation


5/14

4

Since the number of coils N is defined as a discrete set of all even numbers from 2 to 16, 8different coil-to-coil spacing values arise and thus 8 different models must be simulated. Forsimplicity, the coupling of 2 RF coils will be simulated since the contribution of coils spacedfurther in the structure will be negligible. Additionally, the coils are mapped to a planar surfacewhile preserving the coil spacing, substrate height, and conductor dimensions in the cylinder asshown in the second part of figure 2. To compute the coupling, the planar structure is simulated

using HFSS from 0 to 350 MHz with the solution frequency specified at 172 MHz. To ensure allports are matched, the reference impedance of each terminal is set to 92.5 Ohms, the simulatedport impedance of the copper rods. A total of 8 simulations are performed with the coil spacingadjusted for each per equation 2. The raw data is shown in figure 3 with the coupling valuesgraphed in figure 4 versus the number of coils and coil spacing.

N X (cm) X (in) Coupling (dB) Return Loss (dB) Insertion Loss (dB)

2 25.000 9.8425 -50.790 -17.321 -0.27944 17.677 6.9597 -44.405 -16.780 -0.3124

6 12.500 4.9213 -38.499 -16.786 -0.3119

8 9.5671 3.7666 -34.108 -16.600 -0.3166

10 7.7254 3.0415 -30.493 -16.775 -0.3189

12 6.4705 2.5474 -28.028 -17.220 -0.318214 5.5630 2.1902 -25.764 -17.295 -0.3090

16 4.8773 1.9202 -23.342 -18.903 -0.2573Figure 3: Simulated Data for Different RF Coil Rod Spacing at 172 MHz

Figure 4: Coupling vs. Number of Coils and Coil Spacing (Rod) at 172 MHz

2 4 6 8 10 12 14 16-55

-50

-45

-40

-35

-30

-25

-20

Number of Coils

Coupling(dB)

2 3 4 5 6 7 8 9 10

-55

-50

-45

-40

-35

-30

-25

-20

Coil Spacing (in)

Coupling(dB)

Number of Coils vs. Coupling

Coil Spacing vs. Coupling


6/14

5

As expected, the coupling increases significantly as the coil spacing decreases with a maximumvalue of -23.3 dB for N = 16. In addition, the rods remain relatively well matched for a non-planar structure as the return loss does not go above -16.6 dB.

In addition to analyzing the case for copper rods, RF coils can also be implemented with1 Oz copper strips. Using the same methodology to map the cylindrical structure to a planar

surface, the center-to-center strip spacing is still given by equation 2 since the inner radius ofthe substrate is unchanged. The outer radius of the substrate however is reduced to 1 cm alongwith that of the ground plane to allow for the strips to be designed to have a 50 Ohmcharacteristic impedance with a reasonable width. Using LineCalc, a 50 Ohm strip width iscomputed to be 1.2476 for a substrate height of 1 cm and relative dielectric constant of 2.1 forteflon. As with the previous case, a total of 8 simulations are performed varying the center-to-center strip spacing determined by the number of elements. ADS is used to model the scatteringparameters since the close proximity of the strip ports becomes too small to accommodaterecommended HFSS port sizes. The raw simulated data is listed in figure 5 and the coupling isgraphed in figure 6.

N X (cm) X (in) Coupling (dB) Return Loss (dB) Insertion Loss (dB)2 25.000 9.8425 -68.214 -60.255 -0.003

4 17.677 6.9597 -59.743 -63.325 -0.0036 12.500 4.9213 -51.945 -58.259 -0.003

8 9.5671 3.7666 -46.451 -46.509 -0.00410 7.7254 3.0415 -42.413 -45.221 -0.005

12 6.4705 2.5474 -39.288 -50.636 -0.007

14 5.5630 2.1902 -36.944 -61.392 -0.01116 4.8773 1.9202 -35.188 -49.844 -0.018

Figure 5: Simulated Data for Different RF Coil Strip Spacing at 172 MHz

Figure 6:Coupling vs. Number of Coils and Coil Spacing (Strip) at 172 MHz

2 4 6 8 10 12 14 16-70

-65

-60

-55

-50

-45

-40

-35

Number of Coils (in)

Coupling(dB)

1 2 3 4 5 6 7 8 9 10

-70

-65

-60

-55

-50

-45

-40

-35

Coil Spacing (in)

Coupling(dB)

Coil Spacing vs. Coupling

Number of Coils vs.Coupling


7/14

6

As expected, the coupling increases significantly as the strip-to-strip spacing decreases with theworst case being -35.188 dB for N = 16. The return loss data also indicates the ports are wellmatched confirming the strips are properly designed to 50 Ohms. Figures 4 and 6 properlycharacterize the coupling behavior per the RF coil spacing and thus establish a reference formeasuring improvement for the design that will be discussed next.

Design for Coil Decoupling

In order to isolate the individual RF coils, a design must be implemented that preventsthe individual electric and magnetic field components produced by one coil from interacting withadjacent coils. To achieve such isolation, a metal wedge connected to the ground plane isinserted between each coil to terminate any fields that may interact with other conductors.Figure 7 illustrates the wedge design and implementation on a planar substrate using bothcircular rods and strips as RF coils.

Figure 7: Wedge Design and Implementation

To simplify modeling, only two coils are simulated since the coupling between adjacentcoil pairs is much greater in comparison to others that are further spaced. The coil spacing ofparticular interest is with N = 8 elements producing a center-to-center conductor spacing of 3.76inches. Additionally, three wedges are added to the two transmission line circuit such that theoverall structure is symmetrical. The presence of the wedge should significantly decouple theRF coils since any fringing fields should terminate on the wedge itself rather than on theadjacent coil. Also, angled edges on the left and right hand side of the wedge create uniformityin the spacing between the coil and the ground plane and allow for the radiated magnetic field topropagate outward. To characterize the impact the wedges has on the coupling, several HFSS


8/14


9/14


10/14

9

Wedge Implementation for Strip Conductors

As before, the two copper strips are implemented with 3 wedges as illustrated in figure 7.The rod spacing and substrate height are fixed for all simulations while the dimensions for thewedge are varied. A total of 9 different wedge dimensions are simulated each with a differentcombination of width W and height H parameters. Figure 11 shows the simulated couplingvalues for each wedge dimension and figure 12 plots the results providing insight into thebehavior of the data.

Coupling H = 0.45'' H = 0.7'' H = 1.4''

W = 2.5'' -51.34 dB -55.14 dB -68.03 dB

W = 3.0'' -52.29 dB -56.98 dB -71.99 dB

W = 3.5'' -54.10 dB -59.61 dB -78.35 dB

Figure 11: Simulated Coupling for Different Wedge Dimensions at 172 MHz

Figure 12: Coupling for Different Wedge Dimensions at 172 MHz

As with the previous trend, a dramatic reduction in the coupling is found for larger wedgedimensions, particularly those with a height of 0.7 or 1.4. As shown in figure 5, the coupling for2 strips with N = 8 spacing without a wedge is -46.45 dB, while the presence of a wedge with(W, H) = (3.5, 1.4) decreases this value by almost 30 to -78.35 dB. Providing further insight

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

-80

-75

-70

-65

-60

-55

-50

Wedge Height (in)

Couplin

g(dB)

2.5'' Width

3.0'' Width

3.5'' Width


11/14

10

into the results, figure 13 provides HFSS screenshots of the simulated model for a wedge with(W, H) = (3.0, 0.7) indicating the magnitude of the E- and H-Fields on the geometry. Theillustrations of the field magnitudes indicate that the electric field properly terminates on thecopper wedge while the magnetic field is still able to propagate outward. Such behavior isconsistent with the results found for the simulations with the copper rods meeting the designobjectives outlined earlier.

Figure 13:HFSS Screenshot for (W, H) = (3.0, 0.7) with E- and H-Field Magnitudes


12/14

11

Conclusion

The coupling analysis for 2 RF coils implemented with both copper rods and strips onplanar substrates shows a consistent trend with respect to spacing. As the number of uniformlyspaced coils is increased in a fixed cylindrical MRI structure, the coils must be placed closer

together. As this coil-to-coil space decreases, the coupling increases at a very high rate astheoretically expected. The coil configuration of most interest is that of N = 8 uniformly spacedelements producing a center-to-center coil spacing of 3.76 inches. Per HFSS and ADSsimulations, the coupling for the RF coil copper rods is -34.108 dB while the coupling for the RFcoil copper strip is -46.451 dB. Upon implementation of the wedge, both cases produced a vastreduction in the coil-to-coil coupling with values as low as -87.79 dB for the rod case, and -78.35dB for the strip case. In each data set, the decoupling is highest when the wedge width W iswider and the wedge height H is taller with the largest reduction simulated when bothparameters were maximized. The design appears to show great promise in isolating eachindividual RF coil while still allowing the magnetic field to propagate outward towards thespecimen.


13/14

12

References

1. Jin, Jian-Ming. Electromagnetic Analysis and Design in Magnetic Resonance Imaging.Boca Raton: CRC, 1998. Print.

2. Vaughan, J.T. "7T vs. 4T: RF Power, Homogeneity, and Signal-to-noise Comparison inHead Images." Magnetic Resonance in Medicine 46.1 (2001): 24-30. Print.


14/14

13

Appendix A

Simulation files for coupling analysis of 2 coils:

Copper Rod (HFSS):

2Coil_Teflon_2cmH_N 2Coil_Teflon_2cmH_N.hfssresults

Copper Strip (ADS): Botz_Spring12_MSProject_prj

o 2Mstrip_1cm_Teflon

Simulation files for coupling analysis of 2 coils with wedge implemented:

Wedge Implementation with 2 Copper Rods (HFSS): 2Coil_Teflon_3500WedgeX3_NoBend 2Coil_Teflon_4000WedgeX3_NoBend 2Coil_Teflon_4500WedgeX3_NoBend

Wedge Implementation with 2 Copper Strips (HFSS): 2MStrip_Teflon_2500WedgeX3_NoBend 2MStrip_Teflon_3000WedgeX3_NoBend 2MStrip_Teflon_3500WedgeX3_NoBend

modeling analysis of inductive coupling for biomedical applications

Documents