Dennis Klomp^{1}

Ever wanted to build your own multi-tuned RF coil to enable metabolic imaging? This 30 minute session will start from scratch and ends with you capable to make the most advanced multi-tuned, transmit and receive coil array (in theory)...

Coil Efficiency The number one determinant in MR technology for optimal SNR is the RF coil that can be used to transmit RF for excitation and receives the MR signals. The SNR obtained with a receiver coil is proportional to the efficiency of the coil, which according to the principle of reciprocity [1] is equal to the efficiency of the coil as a transmitter. The efficiency of an RF coil is expressed as the magnetic field strength per unit of applied RF power as a quadratic relation (in T/√W). Circularly polarized fields and B1 field strength A magnetic field can be generated by an electrical current flow (I) through a conductor. Per unit current the strength and orientation of this field in the object that is measured can be approximated using the law of Biot-Savart (as long as the wavelength of the RF is larger than the size of the object, which is the case for mouse MR at field strength up to 20T [2], or human head MR up to 3T, or other nuclear MR at even higher fields): (formula in Fig 3)

, (1) where dl is the length of a part of the conductor, r is a vector pointing from the location of the conductor part to the location of the point in space from where the magnetic field strength is calculated, and μ0 is the magnetic permeability constant in vacuum (i.e. 4π x 10-7). In order to create a B1 field that rotates around the main magnetic field, a second conductor is required that generates an equal but orthogonal field with respect to the first conductor. When the electrical current through the orthogonal conductors oscillates with a frequency equal to the Larmor precession, with a 90º-phase difference, a rotating magnetic field (circularly polarized) is generated (Fig. 1). Compared to a single coil setup (linearly polarized field) this quadrature setup requires twice as less power for the same B1, hence improves SNR by 41% (√2). Tuning and Matching An optimal transformation of RF power from an RF amplifier into current through the conductors is obtained when the conjugated impedance (Z*) of the amplifier matches the transformed impedance (Z) of the conductor. The impedance of the conductor can be split into a real part that absorbs power (i.e. resistance R) and an imaginary part that can temporarily store and release power (i.e. admittance X). The resistance of the conductor that generates a magnetic field in a sample consists of three parts: one part (RL) that depends on the conductivity, length and cross-section of the conductor, including skin effects at high operating frequencies; one part (RR) is related to radiation losses, which relates to the operating frequency, size of the conductor and the electro magnetic properties of the surroundings; and finally a part (RS) that is related to the relative power absorbed due to eddy-currents and electric fields in conductive tissue. The admittance of the conductor is linearly proportional to the frequency of operation and the inductance (L) of the conductor, where L can be calculated as (see equation in Figure 4): , (2) where the conductor encloses a loop (coil) with a surface area A. In total, the impedance of the conductor is: Z=RL+RR+RS+jωL, where j=√-1. This impedance needs to be transformed to the impedance of the RF amplifier (typically 50Ω), which can be realized by a simple capacitive network. A parallel capacitor (Ct) can be connected to both ends of the conductor, which creates a parallel impedance Zp (see equation in Fig 5). (3) In case the real part of Zp is tuned to 50Ω (using the appropriate value for Ct), the imaginary part of Zp can be eliminated by adding a capacitor (Cm) in series with Zp with admittance equal to the negative admittance of Zp. In this case the impedance of the inductor parallel to Ct and in series with Cm matches the 50Ω of the RF amplifier (Fig. 2).

1. Hoult DI, Richards RE. Signal-to-noise ratio of nuclear magnetic-resonance experiment. J. Magn. Reson. 1976;24(1):71-85

2. Doty FD, Entzminger G, Kulkarni J, Pamarthy K and Staab JP. Radio frequency coil technology for small-animal MRI. NMR Biomed. 2007; 20: 304–325

3. Adriany G, Gruetter R. A half-volume coil for efficient proton decoupling in humans at 4 tesla. J Magn Reson. 1997 Mar;125(1):178-84.

4. Klomp DW, Renema WK, van der Graaf M, de Galan BE, Kentgens AP, Heerschap A. Sensitivity-enhanced 13C MR spectroscopy of the human brain at 3 Tesla. Magn Reson Med. 2006 Feb;55(2):271-8.

5. Klomp DW, van de Bank BL, Raaijmakers A, Korteweg MA, Possanzini C, Boer VO, van de Berg CA, van de Bosch MA, Luijten PR. (31) P MRSI and (1) H MRS at 7 T: initial results in human breast cancer. NMR Biomed. 2011 Dec;24(10):1337-42.

6. Brown R, Lakshmanan K, Madelin G, Parasoglou P. A nested phosphorus and proton coil array for brain magnetic resonance imaging and spectroscopy. Neuroimage. 2016 Jan 1;124(Pt A):602-611.

7. van der Velden TA, Italiaander M, van der Kemp WJ, Raaijmakers AJ, Schmitz AM, Luijten PR, Boer VO, Klomp DW.Radiofrequency configuration to facilitate bilateral breast (31) P MR spectroscopic imaging and high-resolution MRI at 7 Tesla. Magn Reson Med. 2015 Dec;74(6):1803-10

8. Fitzsimmons JR, Brooker HR, Beck B. A Comparison of double-tuned surface coils. Magn. Reson. Med. 1989; 10: 302–309.

Graphical presentation
of the creation of a circularly polarized magnetic field (B1), using
two (A and B) orthogonally positioned coils in which a sinusoidal current (I) flows
with a 90˚ phase difference.

The
conductors of the RF coil have a net inductance (L) and resistive losses (R),
which are matched by capacitors (C) to the impedance of the RF amplifier.

Equation 1

Equation 2

Equation 3