Magnetic Resonance Microscopy. Группа авторов

following steps:2.5

      Figure 2.5 Schematics of the sample, typically contained in a water tube.

      1 Define the required field of view: diameter Dsamp and length Lsamp. These two parameters define the inner radius of the dielectric ring rh, and its height L, respectively. The outer radius rd is kept as degree of freedom for tuning the mode at the Larmor frequency, and the material properties (permittivity ϵr and loss tangent tan δ) are used to optimize the achievable SNR.

      2 For a given list of permittivity values estimate the required outer radii list for tuning at the Larmor frequency (Ne elements in each list).

Figure 2.6 is an example of such a tuning curve, with a target frequency of 730 MHz (Larmor frequency at 17 T), for a resonator with height 10 mm.

      1 For a given list of loss tangent values (Nt values), estimate for each element of (and the associated outer radius for tuning) the corresponding SNR value (Ne × Nt values).

      Figure 2.6 Example of tuning the first TE_01δ mode frequency of a disk resonator with a given height through its outer radius for varying values of the permittivity.

This array of SNR values can be used as it is for optimizing the ceramic properties, or divided by the corresponding SNR of another probe for comparison. In Figure 2.7, we display the SNR gain (Equation 2.13) over a solenoid coil with the same inner dimensions loaded with the same sample, defined as follows:

       On the left: as a function of the ceramic relative permittivity (vertical axis) and its loss tangent (horizontal axis) for given sample properties (ϵr,samp=50, σsamp = 1 S/m).

       On the right: for the proposed prototype (ϵr = 536, tan δ = 8.10 −4) as a function of the sample relative permittivity and electrical conductivity.

(2.13)

Figure 2.7 Signal-to-noise ratio (SNR) gain displayed as a function of the ceramics properties for a given sample and fixed ring height and inner diameter (left) and of the sample properties for a fixed ceramic probe design (right). From [30].

      With the abacus that can be drawn from such calculations it is possible to design a ceramic probe working under the first TE mode with optimized properties, and to predict the SNR enhancement compared to a reference probe.

      2.3.5 Validation

The accuracy of this SNR estimation model and its constitutive steps was studied for ring resonators with dimensions fitting microscopic samples, and dielectric materials with permittivity adequate for the range of frequencies of MRM. For example, the normalized power loss term in Equation 2.8 has been evaluated from the field distribution calculated in numerical simulations and with the semi-analytical method for varying electromagnetic properties of a sample for a given probe. As can be seen in Figure 2.8, the relative error between the two approaches never exceeds 5.1%. The SNR values predicted by numerical simulations and those obtained with the semi-analytical method are compared in Figure 2.9. The maximum relative error between the two approaches is 8% in the worst-case scenario.

Figure 2.8 Relative error between the numerical simulations (CST Studio, Eigenmode Solver) and the semi-analytical model on the prediction of the normalized power losses term The error is plotted as a function of the sample conductivity and for three different sample permittivities. The ring resonator has the same properties as in [30]. The relative error is always below 5.1%. Figure reproduced with permission from [21].

      Figure 2.9 Comparison of the SNR predictions obtained with numerical simulations and with the developed semi-analytical model (SAM). The maximum relative error between the two approaches is 8%. The ring resonator has the same properties as in [30]. Data reproduced with permission from [21].

      2.4 MRM with Ceramic Coils

      Take-home message: Several experimental proofs of concept have been made in MRM with significant SNR enhancement. Two points that need to be carefully considered are temperature stability and a tuning method that does not involve additional losses.

      MR experiments involving ceramic probes have demonstrated the potential of these coils in microscopy. However, special precautions must be taken since the experimental setup differs significantly from that of conventional coils.

      2.4.1 Practical Considerations and Experimental Setup

      After designing the dielectric resonator to operate under a given resonant mode (TE_01δ or HEM_11δ) for the required B0 field strength and sample dimensions and properties, the ceramic material fitting the electromagnetic properties found for the resonator must be chosen. Ferroelectric materials based on oxide titanites are adequate since the final permittivity and loss tangent are adjusted through the relative proportions of each constituent [11].

To properly excite a resonant mode, the excitation source must induce an electromagnetic field that overlaps with that of the mode, as illustrated in Figure 2.10: the excitation source is in this case equivalent to a magnetic dipole, and its position is chosen so that it is parallel to the magnetic polarization of the desired mode.

      Figure 2.10 Example of excitation source: an electric current loop (magnetic dipole). Position required to excite the TE_01δ (left) and HEM_11δ (right) modes. The magnetic field lines (schematic) of each mode are represented. The static field direction is given by a thin arrow.

Regarding the first TE mode, analogous (in terms of field distribution) to a magnetic dipole parallel to the disk or ring axis, it is practical to use a small circular loop feed that is nonresonant at the Larmor frequency. This loop is positioned above the ceramic ring, with its axis parallel to that of the ring. In this configuration, the circulating current flowing through the loop creates an electric field distribution with the same cylindrical symmetry as that of the TE_01δ mode and therefore excites this mode. Higher-order modes with the same symmetry may be excited as well at their respective frequencies. Based on [29], in the case of small loops, we can maximize the quality factor of the whole probe (loop and dielectric resonator) by optimizing the distance between the loop and the resonator, or by changing the loop diameter at a given position.

In Figure 2.11, the influence of the loop position