Magnetic Resonance Microscopy. Группа авторов
Чтение книги онлайн.
Читать онлайн книгу Magnetic Resonance Microscopy - Группа авторов страница 23
Название: Magnetic Resonance Microscopy
Автор: Группа авторов
Издательство: John Wiley & Sons Limited
Жанр: Химия
isbn: 9783527827251
isbn:
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
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 (TE01δ or HEM11δ) 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 TE01δ (left) and HEM11δ (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 TE01δ 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 on the resonance is investigated with numerical simulations (CST Studio, Frequency Domain Solver), in the case of a disk whose first TE mode is located at 732 MHz (Eigenmode Solver of CST Studio). It was first checked that the excited mode was the TE01δ mode: the magnetic field longitudinal component coincides in each configuration with the total magnetic field amplitude along the disk symmetry axis. As can be observed in Figure 2.11, the resonance frequency is slightly increased by the loop. The left column of Figure 2.11 shows that the maximum magnetic field at the center of the disk coincides with the minimum loop reflection coefficient, meaning the input power of the loop is transferred to the resonant mode of the disk. Also, but not shown in this figure, there exists an optimal loop diameter maximizing the magnetic field amplitude.
Figure 2.11 Influence on (left) the reflection coefficient S11 (minimum value), the magnetic field amplitude (maximum value) at the center of the resonator, and (right) the corresponding frequency of the feeding loop position relative to the dielectric disk (relative permittivity 530, loss tangent 8.10−4, diameter 18 mm, height 10 mm). (a) Varying lateral position. (b) Varying longitudinal position. There is an optimal position of the feeding loop with a minimum reflection coefficient, and a maximum transmitted power to the resonant mode.
In the model proposed above (Section 2.3) for estimating the contribution of the ceramic probe to the SNR, the contribution of the feeding loop is neglected. In fact, this contribution depends on the loop’s geometry and material. For the geometry in Figure 2.11 and the considered probe prototype, the probe efficiency was compared for a lossy copper loop and an ideal loop in a perfect electric conductor; the difference was less than 0.2% between the two values.
The first hybrid mode can be excited as well by the same loop positioned on its lateral side. СКАЧАТЬ