Читать книгу Magnetic Resonance Microscopy - Группа авторов - Страница 38

One way of designing a ceramic probe as depicted in Figure 2.5 consists of studying how the achievable SNR varies with the probe dimensions and/or material properties for a given sample. In the following, the required field of view constrains the ring’s inner diameter and height, the ceramic material properties optimize the SNR value, and the outer diameter and the permittivity are used for tuning the resonance at the Larmor frequency. Therefore, designing the ceramic probe consists of the 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.