Magnetic Resonance Microscopy. Группа авторов

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СКАЧАТЬ ∈_r Imaging zone (height x diameter) Type of probe Dielectric material Exploited distribution Tuning technique [13] Human breast 3 128 1000 15 cm × 10 cm Volume (BaSr)TiO₃ + Mg TE_01δ (5 coupled disks) Interdisk gap adjustment [14] Wrist 7 298 80 10 cm × 10 cm Volume Water HEM_11δ Capacitors (coupling loops electronic network) [15] Cardiac (torso) 7 298 165 Surface (BaSr)TiO₃ TE_01δ (array of 8 resonators) [16] Microscopy 14.1 600 156 24 mm × 4.8 mm Volume CaTiO₃ TE_01δ Overlap with copper foils [17] Microscopy 14.1 600 323 4 mm × 3.8 mm Volume (BaSr)TiO₃ 2 coupled TE_01δ modes Overlap with copper strips [18] Microscopy 17.2 730 536 10 mm × 5.6 mm Volume (BaSr)TiO₃ + Mg TE_01δ Temperature [19] Microscopy 17.2 730 536. 10 mm × 5.6 mm twice Volume (BaSr)TiO₃ + Mg 2 coupled TE_01δ modes Temperature

      2.3 Modeling and Design Guidelines

      Take-home message: It is possible to model the first TE mode of cylindrical dielectric resonators, at the cost of manually writing the mode’s field expression and numerically solving a set of equations.

Conventional MR coils, like the solenoid, have been extensively studied from a theoretical point of view and several design tools are now readily available to optimize their performance. So far, theoretical approaches have been proposed to describe the resonant modes of dielectric resonators, but rarely in the context of their use in MRI. This implies that the noise contributions of the ceramic coil need to be identified and quantified in order to estimate the achievable SNR. Provided that transmit power is enough to reach a desired flip angle (as in the case of MRM), the SNR can be evaluated as for other transceiver probes. In this section, we describe an approximate method to calculate the magnetic and electric fields of the first TE mode (TE_01δ) of a cylindrical resonator sketched in Figure 2.1; however, the methodology used to study this particular mode can be applied to any higher-order or different mode type.

      Figure 2.1 TE_01δ mode of a cylindrical resonator: field-line schematic and notations.

      2.3.1 Dielectric Cylindrical Resonator Modes

      Describing the eigenmodes of dielectric structures relies on a similar methodology as for metallic cavities. Here we focus on resonators with circular cross sections, therefore all the equations will be expressed in a cylindrical coordinates system (ρ, θ, y) with ρ the radius, θ the azimuth, and y the altitude. ρ and θ relate to the Cartesian coordinates system (x, y, z) according to and θ = arctan z / x. The unit vectors associated with this coordinates system are denoted eρ, eθ, and ey.

We start with the Helmholtz equation, in a source-free, linear, homogeneous, and isotropic medium, verified by the electric E and magnetic H fields denoted indifferently U [20, p. 16]. ω is the angular frequency, μ the medium permeability, the medium complex permittivity (with j the unit imaginary number), and k is the complex wavenumber such that with ky and kρ the wavenumber components along the y- and the ρ-directions, respectively. The method of longitudinal components [17] uses the decomposition of the vector field U into its longitudinal Uyey and transverse UT = U − Uyey components. These components are solutions of the scalar and vector Helmholtz equations, respectively.

(2.1)

Assuming that the longitudinal component Uy can be written as the product of three functions, one for each space СКАЧАТЬ