Eigenmode analysis of the scattering matrix for the design of MRI transmit array coils

To obtain efficient operation modes of transmit array (TxArray) coils using a general design technique based on the eigenmode analysis of the scattering matrix.

We introduce the concept of modal reflected power and excitation eigenmodes, which are calculated as the eigenvalues and eigenvectors of S^H S, where the superscript H denotes the Hermitian transpose. We formulate the normalized reflected power, which is the ratio of the total reflected power to the total incident power of TxArray coils for a given excitation signal as the weighted sum of the modal reflected power. By minimizing the modal reflected power of TxArray coils, we increase the excitation space with a low total reflection. The algorithm was tested on 4 dual-row TxArray coils with 8 to 32 channels.

By minimizing the modal reflected power, we designed an 8-element TxArray coil to have a low reflection for 7 out of 8 dimensions of the excitation space. Similarly, the minimization of the modal reflected power of a 16-element TxArray coil enabled us to enlarge the dimension of the excitation space by 50% compared with commonly employed design techniques. Moreover, we demonstrated that the low total reflected power for some critical excitation modes, such as the circularly polarized mode, can be achieved for all TxArray coils even with a high level of coupling.

Eigenmode analysis is an efficient method that intuitively provides a quantitative and compact representation of the coil's power transmission capabilities. This method also provides insight into the excitation modes with low reflection.