Figure 3

Phase-only B₁⁺ RF shim cases for the 16-channel Tic Tac Toe RF coil. This analysis investigates the performance of several configurations using 2-way and 4-way splitters for implementation on the sTx mode. In (a, b), the phase-only RF shim cases, with the amplitude scheme derived from the eigenmodes of the RF coil (described in Fig. 1b) and in reference¹¹, were compared with RF shimming optimizations where the amplitudes of the Tx channels were randomly permutated but can only take on normalized values = 1, 1/√2, or 0.5. Approximately 300,000 optimizations were performed, presented as the colored dots. The cost functions for the RF shimming optimizations were the \({\mathrm{CV}}_{{\mathrm{B}}_{1}^{+}}\), \({\mathrm{CV}}_{{\mathrm{B}}_{1}^{+}}/{\mathrm{min}}_{{\mathrm{B}}_{1}^{+}}\) , and \({\mathrm{max}}_{{\mathrm{B}}_{1}^{+}}/{\mathrm{min}}_{{\mathrm{B}}_{1}^{+}}\), following the flowchart in (c). The region of interest for the B₁⁺ field stats is the entire head from cerebellum excluding the nasal cavities and the ears (Fig. 1c). The black arrows point to the case selected as initial condition for the next optimizations, which was chosen due to having a combination of low \({\mathrm{CV}}_{{\mathrm{B}}_{1}^{+}}\), low \({\mathrm{max}}_{{\mathrm{B}}_{1}^{+}}/{\mathrm{min}}_{{\mathrm{B}}_{1}^{+}}\), and high \({\mathrm{min}}_{{\mathrm{B}}_{1}^{+}}\). The circles represent the RF shim cases with the best \({\mathrm{CV}}_{{\mathrm{B}}_{1}^{+}}\) and the asterisks are the cases with the best \({\mathrm{max}}_{{\mathrm{B}}_{1}^{+}}/{\mathrm{min}}_{{\mathrm{B}}_{1}^{+}}\) for each cost function.