Perturbation analysis of the effects of B₁⁺ errors on parallel excitation in MRI

Design of RF pulses for parallel excitation using phased array transmit coils in MRI requires the B₁⁺ maps that are estimated from B₁⁺ mapping experiments. This paper characterizes the effects of B₁⁺ mapping errors on the resulting excitation pattern using a small perturbation analysis based on linearization of the Bloch equation. The accuracy of the proposed perturbation analysis is validated by Bloch equation simulations based on experimental B₁⁺ maps. The perturbation analysis builds a transparent connection between the B ₁⁺ mapping errors and the resulting excitation errors, and can be used to study the robustness of the designed RF pulses to B ₁⁺ mapping errors. The proposed method may also supply useful metrics for designing RF pulses that are robust to B₁ ⁺ mapping errors.