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 B₁ ⁺ mapping errors and the resulting excitation errors, and can be used to study the robustness of the designed RF pulses to B₁ ⁺ mapping errors. The proposed method may also supply useful metrics for designing RF pulses that are robust to B₁ ⁺ mapping errors.