Complex B₁⁺ mapping with Carr-Purcell spin echoes and its application to electrical properties tomography

To present a new complex-valued B₁⁺ mapping method for electrical properties tomography using Carr-Purcell spin echoes.

A Carr-Purcell (CP) echo train generates pronounced flip-angle dependent oscillations that can be used to estimate the magnitude of B₁⁺ . To this end, a dictionary is used that takes into account the slice profile as well as T₂ relaxation along the echo train. For validation, the retrieved B₁⁺ map is compared with the actual flip angle imaging (AFI) method in a phantom (79 ε₀ , 0.34 S/m). Moreover, the phase of the first echo reflects the transceive phase. Overall, the CP echo train yields an estimate of the complex-valued B₁⁺ , allowing electrical properties tomography with both permittivity and conductivity. The presented method is evaluated in phantom scans as well as for in vivo brain at 3 T.

In the phantom, the obtained magnitude B₁⁺ maps retrieved from the CP echo train and the AFI method show excellent agreement, and both the reconstructed estimated permittivity (79 ± 3) ε₀ and conductivity (0.35 ± 0.04) S/m values are in accordance with expectations. In the brain, the obtained electrical properties are also close to expectations. In addition to the retrieved complex B₁⁺ information, the decay of the CP echo trains also yields an estimate for T₂ .

The CP sequence can be used to simultaneously provide both B₁⁺ magnitude and phase estimations, and therefore allows for full reconstruction of the electrical properties.