Complex B(1) (+) mapping with Carr‐Purcell spin echoes and its application to electrical properties tomography

PURPOSE: To present a new complex‐valued B(1) (+) mapping method for electrical properties tomography using Carr‐Purcell spin echoes. METHODS: A Carr‐Purcell (CP) echo train generates pronounced flip‐angle dependent oscillations that can be used to estimate the magnitude of B(1) (+). To this end, a dictionary is used that takes into account the slice profile as well as T(2) relaxation along the echo train. For validation, the retrieved B(1) (+) map is compared with the actual flip angle imaging (AFI) method in a phantom (79 ε(0), 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 B(1) (+), 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. RESULTS: In the phantom, the obtained magnitude B(1) (+) maps retrieved from the CP echo train and the AFI method show excellent agreement, and both the reconstructed estimated permittivity (79 ± 3) ε(0) 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 B(1) (+) information, the decay of the CP echo trains also yields an estimate for T(2). CONCLUSION: The CP sequence can be used to simultaneously provide both B(1) (+) magnitude and phase estimations, and therefore allows for full reconstruction of the electrical properties.