Multi-echo GRE-based conductivity imaging using Kalman phase estimation method

Purpose: To obtain in vivo electrical conductivity images from multi-echo gradient-echo (mGRE) sequence using a zero-TE phase extrapolation algorithm based on the Kalman method. Methods: For estimation of the zero-TE phase from the mGRE data, an iterative algorithm consisting of a combination of the Kalman filter, Kalman smoother, and expectation maximization was implemented and compared with linear extrapolation methods. Simulations were performed for verification, and phantom and in vivo studies were conducted for validation. Results: Compared with the conventional method that linearly extrapolates the zero-TE phase from the mGRE data, the phase estimation of the proposed method was more stable in situations in which nonlinear phase evolution exists. Numerical simulation results showed that the stability is guaranteed under various nonlinearity levels. Phantom study results show that this method provides improved conductivity imaging compared with the conventional methods. In vivo results demonstrate conductivity images similar to spin echo–based conductivity images with the added benefit of the acquisition of susceptibility images when using mGRE. Conclusion: The proposed method improves zero-TE phase extrapolation, especially in regions of nonlinear phase evolution. Improved conductivity imaging using mGRE can be performed.