Theoretical Performance and Sampling Limits in Steady-State Magnetic Resonance Elastography

In magnetic resonance elastography (MRE), mechanically induced motion is estimated from a time-encoded series of phase-contrast images and used to generate quantitative spatial maps of tissue stiffness. Like most dynamic/parametric applications, MRE has flexibility regarding acquisition parameter assignment, particularly with respect to motion encoding gradients (MEG). In this work, we derive the Cramer-Rao Lower Bound (CRLB) for the complex harmonic signal which completely describes mechanically induced motion in single-frequency, steady-state MRE and use this to define performance limits of experimental MRE setups. This can serve as an objective tool for developing and comparing different protocols. Using this bound, we then identify minimum number of data samples needed for complex harmonic estimation to be well-posed.

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