Multi-frequency Rayleigh damped elastography: in silico studies

Rayleigh damping (RD) is commonly used to model energy attenuation for analyses of structures subjected to dynamic loads. In time-harmonic Magnetic Resonance Elastography (MRE), the RD model was shown to be non-identifiable at a single frequency data due to the ill-posed nature of the imaginary components describing energy dissipation arising from elastic and inertial forces. Thus, parametrisation or multi-frequency (MF) input data is required to overcome the fundamental identifiability issue of the model. While parametrisation allows improved accuracy of the identified parameters, simultaneous inversion using MF input data is a prerequisite for theoretical identifiably of the model. Furthermore, to establish good practical identifiability, frequencies should be separated over a wide range to produce different dynamic response. This research investigates the effects on practical identifiability of the RD model using MF data over different combinations of frequencies in noise-free heterogenous simulated geometry and compares the outcomes to reconstruction result based on single frequency input data. We tested eight frequencies in silico for a phantom type geometry comprises three independent material regions characterised by different mechanical properties. Combinations of two near or well separated frequencies are used to test the separation necessary to obtain accurate results, while the use of four or eight simultaneous frequencies is used to assess robustness. Results confirm expected non-identifiability of the RD model given single frequency input data. Practical identifiability of the RD parameters improved as more input frequencies were used for simultaneous inversion and when two frequencies were well separated. Best quality reconstruction results were achieved using full range data comprising eight available frequencies over a wide range. The main outcome is that high quality motion data over at least two frequencies over a wide range is required for establishing minimal practical identifiability of the model, while quality of the practical identifiability increases proportionally with more input frequencies used. Further simulation studies are required to determine acceptable signal-to-noise ratio (SNR) thresholds in motion data for accurate inversion of the RD parameters.