Biomedical Signal Processing and Control 13 (2014) 270–281 Contents lists available at ScienceDirect Biomedical Signal Processing and Control jo ur nal homep age: www.elsevier.com/locate/bspc Multi-frequency inversion in Rayleigh damped Magnetic Resonance Elastography Andrii Y. Petrov a,∗ , Paul D. Docherty b , Mathieu Sellier b , J. Geoffrey Chase b a Centre for Bioengineering, Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand b Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand a r t i c l e i n f o Article history: Received 6 December 2013 Received in revised form 15 April 2014 Accepted 17 April 2014 Keywords: Magnetic Resonance Elastography Rayleigh damping Multi-frequency inversion Parametric inversion Model identifiability Mechanical properties a b s t r a c t Magnetic Resonance Elastography (MRE) is able to identify mechanical properties of biological tissues in vivo based on underlying assumptions of the model used for inversion. Models, such as the linearly elastic or viscoelastic (VE), can be used with a single input frequency data and can produce a reasonable estimate of identified parameters associated with mechanical properties. However, more complex mod- els, such as the Rayleigh damping (RD) model, are not identifiable given single frequency data without significant a priori information under certain conditions, thus limiting diagnostic potential. To over- come this limitation, two approaches have been postulated: simultaneous inversion across multiple input frequencies and a parametric approach, when only single frequency data is available. This research compares simultaneous multi-frequency (MF) RD reconstructions using both zero-order and power-law (PL) models with parametric reconstructions for a series of tissue-simulating phantoms, made of tofu and gelatine materials, tested at 4 frequencies (50 Hz, 75 Hz, 100 Hz and 125 Hz) that are commonly applied in clinical MRE examinations. Results indicate that accurate delineation of RD based properties and concomitant damping ratio ( d ) using MF inversion is still a challenging task. Specific results showed that the real shear modulus ( R ) can be reconstructed well, while imaginary components representing attenuation ( I and  I ) had much lower quality. However, overall trends correlate well with the expected higher damping levels within the saturated tofu material compared to stiff gelatine in both phantoms. Depending on the phantom configuration, measured  R values within the tofu and gelatine materials ranged from 4.77 to 7 kPa and 15.5 to 16.3 kPa, respectively, while damping levels were 11–19% and 3.1–4.3%, as expected. Correlation of the  R and  d values with previously reported result measured by independent mechanical testing and VE based MRE is acceptable, ranging from 48 to 60%. Both PL and zero-order models produced similar qualitative and quantitate results, thus no significant advantage of the PL model was noted to account for dispersion characteristics of these types of materials. The relatively narrow range of frequencies used in this study limited practical identifiability and can thus produce a potentially false assurance of identifiability of the model parameters. We conclude that application of multiple input frequencies over a wide range, as well as selection of an appropriate model that can accurately account for dispersion characteristics of given materials are required for achieving robust practical identifiability of the RD model in time-harmonic MRE. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction In time-harmonic Magnetic Resonance Elastography (MRE), a single input frequency is a common experimental approach for mechanical property reconstruction. It is less time consuming and ∗ Corresponding author. E-mail addresses: petrov.bme@gmail.com, petrov@hawaii.edu (A.Y. Petrov), paul.docherty@canterbury.ac.nz (P.D. Docherty), mathieu.sellier@canterbury.ac.nz (M. Sellier), geoff.chase@canterbury.ac.nz (J.G. Chase). only requires a single patient examination. A number of stud- ies investigated various models for both static [1,2] and dynamic [3–11] MRE methods using single frequency data. These models include linearly elastic [12–14], viscoelastic (VE) [15–20] and even poroelastic [21–23] models. Two main limitations prevent single frequency approaches from providing accurate approximations of the tissue response. The first is associated with the dispersive nature of the complex shear modulus at different frequencies and thus quantitative estimates acquired at a particular excitation frequency do not represent the true static (at 0 Hz) values of material constants. The second arises http://dx.doi.org/10.1016/j.bspc.2014.04.006 1746-8094/© 2014 Elsevier Ltd. All rights reserved.