Non-identifiability of the Rayleigh damping material model in Magnetic Resonance Elastography Andrii Y. Petrov a,⇑ , J. Geoffrey Chase b , Mathieu Sellier b , Paul D. Docherty 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 article info Article history: Received 7 May 2013 Received in revised form 24 July 2013 Accepted 23 August 2013 Available online 7 September 2013 Keywords: Magnetic Resonance Elastography Nonlinear inversion Rayleigh damping Model identifiability Mechanical properties Medical imaging abstract Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Mag- netic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear visco- elasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a sub- space-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, l I and q I . Results show the non-identifiability of the RD model at a single input frequency based on a structural analysis with a series of supporting experimental phantom results. The estimated real shear modulus val- ues (l R ) were substantially correct in characterising various material types and correlated well with the expected stiffness contrast of the physical phantoms. However, estimated RD parameters displayed con- sistent poor reconstruction accuracy leading to unpredictable trends in parameter behaviour. To over- come this issue, two alternative approaches were developed: (1) simultaneous multi-frequency inversion; and (2) parametric-based reconstruction. Overall, the RD model estimates the real shear shear modulus (l R ) well, but identifying damping parameters (l I and q I ) is not possible without an alternative approach. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction Soft tissue property identification is valuable to a number of medical applications, such as diagnostic purposes [1–3], surgery simulations [4,5], and virtual-reality based techniques. The elastic properties of soft tissues are closely related to their consistency, biological structure, and pathological conditions. Therefore, imaging of mechanical properties of tissue in vivo can improve non-invasive tissue characterisation and help in early diagnosis of various pathologies. Magnetic Resonance Elastography (MRE) can directly visualise and measure tissue elasticity [6–9], and has been applied to resolve stiffness characteristics of a variety human tissues and organs, such as muscle [10–13], breast [14–18], liver [19–21] and the brain [22–30]. MRE acquisition requires application of mechanical waves to tissue within the MRI, phase-contrast MR pulse sequence extended with motion encoding gradient (MEGs), and sophisti- cated inverse problem methods to identify an elastic modulus map of the tissue. The choice of the constitutive model is crucial for accurate reproduction of the observed mechanical response. To date, recon- struction approaches generally assumed tissue to be linearly elas- tic [31], although some groups have employed more advanced models, such as viscoelasticity (VE) [24,27,28] and poroelasticity [32]. Rayleigh damping (RD) is an extension of VE, which utilises an additional damping parameter to provide a more complex description of the elastic energy attenuation. Additional damping effects can improve model accuracy by providing a better data-model correlation [33]. In biological tissue, attenuation, or damping, occurs due to the complex interaction between micro structural components in the soft tissue matrix. Therefore, the model that more accurately maps damping proper- ties might bring additional diagnostic potential with regards to dif- ferentiating tissue structure and composition. Depending on consistency, this particular tissue type can display different damping properties. More specifically, tissue composed from tightly arranged cells displays less damping compared to the 0025-5564/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.mbs.2013.08.012 ⇑ Corresponding author. Tel.: +64 21702062. E-mail addresses: andrew.petrov@pg.canterbury.ac.nz (A.Y. Petrov), geoff.cha- se@canterbury.ac.nz (J. Geoffrey Chase), mathieu.sellier@canterbury.ac.nz (M. Sell- ier), paul.docherty@canterbury.ac.nz (P.D. Docherty). Mathematical Biosciences 246 (2013) 191–201 Contents lists available at ScienceDirect Mathematical Biosciences journal homepage: www.elsevier.com/locate/mbs