Spring-damper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography

Modeling and simulation of underwater acoustic propagation through a random distribution of ice blocks

Acoustic propagation through a random distribution of 1 m ice cubes, from 100 to 1000 Hz, was simulated in a 3D finite element model. The effective sound speed and attenuation as functions of frequency were calculated from the simulated signals. Attempts were made to fit a number of models to the wave speed and attenuation, including single scattering, lossy water, and Biot approximations. An extended Biot model, developed for acoustic propagation in granular seabed sediments, was able to fit the simulation up to 300 Hz. Beyond this frequency, the simulation shows that multiple scattering dominates.

Wave equations for porous media described by the Biot model

Single-mode equivalent space-time representations of the acoustic wave propagating in a Biot poroelastic medium have previously been found only for asymptotic cases: In the low frequency regime, where the viscous skin depth is greater than the characteristic pore size, the time domain equivalent is represented with integer order temporal and spatial loss terms, whereas in the high frequency regime, it is represented with fractional order temporal and spatial loss terms. In the current work, a time domain representation in terms of a partial differential equation is proposed for all three wave solutions of the Biot model across all frequencies, and it is derived from the material response function of the Biot poroelastic medium with suitable approximations for the compressional modes and the dynamic permeability. The dynamic permeability in the time domain is represented by a fractional pseudo-differential operator. Optimal correction factors are introduced into the wave equation to compensate for the discrepancies in the compressional wave dispersion and attenuation. Additionally, the method for incorporating the squirt flow mechanism into the wave equation via the Extended Biot poroviscoelastic model is described. The proposed wave equation has a physical basis and satisfies the passivity criterion.

Harnessing brain waves: a review of brain magnetic resonance elastography for clinicians and scientists entering the field

Brain magnetic resonance elastography (MRE) is an imaging technique capable of accurately and non-invasively measuring the mechanical properties of the living human brain. Recent studies have shown that MRE has potential to provide clinically useful information in patients with intracranial tumors, demyelinating disease, neurodegenerative disease, elevated intracranial pressure, and altered functional states. The objectives of this review are: (1) to give a general overview of the types of measurements that have been obtained with brain MRE in patient populations, (2) to survey the tools currently being used to make these measurements possible, and (3) to highlight brain MRE-based quantitative biomarkers that have the highest potential of being adopted into clinical use within the next 5 to 10 years. The specifics of MRE methodology strategies are described, from wave generation to material parameter estimations. The potential clinical role of MRE for characterizing and planning surgical resection of intracranial tumors and assessing diffuse changes in brain stiffness resulting from diffuse neurological diseases and altered intracranial pressure are described. In addition, the emerging technique of functional MRE, the role of artificial intelligence in MRE, and promising applications of MRE in general neuroscience research are presented.

A multiple relaxation interpretation of the extended Biot model

The biphasic extended Biot poroviscoelastic model takes into account the squirt flow in grain-grain contacts and introduces the bulk and shear relaxation modes associated with it. This model has been criticized for its empirical approach, but here the constitutive equations and the time domain wave equations of the model are derived. This also makes it possible to find single phase viscoelastic equivalents for all three wave solutions of the extended Biot model. Particularly, the viscoelastic equivalents for shear wave propagation can be obtained with considerably fewer parameters than the original model. These equivalents are linear viscoelastic models with springs and dampers for the low frequencies and contain half-order spring-pots for high frequencies. For high frequencies, the non-physicality of the shear relaxation mode is highlighted. The relaxation modes of the extended Biot model are interpreted in the framework of multiple relaxation mechanisms showing that the P- and S-wave modes of the model are not much more complex than that for seawater. The model's near linear frequency dependent attenuation in the intermediate frequency range is the result of weighting each relaxation mechanism appropriately.