Interactive Fluid Coupling Effects of Non-Neighbouring Members.

Broadband, multi-functional and parallel-processing devices are often built on coupled oscillators or arrays of resonators. Different length scales and applications determine the dominating coupling mechanism of the device. In this paper we investigate the effects of interactive fluid coupling between members of a one-dimensional array wherein only one member is actuated. We are specifically interested in studying the influence of non-neighbouring members in small-size arrays comprising of three and five members for different Reynolds numbers and gap widths between members. Our model and analysis is based on the Navier-Stokes equation for incompressible flow which is solved using a boundary integral technique resulting in the hydrodynamic coupling matrix through which added mass and damping effects are inferred. Results clearly suggest that non-neighbouring members play a significant role for most typical array configurations and therefore cannot be ignored. In particular, arrays with more than three members must account for the behaviour of such a device with all member interactions. Thus, predicting the performance of most new and emerging technologies such as sensors and biomedical devices is determined by array effects rather than local, nearest neighbour influences.

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.

Parametric-based brain Magnetic Resonance Elastography using a Rayleigh damping material model.

The three-parameter Rayleigh damping (RD) model applied to time-harmonic Magnetic Resonance Elastography (MRE) has potential to better characterise fluid-saturated tissue systems. However, it is not uniquely identifiable at a single frequency. One solution to this problem involves simultaneous inverse problem solution of multiple input frequencies over a broad range. As data is often limited, an alternative elegant solution is a parametric RD reconstruction, where one of the RD parameters (µI or ρI) is globally constrained allowing accurate identification of the remaining two RD parameters. This research examines this parametric inversion approach as applied to in vivo brain imaging. Overall, success was achieved in reconstruction of the real shear modulus (µR) that showed good correlation with brain anatomical structures. The mean and standard deviation shear stiffness values of the white and gray matter were found to be 3±0.11kPa and 2.2±0.11kPa, respectively, which are in good agreement with values established in the literature or measured by mechanical testing. Parametric results with globally constrained µI indicate that selecting a reasonable value for the µI distribution has a major effect on the reconstructed ρI image and concomitant damping ratio (ξd). More specifically, the reconstructed ρI image using a realistic µI=333Pa value representative of a greater portion of the brain tissue showed more accurate differentiation of the ventricles within the intracranial matter compared to µI=1000Pa, and ξd reconstruction with µI=333Pa accurately captured the higher damping levels expected within the vicinity of the ventricles. Parametric RD reconstruction shows potential for accurate recovery of the stiffness characteristics and overall damping profile of the in vivo living brain despite its underlying limitations. Hence, a parametric approach could be valuable with RD models for diagnostic MRE imaging with single frequency data.

Non-identifiability of the Rayleigh damping material model in magnetic resonance elastography.

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 Magnetic 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 viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-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, µI and ρI. 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 values (µR) 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 consistent poor reconstruction accuracy leading to unpredictable trends in parameter behaviour. To overcome 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 (µR) well, but identifying damping parameters (µI and ρI) is not possible without an alternative approach.

Viscosity of α-pinene secondary organic material and implications for particle growth and reactivity.

Particles composed of secondary organic material (SOM) are abundant in the lower troposphere. The viscosity of these particles is a fundamental property that is presently poorly quantified yet required for accurate modeling of their formation, growth, evaporation, and environmental impacts. Using two unique techniques, namely a "bead-mobility" technique and a "poke-flow" technique, in conjunction with simulations of fluid flow, the viscosity of the water-soluble component of SOM produced by α-pinene ozonolysis is quantified for 20- to 50-µm particles at 293-295 K. The viscosity is comparable to that of honey at 90% relative humidity (RH), similar to that of peanut butter at 70% RH, and at least as viscous as bitumen at ≤30% RH, implying that the studied SOM ranges from liquid to semisolid or solid across the range of atmospheric RH. These data combined with simple calculations or previous modeling studies are used to show the following: (i) the growth of SOM by the exchange of organic molecules between gas and particle may be confined to the surface region of the particles for RH ≤ 30%; (ii) at ≤30% RH, the particle-mass concentrations of semivolatile and low-volatility organic compounds may be overpredicted by an order of magnitude if instantaneous equilibrium partitioning is assumed in the bulk of SOM particles; and (iii) the diffusivity of semireactive atmospheric oxidants such as ozone may decrease by two to five orders of magnitude for a drop in RH from 90% to 30%. These findings have possible consequences for predictions of air quality, visibility, and climate.

Subzone based multi-frequency magnetic resonance elastography using a Rayleigh damped material model.

MR Elastography (MRE) is a relatively novel imaging technique using conventional MRI methods to assess the mechanical properties of tissues. In time-harmonic MRE, a Rayleigh, or proportional, Damping (RD) model incorporates attenuation behavior proportionally related to both elastic and inertial forces, thus providing a more sophisticated description of the elastic energy dissipation occurring in the biological tissue. The overall damping ratio can be extracted from the combined effect of these two components, while an additional measure, called Rayleigh Composition, can be calculated by the ratio between the two components. Thus, RD elastography is capable of not only reconstructing the viscoelastic properties of the material, but also providing additional information about damping behavior and structure. A 3D subzone based reconstruction algorithm using a RD material model has been developed and optimized to reconstruct the viscoelastic properties, damping behavior and elastic energy attenuation mechanism of tissue-simulating damping phantoms across multiple frequencies. Results have shown that all three iterative reconstructed parameters are in relatively close agreement for both the tofu and gelatin materials in both phantom configurations across the frequency range. Preliminary results from in-vivo healthy brain are also presented and discussed.

A computational model of hemodynamic parameters in cortical capillary networks.

The analysis of hemodynamic parameters and functional reactivity of cerebral capillaries is still controversial. To assess the hemodynamic parameters in the cortical capillary network, a generic model was created using 2D voronoi tessellation in which each edge represents a capillary segment. This method is capable of creating an appropriate generic model of cerebral capillary network relating to each part of the brain cortex because the geometric model is able to vary the capillary density. The modeling presented here is based on morphometric parameters extracted from physiological data of the human cortex. The pertinent hemodynamic parameters were obtained by numerical simulation based on effective blood viscosity as a function of hematocrit and microvessel diameter, phase separation and plasma skimming effects. The hemodynamic parameters of capillary networks with two different densities (consistent with the variation of the morphometric data in the human cortical capillary network) were analyzed. The results show pertinent hemodynamic parameters for each model. The heterogeneity (coefficient variation) and the mean value of hematocrits, flow rates and velocities of the both network models were specified. The distributions of blood flow throughout the both models seem to confirm the hypothesis in which all capillaries in a cortical network are recruited at rest (normal condition). The results also demonstrate a discrepancy of the network resistance between two models, which are derived from the difference in the number density of capillary segments between the models.