Viscoelastic Wall Research Articles

Changes in the response of viscoelastic solids to changes in their internal structure

The manner in which a viscoelastic body relaxes or creeps is determined by the viscoelastic body’s internal structure. In this paper, we are primarily interested in the changes in the body’s internal clock due to the changes in its structure. This internal clock’s working can be modified due to the effect of temperature, moisture, and electromagnetic fields, thereby degrading or enhancing the response of the viscoelastic body. Within a purely mechanical context, by degradation or enhancement, one means the decrease or increase in the load carrying capacity. Such degradation or enhancement due to the effect of moisture and temperature in elastic solids has been studied earlier. In this paper, we extend these ideas to the response of viscoelastic solids, particularly through the alteration of the viscoelastic body’s internal clock. To evaluate the efficacy of the model that we have developed, we study a very interesting problem, a biological application wherein the viscoelastic uterine wall’s stress relaxation characteristic changes significantly. The constitutive relation that is developed, and more importantly the methodology that is being put into place, can be used to describe a variety of problems in polymer mechanics and biomechanics and is not limited to the special example that is considered.

Wave induced oscillatory and steady flows in the annulus of a catheterized viscoelastic tube

A perturbation analysis based on equations of motion in Lagrangian form is presented for the oscillatory and time-mean viscous flows induced by a propagating wave of small amplitude in an annulus with a viscoelastic outer wall. Owing to the steady streaming effect, the existence of a catheter in a blood vessel brings in an additional steady pressure gradient, a correction to that predicted by the linear theory, and an additional steady shear stress, which may increase the possibility of hemolysis of red blood cells.

Stability of pressure-driven flow in a deformable neo-Hookean channel

The stability of pressure-driven flow in a rectangular channel with deformable neo-Hookean viscoelastic solid walls is analysed for a wide range of Reynolds numbers (from Re ≪ 1 to Re ≫ 1) by considering both sinuous and varicose modes for the perturbations. Pseudospectral numerical and asymptotic methods are employed to uncover the various unstable modes, and their stability boundaries are determined in terms of the solid elasticity parameter Γ = Vη/(ER) and the Reynolds number Re = RV ρ/η; here V is the maximum velocity of the laminar flow, R is the channel half-width, η and ρ are respectively the viscosity and density of the fluid and E is the shear modulus of the solid layer. We show that for small departures from a rigid solid, wall deformability could have a destabilizing or stabilizing effect on the Tollmien–Schlichting (TS) instability (a sinuous mode) depending on the solid-layer thickness. Upon further increase in solid deformability, the TS mode coalesces with another unstable mode (absent in rigid channels) giving rise to a single unstable mode which extends to very low Reynolds number (<1) for highly deformable walls. There are other types of instabilities that exist only due to wall deformability. In the absence of inertia (Re = 0), there is a short-wave instability of both sinuous and varicose modes arising due to the discontinuity of the first normal stress difference across the fluid–solid interface. For both sinuous and varicose modes, it is shown that inclusion of inertia is important even for Re ≪ 1, wherein a new class of long-wavelength unstable modes are predicted which are absent at Re = 0. These unstable modes are a type of shear waves in an elastic solid which are destabilized by the flow. These long- and short-wave instabilities are absent if a simple linear elastic model is used for the solid. At intermediate and high Re, upstream and downstream travelling waves of both sinuous and varicose modes become unstable. We show that sinuous and varicose modes become critical in different parameter regimes, thereby demonstrating the importance of capturing all the unstable modes. Inclusion of dissipative effects in the neo-Hookean model is generally shown to play a stabilizing role on the instabilities due to both sinuous and varicose modes. The predicted instabilities will be important for the flow of liquids (with viscosity ≥ 10−3 Pa s) in deformable channels of width ≤1 mm, and with shear modulus ≤ 105 Pa.

3P-49 Flow-Mediated Change in Viscoelasticity of Radial Arterial Wall Measured by Automated Detection of Wall Boundaries(Poster Session)

3P-49 Flow-Mediated Change in Viscoelasticity of Radial Arterial Wall Measured by Automated Detection of Wall Boundaries(Poster Session)

A New Closed Cell, Horizontal Magnetic Tweezer

We report on the development of a magnetic force transducer or tweezer that can apply piconewton forces on single DNA molecules in the focus or horizontal plane. Since changes in the DNA's end-to-end extension are coplanar with the pulling force there is no requirement to continually refocus the tethered beads thus considerably simplifying single molecule micromanipulation experiments in our setup. The DNA constructs (γ-DNA end-labeled with a 3μm polystyrene bead and a 2.8μm magnetic sphere) and buffer are introduced into a 200μL to 500 μL closed cell created by using two glass slides separated by 1mm spacers and a thin viscoelastic perimeter wall. This closed cell configuration isolates our sample and produces low-noise force and extension measurements. Breaching the viscoelastic barrier are five pipettes: a 1-2μm inner diameter suction pipette used for capturing the polystyrene bead, a magnet-tipped pipette used to pull the magnetic sphere, a 0.5mm-inner-diameter injection pipette used to introduce proteins of interest, and two 0.5mm-inner-diameter pipettes used to maintain flow. The suction micropipette and the injection pipette are rigidly coupled and positioned by a manual three axis manipulator that can produce continuous displacements of 15mm, 25mm and 25mm in the x-, y-, and z-axis respectively. The magnet-tipped pipette is controlled by a motorized two axis micromanipulator capable of continuously spanning the full width of the cell. A motorized micromanipulator with a defined 157nm step size maneuvers the cell over a 32X/0.40NA objective and between the two mechanical manipulators. Initial tests show the capability of the device to easily and repeatedly find, capture, and manipulate end-labeled DNA constructs.

The Wall Properties Effect on Peristaltic Transport of Micropolar Non‐Newtonian Fluid with Heat and Mass Transfer

The problem of the unsteady peristaltic mechanism with heat and mass transfer of an incompressible micropolar non‐Newtonian fluid in a two‐dimensional channel. The flow includes the viscoelastic wall properties and micropolar fluid parameters using the equations of the fluid as well as of the deformable boundaries. A perturbation solution is obtained, which satisfies the momentum, angular momentum, energy, and concentration equations for case of free pumping (original stationary fluid). Numerical results for the stream function, temperature, and concentration distributions are obtained. Several graphs of physical interest are displayed and discussed.

血管粘弾性インデックスの変化を指標とした機械的侵害刺激に対する疼痛の定量的評価

血管粘弾性インデックスの変化を指標とした機械的侵害刺激に対する疼痛の定量的評価

Flow-Mediated Change in Viscoelastic Property of Radial Arterial Wall Measured by 22 MHz Ultrasound

The endothelial dysfunction is considered to be an initial step in atherosclerosis. Additionally, it was reported that the smooth muscle, which constructs the media of the artery, changes its characteristics owing to atherosclerosis. Therefore, it is essential to develop a method of assessing the regional endothelial function and mechanical properties of the arterial wall. To evaluate the endothelial function, a conventional technique of measuring the transient change in the diameter of the brachial artery caused by flow-mediated dilation (FMD) after the release of avascularization is used. However, this method can not evaluate the mechanical properties of the wall. We previously developed a method for the simultaneous measurements of waveforms of radial strain and blood pressure in the radial artery. In this study, the viscoelasticity of the arterial wall was estimated from the measured stress–strain relationship using the least-squares method and the transient changes in the mechanical properties of the arterial wall ware revealed. From in vivo experimental results, the stress–strain relationship showed a hysteresis loop and viscoelasticity was estimated by the proposed method. The slope of the loop decreased owing to FMD, which resulted in the decrease in estimated elastic modulus. The increase in the area of the loop occurred after recirculation, which corresponds to the increase in the ratio of the loss modulus (depends on viscosity) to the elastic modulus when the Voigt model is assumed. In this study, the variance in estimates was evaluated by in vivo measurement for 10 min. The temporal decrease in static elasticity after recirculation due to FMD was much larger than the evaluated variance. These results show a potential of the proposed method for the thorough analysis of the transient change in viscoelasticity due to FMD.

A Novel Wave Reflection Model of the Human Arterial System

A frequency domain distributed 55 segment arterial model was constructed from the reflection perspective to predict pressure waveforms in the large systemic arteries. At any node, the predicted pressure waveform was the combination of a forward propagating waveform and a number of repeatedly reflected waveforms from any possible sites. This approach ensured that any single reflected waveform could be traced back to its origin, and thus the causal-effect relation would be precisely known. This model was evaluated in terms of branch reflection coefficient, terminal vascular bed behavior, and wall viscoelasticity. It was found that the model predicted pressure waveforms were most sensitive to the branch reflection coefficient, and this led to the adoption of the zero-forward reflection assumption at branches. The model-predicted pressure waveforms compared favorably with realistic blood pressure waveforms, especially in the upper limbs. For lower limbs, finer segmentation could further improve the predictions.

Frequency effects on fatigue crack growth and crack tip domain-switching behavior in a lead zirconate titanate ceramic

The microstructural origins of the effect of frequency on the electrical fatigue behavior of pre-cracked soft ferroelectric Pb(Zr 0.48Ti 0.52)O 3 is investigated by means of a high spatial resolution hard X-ray synchrotron source. It is found that there is a strong link between the frequency of the applied bipolar field, domain-switching behavior in terms of ferroelastic reorientation of the domains around the crack tip and the resultant crack growth. The crack growth is accentuated under increased ferroelastic switching and, in particular, found to be more pronounced under low-frequency loading. The concept of domain wall viscoelasticity is applied to explain why lower frequencies accelerate crack growth under a bipolar electric field.

Validation of a one-dimensional model of the systemic arterial tree

A distributed model of the human arterial tree including all main systemic arteries coupled to a heart model is developed. The one-dimensional (1-D) form of the momentum and continuity equations is solved numerically to obtain pressures and flows throughout the systemic arterial tree. Intimal shear is modeled using the Witzig-Womersley theory. A nonlinear viscoelastic constitutive law for the arterial wall is considered. The left ventricle is modeled using the varying elastance model. Distal vessels are terminated with three-element windkessels. Coronaries are modeled assuming a systolic flow impediment proportional to ventricular varying elastance. Arterial dimensions were taken from previous 1-D models and were extended to include a detailed description of cerebral vasculature. Elastic properties were taken from the literature. To validate model predictions, noninvasive measurements of pressure and flow were performed in young volunteers. Flow in large arteries was measured with MRI, cerebral flow with ultrasound Doppler, and pressure with tonometry. The resulting 1-D model is the most complete, because it encompasses all major segments of the arterial tree, accounts for ventricular-vascular interaction, and includes an improved description of shear stress and wall viscoelasticity. Model predictions at different arterial locations compared well with measured flow and pressure waves at the same anatomical points, reflecting the agreement in the general characteristics of the "generic 1-D model" and the "average subject" of our volunteer population. The study constitutes a first validation of the complete 1-D model using human pressure and flow data and supports the applicability of the 1-D model in the human circulation.

Modelling the mechanical properties of yeast cells

An analytical model has been developed to describe the compression of a single yeast cell between parallel flat surfaces. Such cells were considered to be thin walled, liquid filled, spheres. Because yeast cells can be compressed at high deformation rates, time dependent effects such as water loss during compression and visco-elasticity of the cell wall could be and were neglected in the model. As in previously published work, a linear elastic constitutive equation was assumed for the material of the cell walls. However, yeast compression to failure requires large deformations, with high wall strains and associated rotations. New model equations appropriate to such high strains with rotations were therefore developed, based on work-conjugate Kirchhoff stresses and Hencky strains. This is an improvement on the earlier use of infinitesimal strains, and on the alternative of Green strains and 2nd Piola–Kirchhoff stresses. It is shown that the choice of stress and strain definition has a significant influence on model predictions for given wall material properties, and will affect estimates of the wall elastic modulus or other wall material property parameters obtained by fitting experimental data.

Structural and Nanomechanical Properties of Termitomyces clypeatus Cell Wall and Its Interaction with Chromium(VI)

Alterations of cell surface properties accompanying the complex life cycle of Termitomyces clypeatus have been monitored using atomic force microscopy (AFM). A new hyphae/mycelium is developed on cell division, and the cell wall of the mycelium undergoes a process of internal reorganization (or maturation) followed by morphological and chemical alterations. The changes of the surface ultrastructures during the growth process are correlated to the corresponding changes in relative viscoelasticity and rigidity of the cell wall by employing force spectroscopy. The cell wall rigidity and elasticity are found to be 0.34+/-0.02 N/m and 27.5+/-2.1 MPa, respectively, at the early logarithmic phase, on maturation increase to reach 0.81+/-0.08 N/m and 92.5+/-12 MPa, respectively, at the stationary phase, and thereafter decrease to 0.62+/-0.06 N/m and 61.6+/-6.6 MPa at the death phase. The alterations of the ultrastructural and nanomechanical properties of the cell surface as functions of growth phases affect the interaction involving chromium and T. clypeatus.

Analysis of Viscoelastic Wall Properties in Ovine Arteries

In this paper, we analyze how elastic and viscoelastic properties differ across seven locations along the large arteries in 11 sheep. We employ a two-parameter elastic model and a four-parameter Kelvin viscoelastic model to analyze experimental measurements of vessel diameter and blood pressure obtained in vitro at conditions mimicking in vivo dynamics. Elastic and viscoelastic wall properties were assessed via solutions to the associated inverse problem. We use sensitivity analysis to rank the model parameters from the most to the least sensitive, as well as to compute standard errors and confidence intervals. Results reveal that elastic properties in both models (including Young's modulus and the viscoelastic relaxation parameters) vary across locations (smaller arteries are stiffer than larger arteries). We also show that for all locations, the inclusion of viscoelastic behavior is important to capture pressure-area dynamics.

Flow‐mediated change in viscoelasticity of radial arterial wall measured by 22‐MHz ultrasound

The endothelial dysfunction is considered to be an initial step of atherosclerosis. Moreover, it was reported that the smooth muscle, which constructs the media of the artery, changes its characteristics due to early‐stage atherosclerosis. Therefore, it is essential to develop a method for assessing the regional endothelial function and mechanical property of the arterial wall. There is an ultrasound‐based conventional technique to measure the change in inner diameter of the brachial artery caused by flow‐mediated dilation (FMD) after release of avascularization. In this study, the transient change in the mechanical property of the arterial wall was further revealed by measuring the stress‐strain relationship during each heartbeat. For this measurement, the minute change in thickness (strain) of the radial artery was measured using the ultrasonic phased tracking method, together with the waveform of blood pressure (stress) which was continuously measured at the radial artery. From in vivo experiments, it ...

Viscoelastic Characteristics of In Vitro Vital and Devitalized Rat Aorta and Human Arterial Prostheses

The arterial wall viscoelasticity plays an essential role in the vascular responsiveness to vasoactive drugs or pathologies. The aim of this investigation was to derive and compare resonance curve (RC), natural frequency (f(0)), dynamic modulus of elasticity (E'), and coefficient of viscosity (beta) of (i) vital and devitalized preparations of rat thoracic and abdominal aorta, (ii) human arterial prostheses, and to study the histomorphology of vital and devitalized rat aorta. The method of low frequency forced oscillations was employed. RC of vital preparations showed a hardening type of elasticity whereas in devitalized preparations it was of softening type. E' increased nonlinearly, f(0) decreased and beta increased linearly with equivalent intraluminal pressure (p(eqi)). Distensibility of abdominal aorta was lower than thoracic aorta. Distensibility decreased with increasing p(eqi). E', f(0), and beta increased significantly after devitalization. It was suggested that postmortem viscoelastic characteristics should not be used directly to specify the vital arteries viscoelasticity. RC of human prostheses showed a softening type of elasticity. Arterial prostheses have low circumferential distensibility with E'-values higher than reported in the literature for human arteries. The method of forced oscillations could be employed for studying the arterial wall biomechanics and viscoelasticity of arterial prostheses.

A viscoelastic model of arterial wall motion in pulsatile flow: implications for Doppler ultrasound clutter assessment

The existing computational model studies of pulsatile blood flow in arteries have assumed either rigid wall characteristics or elastic arterial wall behavior with wall movement limited to the radial direction. Recent in vivo studies have identified significant viscoelastic wall properties and longitudinal wall displacements over the cardiac cycle. Determining the nature of these movements is important for predicting the effects of ultrasound clutter in Doppler ultrasound measurements. It is also important for developing an improved understanding of the physiology of vessel wall motion. We present an analytically-based computational model based on the Womersley equations for pulsatile blood flow within elastic and viscoelastic arteries. By comparison with published in vivo data of the human common carotid artery as well as uncertainty and sensitivity analyses, it is found that the predicted waveforms are in reasonable quantitative agreement. Either a pressure, pressure gradient or volumetric flow rate waveform over a single cardiac cycle is used as an input. Outputs include the pressure, pressure gradient, radial and longitudinal fluid velocities and arterial wall displacements, volumetric flow rate and average longitudinal velocity. It is concluded that longitudinal wall displacements comparable to the radial displacements can be present and should be considered when studying the effects of tissue movement on Doppler ultrasound clutter.

Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall

In this paper we continue the study of a fluid-structure interaction problem with the non periodic case. We consider the non stationary flow of a viscous fluid in a thin rectangle with an elastic membrane as the upper part of the boundary. The physical problem which corresponds to non homogeneous boundary conditions is stated. By using a boundary layer method, an asymptotic solution is proposed. The properties of the boundary layer functions are established and an error estimate is obtained.

3P7a-12 Accuracy Evaluation for High-Frequency Ultrasonic Measurement of Viscoelasticity of Radial Arterial Wall by Basic Experiments(Poster Session)

3P7a-12 Accuracy Evaluation for High-Frequency Ultrasonic Measurement of Viscoelasticity of Radial Arterial Wall by Basic Experiments(Poster Session)

Experimental Cyclic Performance of Viscoelastic Gypsum Connections and Shear Walls

The shear capacity of gypsum sheathed shear walls is typically neglected in areas of high seismicity due to the susceptibility of conventional drywall screw connections to damage caused by earthquakes. This paper presents an alternative to the conventional screwed sheathing connection found in wood-framed gypsum shear walls. A viscoelastic (VE) polymer was inserted between the sheathing and the stud framing. A sheathing connection study and shear wall study were performed, and the results of the VE connection show a dramatic increase in stiffness and energy dissipation over the conventional screwed connection. Energy dissipation increases 632% for the sheathing connection and 510% for the shear wall. Stiffness of the shear wall also improves. The VE polymer improves structural performance while resisting damage when subjected to shear displacements up to 18 mm by providing a constant source of energy dissipation. This new VE sheathing connection may allow for weak or nonstructural materials, such as gypsum wallboard, to be used as structural elements for design purposes while reducing the risk of costly damages during seismic events.