A poroelastic continuum model of the cupula partition and the response dynamics of the vestibular semicircular canal.

Using mixture theory, an axisymmetric continuum model is presented describing the response dynamics of the vestibular semicircular canals to canal-centered head rotation in which the cupula partition is modeled as a poroelastic mixture of interpenetrating solid and fluid constituents. The solid matrix of the cupula is assumed to behave as a linear elastic material, whereas the fluid constituent is assumed to be Newtonian. A regular perturbation analysis of the fluid dynamics in the canal provides a dynamic boundary condition, which acts across the cupula partition. Numerical solution of the coupled system of momentum equations provides the spatio-temporal displacement fields for both the fluid and solid constituents of the cupula. Results indicate that at frequencies above 1 Hz, the fluid constituent is dynamically entrained by the solid matrix such that their motions are bound as if to exist as a single component. The resulting high-frequency response is consistent with the macromechanical response predicted by single-component viscoelastic models of the cupula. Below 1 Hz, the dynamic coupling between the fluid and solid constituents weakens and the transcupular differential pressure is sufficient to force fluid through the mixture with little deformation of the solid matrix. Results are sensitive to the precise value of the cupular permeability. One of the most important distinctions between the present analysis and previous impermeable models of the cupula arises at the micromechanical level in terms of the local fluid flow that is predicted to occur within the cupula and around the ciliary bundles and sensory hair cells. Another important result reveals that the permeation dynamics predicted below 1 Hz gives rise to the same low-frequency macromechanical response as would occur with an impermeable viscoelastic structure having a much greater stiffness. Current estimates of the mechanical stiffness of the cupula, based solely on afferent nerve data, may therefore overestimate the true value intrinsic to the solid matrix by as much as an order of magnitude.     

A special theory of biphasic mixtures and experimental results for human annulus fibrosus tested in confined compression

A finite deformation mixture theory is used to quantify the mechanical properties of the annulus fibrosus using experimental data obtained from a confined compression protocol. Certain constitutive assumptions are introduced to derive a special mixture of an elastic solid and an inviscid fluid, and the constraint of intrinsic incompressibility is introduced in a manner that is consistent with results obtained for the special theory. Thirty-two annulus fibrosus specimens oriented in axial (n = 16) and radial (n = 16) directions were obtained from the middle-lateral portion of intact intervertebral discs from human lumbar spines and tested in a stress-relaxation protocol. Material constants are determined by fitting the theory to experimental data representing the equilibrium stress versus stretch and the surface stress time history curves. No significant differences in material constants due to orientation existed, but significant differences existed due to the choice of theory used to fit the data. In comparison with earlier studies with healthy annular tissue, we report a lower aggregate modulus and a higher initial permeability constant. These differences are explained by the choice of reference configuration for the experimental studies.     

Finite element analysis of biological soft tissue surrounded by a deformable membrane that controls transmembrane flow

Background

Many biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids. Mechanical interactions between the solid and the fluid in hydrated porous tissues have been analyzed by finite element methods (FEMs) in which the mixture theory was introduced in various ways. Although most of the tissues are surrounded by deformable membranes that control transmembrane flows, the boundaries of the tissues have been treated as rigid and/or freely permeable in these studies. The purpose of this study was to develop a method for the analysis of hydrated porous hyperelastic tissues surrounded by deformable membranes that control transmembrane flows.

Results

For this, we developed a new nonlinear finite element formulation of the mixture theory, where the nodal unknowns were the pore water pressure and solid displacement. This method allows the control of the fluid flow rate across the membrane using Neumann boundary condition. Using the method, we conducted a compression test of the hydrated porous hyperelastic tissue, which was surrounded by a flaccid impermeable membrane, and a part of the top surface of this tissue was pushed by a platen. The simulation results showed a stress relaxation phenomenon, resulting from the interaction between the elastic deformation of the tissue, pore water pressure gradient, and the movement of fluid. The results also showed that the fluid trapped by the impermeable membrane led to the swelling of the tissue around the platen.

Conclusions

These facts suggest that our new method can be effectively used for the analysis of a large deformation of hydrated porous hyperelastic material surrounded by a deformable membrane that controls transmembrane flow, and further investigations may allow more realistic analyses of the biological soft tissues, such as brain edema, brain trauma, the flow of blood and lymph in capillaries and pitting edema.

     

Influence of Magnetic Field in Three-Dimensional Flow of Couple Stress Nanofluid over a Nonlinearly Stretching Surface with Convective Condition

This article investigates the magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid subject to the convective boundary condition. Flow is generated due to a nonlinear stretching of the surface in two lateral directions. Temperature and nanoparticles concentration distributions are studied through the Brownian motion and thermophoresis effects. Couple stress fluid is considered electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed via boundary layer approach. Nonlinear ordinary differential systems are constructed by employing suitable transformations. The resulting systems have been solved for the convergent series solutions of velocities, temperature and nanoparticles concentration profiles. Graphs are sketched to see the effects of different interesting flow parameters on the temperature and nanoparticles concentration distributions. Numerical values are computed to analyze the values of skin-friction coefficients and Nusselt number.     

A modified theory of the potential and inhomogeneous ion distribution near charged surfaces

A new theory is proposed to calculate the surface potential. The potential is derived from a modified force equilibrium resulting in an algebraic equation. Special boundary conditions are introduced to handle the modified forces. Numeric examples are given based on erythrocyte data and are compared with the Gouy-Chapman theory.     

Biplots for multifactorial analysis of distance

Many data sets in practice fit a multivariate analysis of variance (MANOVA) structure, but do not accord with MANOVA assumptions for their analysis. One way forward is to calculate the matrix of dissimilarities or distances between every pair of individuals, and then to conduct an analysis of distance on the resulting data. Various metric scaling plots can be used to interpret the results of the analysis. However, developments to date of this approach have focused mainly on the individuals in the sample, and little attention has been paid to the assessment of influence of the original variables on the results. The present article attempts to rectify this omission. We discuss the inclusion of biplots on all forms of metric scaling representations in the analysis of distance. Exact biplots will often be nonlinear so we propose a simple linear approximation, and contrast it with other simple linear possibilities. An example from ecology illustrates the methodology.     

Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law Fluid in a Darcy Porous Medium with Plate Suction/Injection

In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the power-law index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined.     

Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis

During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a “staircase” pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.     

The Minimal, Phase-Transition Model for the Cell-Number Maintenance by the Hyperplasia-Extended Homeorhesis

Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.     

External tissue support and fluid–structure simulation in blood flows

The objective of this work is to address the formulation of an adequate model of the external tissue environment when studying a portion of the arterial tree with fluid–structure interaction. Whereas much work has already been accomplished concerning flow and pressure boundary conditions associated with truncations in the fluid domain, very few studies take into account the tissues surrounding the region of interest to derive adequate boundary conditions for the solid domain. In this paper, we propose to model the effect of external tissues by introducing viscoelastic support conditions along the artery wall, with two—possibly distributed—parameters that can be adjusted to mimic the response of various physiological tissues. In order to illustrate the versatility and effectiveness of our approach, we apply this strategy to perform patient-specific modeling of thoracic aortae based on clinical data, in two different cases and using a distinct fluid–structure interaction methodology for each, namely an Arbitrary Lagrangian–Eulerian (ALE) approach with prescribed inlet motion in the first case and the coupled momentum method in the second case. In both cases, the resulting simulations are quantitatively assessed by detailed comparisons with dynamic image sequences, and the model results are shown to be in very good adequacy with the data.     

Computational hydrodynamics of animal swimming: boundary element method and three-dimensional vortex wake structure.

The slender body theory, lifting surface theories, and more recently panel methods and Navier-Stokes solvers have been used to study the hydrodynamics of fish swimming. This paper presents progress on swimming hydrodynamics using a boundary integral equation method (or boundary element method) based on potential flow model. The unsteady three-dimensional BEM code 3DynaFS that we developed and used is able to model realistic body geometries, arbitrary movements, and resulting wake evolution. Pressure distribution over the body surface, vorticity in the wake, and the velocity field around the body can be computed. The structure and dynamic behavior of the vortex wakes generated by the swimming body are responsible for the underlying fluid dynamic mechanisms to realize the high-efficiency propulsion and high-agility maneuvering. Three-dimensional vortex wake structures are not well known, although two-dimensional structures termed 'reverse Karman Vortex Street' have been observed and studied. In this paper, simulations about a swimming saithe (Pollachius virens) using our BEM code have demonstrated that undulatory swimming reduces three-dimensional effects due to substantially weakened tail tip vortex, resulting in a reverse Karman Vortex Street as the major flow pattern in the three-dimensional wake of an undulating swimming fish.     

Thermal and Concentration Stratifications Effects in Radiative Flow of Jeffrey Fluid over a Stretching Sheet

In this article we investigate the heat and mass transfer analysis in mixed convective radiative flow of Jeffrey fluid over a moving surface. The effects of thermal and concentration stratifications are also taken into consideration. Rosseland''s approximations are utilized for thermal radiation. The nonlinear boundary layer partial differential equations are converted into nonlinear ordinary differential equations via suitable dimensionless variables. The solutions of nonlinear ordinary differential equations are developed by homotopic procedure. Convergence of homotopic solutions is examined graphically and numerically. Graphical results of dimensionless velocity, temperature and concentration are presented and discussed in detail. Values of the skin-friction coefficient, the local Nusselt and the local Sherwood numbers are analyzed numerically. Temperature and concentration profiles are decreased when the values of thermal and concentration stratifications parameters increase. Larger values of radiation parameter lead to the higher temperature and thicker thermal boundary layer thickness.     

A continuous method to compute model parameters for soft biological materials

Developing appropriate mathematical models for biological soft tissues such as ligaments, tendons, and menisci is challenging. Stress-strain behavior of these tissues is known to be continuous and characterized by an exponential toe region followed by a linear elastic region. The conventional curve-fitting technique applies a linear curve to the elastic region followed by a separate exponential curve to the toe region. However, this technique does not enforce continuity at the transition between the two regions leading to inaccuracies in the material model. In this work, a Continuous Method is developed to fit both the exponential and linear regions simultaneously, which ensures continuity between regions. Using both methods, three cases were evaluated: idealized data generated mathematically, noisy idealized data produced by adding random noise to the idealized data, and measured data obtained experimentally. In all three cases, the Continuous Method performed superiorly to the conventional technique, producing smaller errors between the model and data and also eliminating discontinuities at the transition between regions. Improved material models may lead to better predictions of nonlinear biological tissues' behavior resulting in improved the accuracy for a large array of models and computational analyses used to predict clinical outcomes.     

Effect of tumor shape and size on drug delivery to solid tumors

ABSTRACT: Tumor shape and size effect on drug delivery to solid tumors are studied, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometries. The governing equations are solved using a numerical method, the element-based finite volume method. Interstitial fluid pressure and velocity are used to show the details of drug delivery in a solid tumor, under an assumption that drug particles flow with the interstitial fluid. Drug delivery problems have been most extensively researched in spherical tumors, which have been the simplest to examine with the analytical methods. With our numerical method, however, more complex shapes of the tumor can be studied. The numerical model of fluid flow in solid tumors previously introduced by our group is further developed to incorporate and investigate non-spherical tumors such as prolate and oblate ones. Also the effects of the surface area per unit volume of the tissue, vascular and interstitial hydraulic conductivity on drug delivery are investigated.     

Use of a membrane-bound fluorophore to characterize diffusion boundary layers around human erythrocytes.

A novel method is used to demonstrate the presence of diffusion boundary layers around erythrocytes following rapid mixing in a stopped-flow spectrophotometer and to estimate the apparent dimensions of the diffusion boundary layers. Pink erythrocyte ghosts labeled on their external surfaces with tetramethyl rhodamine isothiocyanate (TRITC) were mixed in a stopped-flow apparatus with 50 mM NaI in Ringer's solutions. I- is an effective collisional quencher of TRITC fluorescence. TRITC fluorescence after flow stopped decreased monoexponentially with time. The concentration of I- at the cell surface as a function of time was estimated from the dependence of TRITC fluorescence on I- concentration in steady-state experiments. The kinetics of the increase in I- concentration at the cell surface was fit to two diffusional models: a planar erythrocyte ghost bounded by planar diffusion boundary layer and a spherical erythrocyte surrounded by a spherical shell diffusion boundary layer. The planar model best fits the experimental data with a diffusion boundary layer 4.68 microns thick. Using the spherical model the experimental data is best fit by a 6.9 microns diffusion boundary layer.     

A theoretical framework to analyze bend testing of soft tissue

It has been hypothesized that repetitive flexural stresses contribute to the fatigue-induced failure of bioprosthetic heart valves. Although experimental apparatuses capable of measuring the bending properties of biomaterials have been described, a theoretical framework to analyze the resulting data is lacking. Given the large displacements present in these bending experiments and the nonlinear constitutive behavior of most biomaterials, such a formulation must be based on finite elasticity theory. We present such a theory in this work, which is capable of fitting bending moment versus radius of curvature experimental data to an arbitrary strain energy function. A simple finite element model was constructed to study the validity of the proposed method. To demonstrate the application of the proposed approach, bend testing data from the literature for gluteraldehyde-fixed bovine pericardium were fit to a nonlinear strain energy function, which showed good agreement to the data. This method may be used to integrate bending behavior in constitutive models for soft tissue.     

Biphasic poroviscoelastic simulation of the unconfined compression of articular cartilage: I--Simultaneous prediction of reaction force and lateral displacement

This study investigated the ability of the linear biphasic poroelastic (BPE) model and the linear biphasic poroviscoelastic (BPVE) model to simultaneously predict the reaction force and lateral displacement exhibited by articular cartilage during stress relaxation in unconfined compression. Both models consider articular cartilage as a binary mixture of a porous incompressible solid phase and an incompressible inviscid fluid phase. The BPE model assumes the solid phase is elastic, while the BPVE model assumes the solid phase is viscoelastic. In addition, the efficacy of two additional models was also examined, i.e., the transversely isotropic BPE (TIBPE) model, which considers transverse isotropy of the solid matrix within the framework of the linear BPE model assumptions, and a linear viscoelastic solid (LVE) model, which assumes that the viscoelastic behavior of articular cartilage is solely governed by the intrinsic viscoelastic nature of the solid matrix, independent of the interstitial fluid flow. It was found that the BPE model was able to accurately account for the lateral displacement, but unable to fit the short-term reaction force data of all specimens tested. The TIBPE model was able to account for either the lateral displacement or the reaction force, but not both simultaneously. The LVE model was able to account for the complete reaction force, but unable to fit the lateral displacement measured experimentally. The BPVE model was able to completely account for both lateral displacement and reaction force for all specimens tested. These results suggest that both the fluid flow-dependent and fluid flow-independent viscoelastic mechanisms are essential for a complete simulation of the viscoelastic phenomena of articular cartilage.     

Temperature and Concentration Stratification Effects in Mixed Convection Flow of an Oldroyd-B Fluid with Thermal Radiation and Chemical Reaction

This research addresses the mixed convection flow of an Oldroyd-B fluid in a doubly stratified surface. Both temperature and concentration stratification effects are considered. Thermal radiation and chemical reaction effects are accounted. The governing nonlinear boundary layer equations are converted to coupled nonlinear ordinary differential equations using appropriate transformations. Resulting nonlinear systems are solved for the convergent series solutions. Graphs are plotted to examine the impacts of physical parameters on the non-dimensional temperature and concentration distributions. The local Nusselt number and the local Sherwood number are computed and analyzed numerically.