Finite Element Implementation of Neutral Solute Transport in Porous Biological Soft Tissues Under Finite Deformation

2011 ◽  
Author(s):  
Gerard A. Ateshian ◽  
Michael B. Albro ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Transport Properties ◽  
Finite Deformation ◽  
Pore Volume ◽  
Soft Tissues ◽  
Biological Tissues ◽  
Solute Concentration ◽  
Porous Solid ◽  
Solid Matrix ◽  
Waste Products

The physiological function of biological tissues and cells is critically dependent on the transport of various solutes, such as nutrients, cytokines, hormones, and waste products. Transport in such media may be significantly hindered by the porous solid matrix, which may impart anisotropic transport properties to the solutes. Furthermore, large deformations of soft tissues and cells may significantly alter these transport properties due to concomitant alterations in pore volume and structure. Another potential influence of the porous solid matrix is steric volume exclusion resulting from the ratio of solute size and pore size distribution. This steric effect implies that solute concentration inside a tissue or cell may be less than the concentration in a surrounding bath, and this limit on solubility may be exacerbated under finite deformation due to changes in pore volume. Finally, the osmotic pressurization of the interstitial fluid may deviate from ideal physico-chemical behavior and this deviation may be dependent on the state of strain in the solid matrix. Therefore, a finite element framework that can accommodate solid-solute momentum exchanges, strain-induced anisotropy in transport properties and solubility, and strain-dependent non-ideal osmotic response, can provide an important modeling tool in the biomechanics of soft tissues and cells.

scholarly journals Finite Element Implementation of Mechanochemical Phenomena in Neutral Deformable Porous Media Under Finite Deformation

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Michael B. Albro ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Finite Deformation ◽  
Biological Tissues ◽  
Solid Matrix ◽  
Element Formulation ◽  
Momentum Exchange ◽  
Deformable Porous Media ◽  
Chemical Effects ◽  
Highly Nonlinear

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software).

A Sub-Domain Inverse Finite Element Characterization of Hyperelastic Membranes Including Soft Tissues

2003 ◽  
Vol 125 (3) ◽  
pp. 363-371 ◽  
Author(s):  
Padmanabhan Seshaiyer ◽  
Jay D. Humphrey
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soft Tissues ◽  
Nonlinear Behavior ◽  
Local Stress ◽  
Biological Tissues ◽  
Material Behavior ◽  
Inverse Finite Element Method ◽  
Complicated Geometry ◽  
Element Method

Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.

Finite Element Implementation of a Planar Soft Tissue Structural Constitutive Model for Heart Valve Simulations

2013 ◽  
Author(s):  
Rong Fan ◽  
Michael S. Sacks
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Tissues ◽  
Structural Model ◽  
Mechanical Response ◽  
Biological Tissues ◽  
Biaxial Test ◽  
Tissue Microstructure ◽  
Highly Nonlinear ◽  
Insight Into

Constitutive modeling is critical for numerical simulation and analysis of soft biological tissues. The highly nonlinear and anisotropic mechanical behaviors of soft tissues are typically due to the interaction of tissue microstructure. By incorporating information of fiber orientation and distribution at tissue microscopic scale, the structural model avoids ambiguities in material characterization. Moreover, structural models produce much more information than just simple stress-strain results, but can provide much insight into how soft tissues internally reorganize to external loads by adjusting their internal microstructure. It is only through simulation of an entire organ system can such information be derived and provide insight into physiological function. However, accurate implementation and rigorous validation of these models remains very limited. In the present study we implemented a structural constitutive model into a commercial finite element package for planar soft tissues. The structural model was applied to simulate strip biaxial test for native bovine pericardium, and a single pulmonary valve leaflet deformation. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber deformation fiber reorientation and fiber recruitment.

Extended “LMPHETS” Finite Element Models for Coupled Mechano-Electro-Chemical Transport in Soft Tissues

2002 ◽  
Author(s):  
B. R. Simon ◽  
G. A. Radtke ◽  
P. H. Rigby ◽  
S. K. Williams ◽  
Z. P. Liu
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Electrical Potential ◽  
Fluid Pressure ◽  
Nonlinear Material ◽  
Solid Matrix ◽  
Test Problems ◽  
Finite Element Models ◽  
Material Interfaces ◽  
Mobile Species

Soft tissues are hydrated fibrous materials that exhibit nonlinear material response and undergo finite straining during in vivo loading. A continuum model of these structures (“LMPHETS” [1,2]) is a porous solid matrix (with charges fixed to the solid fibers) saturated by a mobile fluid (water) and multiple species (e.g., three mobile species designated by α, β = p, m, b where p = +, m = −, and b = ± charge) dissolved in the mobile fluid. A “mixed” LMPHETS theory and finite element models (FEMs) were presented [1] in which the “primary fields” are the displacements, ui = xi − Xi and the mechano-electro-chemical potentials, ν˜ξ* (ξ, η = f, e, m, b) that are continuous across material interfaces. “Secondary fields” (discontinuous at material boundaries) are mechanical fluid pressure, pf; electrical potential, μ˜e; and concentration or “molarity”, cα = dnα / dVf. Here an extended version of these models is described and numerical results are presented for representative test problems associated with transport in soft tissues.

Interaction Between the Interstitial Fluid and the Extracellular Matrix in Confined Indentation

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Yiling Lu ◽  
Wen Wang
Keyword(s):  
Extracellular Matrix ◽  
Interstitial Fluid ◽  
Soft Tissues ◽  
Dynamic Equilibrium ◽  
Fluid Pressure ◽  
Pressure Oscillation ◽  
Solid Matrix ◽  
Loading Frequency ◽  
Waste Products ◽  
Fluid Movement

The Movement of the interstitial fluid in extracellular matrices not only affects the mechanical properties of soft tissues, but also facilitates the transport of nutrients and the removal of waste products. In this study, we aim to quantify interstitial fluid movement and fluid-matrix interaction in a new loading configuration—confined tissue indentation, using a poroelastic theory. The tissue sample sits in a cylindrical chamber and loading is applied on the top central surface of the specimen by a porous indenter that is fixed on the specimen. The interaction between the solid and the fluid is examined using a finite element method under ramp and cyclic loads. Typical compression-relaxation responses of the specimen are observed in a ramp load. Under a cyclic load, the system reaches a dynamic equilibrium after a number of loading cycles. Fluid circulation, with opposite directions in the loading and unloading phases in the extracellular matrix, is observed. The most significant variation in the fluid pressure locates just beneath the indenter. Fluid pressurization arrives at equilibrium much faster than the solid matrix deformation. As the loading frequency increases, the location of the peak pressure oscillation moves closer to the indenter and the magnitude of the pressure oscillation increases. Concomitantly, the axial stress variation of the solid matrix is reduced. It is found that interstitial fluid movement helps to alleviate severe strain of the solid matrix beneath the indenter. This study quantifies the interaction between the interstitial fluid and the extracellular matrix by decomposing the loading response of the specimen into the “transient” and “dynamic equilibrium” phases. Confined indentation in this manuscript gives a better representation of some in vitro and in vivo loading configurations where the indenter covers part of the top surface of the tissue.

One-Dimensional Mixed Poroelastic-Transport-Swelling (MPHETS) Finite Element Models for Soft Tissues

2000 ◽  
Author(s):  
Jason W. Nichol ◽  
Bruce R. Simon ◽  
Stuart K. Williams
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Transport Model ◽  
Element Model ◽  
Solid Matrix ◽  
Finite Element Models ◽  
Flow Conditions ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Water Species

Abstract A hydrated soft tissue structure can be viewed as a poroelastic transport model, or specifically a porous, incompressible, fibrous solid matrix, which is saturated by an incompressible fluid (water) containing both positively and negatively charged species. We present a one-dimensional finite element model (FEM), derived from a Mixed-Poro-HyperElastic-Transport-Swelling (MPHETS)model. This FEM can be used to model various soft tissues, such as arteries, and provides a powerful tool to study coupled ion transport under various mechanical loading and water/ species flow conditions.

scholarly journals Multiphasic Finite Element Framework for Modeling Hydrated Mixtures With Multiple Neutral and Charged Solutes

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Electric Potential ◽  
Electrostatic Interactions ◽  
Biological Tissues ◽  
Solid Matrix ◽  
Natural Boundary Condition ◽  
Modeling Framework ◽  
Finite Element Software ◽  
Solute Fluxes ◽  
Electroneutrality Condition

Computational tools are often needed to model the complex behavior of biological tissues and cells when they are represented as mixtures of multiple neutral or charged constituents. This study presents the formulation of a finite element modeling framework for describing multiphasic materials in the open-source finite element software febio.1 Multiphasic materials may consist of a charged porous solid matrix, a solvent, and any number of neutral or charged solutes. This formulation proposes novel approaches for addressing several challenges posed by the finite element analysis of such complex materials: The exclusion of solutes from a fraction of the pore space due to steric volume and short-range electrostatic effects is modeled by a solubility factor, whose dependence on solid matrix deformation and solute concentrations may be described by user-defined constitutive relations. These solute exclusion mechanisms combine with long-range electrostatic interactions into a partition coefficient for each solute whose value is dependent upon the evaluation of the electric potential from the electroneutrality condition. It is shown that this electroneutrality condition reduces to a polynomial equation with only one valid root for the electric potential, regardless of the number and valence of charged solutes in the mixture. The equation of charge conservation is enforced as a constraint within the equation of mass balance for each solute, producing a natural boundary condition for solute fluxes that facilitates the prescription of electric current density on a boundary. It is also shown that electrical grounding is necessary to produce numerical stability in analyses where all the boundaries of a multiphasic material are impermeable to ions. Several verification problems are presented that demonstrate the ability of the code to reproduce known or newly derived solutions: (1) the Kedem–Katchalsky model for osmotic loading of a cell; (2) Donnan osmotic swelling of a charged hydrated tissue; and (3) current flow in an electrolyte. Furthermore, the code is used to generate novel theoretical predictions of known experimental findings in biological tissues: (1) current-generated stress in articular cartilage and (2) the influence of salt cation charge number on the cartilage creep response. This generalized finite element framework for multiphasic materials makes it possible to model the mechanoelectrochemical behavior of biological tissues and cells and sets the stage for the future analysis of reactive mixtures to account for growth and remodeling.

DYNAMICAL FINITE ELEMENT MODELING OF SOFT TISSUES AS CHEMOELECTRIC POROUS MEDIA

2011 ◽  
Vol 11 (01) ◽  
pp. 101-130 ◽  
Author(s):  
ZHAOCHUN YANG ◽  
PATRICK SMOLINSKI ◽  
JEEN-SHANG LIN ◽  
LARS G. GILBERTSON
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Water Pressure ◽  
Mixed Finite Element ◽  
Viscoelastic Body ◽  
Biological Tissues ◽  
Element Formulation ◽  
Dynamical Process ◽  
Time Step ◽  
Charge Concentration

An implicit mixed finite element formulation of hydrated soft biological tissues, based on the Simon model, is presented that incorporates the coupling of solid, fluid, and ion phases as well as the viscoelasticity of soft tissue in the dynamical process. The tissues are modeled as a multi-field viscoelastic body subject to finite deformation. In addition to a three-field (u-w-p) modeling of the porous matrix, the study also includes an ion phase for the ionic solution. After presenting the formulation, an efficient staggered solution scheme is presented: within each time step, the ion charge equation is solved first to give the distribution of the charge concentration, the charge induced osmotic water pressure is then employed in solving the u-w-p equations. The resulting u field becomes a forcing term to the solution of the ion charge concentration equations for iteration. This methodology and codes developed for the study have been verified with one-dimensional (1D) analytical solutions. A 2D chemical electric swelling model illustrates the important role of viscoelasticity. A brain tissue impact example demonstrates the potential application of the model.

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