Triphasic Theory for Swelling Properties of Hydrated Charged Soft Biological Tissues

1990 ◽  
Vol 43 (5S) ◽  
pp. S134-S141 ◽  
Author(s):  
V. C. Mow ◽  
W. M. Lai ◽  
J. S. Hou
Keyword(s):  
Osmotic Pressure ◽  
Soft Tissues ◽  
Interstitial Water ◽  
Biological Tissues ◽  
Ion Concentration ◽  
Solid Matrix ◽  
Swelling Properties ◽  
Chemical Potentials ◽  
Triphasic Theory ◽  
Repulsive Forces

Swelling phenomenon of biological soft tissues, such as articular cartilage, depends on their fixed charge densities, the stiffness of their collagen-proteoglycan solid matrix and the ion concentration in the interstitium. Based on the thermodynamic continuum mixture theory, a multiphasic mixture model is developed to describe the equilibrium and transient swelling properties. For articular cartilages in a single salt environment (e.g. NaCl), a three phase model (triphasic theory) suffices to describe its swelling behavior. The three phases are: solid matrix, interstitial water and the mobile salt. The equations of motion in this theory shows that the driving forces for interstitial water and salt are the gradients of their chemical potentials. Constitutive equations for the chemical potentials of the phases and for the total stress under infinitesimal strain but large variation of salt concentration are presented based on the physico-chemical theory for polyelectrolytic solutions and continuum theory. Application of this theory to equilibrium problems yields the well known Donnan equilibrium ion distribution and osmotic pressure equations. The theory indicates that at equilibrium the applied load on the tissue is shared by 1) the solid matrix elastic stress due to deformation; 2) the Donnan osmotic pressure; and 3) the chemical expansion stress due to the charge-to-charge repulsive forces between the charged groups in the solid matrix. For the transient isometric swelling problem, the theory is shown to describe the experimentally observed responses very well.

Implementation of Finite Deformation Triphasic Modeling in the Finite Element Code FEBio

2012 ◽  
Author(s):  
Gerard A. Ateshian ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Soft Tissues ◽  
Mixture Theory ◽  
Solid Matrix ◽  
Osmotic Swelling ◽  
Solute Content ◽  
Counter Ions ◽  
The Matrix ◽  
Triphasic Theory ◽  
Ion Species ◽  
And Diffusion

Many biological soft tissues exhibit a charged solid matrix, most often due to the presence of proteoglycans enmeshed within the matrix. The predominant solute content of the interstitial fluid of these tissues consists of the monovalent counter-ions Na+ and Cl−. The electrical interactions between the mobile ion species and fixed charge density of the solid matrix produces an array of mechano-electrochemical effects, including Donnan osmotic swelling, and streaming and diffusion potentials and currents. These phenomena have been successfully modeled by the triphasic theory of Lai et al. [1], which is based on the framework of mixture theory [2]. Other similar frameworks have also been proposed [3, 4]. The equations of triphasic theory are nonlinear, even in the range of infinitesimal strains. Therefore, numerical schemes are generally needed to solve all but the simplest problems using this framework.

A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage

1991 ◽  
Vol 113 (3) ◽  
pp. 245-258 ◽  
Author(s):  
W. M. Lai ◽  
J. S. Hou ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Charge Density ◽  
Fixed Charge ◽  
Solid Matrix ◽  
Confined Compression ◽  
Fixed Charge Density ◽  
Chemical Expansion ◽  
Chemical Potentials ◽  
Free Swelling ◽  
Triphasic Theory

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by μi = μoi + (RT/Mi)ln[γ±2c (c + c F)] and μW = μow + [p − RTφ(2c + cF) + Bwe]/ρTw, where R, T, Mi, γ±, φ, ρTw and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is σ = − pI − TcI + λs(trE)I + 2μsE, where E is the strain tensor and (λs,μs) are the Lame´ constants of the elastic solid matrix. The chemical-expansion stress (− Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the “pre-stress” in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.

Flows of Electrolytes Through Charged Hydrated Biological Tissue

1994 ◽  
Vol 47 (6S) ◽  
pp. S277-S281 ◽  
Author(s):  
W. M. Lai ◽  
W. Gu ◽  
V. C. Mow
Keyword(s):  
Osmotic Pressure ◽  
Pressure Difference ◽  
Finite Thickness ◽  
Concentration Field ◽  
Ion Concentration ◽  
Solid Matrix ◽  
Hydraulic Pressure ◽  
Neutral Salt ◽  
Apparent Permeability ◽  
Osmotic Pressure Difference

In this paper, analyses of the flows of water and electrolytes through charged hydrated biologic tissues (e.g., articular cartilage) are presented. These analyses are based on the triphasic mechano-electrochemical theory developed by Lai and coworkers (1991). The problems analyzed are 1-D steady permeation flows generated by a hydraulic pressure difference and/or by an osmotic pressure difference across a finite thickness layer of the tissue. The theory allows for the complete determination of the ion concentration field, the matrix strain field as well as the ion and water velocity field inside the tissue during the steady permeation. For flows generated by a hydraulic pressure difference, the frictional drag induces a compaction of the solid matrix causing the fixed charge density (FCD) to increase and the neutral salt concentration to decrease in the downstream direction. Further, while both ions move downstream, but relative to the solvent (water), the anions (Cl−) move with the flow while the cations (Na+) move against the flow. The theory also predicts a well-known experimental finding that the apparent permeability decreases nonlinearly with FCD. For flows generated by an osmotic pressure difference, first, fluid flow varies with the FCD in a nonlinear and non-monotonic manner. Second, there exists a critical FCD below which negative osmosis takes place.

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.

Rapid Critical Point Drying of Tissues in a Parr Bomb

1972 ◽  
Vol 30 ◽  
pp. 400-401
Author(s):  
C.A. Baechler ◽  
W. C. Pitchford ◽  
J. M. Riddle ◽  
C.B. Boyd ◽  
H. Kanagawa ◽  
...  
Keyword(s):  
Critical Point ◽  
Critical Pressure ◽  
Soft Tissues ◽  
Biological Tissues ◽  
Critical Temperatures ◽  
Air Drying ◽  
The Past ◽  
Critical Point Drying ◽  
Great Stress ◽  
Infiltration Techniques

Preservation of the topographic ultrastructure of soft biological tissues for examination by scanning electron microscopy has been accomplished in the past by using lengthy epoxy infiltration techniques, or dehydration in ethanol or acetone followed by air drying. Since the former technique requires several days of preparation and the latter technique subjects the tissues to great stress during the phase change encountered during air-drying, an alternate rapid, economical, and reliable method of surface structure preservation was developed. Turnbill and Philpott had used a fluorocarbon for the critical point drying of soft tissues and indicated the advantages of working with fluids having both moderately low critical pressures as well as low critical temperatures. Freon-116 (duPont) which has a critical temperature of 19. 7 C and a critical pressure of 432 psi was used in this study.

scholarly journals A computational framework for modeling cell–matrix interactions in soft biological tissues

2021 ◽  
Author(s):  
Jonas F. Eichinger ◽  
Maximilian J. Grill ◽  
Iman Davoodi Kermani ◽  
Roland C. Aydin ◽  
Wolfgang A. Wall ◽  
...  
Keyword(s):  
Soft Tissues ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Computational Framework ◽  
Cell Matrix ◽  
Physiological Processes ◽  
Matrix Interactions ◽  
Mechanical Homeostasis ◽  
Cell Matrix Interactions ◽  
Short Time

AbstractLiving soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

Continuum Thermodynamics of Constrained Reactive Mixtures

2021 ◽  
Author(s):  
Gerard A. Ateshian ◽  
Brandon Zimmerman
Keyword(s):  
Heat Supply ◽  
Damage Mechanics ◽  
Reactive Power ◽  
Mixture Theory ◽  
Biological Tissues ◽  
Heat Of Reaction ◽  
Chemical Potentials ◽  
Ideal Gases ◽  
Reactive Processes ◽  
Energy Of Formation

Abstract Mixture theory models continua consisting of multiple constituents with independent motions. In constrained mixtures all constituents share the same velocity but they may have different reference configurations. The theory of constrained reactive mixtures was formulated to analyze growth and remodeling in living biological tissues. It can also reproduce and extend classical frameworks of damage mechanics and viscoelasticity under isothermal conditions, when modeling bonds that can break and reform. This study focuses on establishing the thermodynamic foundations of constrained reactive mixtures under more general conditions, for arbitrary reactive processes where temperature varies in time and space. By incorporating general expressions for reaction kinetics, it is shown that the residual dissipation statement of the Clausius-Duhem inequality must include a reactive power density, while the axiom of energy balance must include a reactive heat supply density. Both of these functions are proportional to the molar production rate of a reaction, and they depend on the chemical potentials of the mixture constituents. We present novel formulas for the classical thermodynamic concepts of energy of formation and heat of reaction, making it possible to evaluate the heat supply generated by reactive processes from the knowledge of the specific free energy of mixture constituents as well as the reaction rate. We illustrate these novel concepts with mixtures of ideal gases, and isothermal reactive damage mechanics and viscoelasticity, as well as reactive thermoelasticity. This framework facilitates the analysis of reactive tissue biomechanics and physiological and biomedical engineering processes where temperature variations cannot be neglected.

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.

Reactive Constrained Mixtures for Modeling the Solid Matrix of Biological Tissues

2017 ◽  
Vol 129 (1-2) ◽  
pp. 69-105 ◽  
Author(s):  
Robert J. Nims ◽  
Gerard A. Ateshian
Keyword(s):  
Biological Tissues ◽  
Solid Matrix
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