A Comparison Between Mechano-Electrochemical and Biphasic Swelling Theories for Soft Hydrated Tissues

2005 ◽  
Vol 127 (1) ◽  
pp. 158-165 ◽  
Author(s):  
W. Wilson ◽  
C. C. van Donkelaar ◽  
J. M. Huyghe
Keyword(s):  
Articular Cartilage ◽  
Material Properties ◽  
Biological Tissues ◽  
Intervertebral Discs ◽  
Ion Concentration ◽  
Confined Compression ◽  
Fixed Charges ◽  
Electrolyte Flux ◽  
Electrochemical Model ◽  
Swelling Model

Biological tissues like intervertebral discs and articular cartilage primarily consist of interstitial fluid, collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans, the total ion concentration inside the tissue is higher than in the surrounding synovial fluid (cation concentration is higher and the anion concentration is lower). This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. In the last decade several mechano-electrochemical models, which include this mechanism, have been developed. As these models are complex and computationally expensive, it is only possible to analyze geometrically relatively small problems. Furthermore, there is still no commercial finite element tool that includes such a mechano-electrochemical theory. Lanir (Biorheology, 24, pp. 173–187, 1987) hypothesized that electrolyte flux in articular cartilage can be neglected in mechanical studies. Lanir’s hypothesis implies that the swelling behavior of cartilage is only determined by deformation of the solid and by fluid flow. Hence, the response could be described by adding a deformation-dependent pressure term to the standard biphasic equations. Based on this theory we developed a biphasic swelling model. The goal of the study was to test Lanir’s hypothesis for a range of material properties. We compared the deformation behavior predicted by the biphasic swelling model and a full mechano-electrochemical model for confined compression and 1D swelling. It was shown that, depending on the material properties, the biphasic swelling model behaves largely the same as the mechano-electrochemical model, with regard to stresses and strains in the tissue following either mechanical or chemical perturbations. Hence, the biphasic swelling model could be an alternative for the more complex mechano-electrochemical model, in those cases where the ion flux itself is not the subject of the study. We propose thumbrules to estimate the correlation between the two models for specific problems.

Influence of the Fixed Negative Charges on the Measured Poisson’s Ratio, Young’s Modulus and Electrical Response of Articular Cartilage

2002 ◽  
Author(s):  
Morakot Likhitpanichkul ◽  
Daniel D. Sun ◽  
X. Edward Guo ◽  
W. Michael Lai ◽  
Van C. Mow
Keyword(s):  
Articular Cartilage ◽  
Deformation Behavior ◽  
Electrical Response ◽  
Compressive Modulus ◽  
Confined Compression ◽  
Physiological Conditions ◽  
Fixed Charges ◽  
Matrix Properties ◽  
The Matrix ◽  
Proteoglycan Content

Under physiological conditions, the solid extracellular matrix (ECM) of articular cartilage derives negative charges from its proteoglycan content [1]. The load-deformation behavior of the tissue (i.e., its apparent mechanical property) comes from not only the intrinsic matrix properties, but also these charges that are attached to the matrix. Study shows that in 1D configurations (such as confined compression), at equilibrium, the osmotic pressure associated with these fixed charges may contribute as much as 50% of the apparent compressive modulus [1–3].

Use of Nanoindentation to Determine Biphasic Material Properties of Articular Cartilage

2008 ◽  
Author(s):  
Gregory J. Miller ◽  
Elise F. Morgan
Keyword(s):  
Mechanical Properties ◽  
Articular Cartilage ◽  
Material Properties ◽  
Small Animal ◽  
Cartilage Degeneration ◽  
Biological Tissues ◽  
Small Animal Models ◽  
Force Displacement ◽  
Articular Cartilage Degeneration

Nanoindentation (NI) has been used with increasing frequency to characterize the mechanical properties of biological tissues. However, the majority of prior studies in this area have focused on hard tissues such as bone, enamel, and dentin [1]. For soft, hydrated tissues and biomaterials, methods of analyzing the force-displacement curves to obtain meaningful information on viscoelastic material properties are still under development. In particular, methods for using NI to quantify the biphasic material properties (aggregate modulus HA, permeability k, Poisson’s ratio ν) of tissues such as articular cartilage have not been established. Such methods could be applied in studies using small animal models to investigate biological and biomechanical mechanisms of articular cartilage degeneration and repair. The overall goal of this study was to develop the use of NI for characterization of the mechanical properties of soft, hydrated materials.

scholarly journals Bi-Component T2 Mapping Correlates with Articular Cartilage Material Properties

2020 ◽  
pp. 110215
Author(s):  
Matthew M. Grondin ◽  
Fang Liu ◽  
Michael F. Vignos ◽  
Alexey Samsonov ◽  
Wan-Ju Li ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Material Properties ◽  
T2 Mapping

Finite Element Modeling of Osmotic Swelling in Tissue-Engineered Cartilage

2008 ◽  
Author(s):  
Liming Bian ◽  
Terri Ann N. Kelly ◽  
Eric G. Lima ◽  
Gerard A. Ateshian ◽  
Clark T. Hung
Keyword(s):  
Articular Cartilage ◽  
Potential Role ◽  
Swelling Pressure ◽  
Type Ii Collagen ◽  
Type Ii ◽  
Osmotic Swelling ◽  
Fixed Charges ◽  
Central Regions ◽  
Significant Research ◽  
Engineered Cartilage

Proteoglycans and Type II collagen represent the two major biochemical constituents of articular cartilage. Collagen fibrils in cartilage resist the swelling pressure that arises from the fixed charges of the glycosaminoglycans (GAGs), and together they give rise to the tissue’s unique load bearing properties. As articular cartilage exhibits a poor intrinsic healing capacity, there is significant research in the development of cell-based therapies for cartilage repair. In some of our tissue engineering studies, we have observed a phenomenon where chondrocyte-seeded hydrogel constructs display cracking in their central regions after significant GAG content has been elaborated in culture. A theoretical analysis was performed to gain greater insights into the potential role that the spatial distribution of proteoglycan and collagen may play in this observed response.

Oscillatory Compressional Behavior of Articular Cartilage and Its Associated Electromechanical Properties

1981 ◽  
Vol 103 (4) ◽  
pp. 280-292 ◽  
Author(s):  
R. C. Lee ◽  
E. H. Frank ◽  
A. J. Grodzinsky ◽  
D. K. Roylance
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Molecular Mechanisms ◽  
Fluid Velocity ◽  
Streaming Potential ◽  
Usual Sense ◽  
Frequency Range ◽  
Confined Compression ◽  
Streaming Potentials ◽  
Compressive Stiffness

The compressive stiffness of articular cartilage was examined in oscillatory confined compression over a wide frequency range including high frequencies relevant to impact loading. Nonlinear behavior was found when the imposed sinusoidal compression amplitude exceeded a threshold value that depended on frequency. Linear behavior was attained only by suitable control of the compression amplitude. This was enabled by real time Fourier analysis of data which provided an accurate assessment of the extent of nonlinearity. For linear viscoelastic behavior, a stiffness could be defined in the usual sense. The dependence of the stiffness on ionic strength and proteoglycan content showed that electrostatic forces between matrix charge groups contribute significantly to cartilage’s compressive stiffness over the 0.001 to 20 Hz frequency range. Sinusoidal streaming potentials were also generated by oscillatory compression. A theory relating the streaming potential field to the fluid velocity field is derived and used to interpret the data. The observed magnitude of the streaming potential suggests that interstitial fluid flow is significant to cartilage behavior over the entire frequency range. The use of simultaneous streaming potential and stiffness data with an appropriate theory appears to be an important tool for assessing the relative contribution of fluid flow, intrinsic matrix viscoelasticity, or other molecular mechanisms to energy dissipation in cartilage. This method is applicable in general to hydrated, charged polymers.

Comparison of the equilibrium response of articular cartilage in unconfined compression, confined compression and indentation

2002 ◽  
Vol 35 (7) ◽  
pp. 903-909 ◽  
Author(s):  
R.K Korhonen ◽  
M.S Laasanen ◽  
J Töyräs ◽  
J Rieppo ◽  
J Hirvonen ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Unconfined Compression ◽  
Confined Compression ◽  
Equilibrium Response

Comparison of biphasic material properties of equine articular cartilage estimated from stress relaxation and creep indentation tests

2021 ◽  
Vol 7 (2) ◽  
pp. 363-366
Author(s):  
Thomas Reuter ◽  
Christof Hurschler
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Material Properties ◽  
Soft Tissues ◽  
Sensitivity Analyses ◽  
Creep Model ◽  
Fe Model ◽  
Relaxation Model ◽  
Marquardt Algorithm ◽  
Indentation Tests

Abstract Mechanical parameters of hard and soft tissues are explicit markers for quantitative tissue characterization. In this study, we present a comparison of biphasic material properties of equine articular cartilage estimated from stress relaxation (ε = 6 %, t = 1000 s) and creep indentation tests (F = 0.1 N, t = 1000 s). A biphasic 3D-FE-based method is used to determine the biomechanical properties of equine articular cartilage. The FE-model computation was optimized by exploiting the axial symmetry and mesh resolution. Parameter identification was executed with the Levenberg- Marquardt-algorithm. Additionally, sensitivity analyses of the calculated biomechanical parameters were performed. Results show that the Young’s modulus E has the largest influence and the Poisson’s ratio of ν ≤ 0.1 is rather insensitive. The R² of the fit results varies between 0.882 and 0.974 (creep model) and between 0.695 and 0.930 (relaxation model). The averaged parameters E and k determined from the creep model yield higher values in comparison to the relaxation model. The differences can be traced back to the experimental settings and to the biphasic material model.

Equivalent Mixed “PHETS” and “MPHETS” Poroelasttc-Transport-Swelling Finite Element Models for Soft Biological Tissues

1999 ◽  
Author(s):  
B. R. Simon ◽  
S. K. Williams ◽  
J. Liu ◽  
J. W. Nichol ◽  
P. H. Rigby ◽  
...  
Keyword(s):  
Finite Element ◽  
Chemical Potential ◽  
Biological Tissues ◽  
Finite Element Models ◽  
Material Interfaces ◽  
Soft Biological Tissues ◽  
Fibrous Matrix ◽  
Charged Species ◽  
Pressure Fields ◽  
Swelling Model

Abstract A soft hydrated tissue structure can be viewed as a “PETS” (poroelastic-transport-swelling) model, i.e., as a continuum composed of an incompressible porous solid (fibrous matrix with fixed charge density, FCD) that is saturated by a mobile incompressible fluid (water) containing mobile positively (p) and negatively (m) charged species. Previously, we described two PETS models — a “semi-mixed” porohyperelastic PHETS model (Simon et al. 1998) and a “fully mixed” MPHETS model (Simon et al. 1999) using FEMs (finite element models) that included geometric and material nonlinearity and coupled electrical/chemical/mechanical transport of the fluid and charged species. Here, we demonstrate the equivalence of the PHETS and MPHETS formulations that are useful when the solid and fluid materials are incompressible and the electrical-chemical potential and mechanical-osmotic pressure fields are discontinuous at material interfaces.

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