A Biphasic Transversely Isotropic Poroviscoelastic Model for the Unconfined Compression of Hydrated Soft Tissue

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
H. Hatami-Marbini ◽  
R. Maulik
Keyword(s):  
Articular Cartilage ◽  
Soft Tissue ◽  
Stress Relaxation ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Viscoelastic Model ◽  
Transversely Isotropic ◽  
Solid Matrix ◽  
Unconfined Compression ◽  
Material Parameters

The unconfined compression experiments are commonly used for characterizing the mechanical behavior of hydrated soft tissues such as articular cartilage. Several analytical constitutive models have been proposed over the years to analyze the unconfined compression experimental data and subsequently estimate the material parameters. Nevertheless, new mathematical models are still required to obtain more accurate numerical estimates. The present study aims at developing a linear transversely isotropic poroviscoelastic theory by combining a viscoelastic material law with the transversely isotropic biphasic model. In particular, an integral type viscoelastic model is used to describe the intrinsic viscoelastic properties of a transversely isotropic solid matrix. The proposed constitutive theory incorporates viscoelastic contributions from both the fluid flow and the intrinsic viscoelasticity to the overall stress-relaxation behavior. Moreover, this new material model allows investigating the biomechanical properties of tissues whose extracellular matrix exhibits transverse isotropy. In the present work, a comprehensive parametric study was conducted to determine the influence of various material parameters on the stress–relaxation history. Furthermore, the efficacy of the proposed theory in representing the unconfined compression experiments was assessed by comparing its theoretical predictions with those obtained from other versions of the biphasic theory such as the isotropic, transversely isotropic, and viscoelastic models. The unconfined compression behavior of articular cartilage as well as corneal stroma was used for this purpose. It is concluded that while the proposed model is capable of accurately representing the viscoelastic behavior of any hydrated soft tissue in unconfined compression, it is particularly useful in modeling the behavior of those with a transversely isotropic skeleton.

A Transversely Isotropic Biphasic Model for Unconfined Compression of Growth Plate and Chondroepiphysis

1998 ◽  
Vol 120 (4) ◽  
pp. 491-496 ◽  
Author(s):  
B. Cohen ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Stress Relaxation ◽  
Growth Plate ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Solid Matrix ◽  
Elastic Model ◽  
Unconfined Compression ◽  
Biphasic Model ◽  
Cylindrical Axis

Using the biphasic theory for hydrated soft tissues (Mow et al., 1980) and a transversely isotropic elastic model for the solid matrix, an analytical solution is presented for the unconfined compression of cylindrical disks of growth plate tissues compressed between two rigid platens with a frictionless interface. The axisymmetric case where the plane of transverse isotropy is perpendicular to the cylindrical axis is studied, and the stress-relaxation response to imposed step and ramp displacements is solved. This solution is then used to analyze experimental data from unconfined compression stress-relaxation tests performed on specimens from bovine distal ulnar growth plate and chondroepiphysis to determine the biphasic material parameters. The transversely isotropic biphasic model provides an excellent agreement between theory and experimental results, better than was previously achieved with an isotropic model, and can explain the observed experimental behavior in unconfined compression of these tissues.

Experimental Verification of the Roles of Intrinsic Matrix Viscoelasticity and Tension-Compression Nonlinearity in the Biphasic Response of Cartilage

2003 ◽  
Vol 125 (1) ◽  
pp. 84-93 ◽  
Author(s):  
Chun-Yuh Huang ◽  
Michael A. Soltz ◽  
Monika Kopacz ◽  
Van C. Mow ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Strain Rate ◽  
Dynamic Loading ◽  
Dynamic Compression ◽  
Solid Matrix ◽  
Supporting Evidence ◽  
Compression Stress ◽  
Unconfined Compression ◽  
Support Mechanism

A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410–417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73–84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1–38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r2=0.966±0.032 for testing at slow strain rate; r2=0.998±0.002 for testing at fast strain rate) and predictions of the dynamic response r2=0.91±0.06. This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.

Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: I—Simultaneous Prediction of Reaction Force and Lateral Displacement

2000 ◽  
Vol 123 (2) ◽  
pp. 191-197 ◽  
Author(s):  
Mark R. DiSilvestro ◽  
Qiliang Zhu ◽  
Marcy Wong ◽  
Jukka S. Jurvelin ◽  
Jun-Kyo Francis Suh
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Solid Phase ◽  
Lateral Displacement ◽  
Transverse Isotropy ◽  
Reaction Force ◽  
Solid Matrix ◽  
Inviscid Fluid ◽  
Unconfined Compression ◽  
Interstitial Fluid Flow

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.

scholarly journals A novel elimination method of preloading force on the unconfined compression tests of soft tissue

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110106
Author(s):  
Jing Yang ◽  
Ming Hu ◽  
Zejie Han ◽  
Deming Zhao ◽  
Tao Qin
Keyword(s):  
Soft Tissue ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Model Parameters ◽  
Compression Tests ◽  
Unconfined Compression ◽  
Estimation Model ◽  
Elimination Method ◽  
The Real ◽  
Material Parameters

Accurate description of the mechanical properties for soft tissues can help surgeon predict the state during surgery. In unconfined compression tests (UCT) of soft tissue, a tiny force is typically applied to determine the starting position of compression. The preloading force will cause the obtained material parameters to deviate from the real parameters. In this paper, a novel elimination method was proposed to eliminate the effect of the preloading force. The effects of preloading force on mechanical response were analyzed by performing unconfined compression numerical tests. Different preloading force were applied in the simulation. The parameters obtained by traditional optimization method were defined as preloading material parameters. In the proposed method, an estimation model between the preloading material parameters and the preloading force was established to estimate real parameters. The proposed elimination method was verified by three sample diameters and material parameters. The results show that the material parameters obtained by proposed method are closer to the real parameters (estimated accuracy exceeds 97%). The proposed method can obtain more accurate constitutive model parameters, and eliminate the effect of preloading force.

Isolation, Loading and Estimating the Poroelastic Properties of a Single Osteon

2009 ◽  
Author(s):  
Gaffar Gailani ◽  
Mohammed Benalla ◽  
Rashal Mahamud ◽  
Stephen Cowin ◽  
Luis Cardoso
Keyword(s):  
Mechanical Properties ◽  
Fluid Flow ◽  
Stress Relaxation ◽  
Reasonable Agreement ◽  
Transverse Isotropy ◽  
Bone Mechanics ◽  
Unconfined Compression ◽  
Stress Relaxation Test ◽  
Tools And Methods

Determining the poroelastic properties of osteons is critical to better understand the role of fluid flow in the nutrition, mechanotransduction, remodeling, homeostasis and loss of bone. The permeability of single osteons is among the key properties that may influence these phenomena. The measurement of permeability of a single osteon remains one of the most demanding tasks in bone mechanics to be developed. Two associated challenges are the size of the osteon and the absence of appropriate tools and methods to perform such measurement. In this communication, we present the development of a new procedure to isolate osteons, the design of a mechanism for loading an osteon and the comparison of the stress relaxation test in unconfined compression experiment with the analytical results for a compressible transverse isotropy model that we previously reported in Gailani and Cowin [1]. These experimentally determined values of permeability and mechanical properties have shown reasonable agreement with the previously reported experimentally and theoretically estimated values.

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.

Relaxation and Creep Quasilinear Viscoelastic Models for Normal Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 159-164 ◽  
Author(s):  
B. R. Simon ◽  
R. S. Coats ◽  
S. L.-Y. Woo
Keyword(s):  
Articular Cartilage ◽  
Soft Tissues ◽  
Least Squares Method ◽  
Viscoelastic Model ◽  
Generalized Least Squares ◽  
Constitutive Law ◽  
Analytical Models ◽  
Creep Data ◽  
Bovine Articular Cartilage ◽  
Generalized Least Squares Method

A quasilinear viscoelastic model was used to develop relaxation and creep forms for a constitutive law for soft tissues. Combined relaxation and cyclic test data as well as preconditioned and nonpreconditioned creep data were used to demonstrate the approach for normal bovine articular cartilage. Values for mechanical parameters in the analytical models were determined using a generalized least squares method.

A Priori Assessment of Adipose Tissue Mechanical Testing by Global Sensitivity Analysis

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Hosein Naseri ◽  
Håkan Johansson
Keyword(s):  
Sensitivity Analysis ◽  
Adipose Tissue ◽  
Soft Tissues ◽  
Global Sensitivity Analysis ◽  
A Priori ◽  
Compression Tests ◽  
Unconfined Compression ◽  
Material Parameters ◽  
Global Sensitivity ◽  
Indentation Tests

In modeling the mechanical behavior of soft tissues, the proper choice of an experiment for identifying material parameters is not an easy task. In this study, a finite element computational framework is used to virtually simulate and assess commonly used experimental setups: rotational rheometer tests, confined- and unconfined-compression tests, and indentation tests. Variance-based global sensitivity analysis is employed to identify which parameters in different experimental setups govern model prediction and are thus more likely to be determined through parameter identification processes. Therefore, a priori assessment of experimental setups provides a base for systematic and reliable parameter identification. It is found that in indentation tests and unconfined-compression tests, incompressibility of soft tissues (adipose tissue in this study) plays an important role at high strain rates. That means bulk stiffness constitutes the main part of the mechanism of tissue response; thus, these experimental setups may not be appropriate for identifying shear stiffness. Also, identified material parameters through loading–unloading shear tests at a certain rate might not be reliable for other rates, since adipose tissue shows highly strain rate dependent behavior. Frequency sweep tests at a wide-enough frequency range seem to be the best setup to capture the strain rate behavior. Moreover, analyzing the sensitivity of model parameters in the different experimental setups provides further insight about the model itself.

scholarly journals A New Hybrid Viscoelastic Soft Tissue Model based on Meshless Method for Haptic Surgical Simulation

2013 ◽  
Vol 7 (1) ◽  
pp. 116-124 ◽  
Author(s):  
Yidong Bao ◽  
Dongmei Wu ◽  
Zhiyuan Yan ◽  
Zhijiang Du
Keyword(s):  
Soft Tissue ◽  
Stress Relaxation ◽  
Surgical Simulation ◽  
Viscoelastic Model ◽  
Stress Strain ◽  
Tissue Model ◽  
The Real ◽  
Strain Stress ◽  
Formula Derivation ◽  
Stability And Accuracy

This paper proposes a hybrid soft tissue model that consists of a multilayer structure and many spheres for surgical simulation system based on meshless. To improve accuracy of the model, tension is added to the three-parameter viscoelastic structure that connects the two spheres. By using haptic device, the three-parameter viscoelastic model (TPM) produces accurate deformationand also has better stress-strain, stress relaxation and creep properties. Stress relaxation and creep formulas have been obtained by mathematical formula derivation. Comparing with the experimental results of the real pig liver which were reported by Evren et al. and Amy et al., the curve lines of stress-strain, stress relaxation and creep of TPM are close to the experimental data of the real liver. Simulated results show that TPM has better real-time, stability and accuracy.

Removal of Sulfated Glycosaminoglycans Has a Differential Effect on Permeability of Bovine Articular Cartilage as Measured by Direct Permeation and Stress Relaxation

2009 ◽  
Author(s):  
Heath B. Henninger ◽  
Clayton J. Underwood ◽  
Gerard A. Ateshian ◽  
Jeffrey A. Weiss
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Soft Tissues ◽  
Water Movement ◽  
Experimental Treatment ◽  
Test Methods ◽  
Confined Compression ◽  
Interstitial Fluid Flow ◽  
Bovine Articular Cartilage ◽  
The Impact

Permeability is defined as the ability of a fluid to pass through a porous medium. The ease of water movement is a determinant of the interstitial fluid flow-dependent viscoelastic properties of hydrated soft tissues and also modulates transport of solutes. For articular cartilage, permeability has been quantified directly via permeation experiments and indirectly by analyzing the data from stress relaxation testing under confined compression. It is unclear whether these different methods result in consistent measurements. This further complicates quantification of the effect of an experimental treatment on permeability such as the removal of sulfated glycosaminoglycans (GAGs) [1, 2]. The objective of this study was to elucidate the impact of sulfated GAGs on the permeability of articular cartilage using direct permeation versus stress relaxation testing, and to assess any differences in permeability calculated from the two test methods.

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