An Experimental and Analytical Evaluation of the Nonlinear Viscoelastic Properties of the Healing Medial Collateral Ligament in a Goat Model

2003 ◽  
Author(s):  
S. D. Abramowitch ◽  
T. D. Clineff ◽  
R. E. Debski ◽  
S. L.-Y. Woo
Keyword(s):  
Stress Relaxation ◽  
Medial Collateral Ligament ◽  
Viscoelastic Properties ◽  
Soft Tissues ◽  
Viscoelastic Behavior ◽  
Collateral Ligament ◽  
Relaxation Experiment ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic

The medial collateral ligament (MCL) is one of the most frequently injured ligaments in the knee. Although it can heal spontaneously after rupture, laboratory studies have shown that the mechanical properties of the healing MCL remain inferior to normal for up to two years after injury (1). Additionally, the healing MCL has been shown to display increased amounts of stress relaxation and creep (2). In order to more completely describe the viscoelastic properties of healing ligaments, we propose to use the Quasi-Linear Viscoelastic (QLV) theory formulated by Fung (1972). This theory has been used to successfully describe the viscoelastic properties of many soft-tissues (3). Recently, our research center has developed an improved approach to determine the constants describing the QLV theory based on data collected from a stress relaxation experiment that utilizes a slow strain rate during loading. This approach allows for experimental errors that commonly result from fast strain rates to be avoided (ex. overshoot) (4). Therefore, the objective of this study were to use this new approach to determine the constants describing the quasi-linear viscoelastic behavior of the healing goat MCL at 12 weeks after injury.

Evaluation of the Viscoelastic Properties of the Intact Medial Collateral Ligament in a Goat Model

1999 ◽  
Author(s):  
Theodore D. Clineff ◽  
Richard E. Debski ◽  
Sven U. Scheffler ◽  
John D. Withrow ◽  
Savio L.-Y. Woo
Keyword(s):  
Medial Collateral Ligament ◽  
Viscoelastic Properties ◽  
Analytical Approach ◽  
Cruciate Ligament ◽  
Collateral Ligament ◽  
Future Studies ◽  
Linear Viscoelastic ◽  
Viscoelastic Theory ◽  
Anterior Cruciate ◽  
Linear Viscoelastic Theory

Abstract The time and history dependent viscoelastic properties have been determined for the normal medial collateral ligament (MCL) of canine (Woo, 1981), porcine anterior cruciate ligament (Kwan, 1993), and human patellar tendon in a cadaver model (Johnson, 1994). The objective of this study was to use a combined experimental and analytical approach to quantify the viscoelastic properties of the intact MCL in a goat model. A thorough understanding of the viscoelastic properties at low strain levels is necessary to future studies of the healing MCL. The quasi-linear viscoelastic theory (QLV) (Fung, 1972) was used to characterize the properties of the MCL during stress relaxation.

The Effects of Refreezing on the Tensile Properties of the Medial Collateral Ligament-Bone Complex: A Rabbit Model

2003 ◽  
Author(s):  
Daniel K. Moon ◽  
Mary T. Gabriel ◽  
Steven D. Abramowitch ◽  
Yoshiyuki Takakura ◽  
Savio L.-Y. Woo
Keyword(s):  
Stress Relaxation ◽  
Tensile Properties ◽  
Medial Collateral Ligament ◽  
Soft Tissues ◽  
Rabbit Model ◽  
Frozen Storage ◽  
Cyclic Stress ◽  
Specimen Preparation ◽  
Freezing And Thawing ◽  
Collateral Ligament

Biomechanical tests of soft tissues, especially those from human cadavers, are generally done after a period of postmortem storage by freezing. In some instances, specimen preparation and testing can be complex and can take place over several days, thus necessitating an additional period of frozen storage before biomechanical evaluation is completed. Studies have been done in the past, which investigated the effects of postmortem freezing on the tensile properties of ligament-bone complexes (Viidik and Lewin 1966; Noyes and Grood 1976; Dorlot 1980; Barad 1982; Nikolaou 1986; Woo, Orlando et al. 1986). It has been shown in our laboratory that careful postmortem freezing for up to three months did not significantly change the mechanical properties of the ligament midsubstance and the cyclic stress relaxation behavior and the structural properties of the ligament-bone complex, but the area of hysteresis was significantly reduced in the stored specimens for the first few cycles of cyclic stress relaxation (Woo, Orlando et al. 1986). Hence, it is important to ensure that an additional freezing and thawing cycle will not further change the tensile properties of these tissues. Therefore, the objective of this study was to evaluate the effects of freezing and thawing twice at 20°C on the structural and viscoelastic properties of femur-medial collateral ligament-tibia complex (FMTC) in a rabbit model.

The Time and History-Dependent Viscoelastic Properties of the Canine Medial Collateral Ligament

1981 ◽  
Vol 103 (4) ◽  
pp. 293-298 ◽  
Author(s):  
S. L.-Y. Woo ◽  
M. A. Gomez ◽  
W. H. Akeson
Keyword(s):  
Medial Collateral Ligament ◽  
Viscoelastic Properties ◽  
Cyclic Stress ◽  
Elastic Response ◽  
Collateral Ligament ◽  
Stress Strain ◽  
Linear Viscoelastic ◽  
Viscoelastic Theory ◽  
Linear Viscoelastic Theory

The viscoelastic properties of the canine medial collateral ligament (MCL) were investigated. Stress-strain relationships at different strain rates, long-term stress relaxation and cyclic stress-strain curves of the MCL were obtained experimentally using a bone-MCL-bone preparation. The experimental data were used in conjunction with the quasi-linear viscoelastic theory as proposed by Fung [15] to characterize the reduced relaxation function, G(t) and elastic response σe (ε) of this tissue. It was found that the quasi-linear viscoelastic theory can adequately describe the time and history-dependent rheological properties of the canine medial collateral ligament.

An Improved Method to Analyze the Stress Relaxation of Ligaments Following a Finite Ramp Time Based on the Quasi-Linear Viscoelastic Theory

2004 ◽  
Vol 126 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Steven D. Abramowitch ◽  
Savio L.-Y. Woo
Keyword(s):  
Stress Relaxation ◽  
Soft Tissues ◽  
Viscoelastic Behavior ◽  
Cyclic Stress ◽  
Elastic Response ◽  
Curve Fit ◽  
Order Of Magnitude ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Theory ◽  
Experimental Values

The quasi-linear viscoelastic (QLV) theory proposed by Fung (1972) has been frequently used to model the nonlinear time- and history-dependent viscoelastic behavior of many soft tissues. It is common to use five constants to describe the instantaneous elastic response (constants A and B) and reduced relaxation function (constants C, τ1, and τ2) on experiments with finite ramp times followed by stress relaxation to equilibrium. However, a limitation is that the theory is based on a step change in strain which is not possible to perform experimentally. Accounting for this limitation may result in regression algorithms that converge poorly and yield nonunique solutions with highly variable constants, especially for long ramp times (Kwan et al. 1993). The goal of the present study was to introduce an improved approach to obtain the constants for QLV theory that converges to a unique solution with minimal variability. Six goat femur-medial collateral ligament-tibia complexes were subjected to a uniaxial tension test (ramp time of 18.4 s) followed by one hour of stress relaxation. The convoluted QLV constitutive equation was simultaneously curve-fit to the ramping and relaxation portions of the data r2>0.99. Confidence intervals of the constants were generated from a bootstrapping analysis and revealed that constants were distributed within 1% of their median values. For validation, the determined constants were used to predict peak stresses from a separate cyclic stress relaxation test with averaged errors across all specimens measuring less than 6.3±6.0% of the experimental values. For comparison, an analysis that assumed an instantaneous ramp time was also performed and the constants obtained for the two approaches were compared. Significant differences were observed for constants B, C, τ1, and τ2, with τ1 differing by an order of magnitude. By taking into account the ramping phase of the experiment, the approach allows for viscoelastic properties to be determined independent of the strain rate applied. Thus, the results obtained from different laboratories and from different tissues may be compared.

The Fractional derivative rheological model and the linear viscoelastic behavior of hydrocolloids

2012 ◽  
Vol 33 (1) ◽  
pp. 141-151 ◽  
Author(s):  
Magdalena Orczykowska ◽  
Marek Dziubiński
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Properties ◽  
Rheological Model ◽  
Xanthan Gum ◽  
Viscoelastic Behavior ◽  
Rheological Parameters ◽  
Rice Starch ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
The Impact

The Fractional derivative rheological model and the linear viscoelastic behavior of hydrocolloids This study was aimed at evaluating the possibility to use the Friedrich-Braun fractional derivative rheological model to assess the viscoelastic properties of xanthan gum with rice starch and sweet potato starch. The Friedrich-Braun fractional derivative rheological model allows to describe viscoelastic properties comprehensively, starting from the behaviour characteristic of purely viscous fluids to the behaviour corresponding to elastic solids. The Friedrich-Braun fractional derivative rheological model has one more virtue which distinguishes it from other models, it allows to determine the relationship between stress and strain and the impact of each of them on viscoelastic properties on the tested material. An analysis of the data described using the Friedrich-Braun fractional derivative rheological model allows to state that all the tested mixtures of starch with xanthan gum form macromolecular gels exhibiting behaviour typical of viscoelastic quasi-solid bodies. The Friedrich-Braun fractional derivative rheological model and 8 rheological parameters of this model allow to determine changes in the structure of the examined starch - xanthan gum mixtures. Similarly important is the possibility to find out the trend and changes going on in this structure as well as their causes.

Comparison of a Novel Nonlinear Viscoelastic Finite Ramp Time Correction Method to a Heaviside Step Assumption

2011 ◽  
Author(s):  
Kevin L. Troyer ◽  
Christian M. Puttlitz
Keyword(s):  
Stress Relaxation ◽  
Soft Tissues ◽  
Viscoelastic Behavior ◽  
Relaxation Modulus ◽  
Correction Method ◽  
Nonlinear Viscoelastic ◽  
Instantaneous Strain ◽  
Relaxation Experiments ◽  
Time Correction

Connective soft tissues exhibit time-dependent, or viscoelastic, behavior. In order to characterize this behavior, stress relaxation experiments can be performed to determine the tissue’s relaxation modulus. Theoretically, the relaxation modulus describes the stress relaxation behavior of the tissue in response to an instantaneous (step) application of strain. However, a step increase in strain is experimentally impossible and a pure ramp load is intractable due to the inertial limitations of the testing device. Even small deviations from an instantaneous strain application may cause significant errors in the determination of the tissue’s relaxation modulus.

A Nonlinear Viscoelastic Model for the Relaxation Behavior of Tendon

2012 ◽  
Author(s):  
Frances M. Davis ◽  
Raffaella De Vita
Keyword(s):  
Stress Relaxation ◽  
Relaxation Function ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Relaxation Behavior ◽  
Successful Model ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic ◽  
Nonlinear Viscoelastic Model

Tendons are viscoelastic materials which undergo stress relaxation when held at a constant strain. The most successful model used to describe the viscoelastic behavior of tendons is the quasi-linear viscoelastic (QLV) model [1]. In the QLV model, the relaxation function is assumed to be a separable function of time and strain. Recently, this assumption has been shown to be invalid for tendons [2] thus suggesting the need for new nonlinear viscoelastic models.

A Compression Relaxometer for Rubber Materials

1973 ◽  
Vol 46 (5) ◽  
pp. 1316-1319
Author(s):  
B. Stenberg ◽  
J. F. Jansson
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Behavior ◽  
Good Function ◽  
Temperature Range ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic

Abstract A relaxometer which permits measurements of stress relaxation for compressed rubber samples is presented. Measurements in the temperature range 316.5 to 412.7° K show the good function of the relaxometer. The relaxometer has also been used in a study of deviations from linear viscoelastic behavior.

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