Summary - Viscoelasticity and Damage of Ligament: Loading and Recovery R. S. Lakes and R. Vanderby
If a weight is hung on an elastic material such as a steel spring, it stretches and remains at that deformed length. When the weight is removed, it immediately recovers its original length. If the same weight is hung on a viscoelastic material, it stretches initially, but continues to stretch over time. When the weight is removed, some of the stretch is immediately recovered and some is recovered gradually with time. If damaged in the stretch, then it will never recover its original length. Ligaments are viscoelastic. They stretch during physical activity and recover during periods of rest. Tissue stretch and recovery is fundamental to its function but not yet well understood. The objective is to experimentally characterize the mechanical behavior of ligaments, both during loading and recovery. This study will include forces that are below and above the threshold of damage. Experimental data will be analyzed with mathematical models. Stretches which produce damage (sprains) can weaken the tissue and put joints at risk for pain and osteoarthritis. Results will be used to guide the best routines for stretching exercises for athletics and rehabilitation, and to provide a framework for the design of artificial ligaments. Results will also be incorporated in the bio-mechanics classes taught by the co-principal investigators and in our popular web site. This grant will train two graduate students for careers in biomedical research. New findings will be presented at conferences and in journal papers.
The biomechanical behavior of connective tissues is important for understanding, quantifying, and treating injuries in these tissues. Mechanical behavior is also important when considering the wide use of grafts, as any graft should match the properties of native tissue for optimal function. One important behavior is the viscoelastic, or time-dependent, properties of tissues. For example, creep and relaxation are important components of tissue behavior, and investigation of such behavior takes careful consideration. Failure to accurately account for time-dependent recovery during unloaded periods will be a source of error when predicting behavior in response to future loads, especially if the unloaded period is short during serial testing. Another important behavior is the post-damage behavior of tissues. Tendons with sub-failure damage have different biomechanical behavior than normal tissues, including both elastic and viscoelastic changes, and therefore have compromised ability to carry out normal functions (i.e. joint movement and stabilization). By anticipating changes in mechanical properties resulting from such damage, it is possible to anticipate alterations in tendon behavior. By developing a method by which to gather information about the stress-strain state of a tissue noninvasively (i.e., via ultrasound), it is possible to move towards in vivo evaluations of human tissues. In the first experiments, tendons and ligaments were subjected to stress relaxation at various strains to determine rate strain-dependence, as well as stress relaxation followed by recovery at a low but nonzero strain to investigate recovery behavior. Relaxation rate in tendon was found to increase with increased input strain in tendon and decrease with increased input strain in ligament, and the rate of recovery was found to be much slower than that of the preceding relaxation (in both tendon and ligament) and also slower than that of a relaxation at the same low strain. The relaxation and recovery behavior of tendon was well described by Schapery’s nonlinear viscoelastic model through the physiologic strain range (0-6% strain). Next, diffuse damage was induced in tendons by subjecting them to an overstretch strain (exceeding the elastic limit) of 6.5, 9, or 13% strain. Stress relaxation and cyclic testing were performed on the tendon prior to and following overstretch such that the ratio of several parameters (such as peak stress, decrease in peak stress during cyclic testing; max stress, decrease in stress during relaxation testing) could be calculated and compared. Diffuse damage induced laxity in the tendon, resulting in decreased stress at a given strain. Damage also reduced the viscoelastic response of the tissue, resulting in less viscoelastic change at a given strain. This behavior led to the development of an "equivalent strain" model, in which tendon was modeled as if it were being subjected to a lower strain. With this model, strain-dependent parameters could be calculated and inserted into a constitutive model. In this study, Schapery’s nonlinear viscoelastic model was used and found to be predictive of post-damage mechanical behavior. Finally, the ability of ultrasound, with acoustoelastic (AE) theory, to characterize mechanical properties was tested. AE theory predicts that as a material is deformed, its acoustic properties are altered, and thus the amplitude of the reflected ultrasound echo (or, the echo intensity) would be changed. In this study it was demonstrated that under steady-state conditions, echo intensity is linearly related to strain and nonlinearly related to stress. During viscoelastic testing, echo intensity increased in a time-dependent fashion. In order to test the ability of the tool to detect mechanical compromise, tendons were subjected to the same diffuse damage model and echo intensity changes were compared before and after damage. Results found that the laxity introduced by diffuse damage resulted in reduced echo intensity changes, further reinforcing the concept of effective strain (echo intensity changes decrease as input strain decreases). A second damage model was performed when a tendinitis-like focal defect was created by injecting collagenase (digesting collagen in a small region of the tendon midsubstance). Focal damage induced in this manner resulted in local alterations in echo intensity changes. The collective body of work focused heavily on accurate characterization of tissue behavior, particularly time- and damage-dependent behaviors, while also analyzing the methods with which the data is gathered and the models used to describe them. The methods and analyses in this study aid in designing experiments that are both informative and time efficient, and gather more physiologically relevant data to better understand the mechanics of soft tissues in the body. Together, this information allows for a better understand of the field of biomechanics, a better understanding of the functional biology of soft tissues, insight into injury mechanisms and how they affect joint function, and metrics with which to measure clinical outcomes during healing and treatment.
