Mathematical modeling of ligaments and tendons

Area of Science:

• Biomechanics
• Biomaterials Science
• Computational Biology

Background:

• Ligaments and tendons are crucial for human body structure and function.
• Extensive research exists on experimental investigations of these tissues.
• Mathematical modeling offers significant insights into their mechanical behavior.

Purpose of the Study:

• To present a comprehensive survey of mathematical modeling developments for ligaments and tendons over the last two decades.
• To categorize and discuss existing mathematical descriptions of these tissues.
• To provide a detailed examination of prominent viscoelastic models.

Main Methods:

• Literature review of mathematical modeling studies on ligaments and tendons from the past 20 years.
• Classification of models into elastic and viscoelastic categories based on time-dependent behavior.
• Detailed discussion of two key viscoelastic models: quasi-linear viscoelasticity (QLV) and single integral finite strain (SIFS).

Main Results:

• Mathematical models for ligaments and tendons are broadly classified as elastic or viscoelastic.
• Elastic models focus on nonlinear mechanical responses without time-dependent effects.
• Viscoelastic models incorporate time-dependent behavior, with QLV being widely used and SIFS being a recent development.

Conclusions:

• Mathematical modeling is essential for understanding ligament and tendon mechanics.
• The evolution of models shows a progression from elastic to more complex viscoelastic descriptions.
• QLV and SIFS represent significant advancements in modeling the time-dependent properties of these tissues.