Complex Deformations of Biological Soft Tissue: Tendons and Ligaments

  • James Gregory

Student thesis: Phd

Abstract

Tendons and ligaments are fibrous soft tissues which are vital for the structural and mechanical integrity of the human body. They possess a unique hierarchical microstructure, starting at the smallest scale with collagen molecules which aggregate to form collagen fibrils -- the most important mechanical component of tendons and ligaments, whose crimped geometry gives rise to complex non-linear stress-strain behaviour at the macroscale. Achieving a complete understanding of the relationship between the micro- and macroscale mechanics of these tissues is of interest to research groups spanning the fields of mathematics, material science, biology, and engineering. Accurate and reliable mathematical models of tendons and ligaments can be applied to predict internal stress distributions in vivo, a feat not possible through direct experimentation alone, providing valuable information to clinicians in instances of tissue damage and rupture. When researchers mathematically model tendons and ligaments, simplifying assumptions -- such as incompressibility and transverse isotropy -- have to be made. In the first part of this thesis, we analyse common assumptions by conducting finite element modelling of tendons and ligaments in idealised geometries. We show that if the direction of the collagen fibres is not carefully considered, unrealistic stress concentrations can form around the edge of the narrowest part of the tendon. We also evaluate the use of the isotropic von Mises yield criterion as an indicator of failure in soft tissue by comparing it with the anisotropic Hill yield criterion. We show that these two criteria produce different failure behaviour, adding to the emerging narrative that isotropic failure criteria are not suitable for biological soft tissues. In the second part of this thesis, we look more closely at failure in tendons and ligaments. We present a new microstructural model, based on the distribution of collagen fibril failure properties, which can produce the full range of stress-strain behaviour observed experimentally. Our model can account for certain features that existing models cannot capture, such as stress plateaus and step-like failure, whilst only including parameters that could, in principle, be measured experimentally. We fit our model to stress-strain data obtained from failure tests of mouse tail tendon fascicles and find good agreement. Most importantly, the parameter values found through fitting align with experimentally-obtained values within the literature.
Date of Award31 Dec 2022
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorAndrew Hazel (Supervisor) & Tom Shearer (Supervisor)

Keywords

  • Multiscale modelling
  • Biomechanics
  • Ligaments
  • Damage
  • Non-linear solid mechanics
  • Soft tissue mechanics
  • Tendons

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