A Mathematical Model of Vibrations and Fluid Flow within Tendons

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute

Abstract

Over the following six months, I further developed my key research question and began the preliminary mathematical work needed to address this. My current hypothesis is that high strain rate forms of tendon loading cause an alteration in the average molecular weight and concentration of hyaluronic acid, a polymer which is the key determinant of tendon fluid viscoelasticity. This has already been seen to occur with synovial fluid within joints, but has not yet been investigated in tendons. My research is focused on developing a mathematical model to understand how alterations in the hyaluronic acid content, and hence viscoelasticity of tendon fluid, affects fluid exudation and local shear stresses. I am also interested in how these outcomes tie in with fibre and fascicle strain rates. Additionally, we have formed several collaborations through which we will investigate how the content and molecular weight of hyaluronic acid changes within tendinopathy.

I have developed a preliminary microscopic tendon model which looks at the effects of fluid viscoelasticity on shear stress and fluid exudation between two rigid fascicles or fibres. I am currently using the Phan-Thien Tanner (PTT) Constitutive equations, commonly used to model synovial fluid flow within joints, to capture the viscoelastic effects of tendon fluid. The next step will be to extend this model to extensible fascicles and fibres. From here I will be looking into developing a macroscopic model, either through homogenisation theory or by adapting current porous media models to account for non-Netwonian properties of the pore fluid (modelled using the PTT equations).

Data Collection and Collaborations
Initially I will carry out rheometer experiments with hyaluronic acid, allowing me to fit parameter values for the PTT equations used within my model. Through our collaborations we will be able to obtain more realistic data for my model, and confirm that hyaluronic acid changes do indeed occur. These collaborations include:

Academic Collaborators
1. Peter Malliaras (Monash University, Australia and my fourth supervisor) and Steven Pearson (Salford University, UK) -
2. Carr Group (NDORMs Oxford)

Industrial Collaborators
3. Tassos Anastassiades - Professor at Queens University, Canada and founder of Anacoti Ltd.


This project falls within the EPSRC mathematical sciences research area, as well as healthcare technologies.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R512333/1 01/10/2017 30/09/2021
2109853 Studentship EP/R512333/1 01/10/2017 30/09/2021 Isabelle Scott