Bayesian inference on microstructural, hyperelastic models of soft tissue deformation.

Abstract

This thesis studies the modelling of soft tissue behaviour and whether Bayesian statistical techniques can be applied to models of soft tissue deformation in order to quantify the level of uncertainty in the values of a model's parameters. Fibrous soft tissues, such as tendon and skin, are ubiquitous in mammals and essential for our daily lives. Changes in the behaviour of these soft tissues, which are associated with changes in their microstructures, have a tremendous impact on people. Understanding how microstructure influences the macroscopic behaviour we observe in experiments is vital, therefore, and advances in our knowledge of soft tissue mechanics have many important applications in wider society. Furthermore, quantifying uncertainty in a model's estimates of parameters is key to understanding how well it can replicate physical behaviour and inform us of the relation between the microscale and the macroscale. Models of fibrous soft tissues can, broadly, follow one of two approaches. Phenomenological models can fit experimental data well and be versatile in terms of the scientific software they can be implemented in, but the parameters included in these models do not have a physical basis for inclusion. Therefore, while these models can be widely used and replicate observed data well, we do not learn anything about the relationship between microstructure and physical behaviour from their results. Microstructural models, by contrast, can be complex, but they enable us to study the effect that the properties and arrangement of tissue constituents have on mechanical behaviour. In this thesis, we complement existing work performed in microstructural modelling by developing a new microstructural model that, through realistic assumptions about the nature of tissue constituents, is tractable and contains only parameters that have a physical basis for inclusion. We show that the model fits mechanical experimental data on tendons and skin well when subjected to standard non-linear optimisation. Furthermore, by assuming that independently and identically distributed noise is present during the collection of the experimental data, we derive a Random Walk Metropolis Markov chain Monte Carlo algorithm that can be used to accurately sample from the posterior distribution of the model's parameters. Additionally, we obtain from the algorithm probable values for the parameters that are realistic, when compared with existing literature values.

Date of Award	31 Dec 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	William Parnell (Supervisor) & Tom Shearer (Supervisor)