Abstract
Individual skeletal muscle fibres exist in several different types, distinguished by the myosin they produce in order to contract. The type of fibres a muscle contains, as well as their locations, impacts the properties of the muscle as a whole. Fibre types are largely a function of recent usage history, controlled by the nervous system. This means fibres are able to change type over time, especially due to exercise patterns or advancing age. It is therefore important
to be able to quantify the spatial distributions of muscle fibres so that the biological drivers of ageing can be better understood.
Much of the previous work to analyse spatial patterns in muscle fibres has focussed on assessing clustering behaviour in the binary fibre types. We review and discuss several approaches that aim to test whether the distribution is random or there is evidence of spatial dependence between neighbouring fibres.
In reality, fibre types exist on a continuum and fibres do not switch types immediately. Instead, this is a gradual process, and while a fibre is changing types it contains more than one type of myosin. These hybrid fibres are of interest because they give insight into the areas where fibres are undergoing type transitions. To account for the hybrid fibres and utilise the extra information they provide, we choose to model the continuous values obtained
through the staining process, which measure the amount of slow myosin a fibre has.
Mixture models are a powerful tool that allow us to assume the stain value for each fibre depends on a latent fibre type, with spatial patterns in the values for each type. This thesis develops models for the stain values, utilising mixture models to assume they come from two underlying subpopulations of fibres. We discuss two classes of models to describe the spatial patterns in the stain values for each type. Conditional autoregressive (CAR) models include a trend based on spatial covariates as well as local dependence between neighbouring fibres. The spatial dependence parameters can be usefully interpreted to summarise the level of correlation between neighbouring fibres across the muscle as a whole. Generalised additive models (GAMs) are a flexible extension to generalised linear models. They permit a non-linear trend in the stain values and the spatial dependence is incorporated through this trend and the inclusion of a smoothing parameter. The parameters of a GAM are not as easy to interpret but they allow visualisation to identify any areas in the muscle with particularly high or low stain values. By also incorporating hierarchical structure in both of these models we are able to summarise the overall spatial trends in the stain values for a group of muscles. In order to demonstrate the utility of these models to describe the spatial distribution of the fibres, we apply the analyses to three groups of soleus muscles from mice differing in age and exercise status.