Modelling porcine muscle fibre patterns
In this thesis we try to model the spatial pattern formed by slow oxidative (SO) fibres in pig muscle. Unlike the other mammals, the muscle fibre pattern in porcine muscle is characterised by cluster of SO fibres dispersed throughout the tissue. The biological interests of modelling such a configuration are, on one hand, its peculiarity, and, on the other hand, the effective contribution of such fibre patterns to the quality of pork meat. Transverse sections of muscle samples are stained to enable discrimination of the fibres of interest. The distribution of the SO clusters is investigated in low magnification cross-sectional images (x5). Each image is regarded as a spatial point process where points are the centroid of the corresponding clusters. Edge effects are minimised by discarding from the analysis those clusters that are touching the edges of the image. The minimum distance found between cluster centres suggests that clusters are distributed throughout the tissue according to some repulsive process. Higher magnification images (x10) are used to study SO fibre clusters in terms of their characteristics, namely the number of constituent fibres, total area and shape. One arrangement of particular interest is that, given the number of constituent fibres, cluster cells are arranged in a concentric configuration. It is believed that the most centrally located fibre in a cluster corresponds to its respective primary fibre, the first constituent cell in any cluster. In this thesis, we suggest models to fit the porcine pattern of fibres based on the minimum inter-cluster distance. All these models are based on using the minimum inter-primary distance established in the very beginning of the cluster process. These models vary essentially in the way in which cells are added to the primary fibre. Basically, cluster cells are either (1) members of the primary’s neighbourhood or are (2) neighbour cells of any of the fibres in the cluster. For each of the methods described above we consider a nearest neighbour (NN) version, i.e., (1) from the primary’s neighbourhood cells are added in increasing order and (2) each new cell added to the cluster is the NN of a fibre of the cluster.