Abstract:
Three-dimensional structural information has been successfully integrated into models of cardiac function at the tissue and organ level, offering insight into the complex relationship between pathological structure and impaired cardiac function. However, spatial information has yet to be incorporated into functional models of cardiac myocytes, in part because sufficient quantitative spatial information does not yet exist. The aim of this study was to establish a framework for using spatial point patterns to quantify and stochastically model the arrangement of myofibrils and mitochondria in cross-section. Positional information was obtained from electron micrographs of rat ventricular myocytes. Each organelle's position was defined by its centre of mass (centroid) and the arrangement of these centroids was analysed as a spatial point pattern. Polynomial models were fitted to provide the most appropriate measure of trends in centroid intensity. Nearest neighbour and pairwise distance functions were used to characterise how the centroids interacted with each other. Monte Carlo tests were used to compare the results of these interaction functions first to simulations of a completely random (Poisson) process, and then to other spatial point process models, to identify the best model for organelle arrangement.. Myofibril and mitochondrion patterns were modelled both separately and together, as hardcore processes. The model that was best able to simulate the observed patterns was the multi-Strauss-hardcore model, which incorporated both myofibrils and mitochondria, with a homogeneous intensity fitted to each. This model incorporated a hardcore radius and a further region of Strauss interaction. These were both separately determined for myofibril-myofibril, mitochondrion-mitochondrion and myofibril-mitochondrion interactions. Results from this model demonstrated that organelles of the same type are less likely to lie close together than organelles of different types - providing a quantitative description of the regularly alternating pattern of myofibrils and mitochondria. This study forms the basis for further inferential studies that can quantitatively characterise cardiac myocyte organisation in both healthy and diseased states. Incorporating such spatial information into computational models of cardiac myocyte function will allow us to explore the effects of altered cell structure on cardiac function on multiple scales.