Geometrical Modelling of Muscle Cells Based on Functional Representation of Polygons

A geometrical modelling tool allowing construction of models of living cells and their organelles would facilitate understanding of biological processes at the cellular level. Here we describe a technique of skeletal muscle cells modelling, and a construction of the model based on the theory of implicit surfaces and their binary operations. The geometry of the cell is defined by means of parallel modelling planes perpendicular to its longitudinal axis. In each plane, the number, shape and topology of cell organelles is defined by means of functionally represented polygons. The model is obtained by interpolation between the planes. This approach allows to generate approximations of surfaces and to estimate the volume and surface densities of organelles in the model.