Morphological Analysis from Images of Hyphal Growth Using a Fractional Dynamic Model

The development of methods capable of accurately characterising the morphology of ?lamentous microbes represents a signi?cant challenge to biotechnologists. This is because the productivity of many industrial fermentation processes is heavily dependent on the morphological form adopted by an organism. It is therefore of signi?cant value if a quantitative model and associated metric(s) for morphological forms determined by complex phenotypes can be determined non-invasively, e.g. through image analysis. Speci?c interest is in the quanti?cation of the branching behaviour of an organism. This is due to the link between branching frequency, biomass and metabolite production. In this paper we present a model for three-dimensional microbial growth that is based on a fractional dynamic model involving separable coordinate geometry. This provides the focus for the approach reported in this paper where microbial growth can be quanti?ed using a sample microscopic digital image. In particular, we study the fractal dimension of fungal mycelial structures by generating a ‘fractal signal’ based on the object boundary. In the analysis of a population of Aspergillus oryzae mycelia, both the fractal dimension and hyphal growth unit are found to increase together over time. Further, through an extensive analysis of different populations of Penicillium chrysogenum and A. oryzae mycelia, cultivated under a variety of different conditions, we show that there is a statistically signi?cant logarithmic correlation between the boundary fractal dimension and hyphal growth unit.