Derivation of a Mathematical Model for Substrate Transport and Reaction in Submerged Fungal Pellet Cultures

A relevant factor determining biomass viability in mycelial pellet cultures is the efficiency of nutrient transport to metabolically active cells within the pellets. In this work, a novel mathematical model is derived by upscaling the substrate mass transport microscale governing equations in submerged, agitated cultures. The model predicts concentration dynamics within and outside the pellets, accounting for both biological and operational parameters across different types of culture vessels. It also incorporates terms associated with pellet growth and shaving. The model was validated using glucose kinetics data obtained from shake-flask cultures of Laccaria trichodermophora pellets. Numerical analysis revealed that deformation of the pellets’ interface due to growth or shaving determines the predicted average glucose concentration, which is one of the key findings of this work, along with the fact that this effect becomes particularly pronounced under conditions of intense agitation.