The study of alternatives to chemical methods of nematode control in agriculture has received significant recent interest. One such method is biological control using nematode trapping fungi such as Arthrobotrys superba. To understand how these fungi can be implemented as effective nematicides, it is essential to study their outgrowth into soil from localized nutrient resources. In this paper, we use a mathematical model to investigate the outgrowth of fungi into an environment essentially without available nutrients capable of supporting net growth. By comparing model solutions with experimental results, we show that in such circumstances, continual mycelial expansion can only be obtained if internal metabolites are actively translocated through the mycelium. Predictions are made concerning the maximal extension possible from a given quantity of nutrients and a testable functional relationship between the two is derived. Using this modelling technique we are able to map not only biomass extent but also biomass distribution at each stage. The type of environmental heterogeneity investigated here is encountered by many species of fungi in nature and is of relevance for the introduction of specific fungi into soil for biological control or bioremediation purposes.