Inside solid substrate particles, there are gradients in oxygen, carbon dioxide, sugar and moisture levels that are caused by growth of fungal hyphae over the particle surface and penetration of hyphae into the particle core. Previous studies have shown that conditions inside particles influence the physiological behavior of the fungus. The gradients have been suggested to cause higher product yield and quality. It is therefore important to have a quantitative understanding of these gradients. Mathematical models are set up to predict the gradients in the concentration of oxygen and other substances in the fungal mat and the core of the substrate particle. We divide the fungal mycelium into three different morphological forms. Coming from the air, we see the aerial mycelium, a wet fungal mat at the particle surface and penetrative mycelium. The wet mat can be divided in an aerobic upper layer and a lower layer that is devoid of oxygen. Oxygen depletion has a large effect on fungal behavior. An essential factor in controlling solid-state fermentations is the rate of fungal heat production. This is proportional to the respiration rate of the fungus, which in turn depends on the oxygen gradient inside the particles. We have discovered that a very important factor is the production of aerial mycelia. Work will now focus on modeling of the formation of aerial mycelia and of fungal growth inside the seed coat where aerial mycelia do not form.