IRG/WP 10-YYXXX THE INTERNATIONAL RESEARCH GROUP ON WOOD PROTECTION Section Y VVVVVVVVVV Modelling hyphal growth of the `bioincising ́ fungus Physisporinus vitreus

The white-rot fungus Physisporinus vitreus preferentially degrades the pit membranes of bordered pits in tracheids and subsequently enhances wood permeability. Thus, P. vitreus can be used to improve the uptake of wood preservatives and environmentally-benign wood modification substances. This process can be used to enhance the use and sustainability of native conifer wood species by the wood industry. Mathematical modelling in combination with laboratory experiments is a powerful and efficient investigation method that enables a deeper insight into complex interactions between biological systems and their environment. The objective of mathematical modelling is not to develop an extremely complex system of equations in an attempt to mimic reality. Rather, it is applied to reduce a complex (biological) system into a simpler (mathematical) system that can be analyzed in more detail and from which key properties can be identified, isolated and investigated. In addition, a verified mathematical model enables to optimize hyphal growth and impact of the P. vitreus. Enhanced uptake of wood preservatives and environmentally-benign wood modification substances of Norway spruce wood and optimized quality control processes would be of importance for the usability, durability and sustainability of wooden structures in civil engineering. In this paper we present a mathematical model of hyphal growth and expansion of P. vitreus in heartwood of Norway spruce. The model enables to investigate the global penetration front of the fungus in wood as function of the control parameters as well as its shape and penetration depth. This model will serve to assist the choice of pellet concentration and reaction times that are required to induce a defined degree of wood permeability by the fungus.