Modelling in vitro growth of dense root networks

An algorithm for the simulation of the growth of root systems on deformable domains

“…Eulerian descriptions are widely used in many areas of physical sciences including fluid mechanics and were applied to root models by Bastian et al (2008). Alternatively, deformable grids can be used to assign physical quantities to a given material cell of the grid.…”

“…Density-based models aggregate root properties into root distribution functions. Changes with time of density distribution functions can then be modelled empirically, for example using sliding exponential profiles King et al, 2003) or mechanistically using partial differential (Acock and Pachepsky, 1996;Bastian et al, 2008). In the latter case, analytical methods can provide simple growth functions (de Willigen et al, 2002;Schnepf et al, 2008).…”

Root growth: homogenization in domains with time dependent partial perforations

“…This root growth model is inspired by [10,16]. It is related to the model studied in [4], where the growth velocity depends on the nutrient concentration with a saturation effect: the roots can only take up to a maximal nutrient concentration. Note that this implies…”

“…For a very dense root network, representative for roots growing in a flooding soil or in medium, one can consider the root density distribution and define a continuous model for the growth of a root network [4]. This model is a system consisting of a transport equation for the root tip density n, and an ordinary differential equation for root length density ρ,…”

A Flexible Mathematical Model Platform for Studying Branching Networks: Experimentally Validated Using the Model Actinomycete, Streptomyces coelicolor

“…Branched networks are highly scalable from bacterial hyphal structures in the μm to mm spatial range and minutes to hours timescales through to colonies of Armillaria bulbosa occupying 150,000 square metres over thousands of year timescales [1]. These scales represent a significant challenge to the modeling of such dynamic recursive structures, yet modeling these systems has been valuable in revealing many emergent properties of branched networks, yielding important details regarding angiogenesis in organs and tumors [2]–[6], transport networks in fungi [1], [7]–[9] and amoebae [2]–[6], [10] and the development of root systems in plants [11], [12]. Often however such models are system specific and lack flexibility.…”