Use of process-based system dynamic models to generate biologically aware 3D trees

Simulations of plant growth using computers have a long story. Botanists and computer scientists have tried to develop methods to create synthetic alternatives of natural objects for over forty years (Deussen and Lintermann, 2006; Prusinkiewicz and Lindenmayer, 2012). Many scientific areas use these models for scientific purposes. For example, in botany models are useful to assess physiological parameters (Henke et al., 2016). The creation of geometrical plant models helps researchers to visually validate biological process such as the interaction of plants with light and environment. Plants models are also used in ecology to visualize information of deep-lying processes, making scientists aware of “invisible” things happening. Examples are represented by the development of plants in reaction to disease or stress and the plants’ grow after pruning (Fabrika et al., 2018). The work presented here has the goal to fill the gap between 3D rendering engine and biological process-based system dynamic models linking the two aspects with a system of ordinary differential equations (ODEs). The link operates in either directions: ODEs system generates the input for 3D engine and the input parameter for the ODEs system is computed in the 3D environment on the other way around (e.g., the amount of light or the quantity of biomass). For example, taking the internode (i.e., the distance between two consecutive nodes in a branch, L [cm]) growth as an exemplificative state variable of the ODE system, the first equation presented in Figure 1 models the growth of the internode i-th by a logistic function depending on water resource (W [cm3 /cm3 ]) and a species-specific growth factor (g, [1/d]). The second system equation presented in Figure 1 defines the availability of water W conditioned by precipitation (R [1/d]), transpiration (plant water uptake) function of the total plant biomass (B [kg]) and evaporation where Lmax ([cm]) is the internode maximum length, r ([1/d/kg2 ]) is the water uptake rate and l ([1/d]) is the evaporation coefficient. During each time step, the ODEs system computes the internode length (Li) passed as input in 3D engine. The 3D system utilizes the given value as an input parameter of its rendering engine, it also computes the total biomass of the synthetic tree (B), and then returns a new value for the ODE system. The ability of the proposed approach is to integrate time process based mathematical models of biological systems in 3D engines. This can deliver several benefits in the field such as seeing at a glance whether a certain model is related to reality (Yi et al., 2018), modelling future plantation trends for production purposes, evaluate possible interventions, and display results clearly also for end users. Additional studies are in progress in this direction to improve both biological modelling and 3D engine rendering.