Frédéric Blaise

Numerical modelling of shape regulation and growth stresses in trees. II. Implementation in the AMAPpara software and simulation of tree growth

Abstract. The main objective of this paper is to present the results of a study of the interactions between the growth and design of a tree with regards to biomechanical factors at the plant level. A numerical incremental model dedicated to the calculation of tree mechanical behaviour has been integrated in the plant architecture simulation software AMAPpara. At any stage of tree growth, a new equilibrium was calculated considering the weight increment applied on the structure, i.e. the mass of new wood layers and vegetative elements, as well as the biomechanical reaction caused by cell maturation strains in both normal and reaction wood. The resulting incremental displacements allowed the tree shape to be modified. The field of growth stresses was calculated within the stem, using a cumulative process taking into consideration the past history of each growth ring. The simulation results of trunk and branch shape, as well as internal stresses, were examined after consideration of different growth strategies. A block of trees was also simulated in order to show the influence of spatial competition on stem curvature and the variability in growth stress.

Simulation of the Growth of Plants — Modeling of Metamorphosis and Spatial Interactions in the Architecture and Development of Plants —

In the past, numerous techniques have been used in the representation of plants. The Plants Modeling Unit of CIRAD developed an original method of plant growth simulation based on botanical notions of plant architecture. But in simulating metamorphosis, the notion of a reference axis which shows all the stages of differenciation in a branch throughout its growth is needed. Also, if we consider the simultaneity of biological events which characterize a plant’s functioning, we can study the environmental (nutrition and precipitation needs) and spatial (crowding, light influence) interactions. The reference axis is structured like a finite automaton and the discrete events simulation (scheduler) is used for the parallel simulation of the growth.

A model simulating interactions between plant shoot and root architecture in a non-homogeneous environment

Modelling of plant structure and growth has undergone major changes in the last few decades. Two major lines of research have been pursued: the integration of ecophysiological knowledge in process-based models which usually lack a description of plant topology and geometry, and the generation of 3-D virtual plants using morphogenetic models, which simulate the architectural development in a stable and homogeneous environment. There is now a trend to merge these two approaches i.e. to link plant architecture and function. This trend is based on the recognition that plant structure: (i) is the joint output of physiological processes and the morphogenetic programme of the plant, (ii) determines its external environment and regulates its functioning accordingly (iii) directly conditions the physiological processes within the plant e.g. allocation of photosynthates. Therefore, double regulation of the ecophysiological processes by the plant and its neighbours, and of the morphogenetic program by the availability of the internal and external resources produced or consumed by these physiological processes, is explicitly considered in the same model. Such an approach is being implemented in the software, AMAPpara, which simulates the parallel functioning and growth of plants which interact with each other. AMAPpara also includes an architectural description of aerial and root systems. The plant morphogenetic program is a priori parameterised according to the selected species i.e. topology, geometry and allometric relationships are considered for botanical elements such as leaves, as well as the maximum life-span of leaves and roots etc. The actual architectural development of the plant is then regulated by physical constraints e.g. competition for space and light, and physiological processes e.g. water transpiration and carbon assimilation. Such processes themselves depend on the structure and biophysical environment of the plant e.g. internal hydraulic architecture, competition for space among neighbouring trees and light interception. This paper presents a new model which investigates the influence of the environment on root system development and the resulting consequences on the growth of the whole plant.

Distance contained centerline for virtual endoscopy

Collision detection and flight path planning are difficult problems in virtual navigation in complex environments, especially in endoscopic navigation inside human organs. We solve these problems in elongated environment through a combination of shape keeping centerline and the distance from each internal point to boundary. Distance contained centerline (DCC) algorithm is presented to extract a line-shaped skeleton and compute the distance from skeleton to each erosion layer. In addition, we combine voxel-coding to remove spurious branches adaptively and reorganize topology accurately. Experiments show that the centerline obtained through DCC represents the complex shape of elongated objects fairly well and guides virtual navigation effectively.