Plant Biomechanics Research Articles

Measurement accuracy and uncertainty in plant biomechanics.

All scientific measurements are affected to some degree by both systematic and random errors. The quantification of these errors supports correct interpretation of data, thus supporting scientific progress. Absence of information regarding reliability and accuracy can slow scientific progress, and can lead to a reproducibility crisis. Here we consider both measurement theory and plant biomechanics literature. Drawing from measurement theory literature, we review techniques for assessing both the accuracy and uncertainty of a measurement process. In our survey of plant biomechanics literature, we found that direct assessment of measurement accuracy and uncertainty is not yet common. The advantages and disadvantages of efforts to quantify measurement accuracy and uncertainty are discussed. We conclude with recommended best practices for improving the scientific rigor in plant biomechanics through attention to the issues of measurement accuracy and uncertainty.

Researches into Structure and Motion of Plants from Mechanical View Point

In the past two or three decades, I have studied a number of topics concerning plant biomechanics or plant biomimetics, such as structure of folding paper observed in leaves and flowers of plants, folding storage and unfolding manner observed in Sensitive Plant, mechanical functions of sepals and petals observed in lily flower bud, vein structure and mechanical properties of a leaf of Santa Cruz Water Lily, mechanical behavior of tendrils with spiral structure supporting cucumber body, adherence in the column of Stylidium caesupitosum and high speed rotation ... etc. From these researches, several interesting ideas or mechanisms adopted by plants have been clarified. For examples, the unfolding vein angle of regularly corrugated simple leaves is chosen as satisfying smooth and earlier unfolding with relatively small energy, the thick main veins of giant water lily have the cross-section with a tear drop shape including many voids to accomplish simultaneously a large bending rigidity and a body as light as possible, very complicated closing motion of a sensitive plant (Mimosa pudica) leaflet can be carried out by a simple rotation of a small pulvinus and a combination of a few installation angles of leaflet on the mid rib, or the incredibly rapid rotation of Stylidium flower column may be performed by the quick release of strain energy stored in a bending part of column. A number of interesting topics are shown here.

On the Relationship between Aquatic Plant Stem Characteristics and Drag Force: Is a Modeling Application Possible?

This paper presents a basic model that shows the relationship between the diameter of a stem and its flexural rigidity. The model was developed from experimental measurements of biomechanical traits (i.e., tensile and bending traits like maximum forces, stresses, moduli of elasticity, flexural rigidity, strain) of three freshwater macrophyte species (Elodea canadensis Michx., Potamogeton pectinatus L., and P. crispus L.), reflecting the seasonal changes in plant biomechanics throughout the vegetative season. These were obtained with the use of a bench-top testing machine in 2016 and 2017. The presented calculations are based on the ratio of drag-to-bending forces, in which the flexural rigidity plays a key role. The proposed model has the form EI = adb, and two approaches based on a regression analysis were applied to determine the parameters of the model—a and b. In the first method, the parameters were identified separately for each day of measurement, while in the second method, the coefficient b was calculated for all data from all days as a unified number for individual plants. The results suggest that coefficient b may provide information about the proportion of changes in drag forces depending on plant stiffness. The values of this coefficient were associated with the shape of the stem cross-section. The more circular the cross-section, the closer the value of the parameter was to 1. The parameter values were 1.60 for E. canadensis, 1.98 for P. pectinatus, and 2.46 for P. crispus. Moreover, this value also depended on the density of the cross-section structure. Most of the results showed that with an increase in stem diameter, the ratio between the drag and bending forces decreased, which led to fewer differences between these two forces. The model application may be introduced in many laboratory measurements of flow–biota interactions as well as in aquatic plant management applications. The implementation of these results in control methods for hydrophytes may help in mitigating floods caused by increases to a river channel’s resistance due to the occurrence of plants.

The strength of plants: theory and experimental methods to measure the mechanical properties of stems.

From the stems of agricultural crops to the structural trunks of trees, studying the mechanical behaviour of plant stems is critical for both commerce and science. Plant scientists are also increasingly relying on mechanical test data for plant phenotyping. Yet there are neither standardized methods nor systematic reviews of current methods for the testing of herbaceous stems. We discuss the architecture of plant stems and highlight important micro- and macrostructural parameters that need to be controlled and accounted for when designing test methodologies, or that need to be understood in order to explain observed mechanical behaviour. Then, we critically evaluate various methods to test structural properties of stems, including flexural bending (two-, three-, and four-point bending) and axial loading (tensile, compressive, and buckling) tests. Recommendations are made on best practices. This review is relevant to fundamental studies exploring plant biomechanics, mechanical phenotyping of plants, and the determinants of mechanical properties in cell walls, as well as to application-focused studies, such as in agro-breeding and forest management projects, aiming to understand deformation processes of stem structures. The methods explored here can also be extended to other elongated, rod-shaped organs (e.g. petioles, midribs, and even roots).

Botanical materials based on biomechanics

Botanical simulation plays an important role in many fields including visual effects, games and virtual reality. Previous plant simulation research has focused on computing physically based motion, under the assumption that the material properties are known. It is too tedious and impractical to manually set the spatially-varying material properties of complex trees. In this paper, we give a method to set the mass density, stiffness and damping properties of individual tree components (branches and leaves) using a small number of intuitive parameters. Our method is rooted in plant biomechanics literature and builds upon power laws observed in real botanical systems. We demonstrate our materials by simulating them using offline and model-reduced FEM simulators. Our parameters can be tuned directly by artists; but we also give a technique to infer the parameters from ground truth videos of real trees. Our materials produce tree animations that look much more similar to real trees than previous methods, as evidenced by our user study and experiments.

Invertebrate biomechanics

Invertebrate biomechanics focuses on mechanical analyses of non-vertebrate animals, which at root is no different in aim and technique from vertebrate biomechanics, or for that matter the biomechanics of plants and fungi. But invertebrates are special - they are fabulously diverse in form, habitat, and ecology and manage this without the use of hard, internal skeletons. They are also numerous and, in many cases, tractable in an experimental and field setting. In this Primer, we will probe three axes of invertebrate diversity: worms (Phylum Annelida), spiders (Class Arachnida) and insects (Class Insecta); three habitats: subterranean, terrestrial and airborne; and three integrations with other fields: ecology, engineering and evolution. Our goal is to capture the field of invertebrate biomechanics, which has blossomed from having a primary focus on discoveries at the interface of physics and biology to being inextricably linked with integrative challenges that span biology, physics, mathematics and engineering.

Homogenization of Biomechanical Models for Plant Tissues

In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and Stokes equations for fluid flow inside the cells. The chemical process in cells and the elastic properties of cell walls and middle lamella are coupled because elastic moduli depend on densities involved in chemical reactions, whereas chemical reactions depend on mechanical stresses. Using homogenization techniques we derive rigorously a macroscopic model for plant biomechanics. To pass to the limit in the nonlinear reaction terms, which depend on elastic strain, we prove the strong two-scale convergence of the displacement gradient and velocity field.

Neighbourhood structure and light availability influence the variations in plant design of shrubs in two cloud forests of different successional status.

Plant design refers to the construction of the plant body or its constituent parts in terms of form and function. Although neighbourhood structure is recognized as a factor that limits plant survival and species coexistence, its relative importance in plant design is not well understood. We conducted field research to analyse how the surrounding environment of neighbourhood structure and related effects on light availability are associated with changes in plant design in two understorey plants (Palicourea padifolia and Psychotria elata) within two successional stages of a cloud forest in Costa Rica. Features of plant neighbourhood physical structure and light availability, estimated using hemispherical photographs, were used as variables that reflect the surrounding environment. Measures of plant biomechanics, allometry, branching and plant slenderness were used as functional plant attributes that reflect plant design. We propose a framework using a partial least squares path model and used it to test this association. The multidimensional response of plant design of these species suggests that decreases in the height-based factor of safety and increases in mechanical load and developmental stability are influenced by increases in maximum height of neighbours and a distance-dependence interference index more than neighbourhood plant density or neighbour aggregation. Changes in plant branching and slenderness are associated positively with light availability and negatively with canopy cover. Although it has been proposed that plant design varies according to plant density and light availability, we found that neighbour size and distance-dependence interference are associated with changes in biomechanics, allometry and branching, and they must be considered as key factors that contribute to the adaptation and coexistence of these plants in this highly diverse forest community.

Microbead encapsulation of living plant protoplasts: A new tool for the handling of single plant cells.

Premise of the study:Understanding plant cell biomechanics has been hampered by a lack of appropriate experimental tools. Here we introduce a protocol for the incorporation of individual plant protoplasts into precisely sized agarose microbeads. This technology may lead to new ways to manipulate the physical and chemical microenvironment of individual plant cells.Methods and Results:Living protoplasts obtained from BY-2 tobacco suspension cultures were continuously incorporated into a stream of agarose microdroplets, collected in cooled mineral oil as gelled microbeads, and then transferred into liquid MS medium for culture. In this first report, we show that spherical microbeads containing living protoplasts can be easily generated in quantity and that these encapsulated cells continue to grow and divide.Conclusions:Microbead encapsulation of protoplasts affords the opportunity to precisely control the physical microenvironment of individual plant cells. Ultimately, this method may help facilitate novel studies in plant biomechanics.

Self‐X Materials and Structures in Nature and Technology: Bio‐inspiration as a Driving Force for Technical Innovation

Over the course of 3.8 billion years of biological evolution, nature has found the answers to many engineering problems. The aim of biomimetics is to analyse and tap biology's potential as a huge reservoir for innovative solutions. Thomas Speck, Professor and Director of the Plant Biomechanics Group (PBG) at the University of Freiburg and the Freiburg Centre for Interactive Materials and Bioinspired Technologies (FIT), Jan Knippers, Professor and Head of the Institute of Building Structures and Structural Design (ITKE) at the University of Stuttgart, and Olga Speck, a researcher at the PBG, scientific coordinator of FIT and manager of the Competence Network Biomimetics at Freiburg, explain how biological material systems with self‐x properties are cost‐efficient, multifunctional, and can be environmentally friendly; and with several billion trial runs, have surely stood the test of time.

Measuring the Mechanical Properties of Plant Cell Walls

The size, shape and stability of a plant depend on the flexibility and integrity of its cell walls, which, at the same time, need to allow cell expansion for growth, while maintaining mechanical stability. Biomechanical studies largely vanished from the focus of plant science with the rapid progress of genetics and molecular biology since the mid-twentieth century. However, the development of more sensitive measurement tools renewed the interest in plant biomechanics in recent years, not only to understand the fundamental concepts of growth and morphogenesis, but also with regard to economically important areas in agriculture, forestry and the paper industry. Recent advances have clearly demonstrated that mechanical forces play a crucial role in cell and organ morphogenesis, which ultimately define plant morphology. In this article, we will briefly review the available methods to determine the mechanical properties of cell walls, such as atomic force microscopy (AFM) and microindentation assays, and discuss their advantages and disadvantages. But we will focus on a novel methodological approach, called cellular force microscopy (CFM), and its automated successor, real-time CFM (RT-CFM).

On measuring the bending strength of septate grass stems.

• Reliable testing methodologies are a fundamental tenet of scientific research. However, very little information is found in the literature explaining how to accurately measure the structural bending strength of plant stems. It was hypothesized that the most commonly employed loading configuration used in bending experiments (placement of loading anvil at an internodal region of the stem or stalk) may significantly alter test results and introduce errors in bending strength measurements of plant stems.• Four types of mechanical tests were performed on bamboo (Phyllostachys aurea), giant reed (Arundo donax), and maize (Zea mays) to investigate how different loading configurations employed during three-point bending experiments affect test results of septate grass stems and to develop a testing protocol that provides reliable measures of stalk bending strength.• RESULTS confirmed the hypothesis that internodal-loaded three-point bending test can produce erroneous bending strength measurements. This testing methodology causes plant stems to break prematurely and produces failure types and patterns incongruent with stalks that broke in their natural (in situ) environment. In contrast, a modified test configuration produces natural failure patterns and more accurate measurements of bending strength.• Reliable measurements of stalk bending strength can be obtained by maximizing the span length of bending tests and placing the loading anvil at stronger and denser nodal tissues. These results are relevant to ecological and evolutionary plant biomechanics studies as well as agronomic breeding studies focused on measuring plant phenotypes such as stalk lodging strength, or on improving bending strength of septate plant stems.

Antisense expression of the fasciclin-like arabinogalactan protein FLA6 gene in Populus inhibits expression of its homologous genes and alters stem biomechanics and cell wall composition in transgenic trees.

Fasciclin-like arabinogalactan proteins (FLAs) play important roles in the growth and development of roots, stems, and seeds in Arabidopsis. However, their biological functions in woody plants are largely unknown. In this work, we investigated the possible function of PtFLA6 in poplar. Quantitative real-time PCR, PtFLA6-yellow fluorescent protein (YFP) fusion protein subcellular localization, Western blotting, and immunohistochemical analyses demonstrated that the PtFLA6 gene was expressed specifically in the xylem of mature stem, and PtFLA6 protein was distributed ubiquitous in plant cells and accumulated predominantly in stem xylem fibres. Antisense expression of PtFLA6 in the aspen hybrid clone Poplar davidiana×Poplar bolleana reduced the transcripts of PtFLA6 and its homologous genes. Transgenic plants that showed a significant reduction in the transcripts of PtFLAs accumulated fewer PtFLA6 and arabinogalactan proteins than did the non-transgenic plants, leading to reduced stem flexural strength and stiffness. Further studies revealed that the altered stem biomechanics of transgenic plants could be attributed to the decreased cellulose and lignin composition in the xylem. In addition expression of some xylem-specific genes involved in cell wall biosynthesis was downregulated in these transgenic plants. All these results suggest that engineering the expression of PtFLA6 and its homologues could modulate stem mechanical properties by affecting cell wall composition in trees.

Biomechanical properties and morphological characteristics of lake and river plants: implications for adaptations to flow conditions

Biomechanical properties and morphological characteristics of stems of eight species of submerged aquatic plants were studied to analyse (1) differences between river and lake specimens, (2) seasonal differences between winter/spring and summer/autumn specimens, and (3) change of biomechanical properties and morphological characteristics along the stems. The data show that river macrophytes display not only characteristic biomechanical traits and morphological characteristics specific to their hydraulic habitats, but also distinctive temporal changes due to seasonally varying water temperature, flow velocity, and growth phase. Furthermore, the data reveal differences between lake and river specimens that could be explained by wind exposure of the lake sampling sites and the species-specific flow requirements of the river macrophytes. Biomechanical properties and morphological characteristics varied along the stem with larger cross-sections and a higher resistance against tension and bending forces at the bottom compared to the top parts, being similar for both lake and river specimens. The acquired and analysed stem biomechanical and morphological data contribute to the plant biomechanics database to underpin a wide range of studies in aquatic ecology, river and wetland management.

Plant biomechanics and mechanobiology are convergent paths to flourishing interdisciplinary research

Plant biomechanics and mechanobiology are convergent paths to flourishing interdisciplinary research

Strong radial variation in wood density follows a uniform pattern in two neotropical rain forests

Summary Wood density (WD) affects plant biomechanics, drought and decay resistance. As a consequence, WD is an important functional trait related to plant demography and ecosystem processes, which is also used to estimate tree biomass. Radial variation in WD (changes from the centre of the stem to the cambium) affects the strength of the entire stem, but also reflects any changes in wood functional properties that might occur during a tree's lifetime. To understand how WD and radial WD gradients, which were defined as the slope of the relationship between WD and distance to the centre, are related to demographic traits of species, we investigated WD in 335 tree species from a Panamanian moist forest and 501 species from an Ecuadorian rain forest and radial density gradients in 118 and 186 species, respectively, and compared WD with tree growth, mortality and size. WD was negatively related to tree growth and mortality. WD tended to increase towards the outside in trees with low initial density and to decrease towards the outside in trees with high initial density. Radial WD gradients were largely unrelated to tree size and demographic traits, but some families had higher or lower WD gradients at a given inner WD. Inner WD was by far the best predictor of radial WD gradients (r2 = 0·39 for Panama and 0·45 for Ecuador) and this relationship was indistinguishable between the two rain forests. This suggests a broadly uniform function of WD variation, likely responding to mechanical requirements during ontogeny. We discuss the factors potentially driving radial increases or decreases in WD and suggest ways to elucidate the relative importance of tree mechanics, hydraulic safety or decay resistance. We also discuss that not accounting for radial WD gradients may result in substantial errors in WD of the whole stem and consequently biomass estimates, and recommend sampling density gradients when obtaining density data from tree cores.

Methodological advances in predicting flow-induced dynamics of plants using mechanical-engineering theory

The modeling of fluid-structure interactions, such as flow-induced vibrations, is a well-developed field of mechanical engineering. Many methods exist, and it seems natural to apply them to model the behavior of plants, and potentially other cantilever-like biological structures, under flow. Overcoming this disciplinary divide, and the application of such models to biological systems, will significantly advance our understanding of ecological patterns and processes and improve our predictive capabilities. Nonetheless, several methodological issues must first be addressed, which I describe here using two practical examples that have strong similarities: one from agricultural sciences and the other from nuclear engineering. Very similar issues arise in both: individual and collective behavior, small and large space and time scales, porous modeling, standard and extreme events, trade-off between the surface of exchange and individual or collective risk of damage, variability, hostile environments and, in some aspects, evolution. The conclusion is that, although similar issues do exist, which need to be exploited in some detail, there is a significant gap that requires new developments. It is obvious that living plants grow in and adapt to their environment, which certainly makes plant biomechanics fundamentally distinct from classical mechanical engineering. Moreover, the selection processes in biology and in human engineering are truly different, making the issue of safety different as well. A thorough understanding of these similarities and differences is needed to work efficiently in the application of a mechanistic approach to ecology.

Wake-Induced Oscillatory Paths of Bodies Freely Rising or Falling in Fluids

Leaves falling in air and bubbles rising in water provide daily examples of nonstraight paths associated with the buoyancy-driven motion of a body in a fluid. Such paths are relevant to a large variety of applicative fields such as mechanical engineering, aerodynamics, meteorology, and the biomechanics of plants and insect flight. Although the problem has attracted attention for ages, it is only recently that the tremendous progress in the development of experimental and computational techniques and the emergence of new theoretical concepts have led to a better understanding of the underlying physical mechanisms. This review attempts to bring together the main recent experimental, computational, and theoretical advances obtained on this fascinating subject. To this end it describes the first steps of the transition in the wake of a fixed body and its connection with the onset and development of the path instability of moving bodies. Then it analyzes the kinematics and dynamics of various types of bodies along typical nonstraight paths and how the corresponding information can be used to build low-dimensional predictive models.

573 Mathematical and geochemical approaches to the physiology and biomechanics of Paleozoic plants

573 Mathematical and geochemical approaches to the physiology and biomechanics of Paleozoic plants

Determination of volumetric elastic moduli of plant leaf cells based on pressure-volume curves

Volumetric elastic modulus (VEM) is an important parameter in biophysics and biomechanics of plants for in particular understanding cell growth. This paper proposes a new relation that can be used for precisely determining VEM. With the aid of this relation, it shows that the exponential approximation of the pressure-volume relationship adopted in most of the literatures in this field may lead to serious errors on VEM.