Quantification of plant structure–function relationships through micro‐CT imaging‐based finite element modeling

SUMMARY

Plants display complex structural tissue arrangements and cell shapes that are intimately related to their functionality and whose precise geometry influences the metabolic and physical processes performed by different organs. Analyzing these structure–function relationships requires accurate information on the complex 3D anatomy and its changes over time at meaningful spatial resolution. A non‐invasive approach, micro‐CT imaging, can produce such 3D or 4D datasets and can be leveraged for finite element (FE) simulations of mechanical and physical processes. This combination of techniques has been employed to study biomechanical properties, gaseous diffusion, light propagation, hydraulics, and thermodynamic processes in plant organs. A deep understanding of structure–function relationships also paves the way to design bio‐inspired structures using plant anatomy as a reference. Here, we illustrate how the combination of micro‐CT‐based imaging and FE modeling can be leveraged in plant science for advanced investigation of structure–function relationships.

Significance Statement

Analyzing the functionality of the multi‐scale architecture of plants benefits from x‐ray‐based imaging combined with multi‐physics modeling.

INTRODUCTION

Plants have a complex hierarchical arrangement of cells and tissues which generate distinctive architectural complexities in each type of organ. The tissue‐specific shapes and structures of cells govern physiological and mechanical processes occurring in and performed by plant organs. A deeper understanding of the structural and functional properties requires accurate characterization of tissue architecture at cellular and subcellular resolution, in three (Gangwar et al., 2021) or four dimensions (4D, as in 3D over time). Confocal laser scanning microscopy can be used to generate such 3D and 4D data, but it is limited in its ability to provide information from deeper regions in bigger samples without resorting to invasive or destructive methods. Two‐photon microscopy and light‐sheet microscopy have helped address these limitations to a certain degree, but, as for all fluorescence‐based methods, they require fluorescent markers. Various electron microscopy‐based 3D imaging techniques such as block face scanning electron microscopy (Harwood et al., 2021) or 3D tomography generate exquisite high‐resolution detail in 3D but are generally only feasible on small tissue volumes comprising a handful of cells, and they are destructive.

X‐ray microcomputed tomography (micro‐CT) has emerged as a suitable tool for imaging live or dried plant samples at cell resolution and on sizeable volumes of tissue. The technique allows visualization of tissue architecture and does not require fluorescent markers. It is non‐invasive and non‐destructive and thus allows for repeated imaging of the same sample over a period of time enabling the documentation of developmental changes (4D imaging) (Box 1).

Box 1. Highlights.

1. Micro‐CT‐based FE modeling is an emerging combination of techniques to assess structure–function relationships in plant biology.

2. Automated software based on convolutional neural network deep learning has enabled the generation of robust image analysis pipelines.

3. Simulation and artificial intelligence models are successful in assessing various traits that are otherwise difficult to discern through conventional experiments.

4. Understanding plant structure–function relations is a key to creating effective bio‐inspired structures.

Micro‐CT has a long history with initial CT systems being developed for medical imaging in the 1970s (Hounsfield, 1973). Improvements over the subsequent decade were aimed at enhancing the resolution to detect smaller details. In the late 1980s, micro‐CT was developed using synchrotron radiation and was applied to an increasing range of materials. By the 1990s, micro‐CT devices were commercially produced and extensively used. The 2000s have seen the emergence of state‐of‐the‐art laboratory‐based micro‐CT (Stock, 2008; Stock, 2019). The technology has been extensively used in fields of biomedicine (Boyd, 2009; Hernandez & Cresswell, 2016; Oliviero et al., 2021; Pahr & Zysset, 2016), paleontology and archeology (Calo et al., 2020; Clark et al., 2023; Stelzner et al., 2023; Sutton, 2008), and geology (Wang & Miller, 2020). As micro‐CT becomes more widely available, its non‐invasive nature requiring minimal sample preparation along with high resolution makes it a versatile tool for plant imaging.

Here, we discuss how 3D data generated from micro‐CT scans can be used as basis for quantitative in silico experimental approaches to investigate the physical behavior of plant samples and correlate these with physiological functioning. Specifically, various applications of finite element (FE) modeling based on micro‐CT 3D datasets are explored (de Araujo et al., 2021; Piovesan et al., 2021). This review provides an overview of micro‐CT based FE methods and explains the principles of this combined approach. The first section focuses on the technology involved in acquiring 3D data. The second explains the processing required to transform the raw data into a format suitable for subsequent FE modeling steps, and the third section explores different types of applications in plant samples in which the 3D datasets are used as input for modeling approaches aiming to analyze different physical aspects of plant functioning.

IMAGE ACQUISITION BY X‐RAY MICROCOMPUTED TOMOGRAPHY

Micro‐CT is a non‐intrusive imaging technique where the samples are visualized using X‐ray scanning (Brodersen et al., 2013; Brodersen & McElrone, 2013; Cochard et al., 2015; Fernández‐Pascual et al., 2019; Harwood et al., 2021; Ho et al., 2016; Lehmeier et al., 2017; Mathers et al., 2018; Mayo et al., 2015; Piovesan et al., 2021; Rousseau et al., 2015; Théroux‐Rancourt et al., 2021; Tomasella et al., 2024). The samples are scanned by an X‐ray beam to produce 2D cross‐section projections (Figure 1). Rotating enables the generation of scans from different angles from which the 3D representation is reconstructed using computational tools (tomographic reconstruction). Image generation relies on differences in density for contrast which in plant samples allow for ready distinction between cells and air spaces. The overall aqueous nature of the cellular structures, including the nucleus and the cell wall, does not generate sufficient contrast to the cytoplasm to be able to distinguish these structures from each other without using contrast agents. Micro‐CT‐based imaging of plant samples is, therefore, particularly useful in airspace‐containing tissues where the cell‐based 3D anatomy of tissues is the desired output.

Figure 1.

Micro‐CT scanning, segmentation and mesh generation for FE modeling. Micro‐CT scanners are lab‐based or at synchrotron facilities consisting of a beam source, a scanning stage and a detector.

(a) Lab‐based systems produce cone‐shaped polychromatic X‐ray beams.

(b) Synchrotron facilities generate monochromatic parallel beams.

(c, d) Series of projection images obtained through sample rotation are subjected to 3D tomographic reconstruction to generate a 3D voxelized dataset.

(e–j) The voxelized dataset is segmented manually or in automated manner to distinguish structures such as tissue types (various grey levels in g) or single cells (various colors in i, j).

(h, k) Reconstruction at the tissue (h) and cell (k) level.

(l) Discretized meshes (yellow) are generated from reconstructed objects and form the basis to perform FE modeling and simulations.

(e–l) Leaf tissue from Arabidopsis thaliana rosette leaves (data set provided by Guillaume Théroux‐Rancourt).

The three main constituents of micro‐CT are the X‐ray source (laboratory or synchrotron‐based), a rotating stage holding the sample, and a digital detector (Figure 1a,b). Most laboratory X‐ray generators produce polychromatic X‐rays, whereas the radiation source in synchrotrons produces parallel monochromatic beams (du Plessis et al., 2017; Mizutani & Suzuki, 2012). The X‐ray source emits focused beams with wavelengths ranging between 0.1 and 10 nm that pass through and around the sample positioned on the rotating stage. The rotation occurs on an axis perpendicular to the direction of the X‐ray beam. The resulting projection slices are collected by the detector at each step of the rotation and are then used to create a complete virtual stack of the object (Figure 1c).

Aside from the density differences in the sample, the quality of the scans depends on the balance between current and voltage of the X‐rays, the distance of the sample from the source of X‐rays, the exposure time at each projection, and a competent digital detector. Depending on these, the scanning parameters need to be optimized for each sample type. Usually, micro‐CT scans require minimal sample preparation such as treatment with contrast enhancing chemicals for tissues with low‐density contrast and enclosing samples with protective covering to prevent dehydration. Contrast in the soft biological samples can be enhanced by using lower voltage and employing contrasting agents such as propidium iodide, phosphotungstic acid, mercury chloride, or uranyl acetate (Pauwels et al., 2013). Denser objects require higher voltage for deep penetration of X‐rays which, however, reduces the contrast in case of a largely homogeneous material. The signal‐to‐noise ratio can be moderated by adjusting the current. A fine balance of these parameters results in high‐resolution images with minimal noise. Another crucial consideration pertains to the placement of the sample. It needs to be firmly fixed on the rotating stage as any tilting or other uncontrolled movement during rotation creates artifacts during data acquisition that affect the reconstruction of the 3D volume (Figure 1d). The dimensions of the sample holder and field of view determine the size of the sample that can be effectively imaged.

IMAGE PROCESSING

To convert the raw image material into a format suitable for subsequent in silico analyses, image stacks are reconstructed using an algorithm based on filtered back projection (Feldkamp et al., 1984). The resulting 3D dataset is made up of voxels, where the brightness of a voxel reflects the density of the material (Figure 1e). Typically, the settings are chosen such that denser materials appear lighter than areas of lower density. While the 3D dataset displays areas with varying signal intensity, this individual voxel‐based information needs to be converted to objects consisting of groups of voxels. For structural and quantitative analyses, these 3D regions of interest must be converted to surface meshes that define objects. This process reduces the complexity of the dataset and involves allocation and segmentation which can be done manually or in automated manner. A basic way to allocate voxels to a group involves thresholding which defines a certain grayscale level to assign a voxel to one subgroup or the other (e.g., cell or air space). The resulting image is binary, that is, it consists of black and white areas (Figure 1f) that in a plant sample with air spaces are annotated “cell” or “air space,” respectively (Figure 1g). To convert this information into objects amenable to further processing, the surface of contiguous groups of voxels with identical annotation is wrapped in a mesh made of simple shapes (elements) and nodes (Figure 1l).

The number of elements and nodes relative to the overall size of the object defines the resolution of the mesh. A finer mesh with higher resolution allows for the representation of smaller structural details but requires higher computational power for processing. Careful optimization of mesh resolution involves refinement and smoothing steps. During refinement, the number of elements and nodes is gradually increased until essential geometrical features are well defined by the mesh. Surface smoothing relocates the nodes of the mesh to achieve a better fit to contours or curved surfaces. Refining and smoothing come at a computational cost and increased processing time. To minimize the computational cost associated with higher mesh resolution, decimation algorithms can be used which reduce the number of nodes in areas of the sample with simpler geometry.

If the first step of the segmentation process is done based on binarization, the result distinguishes two phases (e.g., cell vs. air space) but does not yet identify one cell from the other for cells that are attached, let alone distinguish different cell or tissue types (e.g., epidermis vs. cortex). If that distinction is desired, a second segmentation step is required which detects geometrical features indicating that, despite the continuity of the phase, there is a cell–cell border (Figure 1i,j). This can be done by the detection of local curvature in the surface. In tissues consisting of primarily convex cells, a concave local shape can be interpreted as indicative of a cell border and used to separate an object into two or more distinct ones (Figure 1k). Instead of binarizing and subsequently segmenting based on curvature, other segmentation algorithms can detect individual cells directly based on watershed segmentation applied to the signal intensity of the original 3D image stack or on a region growing algorithm (Agathos et al., 2007).

Manual segmentation produces high accuracy but is time‐intensive and may have low reproducibility since different users may make different judgment calls. Semi‐automated segmentation increases efficiency and consistency but requires extensive manual training. With recent improvements in machine learning, it is now possible to accurately segment biological images in a fully automated manner. To this end, various mathematical algorithms are employed to detect different patterns in a reference image dataset and make predictions for new image datasets of a similar sample type through deep learning methods. These methods are based on neural networks having multiple layers arranged in a nested network architecture which identify the patterns of local curvature and edges to segment the image. Convolution neural networks (CNN) are the most widely used in deep learning to perform convolution operations on multineural networks to extract relevant features of an image during segmentation. Representative, manually segmented and labeled images are used as input (ground truth) for the learning process to train the algorithm on relevant features to recognize and segment. These training datasets require the most computational power in deep learning. To validate the accuracy of segmentation power, the ground truth datasets are used for comparison and provide validation for the accuracy and reliability of the model. U‐NET, a type of CNN, and deep learning have been used for automatic segmentation of various plant organs. Various computational software packages such as ImageJ, IMARIS, Dragonfly, AVIZO, Amira, Labellerr, Encord, 3D Slicer, ITK‐Snap, MONAI, Killi, LabelMe, CVAT, PlantSeg, and Cellpose are available for segmentation purposes.

TOWARD MECHANISTIC INSIGHT USING FINITE ELEMENT MODELING

Once the architecture of a plant's organ or tissue is captured through imaging and converted to a 3D mesh that outlines the geometrical features, it can be used to model and simulate functionalities and processes that affect metabolism such as mechanical behavior, gaseous flow as well as hydraulic and thermodynamic processes (Figure 2). Each of these approaches requires information on the physical properties of the material or phase to be simulated and on the boundary conditions defining the system. Depending on the purpose of the simulation, the constitutive properties required may be descriptors of mechanical properties and/or thermal or fluid dynamic attributes. Furthermore, the properties of the environment need to be defined such as pressure, external load application or displacement.

Figure 2.

Schematic representation of and examples for bio‐physical models based on plant anatomical structures.

(a) Schematic illustration of biological processes and properties and location of analyzed tissues.

(b) Inflorescence tank of Nidularium innocenti. (b₁) 3D micro‐CT reconstruction; (b₂) FE tetrahedral elements mesh in longitudinal cut view with regions of plant (green) and environment (white); (b₃) FE prediction of plant tissue temperature due to heat transfer to water caught in tank (red indicates highest temperature increase); from Nogueira et al. (2019) with permissions.

(c) Segment of maize leaf. (c₁) Color labels on the 3D micro‐CT reconstruction indicate epidermis (gray), cytosol (teal), vascular tissue (blue), chloroplasts of mesophyll (red), and bundle sheath (green). (c₂) Light absorbance ranging from high (red) to low (blue) as predicted by light propagation model; from Retta et al. (2023) with permissions.

(d) Segment of tomato leaf. (d₁) 3D reconstruction based on synchrotron radiation X‐ray computed laminography showing epidermis (gray), cytosol (yellow), chloroplasts (green), vacuole (blue). (d₂) CO₂ distribution in the mesophyll cells at 21% ranging between 356 (red) and 21 (blue) μmol mol⁻¹ as simulated based on a gas diffusion model; from Ho et al. (2016) with permissions.

(e) Segment of Aechmea penduliflora leaf. (e₁) 3D reconstruction of leaf tissue based on micro‐CT imaging; (e₂) 3D reconstruction of intercellular air space volume indicating diffusive path lengths from the stomate (white arrows) between 0 (blue) and 900 μm (red); from Earles et al. (2019) with permissions.

(f) Fluid flow through Dalbergia ruddae wood microstructure imaged through micro‐CT. Colored lines indicate speed of fluid flow predicted by CFD model with red indicating high and blue indicating low velocity. Unpublished figure provided by Luis Olmos. Refer to Rivera Ramos et al. (2023) for details.

(g) Section of bark (cork) from Quercus suber. (g₁) 3D reconstruction from micro‐CT scan; (g₂) FE model predicting von Mises stress under compressive load application leading to 8% strain and (g₃) 50% strain. Unpublished figures provided by Felipe Luís Palombini. Refer to Palombini et al. (2023) for details.

FE analysis uses the mesh created in the previous step as input structure to solve the overall physical behavior of an object through equations applied on the individual elements of the mesh. For the purpose of the modeling, the mesh can be refined or otherwise modified. While a finer mesh is usually preferred to accurately represent all the geometrical traits, it comes at the cost of high computational requirements which can be dramatic in this simulation step. It is, therefore, typical to perform sensitivity testing where the simulations are run at different mesh resolutions to identify the resolution that satisfies the quality requirements while limiting the demands on the computing power. This may involve attributing different element sizes to different features with bigger elements being assigned in areas that are simply shaped or relatively flat surfaces. Importantly, the power and efficiency of the models is validated through experiments to compare predictions made by the model with empirical experimental data. There are various commercially available software packages to perform FE analysis such as ANSYS, SDRC/IDEAS, NASTRAN/PATRAN, HYPERMESH, LS DYNA, ABAQUS, SIEMENS PLM NX, NISA, COMSOL, and KEBIR. Careful selection of the software should depend upon the parameters of the model, the physics to be simulated, and the desired type of simulations and predictions.

Mechanical modeling

Mechanical simulations allow predicting how a structure deforms under the application of a load. This could be an internal load—for example, the load created by turgor pressure on the cell wall—or it could be an external load such as the force exerted by gravity or wind on tree branches. These simulations require the solid phase of the structure to be represented by a volumetric mesh that can be generated based on the superficial mesh resulting from the segmentation. Furthermore, each element making up the physical structure needs to be assigned material properties such as Young's modulus, viscoelastic properties, and/or Poisson's ratio. Obtaining these values experimentally can represent a challenge since they require mechanical testing of the biological specimen, ideally at the cell or tissue scale. Methods used for this purpose include creep or relaxation tests, compression and bending tests, and make use of instron instruments, atomic force microscopy (AFM) or nanoindentation (Bidhendi & Geitmann, 2018; Bidhendi & Geitmann, 2019). In the absence of bona fide experimentally determined values for mechanical properties of the specific specimen analyzed, these must be based on educated guesses and reasonable assumptions (Bidhendi & Geitmann, 2018).

The characterization of the mechanical behavior of plants is relevant both in the context of the consumption and usage of plant parts (e.g., texture of a food ingredient, mechanical stability as construction material) and our understanding of plant functioning (e.g., cellular growth processes resulting from the deformation of cell wall under turgor pressure; structural stability of plant organs against external forces such as gravity). Some research questions allow for significant simplifications in the representation of plant structure such as modeling a wood beam as a uniform block of homogeneous material for the purpose of assessing its bending resistance. However, where the goal is to identify the role of microscopic features for macroscopic traits (e.g., the effect of the relative abundance and cell wall characteristics of earlywood and latewood on the bending behavior of mentioned wood beam), microscopic structure must be gathered, and the modeling must straddle multiple length scales. A multi‐scale approach allows considering the heterogeneous and hierarchical structure of tissues and organs in their mechanical behavior (Karlen et al., 2024; Palombini et al., 2023). Micro‐CT‐based FE modeling can be leveraged to disentangle the individual contributions of different tissues to the overall mechanical properties of an organ under load. In that vein, a study on bamboo involved X‐ray imaging of extended tissue regions and FE modeling to identify maximum load bearing tissues under compression (Palombini et al., 2019; Palombini et al., 2020; Palombini et al., 2022). The models indicate that the substantial mechanical strength of bamboo is related to the arrangement of porous parenchyma combined with thick sclerenchyma tissue located above the nodes and vascular branching. The cortex region of the bamboo stem consists of cell layers with lower porosity and high density providing added mechanical stability. Combined, these morphological features distribute stress across the organ and help withstand compression and axial loads (Palombini et al., 2019; Palombini et al., 2020). Similarly, micro‐CT‐based FE modeling revealed the anisotropy in mechanical behavior of Quercus suber cork tissue as it relates to cell shape and orientation and showed that natural corrugations in the cell wall function as stress concentrators directing cell wall folding under compression (Palombini et al., 2023) (Figure 2g).

In these studies, the FE models generated for the purpose of testing the effects of constitutive properties were constructed on gray‐level‐based numerical models. Two distinct discretizing approaches were compared—one used voxel‐based generation of meshes, and the other was geometry‐based where images were first segmented and then a mesh was generated. In the voxel‐based method, each voxel is directly transformed into an element in the mesh. In contrast, in the geometry‐based method, voxels are binarized using thresholding; then, a mesh is generated which can be further refined to obtain an accurate global shape. The combination of gray‐level analysis with a geometry‐based discretizing method to create models proved to be more accurate (Palombini et al., 2020).

FE modeling helps understand not only elastic and reversible mechanical behavior such as bending and compression but also serves to characterize failure behavior such as breakage and fracture formation. An FE model of rice seeding stalks illustrates this, and agricultural relevance was demonstrated through the experimental validation by compression and tensile tests simulating the typical load applications that a rice seedling experiences during the transplanting process (Xue et al., 2023). The results showed that the ability of the outer sheath of the rice stalk to bear maximum mechanical stress was attributed to its material density and elastic modulus as well as the effect of turgor pressure on its biomechanical properties (Xue et al., 2023). Due to their different growth patterns, in oat and wheat crops, stem strength was studied under aerodynamic force exerting a bending load. FE simulation of the load application scenario was validated through controlled wind tunnel experiments. The model predicted higher strength of wheat stems in comparison to oats, resulting from differences in stem morphology with a higher fraction of parenchyma cell wall and lignin in wheat (Gangwar et al., 2023). The morphological features associated with higher strength and transverse stiffness found in wheat provide guidance for breeding of lodging‐resistant varieties in other crop species. Similarly, FE modeling was used to extract the mechanical properties of stem material in oats, validated by a four‐point bending test (Gangwar et al., 2021). The model was used to predict the effects of morphological traits and biochemical composition on mechanical properties in various genetic mutants of Arabidopsis thaliana and compare them to experimental data (Gangwar et al., 2021). Thus, FE models, validated through various mechanical experiments, can be efficiently used to predict which structural traits to focus on when selecting plant cultivars for higher mechanical stability.

To understand how mechanical bending deformation is translated into intracellular signals, Saikia et al. (2021) used computational analysis to characterize the mechanical transduction activity in the sensory hair of the Venus flytrap. An FE‐based model of the multicellular sensory hair architecture was generated based on morphometric data from micro‐CT imaging. To assess the dependency of the cellular response on the stimulus loading rates, the model incorporated the viscoelasticity of the cell wall and intercellular fluid transport. The findings suggest that mechanosensitive ion channels, expected to be stretch‐activated and localized in the plasma membrane of the sensory cells, are sensitive to the rate at which stretch resulting from hair bending is applied on the cell walls (Saikia et al., 2021).

Organ bending can also occur without externally applied load and serves to effect actuation. While in some plant systems, bending results from changing turgor pressure differentials (Sleboda et al., 2023); in others, it is generated by the hygroscopic behavior of cell walls swelling and contracting under different humidity conditions. To simulate the latter behavior in pine cone scales, their structural changes in dry and wet states were observed using micro‐CT and used to inform an FE model that simulates the effect for their deformation (Eger et al., 2022). The structural and kinetic investigations combined with the in silico simulation revealed that the behavior of and interaction between the involved tissues is significantly more complex than a simple bilayer mechanism that has been assumed to drive the motion.

Micro‐CT‐based FE simulations have been used to analyze leaf structure and mechanics (Liu et al., 2018). Leaves are constantly subject to self‐loading stress and, in addition, are frequently exposed to bending and twisting under high wind conditions. The structural complexities of leaves provide mechanical stability to withstand such loads. Given the detrimental effect on plant performance resulting from leaf damage, it is of interest to understand how these lightweight sandwich structures behave exactly. Structural properties of Typha leaves were characterized by micro‐CT and SEM, and the mechanical properties were obtained through axial compression, tension, and lateral bending tests. FE modeling of three different internal arrangements of long and slender Typha leaves revealed the influence of tissue anatomy on the ability to counteract compression and bending stresses (Liu et al., 2018). The ideal internal arrangement effectively distributes loads and counteracts stresses resulting from bending or buckling. Mechanical testing and morphological analysis of peltate leaves of Stephania japonica informed a mechanical model that enabled studying their behavior under different simulated conditions such as complex stress states that are experimentally not achievable but provide more detailed insight (Macek et al., 2023). Using FE simulations, the distribution of mechanical stress and the nature of deformations resulting from load application served to predict how different tissue layers withstand mechanical load in these leaves (Macek et al., 2023). Similar models were used to analyze the role of specific tissue layers in withstanding mechanical load applications such as those generated by gravitational pull, wind, or rain on the peltate leaves of Colocasia fallax and Tropaeolum majus, thus providing insight into the engineering concepts supporting the umbrella‐like structure of these leaves (Sacher et al., 2019).

Modeling gas phase behavior

Photosynthesis performance is influenced by the efficiency of gas flow into and through the photosynthetic tissue—the mesophyll. It is well known that gas flow depends on the abundance of functional stomata, the shape and density of mesophyll cells, the porosity of the mesophyll, and the architecture of the intercellular air space network. However, untangling the consequence of changing a single trait on photosynthetic efficiency is often difficult because of its additive effects. Modeling gas flow based on true leaf inner architecture is, therefore, extremely useful to predict the relative importance of individual traits. The physical parameters required for the modeling include pressure and diffusion rates, and the resulting predictions for overall gas flow through a tissue can be validated experimentally by measuring the same through nuclear magnetic resonance (NMR) and gas exchange systems. The mechanical properties of the solid/liquid phase (cells) of the tissue are largely irrelevant in this approach and the mesh instead serves to describe the shape of the interface between cells and airspace (where some models consider gas diffusion rates through cell wall material) and the 3D geometry of the airspace (Figure 2e).

The gas space geometry in leaves has been visualized to study diffusion reactions (Baillie & Fleming, 2020; Berghuijs et al., 2016; Earles et al., 2019; Harwood et al., 2021; Ho et al., 2016; Lehmeier et al., 2017; Retta et al., 2019; Retta et al., 2023; Xiao et al., 2016) (Figure 2d). A recent model called eLeaf has been developed to study rice leaf anatomy (Xiao et al., 2023). It uses accurate leaf anatomy data obtained by a combination of micro‐CT, confocal microscopy, and transmission electron microscopy. By combining anatomical information extracted at different length scales, an accurate 3D representation of leaf anatomy is generated. Next, a 3D diffusion reaction model is applied which is solved by FE methods. Théroux‐Rancourt and colleagues validated their model experimentally by measuring the effect of elevated CO₂ concentrations in the environment on photosynthesis. The model predicts that the photosynthetic rate is independent of changes in porosity of the leaves whereas cell size has an influence (Théroux‐Rancourt et al., 2021).

Watts and colleagues also used FE methods to model 2D diffusion of CO₂ and photosynthesis, assuming mesophyll tissue to be a homogenous porous medium (Watts et al., 2024). The study focused on mechanisms by which amphistomatous leaves adapted to maximize CO₂ diffusion under different light conditions. The analysis indicated stomatal spacing to be over dispersed as opposed to an ideally dispersed or random pattern. The stomatal pattern on both sides of the amphistomatous leaves of Arabidopsis thaliana was found to be independent of each other. Through simulations and photosynthesis modeling, it was concluded that stomatal co‐ordination in both sides of the leaf has little effect on improving photosynthesis rate. This suggests that there must be other ways of improving CO₂ diffusion, such as a correlation of stomatal size to mesophyll volume for maximum diffusion.

Analyzing the role of light propagation

Photosynthetic efficiency of a leaf is critically influenced by the way in which light propagates through the photosynthetic tissue and is absorbed by chloroplast‐containing cells (Hanba et al., 2023). The shape and arrangement of the different tissue layers affect scattering and the attenuation of light intensities. Epidermal cells facilitate light rays to reach columnar palisade mesophyll cells which aid in deeper penetration of light to spongy tissue layers where they are scattered enhancing absorption (Karabourniotis et al., 2021; Vogelmann et al., 1996). Combined, several anatomical features facilitate light propagation through tissues and generate a heterogeneous light intensity gradient within the leaf. The effect of directionality and quality of light along with anatomical features determines the photosynthetic rate (Brodersen et al., 2008; Brodersen & Vogelmann, 2010; Earles et al., 2017; Nikolopoulos et al., 2024). To understand this complex interaction, various models have been proposed that simulate optical properties through ray‐tracing models (Bousquet et al., 2006; Govaerts et al., 1996; Karabourniotis et al., 2021; Kumar, 2009; Ustin et al., 2001; Watté et al., 2015). Xiao et al. (2016) developed a 3D model to evaluate the effect of various anatomical properties on internal light intensity and light use efficiency. The model indicates a key role of mesophyll cells and bundle sheath cells in creating a heterogeneous light environment within the leaves. It helped reveal that bundle sheath extensions aid in optimal light use efficiency by altering internal light scattering and propagation. The model also indicates the role of chloroplast positioning in effective light use efficiency (Xiao et al., 2016). A 3D model for tomato leaf demonstrated that changes in chloroplast positioning in response to light intensities influence the rate of CO₂ gas diffusion within the leaf (Ho et al., 2016) (Figure 2d). The next step was to couple these ray‐tracing models with gas exchange models to allow studying correlations of light intensity, plant anatomy, and photosynthetic capacity. The multi‐modular computational model eLeaf simulates internal light distribution along with physiological and biochemical parameters based on a ray‐tracing algorithm combined with a 3D reaction–diffusion model simulating CO₂ movement and a metabolic model simulating the effect of photosynthetic metabolism. It predicts interactive effects of internal CO₂ concentration and light intensity on photosynthesis. The modeled photosynthetic assimilation rates are comparable to experimentally observed rates indicating the efficiency of the model to test the effects of individual features on photosynthesis. The model suggests, for example, that, counterintuitively, in the presence of low light intensity, high CO₂ concentrations affect photosynthesis negatively (Xiao et al., 2023).

Leaves grown under high light intensities are generally thicker in comparison to leaves grown under lower intensities to facilitate maximum photosynthesis (Borsuk & Brodersen, 2019; Retta et al., 2024; Théroux‐Rancourt et al., 2023). Chloroplast arrangement within the mesophyll cells also differs in response to light intensities ensuring maximum absorbance. This arrangement or organelle movement in response to light is influenced by the cell shape (Borsuk & Brodersen, 2019; Gotoh et al., 2018; Kato et al., 2022; Kitashova et al., 2021; Maai et al., 2020). Retta et al. (2023) created a 3D model of maize leaves where gas exchange and light propagation were coupled to photosynthetic energetics (Figure 2c). A meshed Monte Carlo method was used to model light propagation, and gaseous exchange was simulated by reaction diffusion modeling to test the effect of chloroplast movement on photosynthesis. The alignment of chloroplasts in mesophyll cells toward bundle sheath cells (aggregative arrangement) in high light intensities resulted in better light absorption and enhanced photosynthetic rate. The capability of this 3D model to resolve the functional complexities of photosynthesis in C4 plants was enhanced in comparison to simpler 2D models. Understanding the key mechanism responsible for enhanced performance can be a basis for improving photosynthetic rates in C4 plants through genetic engineering (Retta et al., 2023). In a study by Borsuk et al. (2024), optical and photosynthetic properties of palisade mesophyll cells with two different geometries (lobed and columnar) were studied in relation to chloroplast localization and light quality. To understand the structure–function relationship, accurate 3D models for palisade cells were created from micro‐CT scans, and optical properties were analyzed through ray‐tracing simulation. The results suggest acclimation of lobed cells having maximum absorption under diffuse light with chloroplasts arranged at the periclinal walls. In comparison, chloroplast localization is more sensitive to light directional quality in columnar palisade cells. Lobing of mesophyll cells also increases productivity by increasing mesophyll surface area to volume ratio (Borsuk et al., 2024). This work provides an insight into how lobing and the shape of individual cells affect overall optical properties in leaves.

Fluid flow modeling

Hydraulics is an important structure‐dependent process in plants since failure‐free translocation of water through xylem conduits is crucial for optimal functioning. The efficiency of the process is influenced by leaf water potential, flow of water, the probability of embolism (air pocket) formation, and the degree of recovery from the same. The anatomical dimensions of vessels, their perforations, wall thickenings, and their connectivity crucially affect overall water transport through an organ, but how these microscopic features add up to the trait observed at macroscopic scale is difficult to assess. Previously employed techniques such as histological sectioning and light microscopy, vessel air‐injection methods, and hydraulic conductivity methods failed to accurately take into account the heterogeneous 3D anatomy of the vessel network. Furthermore, most of these methods are destructive preventing time course studies. Synchrotron and lab‐based micro‐CT are emerging as the most suitable tools to support the investigation of plant hydraulics. Their capability to differentiate between water‐ and gas‐filled areas combined with appropriate spatial and temporal resolution allows for ready imaging of xylem and phloem vessels in intact plants (de Araujo et al., 2021; Tomasella et al., 2024). Thus, X‐ray micro‐CT has been used in order to understand how the development of xylem, its morphology, and the connectivity of the vessel network affect the susceptibility to the formation of air pockets (Brodersen et al., 2013; Brodersen & McElrone, 2013; Cochard et al., 2015; Robinson et al., 2023; Schoeman & Drew, 2023; Tomasella et al., 2024). Synchrotron micro‐CT was employed to study the internal architecture and embolism in maple and birch saplings. A connectivity analysis revealed the network of interconnected embolisms in xylem and the higher contribution of large volume embolisms to the total embolism volumes. The results revealed uniformly distributed embolisms in birch in comparison to fewer embolisms occurring near the cambium in maple saplings. This distribution in maple suggests elevated susceptibility to embolism in older vessels (Robinson et al., 2023).

The flow of fluids through plant structures is commonly simulated using computational fluid dynamics (CFD)—a special application of FE modeling. CFD requires input parameters such as internal pressure, fluid velocity, and rates of diffusion. It has been employed to study embolism in grapevine under different draught simulations and established that traits of the xylem network such as the number of vessels, their connectivity, and location greatly influence the vulnerability or resistance of the xylem system to embolism (Wason et al., 2021). Resistance to water flow through the xylem increases with the complexity of inner surface structures. At constant flow, the total vessel resistance is a combination of resistance provided by smooth vessel surfaces, secondary wall thickenings, and perforation plates. Modeling enabled ranking the relative importance of these features and predicted a linear relationship between anatomical traits such as height and width of the perforation plate, pit depth, and flow resistance. Concretely, increased height and width of perforation plates and pit depth result in higher flow resistance, whereas higher inner diameter of the vessel and higher permeability of the pit membrane correlate negatively with flow resistance (Xu et al., 2020). Elevated pits in the secondary wall thickening also provide resistance to water flow under low irrigation (de Araujo et al., 2021). CFD simulations of water transport in Khaya grandifoliola under varying conditions of water availability predict that, during embolism, increased vessel connectivity due to higher pit numbers would assist in redirecting water flow without altering conductivity. This reduces the effect of high resistance generated by smooth vessels and thereby lowers total resistance to flow under non‐irrigated conditions (de Araujo et al., 2021).

To test the theoretical predictions, the vessel network of grapevine stem was reconstructed from micro‐CT images and in vivo flow of water was documented using magnetic resonance imaging (MRI). The results demonstrated a deviation from the theoretically predicted rates of water flow. Variations in vessel length, diameter, and connectivity of vessels with different diameters in the network result in differential pressure gradients in xylem conduits, and this heterogeneity leads to a redirection of a part of the water flow from vessels with larger diameter toward vessels with smaller diameter. Rather than the sum of its parts, the network pattern of xylem vessels with different diameter connected together appears to dictate the transverse gradients and in turn the overall flow at the scale of the stem. The findings highlight the necessity to include these heterogeneous xylem traits in models to realistically assess xylem anatomy and its effects on flow dynamics (Bouda et al., 2019). To understand the evolutionary relationship between xylem anatomy diversification and drought resistance, Bouda et al. simulated various xylem strand shapes in early vascular plants. Their model analysis suggests the selective diversification in conduit network topology and xylem strand shape from early cylindrical forms to more complex lobed forms increased embolism resistance conferring to vascular plants the ability to adapt to a dry habitat (Bouda et al., 2022).

While 3D structure is a crucial parameter for the network properties of the xylem and the fluid flow behavior, the biochemical properties are relevant as well. To assess whether there might be an effect of the metabolic activities in the xylem parenchyma on embolism, Secchi and colleagues imaged poplar plants with micro‐CT while modulating the apoplastic pH or metabolic activity of the stem (Secchi et al., 2021). Their study revealed that the accumulation of sugars in the apoplast is necessary for the recovery and removal of embolism during rehydration. Flow of sugars and ions from neighboring cells into the xylem apoplast creates an osmotic gradient that facilitates diffusion of water into the embolized vessels. The authors concluded that the hydraulic recovery of stems in poplar is dependent on energy and occurs in coordination with accumulation of sugars (Secchi et al., 2021). Similarly, changes in tissue anatomy were observed during the desiccation and rehydration process in desiccation‐tolerant Pentagramma triangularis fern. The proposed model suggests the contributions of capillary rise, root pressure, and higher sucrose concentration in chlorenchyma cells in successfully rehydrating xylem conduits. In addition, flexible xylem conduits (due to the presence of pectin, proteins, and reduced amount of lignin) play a pivotal role in rehydrating conduits that withstand breakage during desiccation (Holmlund et al., 2019). Similarly, tissue anatomy affects the probability of crack generation during wood drying. CFD simulations performed on 3D tissue volumes obtained through X‐ray tomography from Eucalyptus wood revealed the effect of microfeatures such as bulges and cracks on the drying behavior of the wood. Lumen connectivity analysis indicated lower permeability in the tangential direction attributed to higher tortuosity of the flow path (Rivera Ramos et al., 2021). A similar approach was used to observe flow dynamics in Dalbergia ruddae wood and the permeability changes attributed to the presence of gums. Simulations indicated decreased permeability in the longitudinal direction due to them blocking vessels (Rivera Ramos et al., 2023) (Figure 2f). Structural insight from micro‐CT data performed on various species combined with the CFD‐based predictions can help establish missing links in the structure–function relationship related to plant hydraulics that inform our conceptual understanding of the evolutionary pressures that led to their development (Rivera‐Ramos et al., 2024).

Thermal modeling

Thermodynamic analyses help understand how plants control their temperature, are impacted by, and deal with temperature changes as well as heat and cold stress. At the metabolic level, heat shock proteins are activated in response to high temperatures, whereas anti‐freeze proteins and accumulation of sugar help sustain plants during lower temperatures (Satyakam et al., 2022). Effects of temperature‐dependent changes manifest during vegetative and reproductive stages (Jagadish et al., 2021; Moore et al., 2021; Stokes & Geitmann, 2024). Higher temperatures can, for example, result in early flowering, sterility, and faulty seed set. To withstand adverse temperature changes, plants regulate their optimal temperature at the physiological multi‐scale level. Certain morphological features protect sensitive organs from freezing temperatures such as scales surrounding buds or fern leaves curling (Wang et al., 2020). Flat organ morphologies exploit evaporation or convection for cooling, and a change in organ orientation in response to high light intensity protects from the heating effect of intense sunlight. Analyzing the detailed functioning of structural and geometrical features requires thermodynamic modeling that benefits from microscopic structural data as input and requires parameters such as boundary temperature, air velocity, radiation, and thermal properties.

In leaves, temperature affects the physio‐chemical processes that convert light radiation energy into chemical energy. Excess energy is dissipated as heat (heat transfer, respiration, and transpiration) to maintain the leaf tissue temperature (Jagadish et al., 2021; Zhu et al., 2022). Leaf traits that influence heat dissipation include macroscopic traits such as leaf placement and shape as well as microscopic traits such as the number and positioning of stomata (Xu et al., 2021). 3D modeling of heat and mass transfer in leaves correlates environmental factors such as temperature, radiation, and humidity to transpiration rates. The model proposed by Zhu et al. (2022) provides a linear relationship of leaf temperature with respect to environmental factors.

The arrangement and orientation of leaves influences water vapor diffusion and heat transfer (Bridge et al., 2013). Model simulations established that increased petiole length and angle of leaves with respect to soil surface result in increased transpiration rate allowing to counteract the effects of elevated temperature. This is achieved by elevating airflow surrounding the leaves and reducing boundary layer resistance. Heat and mass transfer simulations in line with different leaf orientations (Plas et al., 2024) revealed that leaf temperature and humidity are influenced by the airflow and stomatal resistance in controlled conditions. This recently developed model is a reduced order model based on CFD values to predict leaf temperature and humidity. It provides rapid predictions and has higher efficiency for utilizing computational power as the model requires fewer CFD simulations. These models are excellent tools to predict plant behavior under various climatic conditions in greenhouses and closed plant growth systems, thus providing a tool to increase plant productivity in indoor cultivation.

Thermal modeling also allows for evaluating and predicting plant physiological and tissue‐specific responses to combinations of factors such as changes in atmospheric CO₂ and temperature. A model based on energy balance and gas exchange data predicted that leaf structure and leaf size have a greater influence on tissue temperature than variations in CO₂ (Konrad et al., 2021). Leaf size affects the boundary layer thickness around the leaves and thus impacts heat loss. These models have been instrumental in recognizing essential structural features relevant to temperature maintenance in flat tissues under changing environments.

How flowers manage temperature changes is of particular interest given the sensitivity of reproductive processes to temperature stress. A novel application of micro‐CT‐based FE analysis revealed the role of water as a protective barrier in Nidularium innocentii flowers (Nogueira et al., 2017; Nogueira et al., 2019). A 3D model of an inflorescence was generated based on high‐resolution micro‐CT imaging data (Figure 2b). Heat transfer FE analysis was used to predict the effect of external environmental conditions on the inflorescence with and without water accumulation in surface cavities. This combinational technique revealed that collected water acts as a thermal stabilizer whereas, in the absence of water, the inflorescence displays a heat stress response (Nogueira et al., 2019). Future models generated with accurate tissue structural data and FE analysis will enable simulation under varied micro‐climates and gaseous concentrations to accurately predict plant responses under a variety of conditions at different time scales and validated through in‐field and experimental data. These simulations will facilitate selecting and engineering temperature‐tolerant traits for breeding purposes.

BIO‐INSPIRED DESIGN

Plants have been a major inspiration for effective manmade designs. The complex multi‐scalar architecture characterizing plants arisen through the course of evolution has provided them with metabolic functionality and mechanical stability to withstand varied environmental conditions in a way that surpasses even the smartest manmade “smart materials.” These properties of plants have been studied to design structures for industrial applications (Mader et al., 2020; Speck & Speck, 2021). The effect of structural complexity on function is studied using various techniques. Micro‐CT‐based FE modeling has emerged as an effective combination to analyze the effect of structural components at multiple scales. Through FE simulations, the behavior of a structure under differential conditions is analyzed to understand the link between morphology and overall mechanical properties. This knowledge can then be translated to create structural designs with different load bearing mechanical properties such as those inspired by bamboo stalks (Palombini et al., 2020; Palombini et al., 2022). Structural properties and mechanical attributes of branched stems have also been studied using this combinational method and applied to create improved joint structures (Masselter et al., 2013). Mechanical properties and damage in plant fibers have been documented using FE simulations based on fiber ultrastructure. This provides a better understanding of damage in fibers and their effects on their mechanical properties for improving plant‐based bio‐composites (Masselter et al., 2021; Richely et al., 2022). FE modeling can also be employed to understand the mechanism of plant movements such as those mediated by bulliform cells which have served as an inspiration to create cellular actuators (Mader et al., 2020). Hygroscopic plant movements in response to external humidity inspire mechanical models such as humidifying systems, sensors, and folding systems (Bae & Kim, 2023; Guo et al., 2024). Such efforts can further be enhanced by the addition of micro‐CT data to the existing model. Micro‐CT‐based FE analysis can also be used to study the additive effect of individual tissues on organ mechanics, including aerenchyma‐type tissues. This proves as a basis to create mechanically stable structures which are lightweight. With the help of advanced microscopy and computational techniques, knowledge of structure–function properties of plants can be acquired in an unprecedented manner informing in entirely new ways the design of bio‐inspired structures.

CONCLUSION

With increasing accessibility of lab‐based X‐ray micro‐CT imaging, improved computational power and sophistication, computational modeling is leveraged in a growing number of plant science applications. FE models can readily predict aspects of multi‐scale structure–function relationships that are otherwise difficult to assess through conventional experiments. However, there are limitations to the effective use of this technology. The extensively large datasets generated are difficult to manage and require extensive computational power to process. Segmentation of desired features in low‐contrast samples is a challenge and requires intensive manual input highlighting the need for effective image analysis strategies that require minimal manual input and produce desired feature information from large datasets.

Simulation models are typically designed to fit specific datasets and are often difficult to adapt to other studies. Improvements in deep learning algorithms for image analysis, particularly the use of rapidly developing U‐NET networks, are transforming the tedious task of segmenting complex biological images to a fully automated process. Exploiting the power of deep learning will result in the development of segmentation software with minimal training required and processing of different types of data. Thus, requirement‐based improvements in the segmentation software will enable the generation of standardized pipelines and robust as well as accurate models employable to a variety of species. Apart from segmentation, another limitation is the difficulty to predict and validate the effect of a single variable on the overall process due to interconnected parameters. Interdisciplinary studies could provide experimental data for such parameters to understand and predict the effect of a single variable on the physiological process. Various biophysical models have been put forward to study different morphological features; together, these models provide a comprehensive picture of the effects of structure on overall physical processes. With further enhancements in computational power, it will be possible to create online platforms serving as database libraries supporting future studies and the generation of a comprehensive model of a given biological process including all the interdependent traits (Box 2).

Box 2. Outstanding Questions.

1. How can the accuracy of segmentation pipelines be improved through deep learning and enhanced computational power?

2. How effective will a generalized model be in predicting diverse species' behavior under increasing temperature and CO₂ conditions?

3. How can the data sharing platforms be optimized to create an open‐access computationally powerful database library for collaborative research?

4. How can micro‐CT equipment be modified to accommodate minimum radiation damage along with simultaneous measurements of physiological processes?

5. How can micro‐CT combined with modeling be leveraged to establish evolutionary links?

Improved micro‐CT image acquisition with lower radiation damage is another requirement to effectively study plant development over time (4D). Modified imaging chambers and adjustable sample holders for different plant samples ranging from in vitro to field‐grown plants will facilitate the developmental imaging. Correlative imaging also takes a step further to generate multiscale models including functional process predictions based on parameters at different levels and multi‐physics models that combine, for example, solid mechanics with fluid flow and thermodynamic aspects. Micro‐CT and FE simulations in combination with other techniques can establish a better understanding of the three‐way interaction between structure, mechanics, and physiology. The critical knowledge about structure–function relationship acquired by this approach can be translated to create effective designs for industrial purposes.

CONFLICT OF INTEREST

The authors do not have any conflict to declare.

DATA AVAILABILITY STATEMENT

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.