A refined method for digitally modeling small and complex plant structures in 3D: An example from the grasses (Poaceae).

PREMISE OF THE STUDY: A refined procedure is described for modeling small, intricate plant structures using computer-aided design software. The procedure facilitates the study of wind pollination in the family Poaceae and provides virtual biological illustrations for public outreach. METHODS AND
RESULTS: Spikelets were fixed in gFAA, dehydrated using ethanol and xylene, embedded in paraffin wax, and then sectioned with a rotary microtome. Images of serial sections were used as a reference for modeling the shape of bracts with splines in a computer-aided design program. Virtual models produced by this method have many potential uses; examples include geometric morphometric analyses and simulations of computational fluid dynamics.
CONCLUSIONS: This protocol is a synthesis of modern biological illustration and engineering technology. Virtual models facilitate quantitative experiments that may address questions about reproductive biology, conditions shaping the form of anatomical support, or the morphological evolution of structures of biomechanical interest.

The creation of three‐dimensional (3D) models is a valuable tool for exploring a wide range of questions in biological research. The choice of technique used to generate 3D models in a particular study is important for the resolution quality, the investment of time, and production cost. Modeling intricate plant structures generally involves extracting two‐dimensional (2D) images of a desired structure, interpreting those shapes, and then recreating the morphology in 3D. High‐resolution X‐ray computed tomography has been used to construct virtual 3D models of plant structures (Dhondt et al., 2010) and even fossilized plants (Gee, 2013) by extracting 2D slices linearly through a structure, and then reconstructing a 3D surface from those images. Another method, optical photogrammetry (Eulitz and Reiss, 2015), accomplishes the same task by rotating the object to collect 2D images from multiple angles. The method that we describe here operates similarly to X‐ray computed tomography, but uses refined microscopy techniques to produce conventional anatomical slides containing serial sections. Imaging those serial sections with standard light microscopy effectively replaces extracting layers with X‐rays. Virtual 3D models are then constructed by manually designing individual splines to create the architecture of the plant structure. The advantages of the 3D modeling technique described in this paper as compared to X‐ray computed tomography are cost efficiency, simultaneous production of microscope slides for anatomical study, and the creation of an easily editable virtual model before the creation of the surface mesh. An advantage over photogrammetry is the ability to accurately recreate internal structures with a high level of detail.

An example of the utility of this method is our work on the flowers of the grass family. Poaceae is the fifth most diverse flowering plant family and one of the most ubiquitous in terrestrial distribution (Stevens, 2001 onwards; Kellogg, 2015). It is the largest plant family to rely primarily on wind pollination and is thus unique among the five most diverse families. The small size, concealing architecture of the floral units (spikelets), and compound arrangement of parts makes grass synflorescences notoriously difficult to study, especially with respect to pollination biology. We have developed a protocol to model the spikelets in 3D using computer‐assisted design (CAD) software. The models enable visual exploration of spikelets through virtual dissection. The same models can be subjected to simulations to test a suite of new hypotheses regarding mechanical properties and aspects of pollination biology. These digital models facilitate scientific research, explanatory taxonomic videos, and public outreach with the same virtual object. The spikelet of the unquestionably important and often taxonomically feared Poaceae is an ideal structure to demonstrate this new method.

The grass spikelet is a compact structure of bracts (glumes, lemmas, paleas) that envelop each other and the developing grain. Understanding the positions and shapes of the bracts is the principal method of taxonomic identification in the grass family. These structures are traditionally represented by 2D illustrations; however, it is challenging to accurately represent 3D structures and their concealing arrangement with conventional botanical illustration. Static illustrations cannot permit adjustable transparency of parts to allow the visualization of the intricate interiors of botanical structures, nor can they be used for downstream analyses. The dynamic 3D models produced by our method exist in a gradient between classical botanical illustration and virtual reality. If morphometric integrity is retained in three dimensions, the same model can be used to visualize the composition of a spikelet in a plant systematics class or provide surfaces for geometric morphometric studies (Adams, 2014). Video animations that rotate spikelets, virtually dissect spikelets or parts of the grass synflorescence, and animate taxon‐specific morphology may be used as helpful online resources to accompany taxonomic keys or botany courses.

Anatomically accurate, digital 3D models of plant structures can be used in a variety of research applications. For example, we plan to import these 3D spikelet models into computational fluid dynamics simulations to analyze wind flow around reproductive structures. Modifications can be made to the virtually modeled object relatively easily in order to experimentally test how individual parts of the spikelet, such as glumes or awns, contribute to the aerodynamics of the system. These 3D models could be used for ancestral state reconstructions and provide a means to explore observed and unobserved areas of morphospace (Runions et al., 2017). The frontiers of computer technology have been integrated with biology to produce major advances in genomics and bioinformatics; we aim to apply the same computational edge to studies of morphology.

METHODS AND RESULTS

This procedure is useful for the 3D modeling of any small, compartmentalized plant material, but our description of the method will refer specifically to the example of grass spikelets. Multiple spikelets are removed from living plants by cutting the pedicel 2 mm below the lowest glume at anthesis or stigma exsertion (Fig. 1A). Multiple spikelets are used to increase the available material in later phases of the process to minimize the risk of damaging all material. Redundancy of material also allows the final modeling to incorporate an average of structures instead of relying on a single sample. Spikelets are separated into three groups for three different degrees of dissection (Fig. 1B) before fixation, dehydration, paraffin embedding, and sectioning (Appendix 1) to permit alternate views of the structure that are necessary for accurate 3D modeling. These groups are as follows:

Figure 1

A flow diagram illustrating the dissection and microscopy techniques applied to spikelets in order to obtain images of cross sections. The procedure includes (A) collecting fresh material and vouchering the specimen, (B) dissecting some spikelets while taking photographs, (C) fixing the material in gFAA and then dehydrating in a graded series of ethanol and xylene, (D) embedding in paraffin wax, (E) serial sectioning at 10 μm thickness with a microtome, mounting sections on a slide, and photographing to produce (F) images that will be used as references for 3D modeling.

A set of spikelets is processed whole. This batch can produce the most complete set of continuous serial sections, but is often hindered by air bubbles trapped within the spikelet compartments. Gently forcing air bubbles out with a blunt dissection probe facilitates a more complete infiltration of fixatives and subsequent fluids.

A set of spikelets is cut transversely at a point above all bract insertions to expose the interior of the spikelet to increase infiltration of fluids, allowing more complete embedding and smoother sectioning. This set allows for serial sections, which progress along the rachilla, to be made, and provides a reference for each bract's location and attachment. If working with a taxon with an elongated spikelet with more than two florets (e.g., Poa L. or Eragrostis Wolf), it will be necessary to cut the spikelets into segments along the length of the rachilla.

A third set of spikelets is dissected completely in order to remove individual bracts. Several spikelets contribute their individual parts, such that separate vials each consist exclusively of lower glumes, upper glumes, fertile lemmas, etc., and are labeled accordingly. This set allows sections to be made of each bract without other material interfering or dulling blades. Sectioning individual bracts provides the clearest anatomical view and informs the modeling of each bract, but only in combination with the other preparations can the bract placements and overall spikelet structure be recreated.

Material was taken from Danthoniopsis dinteri (Pilg.) C. E. Hubb., Panicum virgatum L., and Poa pratensis L., all grown in a greenhouse, during the development of this procedure. Herbarium material may also be used, if spikelets were not deformed during the pressing and drying processes, by soaking in Pohl's solution (Pohl, 1965) prior to fixation. The spikelets (whole and cut) or dissected bracts are placed in scintillation vials and then fixed in gFAA (1% glutaraldehyde added to formaldehyde–acetic acid [Sass, 1958]) for a minimum of 24 h before further processing (Appendix 1). The liquid contents of the vials are then carefully removed and replaced with ethanol (ETOH). We have found that progressing from gFAA to 70% ETOH, 90% ETOH, 95% ETOH, 100% ETOH, and ending with a second round of 100% ETOH, in hourly steps allows timely dehydration, but at a rate slow enough to prevent cells from lysing, which could cause the shape of the organs to become distorted. Placing the vials in a rotator, or using an aspirator, may assist complete infiltration. The samples are gradually transferred from pure ETOH to xylene prior to the addition of paraffin wax. The vial is placed in a 60°C oven, and paraffin wax is added. The vial lid is unscrewed to allow the xylene to evaporate, leaving the plant material in melted paraffin wax.

Paraffin wax is poured into a mold before the desired plant material is removed from the vial and placed in an upright position at the center of the mold with the pedicel touching the bottom of the mold (Fig. 1D). After the paraffin has hardened, material is sectioned at 10 μm using a rotary microtome (Fig. 1E). Serial sections are placed on a glass slide with Haupt's solution (Bissing, 1974), stained so that they can be imaged, and then sealed with Permount and a coverslip (Sass, 1958). Images are taken at appropriate magnifications, which may vary depending on species and the size of spikelets, using a light microscope and saved as TIF files. These images provide a framework for accurately sculpting the shape of the spikelet in the CAD software. Complete spikelets under a dissecting scope are imaged to provide additional reference material.

For 3D modeling (Video S1), we use two CAD programs with alternate advantages. Modeling begins in a program called Cinema 4D (MAXON Computer GmbH, Friedrichsdorf, Germany). The microscopy cross‐section TIF files are imported into the modeling environment and oriented parallel to the X–Z plane. The shape of each bract in cross section is traced from the image using a Bezier spline drawing tool. Reference images of the whole spikelet from a side view are imported, oriented in the correct direction, and then traced (Appendix 1). The cross‐section images are moved to the proper height by vertically transposing the splines until they intersect the correct points in the side‐view splines. The splines are organized as sets of sequential splines and placed in a Loft object, which creates a continuous surface between splines. The separate Loft objects are then oriented together to form the entire spikelet. Cinema 4D produces beautiful rendered images and includes a wide range of textures, lighting, and animation techniques. However, as Cinema 4D is an artistically oriented software, it lacks the technical capacities of true nonuniform rational basis splines (referred to as NURBS). The object is therefore transferred to another program called Rhinoceros 5 (Rhinoceros 5 SR13; Robert McNeel & Associates, Seattle, Washington, USA) and the plugin Grasshopper (version 27 August 2014; Robert McNeel & Associates), which are scripts‐based, engineering‐grade CAD software. The transfer consists of removing splines from their Loft object in Cinema 4D and exporting them in a format compatible with both programs (.dxf), importing them into Rhinoceros 5, converting the Bezier splines into Basic splines, and then re‐lofting them using a Grasshopper script. The Rhinoceros 5 version of the spikelet model provides a surface mesh for computational fluid dynamics simulations to calculate aerodynamic properties.

Previous methods for analyzing aerodynamic properties of grass spikelets relied on conventional wind tunnels (Niklas, 1985) or measurements taken in the field (Friedman and Harder, 2004). Virtual simulation of computational fluid dynamics allows for the calculation of the Navier–Stokes equation (Temam, 1984), which provides air pressure and speed vectors for points within the simulated space. This is an enormous resource for testing hypotheses pertaining to structures and their relationship to the surrounding air currents. We know of one instance in the literature of computational fluid dynamics simulated around a virtual grass synflorescence (Cresswell et al., 2010). This study avoided modeling the intricate bract shapes by substituting all parts with half spheres. Although all models are approximations, our method of modeling the shape of each bract is an improvement over this study because it recreates the structure of spikelets more accurately. Virtual models produced by X‐ray computed tomography are sample‐specific and may contain abnormalities of the limited (possibly singular) sample size or exhibit deformations from noise during the acquisition of 2D images. If the purpose of a model is to provide a surface for simulating computational fluid dynamics, the intricacies of the botanical morphology should be approximated in the virtual model to accurately portray the biological inspiration.

As an educational tool, virtual models are an improvement upon 2D line drawing by providing the ability to rotate an object in 3D, visually zoom into regions of interest, and dissect the object to show how structures are oriented internally. The 3D models of grass spikelets we create with this procedure are uploaded to the 3D model repository website Sketchfab (https://sketchfab.com/pklahs) for public viewing. Because these models are constructed with points and splines in 3D space, they can be used in geometric morphometric analyses; ancestral reconstruction of 3D form; or for calculations of surface area, volume, and other 3D descriptors of shape and size. Morphometric studies require precision as to which landmarks are chosen to represent the nature of a structure's shape. The virtual models consist of many recorded points from which sets of informative points can be selected and provide a setting in which very precise measurements can be taken.

CONCLUSIONS

This method produces 3D surface models that can be used for geometric morphometric analysis and in silico simulation studies on the structural properties of plants and their interaction with environmental forces. For example, we intend to use the grass spikelet models generated in this study to assess their properties under different computational fluid dynamics models to address hypotheses of spikelet aerodynamics. Structural modifications to spikelets, ranging from impractical to impossible in vivo, can be made to the virtual model relatively easily to test hypotheses of structural influence of individual parts on the entire system. For example, awns can be added or removed from bracts, or individual bracts scaled in size, before conducting the aerodynamic simulations to explore their potential effects on wind pollination. Exploring the interactions of these structures will provide insights into the evolution of reproductive structures in the grass family. Application of this procedure is not limited to grass spikelets, and is immediately applicable to other types of flowers or even vegetative parts. Virtual models created with this method can be used to address a wide range of structural questions, all while presenting the beauty of botanical morphology in a novel way.

VIDEO S1. An animation of the steps required for 3D modeling of spikelets using Cinema 4D software. This video is an MP4 file and is available under the Supporting Information section at the end of the article, or can be viewed from the https://youtu.be/BAqwqSD0e9E.

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