664 Materials and methods
The Naturalis Biodiversity Center in Leiden, Netherlands, houses a legacy collection of acetate peels of blastoids produced in the late 1960s (Breimer and van Egmond, 1968). A typical specimen in this collection was serially sectioned perpendicular to the polar axis producing between 50 and 100 acetate peels. Etched and unetched peels were produced at each interval. Although the specimens were destroyed during the sectioning process, the peels are in pristine condition considering their age and remain an important source of detailed information about the internal morphology of blastoids. Eventually, the peels will be digitized and available online as part of the Naturalis Bio- diversity Center’s digitization initiative. Using individual acetate peels from this collection, Breimer and Macurda (1972) proposed major evolutionary trends in fissiculate blastoids. Morphologic information from the majority of the peels has never been published. Peels from representatives of 40 genera were scanned individually at 3,600 dpi with 8-bit grayscale using a Braun slide scanner with the goal of using the digitized peels to virtually recreate the internal and external blastoid morphology. Many 3D reconstruction software alternatives are available
to transform tomographic data sets into 3D reconstructions (Cunningham et al., 2014). SPIERS (Serial Palaeontological Image Editing and Rendering System) is a widely used, freely available package of three programs for the reconstruction and visualization of tomographic data sets (http://www.spiers-
software.org). Using SPIERS to construct 3D visualizations from serial sections and acetate peels is challenging if the serial sections are not equally spaced and if fiduciary markings to aid alignment are not present. Although most modern data sets from serial sections do not suffer these problems, many legacy data sets, including ours, do have these issues. To reconstruct blastoids from the acetate peels, we developed
Journal of Paleontology 91(4):662–671
theca with hydrospires, and brachiolar filtration fan (Fig. 4) was produced in Rhinoceros by adding the stem and brachioles to the 3D model produced from the acetate peels. The orientation of the stem and filtration fan followed the Type 1 feeding model of Breimer and Macurda (1972).
spire model of Monoschizoblastus rofei was prepared for fluid flow simulation by hollowing (Fig. 3.2) and adding hydrospire pores. We added 30 hydrospire pores to each hydrospire in accordance with our observations of a similarly sized specimen of Monoschizoblastus rofei in our collections. The length of the pore canals was based on the thickness of the thecal plates in the original sectioned specimen. An enhanced model of Monoschizoblasus rofei with stem,
was reconstructed from 95 acetate peels using the workflow described in the preceding. A model of the internal anatomy of Monoschizoblastus rofei (Etheridge and Carpenter, 1886) (Fig. 2) was similarly reconstructed from 76 peels. The hydro-
Computational fluid dynamic simulations of fluid flow through blastoid hydrospires
a visualization workflow (Fig. 1) based on Rhinoceros software, a NURBS- (nonuniform rational basis spline) based 3D com- puter graphics and CAD (computer-aided design) software that produces mathematically precise representations of curves and freeform surfaces. Because Rhinoceros is widely used in rapid prototyping, computer-aided design and manufacturing, and graphic design, it easily interfaces with a variety of other 3D visualization software packages and 3D printers. Rhinoceros makes no assumptions about vertical spacing of tomographic slices, and the user can interactively edit the vertical spacing as the model is reconstructed. The acetate peels of the blastoids lack homologous points
of reference and must be manually realigned using Photoshop. Once peels are digitized and registered, the specimen outline is clipped from the background and stacked into layers to virtually recreate the blastoid that had been destroyed through serial sectioning. Morphologic characters of interest from individual digitized peels can be characterized as regions of interest (ROI) and are segmented on separate layers using Photoshop. The layers are exported into Illustrator and converted to an AutoCAD drawing file. The ROIs are lofted into 3D models using Rhino software and can be viewed electronically or con- verted to physical models by 3D printing. The internal anatomy of a specimen of Pentremites godoni (DeFrance, 1819) (Fig. 1)
rofei was calculated using the computational fluid dynamics (CFD) module of Solidworks, a widely available computer-aided design (CAD) and computer-aided engineering (CAE) software package. A life-size (thecal length 10mm) hydrospiremodel was placed into the CFD domain and simulated on the basis of ~931,000 fluid cells (Fig. 3.4–3.7). The hydrospire model was surrounded by a fluid domain of rectangular solid shape. The distance between the inlet and the hydrospire model was about two times the thecal length; between the model and the outlet was three times the thecal length. Simulations using larger computational domains did not result in significant changes of the observed flow patterns. Mesh refinement showed good convergence; an increase in cell number did not result in significant changes of velocities. The fluid domain used seawater parameters (average density = 1,026.021kg/m3, dynamic visco- sity = 0.00122Pa·s),with unidirectional flow from the external side of the hydrospire (the side having the hydrospire pores). Initial water velocity into the hydrospire pore was set at 0.6 × 10−3m/sasdefined by Huynh et al. (2015) from estimates by Paul (1978) with turbu- lence set at 4%. The fluid domain had free-slip wall conditions to best approximate an open-water domain. We also used free-slip conditions in the internal walls of the hydrospire as a default con- dition. The Reynolds number for the hydrospire measured at the hydrospire pore is 0.787, similar to results reported by Huynh et al. (2015), who concluded that a laminar flow regime existed inside blastoid hydrospires. Water entering the hydrospire fold flows more or less horizontally at a significantly reduced velocity until it reaches
Our initial goal was to virtually re-create the experiment by Huynh et al. (2015) and test the hypotheses of water flow through hydrospires developed by Schmidtling and Marshall (2010) and Huynh et al. (2015). We used the model of Monoschizoblastus rofei because it has the simplest configura- tion of hydrospires seen in blastoids: 10 single hydrospires (Fig. 2) each emptying into a single spiracle with the exception of the anal interray hydrospires, which empty into an anispiracle (Fig. 3.1). Fluid flowthrough the hydrospire model ofMonoschizoblastus
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