DOI: 10.5061/dryad.280gb5n14
title: Generative design as a tool to analyze the uncertain loading regimes of intricate skeletal structures

description: The morphology of a skeletal structure is driven in part by the forces it
 endures over evolutionary time. We demonstrate that generative design, an
 iterative engineering tool, can yield insight into the loading regimes of
 complex skeletal elements. With only a simple model of the spatial
 constraints and potential forces seen by a skeletal element, we generated
 analogous structures. We used this technique to provide insights into the
 specialization of the radial elements of batoid pectoral fins, a case that
 would be challenging to analyze by conventional means. Particular
 configurations of generative designs resulted in structures with a
 morphology remarkably similar to that of real radials. We suggest that
 these cases reveal the loading configurations that the real radials have
 evolved to withstand.
description: We imaged material from two batoid fish species from the
 collection of the Biomechanics Lab at Friday Harbor Labs. The longtailed
 river stingray, <em>Plesiotrygon iwamae</em>, is an undulatory
 swimmer with a rounded pectoral fin profile producing multiple wave
 periods along the wing per flap. The banded eagle ray,
 <em>Aetomylaeus nichofii</em>, is an oscillatory swimmer with
 a triangular fin profile generating a half wave period per flap. We
 dissected the skeleton of the pectoral fin from both species and micro-CT
 imaged the samples on a Bruker Skyscan 1173. We produced volume and
 surface renderings of radials with the free, open source software 3D
 Slicer. Fusion 360 (Autodesk, San Francisco), was used
 under educational license for computer aided design (CAD) and solving the
 generative design cases. The simulation requires geometric dimensions,
 loadings, and material properties. We elected to use a model with
 biologically based aspect ratio and arbitrary size, loading, and
 properties. We specified geometric constraints - a pair of circular
 end-caps with a central cylindrical obstruction, to simulate the stingray
 radial. The cartilage of the radials only calcifies at the outer surface
 (perichondrium), and this was captured in the generative design model by
 requiring supporting material to lie outside a central core.
 Histology shows this relationship between the mineralized
 tesserae and the unmineralized core. This informed our positioning of a
 ‘forbidden’ zone for the generative designs. We
 constrained one end cap position in all three directions and three
 rotations, then added various combinations of compressive, tensile, and
 torsional loads to the other end. The length between the ends was 300 mm,
 the ends were each 5 mm thick, the diameter of the ends was 50 mm, and the
 diameter of the cylindrical obstruction was 24 mm. For small structures
 like radials, we recommend increasing the size of the model as we have
 done. The program works at a resolution defined on a unitless
 Low(0)-High(10) scale in the study settings. Models which are too small
 end up lacking in complexity as the program is unable to generate any
 smaller geometry. Compressive loads ranged from 100 N-10.000 N, and the
 torsional loads from 0.1 Nm-100 Nm. For all trials,
 gravity was suppressed and the objective was set to ‘Minimize Mass’ with a
 safety factor of 1.00 and the displacement option deselected, as in our
 case we were not defining a maximum allowed deflection under loading. The
 ‘manufacturing method’ was set as 'Additive' only and was
 oriented in the Z+ Axis with 45° overhang and 3 mm allowed minimum
 thickness. We posit that using an additive procedure to set a minimum
 thickness simulates the "building blocks" of a structure.
 Radials are made up of mineralized tesserae meaning that a minimum
 thickness larger than cell-size exists. We used HP 3D CB PA 12 plastic
 from the Fusion 360 Additive Material Library. We added a slotted cylinder
 around the central obstacle body defined as a “Starting Shape” to speed up
 the solving process. With no starting shape, the initial iteration is
 determined based on the position and geometry of the preserved bodies. A
 starting shape circumvents that first step. We ran the program under
 compression, and torsion individually to establish the effect of each
 loading regime on geometry.  We tested a quantitative
 method for comparing the results of a generative study to a morphology
 using unitless volume fraction representing space filled.
 For the generative models, the total volume is defined to be that
 of the entire cylindrical region including the end caps. For the radials,
 an total volume was approximated as the cylinder found using the averages
 of the major and minor axes of both end caps. 
description: # Generative design as a tool to analyze the uncertain loading regimes of
 intricate skeletal structures
 [https://doi.org/10.5061/dryad.280gb5n14](https://doi.org/10.5061/dryad.280gb5n14) We have submitted our raw microCT image stacks (**CT_data.zip**), 3D meshes of structures produced using our generative design method (**Generative_Design_Models.zip**), 3D meshes of indvidual batoid radials (**Radial_Models.zip**), Shape data taken from both sets of meshes and used to calculate volume fractions (**Volume_Fraction.csv**). ## Descriptions ### **CT\_data.zip** * Folder *RayWing01_14.9um_2k_Rec2* : BMP image stack of 14.9 micron resolution scan of a section of pectoral fin from a preserved speciment of *Plesiotrygon iwamae* produced on Brucker Skyscan 1173. * Folder *RayWing02_13.8um_2k_Rec* : BMP image stack of 13.8 micron resolution scan of a section of pectoral fin from a preserved speciment of *Aetomylaeus nichofii* produced on Brucker Skyscan 1173. ### **Generative\_Design\_Models.zip** * File convention: * One number : STL mesh of resultant structure of trials using only compressive or torsional load in N, kN; or Nmm, kNmm, respectively * Two numbers : STL mesh of resultant structure of trials using combined compressive and torsional loads. First number is compression in N or kN. Second number is torsion in Nmm or kNmm. ### **Radial\_Models.zip** * File convention: * *Anichofii...* : STL models of single radials made in 3D slicer from *RayWing02_13.8um_2k_Rec* scan of *Aetomylaus nichofii* * *Piwamae...* : STL models of single radials made in 3D slicer from *RayWing01_14.9um_2k_Rec2* scan of *Plesiotrygon iwamae* * *...Proximal* : Radial segmented came from close to the body trunk * *...Distal* : Radial segmented came from near the fin tip ### **Volume\_Fraction.csv** Measurements taken from **Radial_Models.zip**, **Generative_Design_Models.zip** using Fusion 360 Columns : * *Length* : from outer faces of end cap features * *Major 1, Minor 1, Major 2, Minor 2* : Applicable only for radials. Major and minor dimensions of approximately eliptical faces of end caps. 1 or 2 for each of the two end caps. * *Average Diameter* : Applicable only for radials. Average of *Major 1, Minor 1, Major 2, Minor 2* * *Area* : end cap face area approximated as a cylinder using *Average Diameter* for radials, and a radius of 50 mm for generative designs. * *Total Volume* : *Area* times *Length* * *Mineral Volume* : Mesh volumes * *Vf* : *Mineral Volume* over *Total Volume* reported as a percentage Rows : * *Distal* : * Radial meshes from both species * *Proximal* : * Radial meshes from both species * *Compression* : * Generative design meshes from compression only trials * *Torsion* : * Generative design meshes from torsion only trials * *Combination* : * Generative design meshes from combined loading trials, first number compression, second torsion