Snake fangs: 3D morphological and mechanical analysis by microCT, simulation, and physical compression testing

Snake fangs: 3D morphological and mechanical analysis by microCT, simulation, and physical... This Data Note provides data from an experimental campaign to analyse the detailed internal and external morphology and mechanical properties of venomous snake fangs. The aim of the experimental campaign was to investigate the evolutionary development of 3 fang phenotypes and investigate their mechanical behaviour. The study involved the use of load simulations to compare maximum Von Mises stress values when a load is applied to the tip of the fang. The conclusions of this study have been published elsewhere, but in this data note we extend the analysis, providing morphological comparisons including details such as curvature comparisons, thickness, etc. Physical compression results of individual fangs, though reported in the original paper, were also extended here by calculating the effective elastic modulus of the entire snake fang structure including internal cavities for the first time. This elastic modulus of the entire fang is significantly lower than the locally measured values previously reported from indentation experiments, highlighting the possibility that the elastic modulus is higher on the surface than in the rest of the material. The micro–computed tomography (microCT) data are presented both in image stacks and in the form of STL files, which simplifies the handling of the data and allows its re-use for future morphological studies. These fangs might also serve as bio-inspiration for future hypodermic needles. fangs with an enclosed venom-conducting canal, and (3) open Introduction groove fangs with venom ejected along the groove surface due The fangs of venomous snakes are highly modified for pierc- to high viscosity of the venom. ing the skin and ejecting venom into prey, providing venomous In a recent experimental microCT campaign, we conducted snakes with a significant evolutionary and ecological advan- a phylogenetically informed analysis of fang phenotypes [1]. By tage. Snake fangs vary considerably in size and shape, and this using static load simulations applied to the micro–computed to- morphological variation can be attributed to differences in body mography (microCT) data of each fang, we found that, despite size, diet, and feeding behaviour. In advanced snakes, 3 types differences in shape and size, stress distributions after apply- of venom-conducting fangs can be found: (1) closed fangs with ing a load were similar between the 3 fang phenotypes. The re- an enclosed venom-conducting canal and suture line on the top sults of the study suggest that fangs might be biomechanically surface where the 2 sides seem to close up, (2) entirely fused Received: 4 August 2017; Revised: 21 November 2017; Accepted: 7 December 2017 The Author(s) 2017. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 2 Plessis et al. optimized. This Data Note is meant to highlight this exceptional least 10 points selected along the top of the fang from base to dataset, providing details on the analysis and providing addi- tip. As fang size variations occur also within species, the orig- tional results not included in the original paper. This includes inal skull belonging to each fang was also scanned using mi- advanced morphological comparisons, more detailed load sim- croCT, and skull length was measured from front to back as a rel- ulation results and physical compression test data, and extrac- ative size correction factor. In this way, relative fang size could tion of elastic modulus values. The fang models used for sim- be calculated from fang length/skull length. The polyline used ulations and for morphological measurements are included in to measure fang length was also used to fit a “best-fit” circle to the form of image stacks and segmented STL (sterolithography) the curvature of the fang, and the curvature was measured as files. These STL files are significantly smaller than full microCT the segment angle, i.e., the total angle covered by the fang on its datasets and provide dimensionally accurate 3D models of the best-fit circle. As the fang is a structure of varying thickness, a fangs. This simplified format hopefully allows a wider usage of diameter value is difficult to calculate. In this work, the fang di- the dataset by other researchers. ameter was measured using a best-fit circle to the approximate middle of the fang in the cross-sectional slice image. A central section was selected by using a 10% region of interest around this mid-point of each fang and analysing that section for ma- Materials and Methods terial fraction (BV/TV) and wall thickness analysis. High-resolution x-ray CT scans were recorded at the Stellen- Physical compression tests were performed with a Deben bosch University CT facility [2], using optimized parameters for CT500 microtest stage (500N max). The fang was glued to a highest-quality scanning using nanoCT [3]. Voxel sizes were be- polymer disk and placed on the top jaw of the stage, while a tween 1 and 8 μm depending on fang size. Each fang was in- polymer disk was placed on the bottom jaw, with rigid foam dividually loaded in rigid foam in a vertical orientation, with on top of it. The fang was slowly moved toward the foam in the foam attached to a glass rod. Scan settings included 60 kV compression mode at 0.2 mm/min, and the foam was pierced and 240 μA with the fast-scan option, resulting in ∼1 hour per with no measured load (sensitivity ∼0.1 N). Live x-ray images sample scan time. Datasets were processed in VGStudioMax 3.0, were recorded of the compression process, and successful load tests were recorded for 2 fangs. Live x-ray videos are attached and static load simulations were performed using the Structural Mechanics Simulation module. This module makes use of voxel- as Supplementary Material. For calculation of stress, the cross- based load simulation, similar to finite element modelling, but sectional area of the fang at the failure location was taken. For without the need for meshing of surfaces. The simulation re- calculation of strain, the total fang length was taken. quires a binary segmentation in the form of a surface determi- nation but does not require a mesh. Nevertheless, a mesh is also generated for simple data handling and can in principle also be Results and Discussion used for simulation, with appropriate remeshing or creation of artificial voxel data based on the mesh file—this is discussed in MicroCT images of the night adder Causus rhombeatus (NCBI more detail in the Supplementary Material. In this work, a nom- Taxon ID: 44735) are shown in Fig. 1. The series of images, from inal load of 5 N was applied to the tip of the fang (in a region left to right and top to bottom, show the whole-head microCT covering roughly half the distance to the venom canal exit ori- scan (first the exterior skin view, then a transparent view show- fice) and applied along the direction of the tip. For this, 2 regions ing upper jawbone and skull, then rotated jawbone with circles of interest (ROIs) were defined, 1 at the base, which is the fixed indicating the location of fangs [including replacement fangs] in ROI, and 1 at the tip as described above, covering half the dis- mobile anterior position). A high-resolution scan of 1 fang of this tance from tip to venom exit orifice. The region between venom type is shown at the bottom right, with an entirely fused venom exit orifice and tip was used as the reference to align the axes, canal. for applying a load in plane (directly parallel to the tip region). A microCT scan of a fang allows viewing of internal struc- Young’s modulus values were taken from the literature as 20 GPa tures such as the venom canal and the pulp cavity, as seen in [4] and Poisson’s ratio 0.3. The fang was held at its base and the Fig. 2, while a microCT slice image shows more detail of the load applied, with other parameters based on a compromise be- structure (e.g., the thin wall between the venom canal and pulp tween simulation time and convergence of the simulation result cavity), and a cropped 3D view puts this into perspective. Con- to a low error value. In this series of simulations, the number of sidering that many fangs are very small (some <1 mm) and sam- iterations used was 2000, with a simulation cell size equal to 4. ples are rare, this nondestructive approach allows a unique in- The resulting Von Mises stress distributions could be analysed sight into these types of structures, allowing slicing virtually at visually and quantitatively using in this case a 10% maximum any angle. interval from the statistical stress results. This means that local The 3 types of fangs investigated are shown with represen- maxima (such as stress hotspots in sharp points) are effectively tative examples in Fig. 3, with CT cross-sectional view also indi- smoothed out and an average is found for each fang, irrespective cating the pulp cavity and venom canal. of individual stress concentration regions. The idea is to find av- As many variations exist in fang morphology, a detailed anal- erage stress values, depending on the bulk morphology of each ysis was conducted in an attempt to correlate morphological fang. This method has recently been applied successfully in a features with fang types. The first such measurement was the study of tensile stresses around defects inside titanium alloy relative fang length. Because fang size depends highly on the castings [5], as well as analysing stress distributions in girdled size of the individual, skull length was calculated to correct for lizard osteoderms when a load is applied to simulate a bite of a this. Each snake’s skull was scanned, and its length was used predator [6]. to calculate a relative fang length. As seen in Fig. 4A, the closed Advanced morphological analysis was performed using the fused fangs are slightly longer on average, while the open groove metrology toolbox of VGStudioMax 3.0. An advanced surface de- fangs are slightly shorter. The “slender ratio” is a measure of termination is used to find the material edge, after which vari- length in relation to fang total diameter, taken at the middle ous tools are used for different morphological analyses. In par- of the fang (Fig. 4B). In this case, again, the closed fused fangs ticular, the fang length was measured using a polyline with at seem more slender. The relative wall thickness (Fig. 4C) was Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Snake fangs 3 Figure 1: Location of fangs in night adder (Causus rhombeatus). Figure 2: Internal structure of fang visualized using microCT data. Venom canal is in green and pulp cavity in orange in 3D view; sliced and cropped 3D views to the right show wall thickness and curvature of the structure. calculated as the average wall thickness at the middle of the same as used for the wall thickness) was analysed for material fang (10% of length of fang), in relation to the fang diameter fraction, including the venom canal, even in the open groove at the middle (i.e., size corrected). The wall thickness is impor- fang (using an advanced segmentation process). In this case, the tant as a thin wall will result in a weaker structure. However, volume fractions of material are similar, with the open groove the size-corrected wall thickness is very similar across all fang fang type having a slightly higher material volume fraction. types, with open groove fangs having slightly thicker walls on Finally, the curvature was measured using a method whereby average. A similar measure is the material volume fraction or the top curve of the fang was used to fit a circle, and the angle BV/TV value (Fig. 4D), which is used widely in biomedical analy- covered by the length of the fang on this circle was measured sis, e.g., for trabecular bone. The middle section of the fang (the as the segment angle (Fig. 4E). A higher value indicates a higher Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 4 Plessis et al. along the top and bottom of the fang running from the tip to more than half the fang length (Fig. 5A). The closed nonfused fangs have small ridges on each side of the tip laterally (Fig. 5B). The closed fused fangs have sharp edges only near the tip along the top and bottom, but extending only to the venom exit ori- fice (Fig. 5C). The larger edges found in the open groove fang type could be correlated to its posterior position in the max- illa and feeding behaviour that entails bite and hold (chew). This type of bite is expected to have a lower strike force, thereby re- quiring sharper and more pronounced edges to assist in break- ing the skin of the prey. Both the open groove and closed fused types have sharp edges along the top and bottom, and both these types have mobile positions in the maxilla. The mobility allows a wider range of strike angles, and the vertical edges might be more effective over more angles. The closed unfused type is found in a fixed anterior position and has lateral edges. It can be imagined that once a bite has taken place and the fang is embedded in the prey, it may be subjected to lateral forces. Pre- sumably, the lateral blades assist in removal of the fang in such situations. In order to directly compare the structural mechanics of the fang phenotypes, taking all morphological parameters directly into account, image-based load simulation was performed on each fang. A fixed load was applied to the tip of every fang with its base held in place. The resulting Von Mises stress was visual- ized as shown in Fig. 6 and measured in a 10% interval at maxi- mum in the statistical results for each simulation. As fang sizes differ, the results are expected to depend on fang radius with a power law. This is shown in Fig. 7A for each fang type indicated, from data in Broeckhoven and du Plessis [1]. By using the fang diameter at the middle and calculating a theoretical stress value for the same force applied in the simulation, a simplified theo- retical stress value could be calculated for each fang (corrected for differences in material volume fraction, neglecting the cur- vature and the cone shape). By showing the simulation stress re- sults in comparison with theoretical stress values (Fig. 7B), it can be shown that all fangs have shapes that respond similarly to ap- plied static loads and no fang types are unexpectedly stronger or weaker than others due to their shape or internal cavity sizes, wall thickness, or combinations of morphological factors. In ad- dition, simulations were performed with the load applied later- ally to the tip (at 90 degrees), and the maximum stresses were recorded. These maximum stresses correlate linearly with max- imum stress for the parallel load as shown in Fig. 7C, indicating that all fangs are equally strong laterally (and none are weaker than others for lateral loads). The lateral loads cause an increase in stress by a factor of 3 compared with linear loading. In an effort to validate the simulation results, dried, nonpre- Figure 3: Cross-sectional slice images of 3 fang types: (A) open groove, (B) closed served fangs were subjected to mechanical load tests. In Fig. 8, nonfused, and (C) closed fused phenotype. a sequence of microCT images shows sequential loading and imaging, showing the failure occurring first at the tip and then curvature, with the closed fused fangs having the highest curva- near the top of the venom canal exit orifice. ture and the open groove fangs having the lowest curvature on Mechanical loading to failure was successfully completed for average. 2 fangs. It was found that the maximum force at yield is between All the above results indicate that closed fused fangs are rela- 2 and 4 N. This is surprisingly low even considering the small tively longer, more slender (i.e., long and thin), and more curved size of the fangs (5 mm). Stress strain curves were obtained and than other fang types. Open groove fangs are less curved and are shown in Fig. 9, indicating that the yield stress is near 25–35 shorter but have thicker walls and higher material volume frac- MPa and the Young’s modulus (of the entire structure including tions, presumably to compensate for their smaller size. Large cavities) is ∼500 MPa. variations exist, as can be expected within each category. An in- These values allow an estimation of the material Young’s teresting observation was that sharp edges are found on many modulus using the material volume fraction and assuming the material acts as an open cell foam. Initial simulations us- fangs, most likely meant to assist in piercing. It was found that each fang type has a specific type of sharp edge associ- ing 20 GPa for Young’s modulus of the fang material result in much higher estimation of the effective Young’s modulus of the ated with it. The open groove fangs have a long sharp ridge Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Snake fangs 5 Figure 4: Morphological measurements obtained for 20 snake species (1 sample per species), grouped as (left) closed fangs with suture line, (middle) fused fang, and (right) open groove fangs. Morphometrics shown are (A) relative fang length, (B) fang length over diameter (slender ratio), (C) wall thickness over diameter (size- corrected wall thickness), (D) material volume fraction (BV/TV), (E) curvature measured as circular segment angle. entire structure. A lower value of 1.25 GPa was thus estimated Conclusions and applied in the simulation of this fang type. The resulting Venomous snake fangs were analysed by microCT using ad- displacement found by simulation allows calculation of the ef- vanced morphological analysis and structural mechanics sim- fective Young’s modulus of the entire structure, 365 MPa in this ulations. It was found that the 3 fang phenotypes that occur case. This value of Young’s modulus is therefore more reason- in various lineages of snakes all had distinctive characteris- able (corresponding roughly to the 500 MPa obtained by com- tics besides the morphology of the venom-conducting canal. pression testing). This value of ∼1.25 GPa, which is the average The open groove fangs appear to be shorter and less curved, Young’s modulus of the fang material, is much lower than the while closed, fused fangs are longer, relatively thin, and more 20 GPa found by indentation in previous studies. This highlights curved. Sharp edges are located in different places in each fang the possibility that the elastic modulus varies locally across the type, and could be correlated to bite behaviour. Incorporating fang, and especially that it might be higher on the surface (where all morphological information, structural mechanics simula- indentation normally takes place) or might vary between species tions were performed on the microCT data. Results obtained as well. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 6 Plessis et al. Figure 5: Sharp edges occurring in different places in different fang types shown here are representative examples of (A) long sharp edges along top and bottom of open groove fangs, (B) sharp edges around the horizontal sides of the tip of closed fangs, and (C) sharp edges along the top and bottom of the tip of entirely fused fangs. Figure 6: Von Mises stress distributions visualized for every fang type, with videos in the Supplementary Material. In order: Naja nivea, Causus rhombeatus, in the form of stress values indicate that fang types all Dispholidus typus. respond similarly to applied loads, both parallel and laterally. Lateral loads induce stresses 3 times higher than parallel loads. Availability of supporting data Physical compression tests were conducted on 2 snake fangs. Stress strain curves recorded for these 2 fangs allow calcula- Supporting microCT data are available as image stacks and STL tion of elastic modulus of the fang structure (500 MPa) includ- files from the GigaScience database (GigaDB), alongside videos of ing its venom canal and pulp cavity. The location of failure snake fang physical compression testing [7]. in physical tests correlates well with the stress distributions from load simulations. These results indicate that the piercing Abbreviations and cutting ability of fangs is pivotal to their success, as the fangs do not appear to be physically very strong (yield stress 3D: 3-dimensional; CT: computed tomography; Pa: pascal; ROI: ∼25–35 MPa). regions of interest. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Snake fangs 7 Figure 7: Von Mises stress values shown as a function of (A) fang middle radius [1] and (B) theoretically calculated stress for a rod of the same radius with measured material volume fraction. (C) Stress values for parallel load compared with those for lateral loads. Figure 8: A sequence of microCT scans showing progressive failure in a single Naja nivea fang. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 8 Plessis et al. Figure 9: Stress strain curves obtained for 2 fangs of Naja nivea, different specimens than the 1 shown in Fig. 8. Both of these curves were obtained during live x-ray imaging, with both videos available in the Supplementary Material. tomography laboratory. Nucl Instrum Methods Phys Res Sect Competing interests B 2016;384:42–49. A. du Plessis and S.G. le Roux manage and operate the Stellen- 3. du Plessis A, Broeckhoven C, Guelpa A, le Roux SG. Labora- bosch University CT Facility. tory x-ray micro-computed tomography: a user guideline for biological samples. Gigascience 2017;6(6):1–11. 4. Jansen van Vuuren L, Kieser JA, Dickenson M, Gordon KC, Acknowledgements Fraser-Miller SJ. Chemical and mechanical properties of snake fangs. J Raman Spectrosc 2016;47(7):787–95. The National Research Foundation of South Africa is acknowl- 5. du Plessis A, Yadroitsava I, le Roux SG, Yadroitsev I, Fieres J, edged for its support through equipment grants for micro-CT Reinhart C, Rossouw P. Prediction of mechanical performance instruments and rated researcher incentive funding for A. du of Ti6Al4V cast alloy based on microCT-based load simulation. Plessis. J Alloys Compd 2017; doi:10.1016/j.jallcom.2017.06.320. 6. Broeckhoven C, du Plessis A, Hui C. Functional trade-off between strength and thermal capacity of dermal armor: References insights from girdled lizards. J Mech Behav Biomed Mater 1. Broeckhoven C, du Plessis A. Has snake fang evolution lost 2017;74:189–94. its bite? New insights from a structural mechanics viewpoint. 7. du Plessis A, Broeckhoven C, le Roux SG. Snake fangs: 3D Biol Lett 2017;13(8):20170293. morphological and mechanical analysis by microCT, simula- 2. du Plessis A, le Roux SG, Guelpa A. The CT Scanner Facility tion and physical compression testing. GigaScience Database at Stellenbosch University: an open access X-ray computed 2017. http://dx.doi.org/10.5524/100389. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png GigaScience Oxford University Press

Snake fangs: 3D morphological and mechanical analysis by microCT, simulation, and physical compression testing

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Abstract

This Data Note provides data from an experimental campaign to analyse the detailed internal and external morphology and mechanical properties of venomous snake fangs. The aim of the experimental campaign was to investigate the evolutionary development of 3 fang phenotypes and investigate their mechanical behaviour. The study involved the use of load simulations to compare maximum Von Mises stress values when a load is applied to the tip of the fang. The conclusions of this study have been published elsewhere, but in this data note we extend the analysis, providing morphological comparisons including details such as curvature comparisons, thickness, etc. Physical compression results of individual fangs, though reported in the original paper, were also extended here by calculating the effective elastic modulus of the entire snake fang structure including internal cavities for the first time. This elastic modulus of the entire fang is significantly lower than the locally measured values previously reported from indentation experiments, highlighting the possibility that the elastic modulus is higher on the surface than in the rest of the material. The micro–computed tomography (microCT) data are presented both in image stacks and in the form of STL files, which simplifies the handling of the data and allows its re-use for future morphological studies. These fangs might also serve as bio-inspiration for future hypodermic needles. fangs with an enclosed venom-conducting canal, and (3) open Introduction groove fangs with venom ejected along the groove surface due The fangs of venomous snakes are highly modified for pierc- to high viscosity of the venom. ing the skin and ejecting venom into prey, providing venomous In a recent experimental microCT campaign, we conducted snakes with a significant evolutionary and ecological advan- a phylogenetically informed analysis of fang phenotypes [1]. By tage. Snake fangs vary considerably in size and shape, and this using static load simulations applied to the micro–computed to- morphological variation can be attributed to differences in body mography (microCT) data of each fang, we found that, despite size, diet, and feeding behaviour. In advanced snakes, 3 types differences in shape and size, stress distributions after apply- of venom-conducting fangs can be found: (1) closed fangs with ing a load were similar between the 3 fang phenotypes. The re- an enclosed venom-conducting canal and suture line on the top sults of the study suggest that fangs might be biomechanically surface where the 2 sides seem to close up, (2) entirely fused Received: 4 August 2017; Revised: 21 November 2017; Accepted: 7 December 2017 The Author(s) 2017. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 2 Plessis et al. optimized. This Data Note is meant to highlight this exceptional least 10 points selected along the top of the fang from base to dataset, providing details on the analysis and providing addi- tip. As fang size variations occur also within species, the orig- tional results not included in the original paper. This includes inal skull belonging to each fang was also scanned using mi- advanced morphological comparisons, more detailed load sim- croCT, and skull length was measured from front to back as a rel- ulation results and physical compression test data, and extrac- ative size correction factor. In this way, relative fang size could tion of elastic modulus values. The fang models used for sim- be calculated from fang length/skull length. The polyline used ulations and for morphological measurements are included in to measure fang length was also used to fit a “best-fit” circle to the form of image stacks and segmented STL (sterolithography) the curvature of the fang, and the curvature was measured as files. These STL files are significantly smaller than full microCT the segment angle, i.e., the total angle covered by the fang on its datasets and provide dimensionally accurate 3D models of the best-fit circle. As the fang is a structure of varying thickness, a fangs. This simplified format hopefully allows a wider usage of diameter value is difficult to calculate. In this work, the fang di- the dataset by other researchers. ameter was measured using a best-fit circle to the approximate middle of the fang in the cross-sectional slice image. A central section was selected by using a 10% region of interest around this mid-point of each fang and analysing that section for ma- Materials and Methods terial fraction (BV/TV) and wall thickness analysis. High-resolution x-ray CT scans were recorded at the Stellen- Physical compression tests were performed with a Deben bosch University CT facility [2], using optimized parameters for CT500 microtest stage (500N max). The fang was glued to a highest-quality scanning using nanoCT [3]. Voxel sizes were be- polymer disk and placed on the top jaw of the stage, while a tween 1 and 8 μm depending on fang size. Each fang was in- polymer disk was placed on the bottom jaw, with rigid foam dividually loaded in rigid foam in a vertical orientation, with on top of it. The fang was slowly moved toward the foam in the foam attached to a glass rod. Scan settings included 60 kV compression mode at 0.2 mm/min, and the foam was pierced and 240 μA with the fast-scan option, resulting in ∼1 hour per with no measured load (sensitivity ∼0.1 N). Live x-ray images sample scan time. Datasets were processed in VGStudioMax 3.0, were recorded of the compression process, and successful load tests were recorded for 2 fangs. Live x-ray videos are attached and static load simulations were performed using the Structural Mechanics Simulation module. This module makes use of voxel- as Supplementary Material. For calculation of stress, the cross- based load simulation, similar to finite element modelling, but sectional area of the fang at the failure location was taken. For without the need for meshing of surfaces. The simulation re- calculation of strain, the total fang length was taken. quires a binary segmentation in the form of a surface determi- nation but does not require a mesh. Nevertheless, a mesh is also generated for simple data handling and can in principle also be Results and Discussion used for simulation, with appropriate remeshing or creation of artificial voxel data based on the mesh file—this is discussed in MicroCT images of the night adder Causus rhombeatus (NCBI more detail in the Supplementary Material. In this work, a nom- Taxon ID: 44735) are shown in Fig. 1. The series of images, from inal load of 5 N was applied to the tip of the fang (in a region left to right and top to bottom, show the whole-head microCT covering roughly half the distance to the venom canal exit ori- scan (first the exterior skin view, then a transparent view show- fice) and applied along the direction of the tip. For this, 2 regions ing upper jawbone and skull, then rotated jawbone with circles of interest (ROIs) were defined, 1 at the base, which is the fixed indicating the location of fangs [including replacement fangs] in ROI, and 1 at the tip as described above, covering half the dis- mobile anterior position). A high-resolution scan of 1 fang of this tance from tip to venom exit orifice. The region between venom type is shown at the bottom right, with an entirely fused venom exit orifice and tip was used as the reference to align the axes, canal. for applying a load in plane (directly parallel to the tip region). A microCT scan of a fang allows viewing of internal struc- Young’s modulus values were taken from the literature as 20 GPa tures such as the venom canal and the pulp cavity, as seen in [4] and Poisson’s ratio 0.3. The fang was held at its base and the Fig. 2, while a microCT slice image shows more detail of the load applied, with other parameters based on a compromise be- structure (e.g., the thin wall between the venom canal and pulp tween simulation time and convergence of the simulation result cavity), and a cropped 3D view puts this into perspective. Con- to a low error value. In this series of simulations, the number of sidering that many fangs are very small (some <1 mm) and sam- iterations used was 2000, with a simulation cell size equal to 4. ples are rare, this nondestructive approach allows a unique in- The resulting Von Mises stress distributions could be analysed sight into these types of structures, allowing slicing virtually at visually and quantitatively using in this case a 10% maximum any angle. interval from the statistical stress results. This means that local The 3 types of fangs investigated are shown with represen- maxima (such as stress hotspots in sharp points) are effectively tative examples in Fig. 3, with CT cross-sectional view also indi- smoothed out and an average is found for each fang, irrespective cating the pulp cavity and venom canal. of individual stress concentration regions. The idea is to find av- As many variations exist in fang morphology, a detailed anal- erage stress values, depending on the bulk morphology of each ysis was conducted in an attempt to correlate morphological fang. This method has recently been applied successfully in a features with fang types. The first such measurement was the study of tensile stresses around defects inside titanium alloy relative fang length. Because fang size depends highly on the castings [5], as well as analysing stress distributions in girdled size of the individual, skull length was calculated to correct for lizard osteoderms when a load is applied to simulate a bite of a this. Each snake’s skull was scanned, and its length was used predator [6]. to calculate a relative fang length. As seen in Fig. 4A, the closed Advanced morphological analysis was performed using the fused fangs are slightly longer on average, while the open groove metrology toolbox of VGStudioMax 3.0. An advanced surface de- fangs are slightly shorter. The “slender ratio” is a measure of termination is used to find the material edge, after which vari- length in relation to fang total diameter, taken at the middle ous tools are used for different morphological analyses. In par- of the fang (Fig. 4B). In this case, again, the closed fused fangs ticular, the fang length was measured using a polyline with at seem more slender. The relative wall thickness (Fig. 4C) was Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Snake fangs 3 Figure 1: Location of fangs in night adder (Causus rhombeatus). Figure 2: Internal structure of fang visualized using microCT data. Venom canal is in green and pulp cavity in orange in 3D view; sliced and cropped 3D views to the right show wall thickness and curvature of the structure. calculated as the average wall thickness at the middle of the same as used for the wall thickness) was analysed for material fang (10% of length of fang), in relation to the fang diameter fraction, including the venom canal, even in the open groove at the middle (i.e., size corrected). The wall thickness is impor- fang (using an advanced segmentation process). In this case, the tant as a thin wall will result in a weaker structure. However, volume fractions of material are similar, with the open groove the size-corrected wall thickness is very similar across all fang fang type having a slightly higher material volume fraction. types, with open groove fangs having slightly thicker walls on Finally, the curvature was measured using a method whereby average. A similar measure is the material volume fraction or the top curve of the fang was used to fit a circle, and the angle BV/TV value (Fig. 4D), which is used widely in biomedical analy- covered by the length of the fang on this circle was measured sis, e.g., for trabecular bone. The middle section of the fang (the as the segment angle (Fig. 4E). A higher value indicates a higher Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 4 Plessis et al. along the top and bottom of the fang running from the tip to more than half the fang length (Fig. 5A). The closed nonfused fangs have small ridges on each side of the tip laterally (Fig. 5B). The closed fused fangs have sharp edges only near the tip along the top and bottom, but extending only to the venom exit ori- fice (Fig. 5C). The larger edges found in the open groove fang type could be correlated to its posterior position in the max- illa and feeding behaviour that entails bite and hold (chew). This type of bite is expected to have a lower strike force, thereby re- quiring sharper and more pronounced edges to assist in break- ing the skin of the prey. Both the open groove and closed fused types have sharp edges along the top and bottom, and both these types have mobile positions in the maxilla. The mobility allows a wider range of strike angles, and the vertical edges might be more effective over more angles. The closed unfused type is found in a fixed anterior position and has lateral edges. It can be imagined that once a bite has taken place and the fang is embedded in the prey, it may be subjected to lateral forces. Pre- sumably, the lateral blades assist in removal of the fang in such situations. In order to directly compare the structural mechanics of the fang phenotypes, taking all morphological parameters directly into account, image-based load simulation was performed on each fang. A fixed load was applied to the tip of every fang with its base held in place. The resulting Von Mises stress was visual- ized as shown in Fig. 6 and measured in a 10% interval at maxi- mum in the statistical results for each simulation. As fang sizes differ, the results are expected to depend on fang radius with a power law. This is shown in Fig. 7A for each fang type indicated, from data in Broeckhoven and du Plessis [1]. By using the fang diameter at the middle and calculating a theoretical stress value for the same force applied in the simulation, a simplified theo- retical stress value could be calculated for each fang (corrected for differences in material volume fraction, neglecting the cur- vature and the cone shape). By showing the simulation stress re- sults in comparison with theoretical stress values (Fig. 7B), it can be shown that all fangs have shapes that respond similarly to ap- plied static loads and no fang types are unexpectedly stronger or weaker than others due to their shape or internal cavity sizes, wall thickness, or combinations of morphological factors. In ad- dition, simulations were performed with the load applied later- ally to the tip (at 90 degrees), and the maximum stresses were recorded. These maximum stresses correlate linearly with max- imum stress for the parallel load as shown in Fig. 7C, indicating that all fangs are equally strong laterally (and none are weaker than others for lateral loads). The lateral loads cause an increase in stress by a factor of 3 compared with linear loading. In an effort to validate the simulation results, dried, nonpre- Figure 3: Cross-sectional slice images of 3 fang types: (A) open groove, (B) closed served fangs were subjected to mechanical load tests. In Fig. 8, nonfused, and (C) closed fused phenotype. a sequence of microCT images shows sequential loading and imaging, showing the failure occurring first at the tip and then curvature, with the closed fused fangs having the highest curva- near the top of the venom canal exit orifice. ture and the open groove fangs having the lowest curvature on Mechanical loading to failure was successfully completed for average. 2 fangs. It was found that the maximum force at yield is between All the above results indicate that closed fused fangs are rela- 2 and 4 N. This is surprisingly low even considering the small tively longer, more slender (i.e., long and thin), and more curved size of the fangs (5 mm). Stress strain curves were obtained and than other fang types. Open groove fangs are less curved and are shown in Fig. 9, indicating that the yield stress is near 25–35 shorter but have thicker walls and higher material volume frac- MPa and the Young’s modulus (of the entire structure including tions, presumably to compensate for their smaller size. Large cavities) is ∼500 MPa. variations exist, as can be expected within each category. An in- These values allow an estimation of the material Young’s teresting observation was that sharp edges are found on many modulus using the material volume fraction and assuming the material acts as an open cell foam. Initial simulations us- fangs, most likely meant to assist in piercing. It was found that each fang type has a specific type of sharp edge associ- ing 20 GPa for Young’s modulus of the fang material result in much higher estimation of the effective Young’s modulus of the ated with it. The open groove fangs have a long sharp ridge Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Snake fangs 5 Figure 4: Morphological measurements obtained for 20 snake species (1 sample per species), grouped as (left) closed fangs with suture line, (middle) fused fang, and (right) open groove fangs. Morphometrics shown are (A) relative fang length, (B) fang length over diameter (slender ratio), (C) wall thickness over diameter (size- corrected wall thickness), (D) material volume fraction (BV/TV), (E) curvature measured as circular segment angle. entire structure. A lower value of 1.25 GPa was thus estimated Conclusions and applied in the simulation of this fang type. The resulting Venomous snake fangs were analysed by microCT using ad- displacement found by simulation allows calculation of the ef- vanced morphological analysis and structural mechanics sim- fective Young’s modulus of the entire structure, 365 MPa in this ulations. It was found that the 3 fang phenotypes that occur case. This value of Young’s modulus is therefore more reason- in various lineages of snakes all had distinctive characteris- able (corresponding roughly to the 500 MPa obtained by com- tics besides the morphology of the venom-conducting canal. pression testing). This value of ∼1.25 GPa, which is the average The open groove fangs appear to be shorter and less curved, Young’s modulus of the fang material, is much lower than the while closed, fused fangs are longer, relatively thin, and more 20 GPa found by indentation in previous studies. This highlights curved. Sharp edges are located in different places in each fang the possibility that the elastic modulus varies locally across the type, and could be correlated to bite behaviour. Incorporating fang, and especially that it might be higher on the surface (where all morphological information, structural mechanics simula- indentation normally takes place) or might vary between species tions were performed on the microCT data. Results obtained as well. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 6 Plessis et al. Figure 5: Sharp edges occurring in different places in different fang types shown here are representative examples of (A) long sharp edges along top and bottom of open groove fangs, (B) sharp edges around the horizontal sides of the tip of closed fangs, and (C) sharp edges along the top and bottom of the tip of entirely fused fangs. Figure 6: Von Mises stress distributions visualized for every fang type, with videos in the Supplementary Material. In order: Naja nivea, Causus rhombeatus, in the form of stress values indicate that fang types all Dispholidus typus. respond similarly to applied loads, both parallel and laterally. Lateral loads induce stresses 3 times higher than parallel loads. Availability of supporting data Physical compression tests were conducted on 2 snake fangs. Stress strain curves recorded for these 2 fangs allow calcula- Supporting microCT data are available as image stacks and STL tion of elastic modulus of the fang structure (500 MPa) includ- files from the GigaScience database (GigaDB), alongside videos of ing its venom canal and pulp cavity. The location of failure snake fang physical compression testing [7]. in physical tests correlates well with the stress distributions from load simulations. These results indicate that the piercing Abbreviations and cutting ability of fangs is pivotal to their success, as the fangs do not appear to be physically very strong (yield stress 3D: 3-dimensional; CT: computed tomography; Pa: pascal; ROI: ∼25–35 MPa). regions of interest. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Snake fangs 7 Figure 7: Von Mises stress values shown as a function of (A) fang middle radius [1] and (B) theoretically calculated stress for a rod of the same radius with measured material volume fraction. (C) Stress values for parallel load compared with those for lateral loads. Figure 8: A sequence of microCT scans showing progressive failure in a single Naja nivea fang. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018 8 Plessis et al. Figure 9: Stress strain curves obtained for 2 fangs of Naja nivea, different specimens than the 1 shown in Fig. 8. Both of these curves were obtained during live x-ray imaging, with both videos available in the Supplementary Material. tomography laboratory. Nucl Instrum Methods Phys Res Sect Competing interests B 2016;384:42–49. A. du Plessis and S.G. le Roux manage and operate the Stellen- 3. du Plessis A, Broeckhoven C, Guelpa A, le Roux SG. Labora- bosch University CT Facility. tory x-ray micro-computed tomography: a user guideline for biological samples. Gigascience 2017;6(6):1–11. 4. Jansen van Vuuren L, Kieser JA, Dickenson M, Gordon KC, Acknowledgements Fraser-Miller SJ. Chemical and mechanical properties of snake fangs. J Raman Spectrosc 2016;47(7):787–95. The National Research Foundation of South Africa is acknowl- 5. du Plessis A, Yadroitsava I, le Roux SG, Yadroitsev I, Fieres J, edged for its support through equipment grants for micro-CT Reinhart C, Rossouw P. Prediction of mechanical performance instruments and rated researcher incentive funding for A. du of Ti6Al4V cast alloy based on microCT-based load simulation. Plessis. J Alloys Compd 2017; doi:10.1016/j.jallcom.2017.06.320. 6. Broeckhoven C, du Plessis A, Hui C. Functional trade-off between strength and thermal capacity of dermal armor: References insights from girdled lizards. J Mech Behav Biomed Mater 1. Broeckhoven C, du Plessis A. Has snake fang evolution lost 2017;74:189–94. its bite? New insights from a structural mechanics viewpoint. 7. du Plessis A, Broeckhoven C, le Roux SG. Snake fangs: 3D Biol Lett 2017;13(8):20170293. morphological and mechanical analysis by microCT, simula- 2. du Plessis A, le Roux SG, Guelpa A. The CT Scanner Facility tion and physical compression testing. GigaScience Database at Stellenbosch University: an open access X-ray computed 2017. http://dx.doi.org/10.5524/100389. Downloaded from https://academic.oup.com/gigascience/article-abstract/7/1/1/4750779 by Ed 'DeepDyve' Gillespie user on 16 March 2018

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GigaScienceOxford University Press

Published: Jan 1, 2018

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