https://orcid.org/0000-0001-7367-3212
Synopsis
Quantifying the material properties of hard biological materials can improve understanding of the relationships between form, function, and performance. This study illustrates the use of nanoindentation as a tool for evaluating material properties in a comparative biology framework. We provide a step-by-step guide for comparative and evolutionary biologists illustrating the collection and analysis of nanoindentation data from samples of artiodactyl skull bones. We assess the impact of methodological decisions on the output of nanoindentation tests. We also investigate whether evolutionary variations in skull bone properties are present between artiodactyl species that engage in intraspecific head-to-head combat and those that do not. Elastic modulus exhibited little variation among numbers of indents performed per test and per bone sample. The average elastic modulus was significantly lower when bones were hydrated with deionized water. The skulls of artiodactyls exhibited a gradient of elastic modulus values in which the anterior of the skull is less stiff than more posterior locations. Species involved in head-to-head combat showed little difference in elastic modulus values compared to non-combat species. This suggests that ecological factors influence the evolutionary diversity of bone material properties, rather than strictly phylogenetic constraints. In a phylogenetic context, nanoindentation reveals tetrapod bone heterogeneity and provides insights into the evolution of these traits.
Introduction
The mechanical performance of biological structures is strongly influenced by the properties of the materials from which they are built (Currey 1979, 1984). Material properties such as density, stiffness, and hardness can define the physical limitations of structures with different compositions, providing critical insight into the likelihood that a structure will succeed or fail in performing a given task. Quantifying material properties is therefore an important component of functional morphology, as it aids in understanding the relationships between form, movement, and performance for biological structures and whole organisms (Blob and Snelgrove 2006; Oyen 2008b; Wilson et al. 2009; Tseng and Stynder 2011; Taft et al. 2017; Habegger et al. 2020). For ecologists, these properties can help establish the physical capabilities of an organism within its environment and provide insights into its biological interactions (Wall 1983; Koehl 1996; Tseng and Flynn 2015). Moreover, examining the properties of biological materials from a comparative perspective can shed light on the selective pressures that have shaped morphological evolution over time (Currey 1987; Blob and LaBarbera 2001; Erickson et al. 2002; Blob and Snelgrove 2006; Bruet et al. 2008; Houssaye 2009; Olesiak et al. 2010; Butcher et al. 2011).
Early efforts to consider biological materials properties in comparative and evolutionary contexts were advanced by Currey (1979, 1987), who highlighted variation in the properties of bone across species that spanned diverse phylogenetic lineages and structures with different functional demands. More recently, experiments have investigated how material properties affect movement and function of organisms (Ferrara et al. 2013), how that relate to performance in their habitats (Pérez-Barbería and Gordon 1999; Gray et al. 2007; Houssaye 2009; Chen et al. 2012), and how properties of hard biological materials may have evolved (Blob and LaBarbera 2001; Erickson et al. 2002; Blob et al. 2014). However, comparative studies have led to conflicting interpretations of the extent and significance of diversity in the properties of biological materials. For example, in studies of bone material properties, some have indicated that properties of particular bones may be evolutionarily constrained across taxa (Erickson et al. 2002), whereas others have shown that properties correlate with bone function and biomechanical demands (Blob and Snelgrove 2006). Thus, many questions remain about the extent of variation in the material properties and microstructure of bone (and other hard biological materials) within and between taxa.
Historically, many efforts to evaluate the material properties of hard biological materials, especially bone, employed techniques with foundations in beam theory, which is based on principles of elasticity (Currey 1987; Summers and Long 2005; Habegger et al. 2015). However, these approaches have important assumptions that can limit the types of specimens to which they can be applied. For example, 3- and 4-point bending tests assume that a sample to be tested is made of a homogeneous material, has a uniform cross-section, and is long in proportion to its depth (i.e., essentially “beam” shaped: Van Lenthe et al. 2008; Kourtis et al. 2014). Long bones of vertebrate limbs rarely meet these assumptions; moreover, bones that do not resemble a beam (e.g., skull bones) are especially challenging to test as intact elements. For such elements, it is often necessary to remove a sizable piece of the specimen to sculpt it into a “beam” shape that can be gripped in a testing apparatus. Mechanical testing (i.e., tension, compression, and bending) is also destructive for such specimens and samples, which severely limits the range of items that can be tested because destructive sampling is often restricted for species or specimens that are rare or difficult to obtain (Faisal et al. 2018).
Small-scale physical experimentation methods, such as micro- and nanoindentation, overcome many of the limitations associated with macro-scale mechanical testing, such as the need for specimens to have a specific geometry. This technique has proven to be very effective in investigating how tooth structure supports mechanical function from both biomedical (Balooch et al. 1998; Fong et al. 1999; Habelitz et al. 2002; Field et al. 2014; Ghadimi et al. 2014) and comparative (Angker and Swain 2006; Whitenack et al. 2011; Kundanati et al. 2019; Gorb and Krings 2021; Arevalo et al. 2022; Shohel et al. 2022; Wilmers et al. 2024) perspectives. To date, most comparative indentation studies have been limited to one or two species (Whitenack et al. 2010; Chen et al. 2012; O'Brien et al. 2014; Ma et al. 2018; Wurmshuber et al. 2023; Wilmers et al. 2024) or a small selection of species (Field et al. 2014; Kundanati et al. 2019; Gorb and Krings 2021), with the aim of either relating structural properties to ecological function or generating biomimetic insights (although see Shohel et al. 2022). By expanding small-scale indentation studies to a phylogenetically informed selection of species, we propose to generate novel quantitative insights into evolutionary patterns in the material properties of hard biological materials like bone and teeth.
Nanoindentation is one of a suite of techniques that can be used to evaluate material properties of biological specimens, focusing at the nanoscale. It operates on a basic principle dating back to the 1980s (Pethicai et al. 1983; Oliver and Pharr 1992) that is commonly used by many nanoindentation systems. This involves simultaneously measuring the load and indenter displacement during a loading cycle without the need to manually measure the residual indent, as is necessary in Vickers microindentation (Broitman 2017). The specimen under examination is subjected to a precisely controlled indentation using a tip of known geometry and made from a material of known properties (Pharr 1998). Characteristics of the resulting load-displacement curve [peak load (Pmax)] can give information on several experimental variables (Fig. 1). Values of variables, including peak load, displacement at peak load (Pmax), maximum contact depth (hmax), residual penetration depth (hf), the slope of the initial unloading curve, and the known characteristics of the indenter tip, (i.e., area function), then enable the calculation of a variety of material properties. These properties include hardness (resistance to permanent deformation), Young's modulus (resistance to elastic deformation), and toughness (resistance to fracture) (Pharr 1998). A Berkovich diamond indenter tip is commonly used to indent the material, as it maintains a consistent contact area with depth, though there are other types of indenter tips with differing geometries and, therefore, different contact areas (Ebenstein and Pruitt 2006; Oyen 2013). For example, a spherical indenter is often preferred for softer materials, such as gel polymers, especially when used with multiple load/unload cycles (Ebenstein and Pruitt 2006). In bone studies, spherical indenters have been used to better address bone's viscoelastic properties, as they help minimize plastic deformation and stress concentrations, reducing damage to tissues and allowing for clearer distinction between elastic and plastic behaviors (Angker and Swain 2006; Ebenstein and Pruitt 2006; Rodriguez-Florez et al. 2013). Unlike the Berkovich indenter, a spherical indenter is not self-similar, introducing depth-dependent changes in stress as the indenter penetrates deeper into the material. Spherical indenters are available in various sizes, allowing for measurements across different hierarchical levels of bone structure (Paietta et al. 2011).
(A) Modified from Oliver and Pharr (1992), Fig. 19 schematic of indentation geometry showing variables used in calculations of elastic modulus. (B) Modified from Oliver and Pharr (1992), Fig. 20 schematic of the resulting load-displacement curve from the indentation geometry in (A). It depicts maximum load (Pmax), maximum contact depth (hmax), residual penetration depth (hf), and the slope of the initial unloading curve (S). Three basic equations used to calculate elastic modulus (E) from the indentation geometry are as follows: (1) |${h_c} = {h_{{\rm{max}}}} - \frac{3}{4}\frac{{{P_{{\rm{max}}}}}}{{dP/dh}}$|, (2) |$A = \pi {a^2},$| (3) |$E = \frac{1}{2}{( {\frac{{dP}}{{dh}}} )_{{h_{{\rm{max}}}}}}\sqrt {\frac{\pi }{A}} $|.
It is important to recognize that indentation methods measure material properties rather than mechanical properties. Mechanical properties are influenced by the shape and size of the material, whereas material properties are intrinsic to the material itself (Wainwright et al. 1976). For example, stiffness describes how much a particular structure will deform under a given load, whereas Young's modulus describes how a material behaves under stress and strain. Small-scale indentation provides the nanomechanical properties of hard biological materials at submicron levels without being affected by specimen size, shape, and macroporosity (Managuli et al. 2023). This method requires only small samples, facilitating the investigation of localized differences and small-scale features, such as individual lamellae (Rho et al. 1997; Oyen and Cook 2009; Hargrave-Thomas et al. 2015). Moreover, the indentation test itself leaves no macro-scale damage (though some sample preparation may be necessary: Valtierra et al. 2022) and avoids issues commonly seen in macro-scale testing, as biological layers often exceed the nanoscale and resist complications like buckling (Currey 1984).
Applications of indentation testing methods have been limited in integrative and comparative biology, with the notable exception of studies on human and vertebrate dental tissues. The most common micro-indentation tests (Vickers test and Knoop test) measure hardness by determining a material's resistance to penetration. A load is applied to the sample's surface, and the practitioner then measures the size of the resulting indent. A crucial distinction for nanoindentation tests is that both the load applied to a specimen and the displacement of its material are measured throughout the test. This continuous monitoring enables the generation of a stress–strain curve, offering deeper insights into the material's mechanical properties at the nanoscale. It should be noted, however, that this continuous testing method usually associated with nanoindentation could be applied at the micro-scale, as the only technical distinction between micro- and nanoindentation is the scale of the test. Nanoindentation was initially optimized for engineered materials that are stiff, isotropic, and homogeneous, but has since been adapted for biological materials (see reviews by Rayfield 2007; Lewis and Nyman 2008; Arnold et al. 2017; Broitman 2017; Managuli et al. 2023). Most recent advancements in nanoindentation methods for bone material properties have been driven by the biomedical field, as estimates of bone hardness and stiffness are valuable for applications, including orthopedic surgery and the treatment of conditions like osteoporosis (Hengsberger et al. 2002; Donnelly 2011; Zhao et al. 2018). However, these efforts are now also driven by researchers wanting to develop and test bioinspired hard materials like biomimetic bone (Oyen 2008b), enamel (Ghadimi et al. 2014; Wilmers et al. 2024), and soft tissues like the lining of the human uterus (Fodera et al. 2024).
Applications of nanoindentation to non-medical studies of bone can be found in the fields of paleontology and archeology. For example, studies have investigated how bone is altered geologically after death and how properties change through fossil preservation (Lerner et al. 2007; Olesiak et al. 2010; Erickson et al. 2012). Nanoindentation testing of bone has not been as widely adopted by comparative biologists (although see Kupczik et al. 2007; Bruet et al. 2008; Olesiak et al. 2010; Ferrara et al. 2013). This is surprising, given the potential benefits of these methods for a range of applications. For example, the data returned by nanoindentation methods can be used to investigate safety factors of biological materials and also provide more accurate input information for computational models of hard structures such as finite element analyses (FEAs), which can predict material stress under theoretical loading conditions that are not possible to generate through empirical experiments (Dumont et al. 2005; Ross 2005; Strait et al. 2005; Farke 2008; Snively et al. 2015).
The purpose of this paper is to provide organismal and evolutionary biologists with an introduction to nanoindentation methods and how to implement them, highlighting their advantages and aiming to facilitate further interdisciplinary studies on the properties of biological hard materials. These methods, which are well established in other fields, can be a valuable tool for biologists, especially in a comparative framework. We illustrate this utility using bone samples extracted from the skulls of even-toed hoofed mammals (Artiodactyla). We outline general nanoindentation methodology and testing procedures, with the goal of making these methods more accessible to comparative biologists. We address sample preparation, nanoindentation testing, and the interpretation of results. Validation of the method is demonstrated by presenting results from indentations performed within a scanning electron microscope (SEM), visually confirming the appropriate surface roughness of bone specimens for this technique. By simplifying the learning curve of nanoindentation for applications in comparative biology through this review, we hope to emphasize the collaborative potential between biologists, materials scientists, and engineers and encourage interdisciplinary work across these fields.
This study investigates four research questions. The first two questions focus on the impact of methodological decisions on the outcome of nanoindentation tests: (1) does the number of indents performed on a bone sample influence the resulting values obtained for material properties, such as elastic modulus; and (2) does the elastic modulus differ between dry and re-hydrated bone cores. Our third and fourth questions illustrate the application of nanoindentation methods in a comparative biological context, asking (3) are there functional patterns in the variation of bone properties across different bone locations within the artiodactyl skull, (4) and whether evolutionary variations in skull bone properties are present between species that engage in intraspecific head-to-head combat and those that do not. Previous studies on a variety of tetrapod taxa (e.g., reptiles, carnivores, primates, and sheep) have shown non-uniform strain distributions across regions of the skull and jaw (Ross and Metzger 2004), with higher strains in the mandible and lower strains around the neurocranium, influenced by localized strain through muscle activity. Many artiodactyls engage in intraspecific combat for reproductive success, using head ornamentation to fight conspecifics. This places a unique force on the head ornaments and bones of the skull (Kitchener 1988). Based on this, we expect the skull bones of species that use intraspecific combat to exhibit lower elastic moduli to absorb forces associated with combat.
Sample preparation
Extracting test specimens
It is worth noting that hard biological materials don't necessarily have to be cored to be compatible with nanoindentation; they simply need to fit into the nanoindenter and be adequately restrained during testing so that the sample is presented square to the indenter axis and held firmly with the minimum amount of compliance (Fischer-Cripps 2004). If the sample does not need to be cut and can be adequately restrained, nanoindentation is virtually non-destructive (Faisal et al. 2018). However, a sample usually has to be extracted from a specimen to fit within the indenter and most biological specimens must be polished to decrease surface roughness for accurate indentation. When extracting a sample from an original intact item, such as a skull, the goal should be to obtain the sample with minimal damage to the original specimen while obtaining a usable sample for nanoindentation. We recommend a diamond-tipped coring bit attached to a standard impact power drill to sample hard biological materials without causing excessive damage to the original specimen (Fig. 2). To successfully core the sample without leaving marks and scratches, begin with the bit at a ∼45° angle to the material surface. As the bit sinks into the sample, straighten the drill to a 90° angle. This greatly increases the stability of the drill on the sample and decreases excess movement and scratches. When drilling into a dried specimen, it is important to apply a small amount of water to the drilling surface throughout the process so that the core stays intact during drilling. This can be performed using a squeeze bottle with a narrow nozzle so that water can be placed precisely and added as needed (Fig. 2). When drilling a fresh specimen, it may or may not be necessary to use water as a lubricant; however, it is still recommended to reduce the heat conveyed to the specimen by friction with the drill bit. The material core often does not stay in the coring bit, so it is important to locate the core sample before removing the drill bit from the specimen.
(A) Coring process of the occipital bone of Grant's gazelle (Nanger granti). The diamond tipped coring drill bit was used with a standard impact drill and the core is started at ∼45° angle; (B) close up of the drilling proves with the water lubrication. Two drill holes can be seen that indicate when the effect of coring.
Embedding and grinding
Several preparatory steps are necessary to ensure that an extracted sample is suitable for nanoindentation. Firstly, the material to be tested must be firmly stabilized to prevent any shifts during testing, as even minor movements can significantly impact testing output at such a small scale. A common approach to stabilization is to embed the specimen in a non-infiltrating epoxy, such as Caroplast (Carolina Biological Supply Company, Burlington, NC) (Fig. 3A). Because it does not infiltrate most hard biological material, and itself has a low-modulus value, Caroplast embedding has minimal effects on the measured properties of hard biological specimens (Olesiak et al. 2007; Olesiak et al. 2010). This allows practitioners to easily distinguish if an indent cycle has mistakenly measured properties from the medium surrounding the specimen, rather than the specimen itself. Embedding can be accomplished by securing specimens in small wells with non-stick walls, such as silicone ice cube trays or baking molds. Alternatively, companies specializing in metallurgy and material analysis offer ring forms and castable molds for embedding purposes. Care should be taken to orient the specimen in a way that the surface intended for testing faces the exposed surface of the mounting medium to facilitate later polishing. If the sample will not stand on its own in the desired orientation, it can be superglued to the bottom of the mold. The sample should be completely poured over with the embedding medium because the hardened medium will be ground down in subsequent steps. Curing of a mounting medium can take 48 h or longer and is best performed in a fume hood. Additionally, most embedding media generate heat during the curing process, which can be dissipated by curing in a water bath, or other thermally conductive materials (Montalbano and Feng 2011)
(A) Silicone baking mold with two bone cores embedded in Caroplast after they have cured; the (B) the grinding and polishing wheel used with the 400–1200 grit sandpaper and the diamond solution; (C) vibratory polisher with one bone core attached to the circular metal holder being polished for 1.5–2 h in the colloidal silica suspension (blue). Both the grinding wheel and vibratory polisher are located at the Center for Integrated Nanotechnologies (CINT).
After the embedding medium is set, the embedded specimen can be removed from its mounting well to grind the testing surface. The purpose of this step is two-fold: (1) to grind away excess medium until the biological material surface is revealed and (2) to buff out large indentations and/or cracks in the sample surface before fine polishing. Coarse grinding can be performed by hand with a polishing wheel (Fig. 3B), commonly available in lab facilities focusing on histology or several geological disciplines (e.g., mineralogy). Additionally, the embedded sample can be cut using a fine cutting saw if necessary to produce the flat surface needed for polishing and indentation. Contingent on embedding material and sample type, initial grinding can usually be accomplished using 400 grit pads and the time needed depends on how deeply the specimen is embedded. Once the specimen's surface is exposed, grinding can proceed with a 600-grit pad to remove gross surface flaws, rotating the surface of the specimen being polished by 90° (in the plane of the wheel) at regular intervals to eliminate scratches in the opposite direction, and taking care to not grind away an excessive amount of the specimen itself. During each stage of grinding, it is important to visually inspect the testing surface to qualitatively assess the amount of sample exposed from the medium using either a digital microscope (Keyence VHK) or a profilometer. Grinding is considered complete once the embedding medium is entirely removed from the sample surface.
Polishing and surface roughness
For nanoindentation to work properly on bone and other biological hard materials, an appropriate surface roughness is needed, which is often lower than the natural surface roughness of the sample. This is accomplished by sequential polishing steps. Using the same wheel used for grinding, samples can be polished with high-grit sandpaper (800 and 1200), and then finer scale fluids with a polishing pad (e.g., 1µm diamond fluid, Pace Technologies DIAMAT solution). These grit sizes buff out moderately sized cracks and scratches, with each step proceeding for roughly 4–5 min in alternating orientations to the polishing wheel, as described for grinding. It is important to move to higher grit sandpaper sequentially so that large scratches do not remain in a polished sample. Further polishing requires different approaches. After physical polishing, chemo-mechanical polishing can be performed using a vibratory polisher (Fig. 3C). Typical protocols involve treatment for 1.5–2 h using a colloidal silica suspension (Pace technologies SIAMAT Blue) in conjunction with a polyurethane pad. After attaching the pad to the vibratory polisher, enough colloidal silica suspension is added to barely cover the pad completely. The embedded sample should be secured to a specimen holder for the polishing machine (many of which are made for round samples), and then placed face down onto the pad to begin polishing. Like the grinding step, the sample should be periodically visualized under a digital microscope or profilometer to qualitatively assess the roughness of the testing surface. If the sample is still excessively rough, which is determined subjectively by eye or a nanoindentation test failure, a further step of polishing to the atomic level can be performed using an ion mill; however, this step is typically not essential for successful nanoindentation testing.
Example artiodactyl dataset
Following the procedures outlined above, samples were extracted from artiodactyl skulls housed at Clemson's Campbell Museum of Natural History from five major clades (Hippopotamidae, Suidae, Camelidae, Cervidae, and Bovidae). Small bone cores were extracted at five locations along the skull and rostrum (i.e., anterior and posterior mandible, premaxilla, nasal, and occipital) to assess if elastic modulus differs across the skull and jaw bones, with the expectation that the occipital bone of combat species will exhibit lower elastic modulus due to a required decreased resistance to deformation to allow for absorption and dissemination of forces across the back of the skull during combat (Fig. 4). During drilling, water was used to lubricate and cool the bone and extract an intact bone core. Bone core specimens were stored dry at room temperature. Cores were embedded in Caroplast medium using rectangular silicone baking molds, with cores that did not sit stable being superglued to the bottom of the mold. Embedded specimens were left to cure in the molds for a minimum of 24 h, taking care that the specimens did not migrate before the Caroplast solidified. Samples were then removed from the silicone molds and allowed to harden for an additional 24 h.
White-tailed deer (Odocoileus virginianus, CU665) skull depicting the five bone locations that were sampled on all artiodactyl specimens in this study. This specimen was not included in the sampling, as a male deer was selected due to the study's focus on combat-related questions.
The samples were taken to the Center for Integrated Nanotechnologies (CINT) (Albuquerque, NM) for subsequent grinding, polishing, and testing. Embedded samples were first ground using a 400-grit polishing pad on a Pace Technologies grinding wheel. During this step, a Keyence digital microscope was used to visually assess when the medium was removed, and the bone was exposed. Then, each sample was polished with 600,800 and 1200 grit sandpaper, each for 4–5 min until surface scratches were eliminated while alternating the direction of the sample on the wheel roughly every 30 s. Samples were polished with a 1-µm diamond fluid that was added to a polishing pad on the wheel for the same time interval as the high grit sandpaper. Then, the samples were rinsed off and attached to a specimen holder for a vibratory polisher. Because these samples were rectangular in shape, they were super glued to a weight (holder) and placed face down on the vibratory polishing surface that was covered with colloidal silica. Up to four samples were loaded at a time and were polished for ∼1.5 h. Following that step, a small blade was used to remove them from the holder. If necessary to remove the sample from the holder, the whole apparatus was placed in a sonicator to detach the embedded sample from the polishing holder. Polished bones were imaged using the digital microscope and/or profilometer before indentation testing (Fig. 5). Further polishing with an ion mill was not applied as it was not necessary to further decrease the surface roughness on these samples (Fig. 5).
The four images were taken of the same polished pronghorn (Antilocapra americana) anterior mandible bone core; (A) light microscope image, (B) laser and optical image provide contrast to visualize surface roughness, (C) heat map image, with warmer colors representing high areas and cool colors representing low areas, provides a topology of the surface and shows low (cool colors) areas to avoid in testing, and (D) rotating 3D image provides an overall visualization of the bone core. Green arrows indicate possible smooth areas to target for nanoindentation.
Nanoindentation test procedures
Testing overview
First, the embedded and polished sample needs to be secured to the platform, often using a magnet embedded within the platform. A small metal disc is super-glued to the bottom of the embedded sample, which is then placed on the magnetic platform area (Fig. 6B). Prior to indenting, there is an automated x−y stage that allows the tester to navigate the tip to different areas of the sample. At this step in the procedures, software controlling the indenter will also allow a practitioner to choose to perform many individual indents across the surface of material, typically in a grid array (Oyen 2013).
(A) The Hysitron Triboindenter at CINT used for nanoindentation testing; (B) metal stage of the Hysitron Triboindenter with three bone samples attached and ready for indentation. The silver pucks superglued to the bottom of the sample are visible through the embedding medium. They allow for magnetic attachment to the stage.
When the test is initiated, a diamond-tipped probe is driven into the sample until a predetermined load or depth is reached. Nanoindentation systems are commonly load controlled, meaning that the tip will indent the material until a specified load is reached. In a load-controlled test, the choice of maximum load is contingent upon the gross material properties; generally softer materials require lower loads compared to harder or stiffer ones. The desired depth of penetration, often driven by specific layer or area testing requirements, is another crucial factor to consider when setting maximum load because it needs to eliminate the influence of surface roughness (Rho et al. 1997). Some nanoindentation systems can conduct depth-controlled testing, where the practitioner sets a specified depth, and the load that is required to reach that depth is used. This can be advantageous, as it removes the inconsistency of contact area in load-controlled tests (Wolfram et al. 2010). The tip will penetrate to a specified, consistent depth during each test, allowing the load to vary, which ensures the same contact area for each indent. The available instrument settings will ultimately determine the boundaries of the load and depth control possibilities. Once the settings are specified, high-resolution sensors and actuators continuously control and record three variables: load (P), displacement (h), and time (t) (Rho 1999; Oyen 2013; Broitman 2017). As the indenter is driven into the material, the material undergoes plastic and elastic deformation, and creates a load-displacement curve (Fig. 1). The shape of the overall curve, or trace, can give indications about the deformation mode of the material throughout the test (Oyen and Cook 2009). The linear aspect of the unloading trace in the load-displacement curve is important for calculating elastic modulus, as it represents the elastic deformation of the material as the tip is retracted.
Several characteristics make hard biological materials more complicated to test than an engineered, homogenous metal (Hoffler et al. 2005). For example, bone is a heterogeneous, hierarchical material composed of mineralized collagen fibrils and pores at the tissue level, which are bundled to form osteons and lamellae (Lakes 1993). This hierarchical nature and porosity can influence the nanoindentation output, so the tester must determine what penetration depth is most appropriate for the specific scientific question. Additionally, bone is anisotropic, meaning its material properties depend on the orientation of the load. Therefore, maintaining consistent orientations is essential when investigating bone in a comparative context (Swadener et al. 2001; Wolfram et al. 2010; Casanova et al. 2017). Increased indentation depth (sampling volume) will capture progressively larger structural features of the material; thus, controlling indentation depth allows for precise measurements of specific structural levels (Mittra et al. 2006; Paietta et al. 2011). Porosity can complicate the Oliver–Pharr interpretation of hardness and modulus by affecting the consolidation of micropores during testing (Oyen 2008a). This highlights the importance of thoroughly visualizing and imaging samples beforehand. Most biological hard materials, such as bone, also exhibit viscoelastic properties, meaning that they demonstrate both viscous and elastic responses under strain. These responses play a crucial role in the material's force distribution. In nanoindentation testing, viscoelasticity may cause bone and other biological hard tissues to exhibit time-dependent creep behavior under constant load, because the movement of water through the hydrated material as it is loaded effects properties like Young's modulus. At high loading rates, bone acts as a linear elastic material without creep behavior, as the liquid does not have time to move through the material during the test. However, when loading rate is slow, diffusion takes place and the bone acts as a viscoelastic material (He and Swain 2009; Yu et al. 2011; Lee et al. 2013). To account for viscoelasticity, a hold period at maximum load is implemented to allow viscous relaxation before initiating the unloading phase, which is essential for accurately calculating properties like Young's modulus (Bembey et al. 2006; Oyen and Cook 2009; Oyen 2013).
The Oliver–Pharr method uses a power law expression to calculate Young's modulus at peak load (S). Together with a geometric parameter of the indenter tip, this process computes the contact depth (hc), which, in turn, is used to determine the contact area of the indent. This projected contact area is crucial for calculating material properties accurately. To estimate contact area, the method uses an area function (also called the shape function or tip function), which relates the cross-sectional area of the indenter to the distance to the tip of the indenter. This is straightforward to calculate for a perfect Berkovich tip. However, an indenter tip will always have defects due to wear and other factors, so this area function will have to be estimated for each individual tip at the time of its use. To accommodate such issues, a calibration procedure that measures the machine compliance and assesses the tip area function by indenting a material with known properties is conducted at the beginning of each testing session, allowing for the calculation of deviations from the ideal geometry. This calibration is commonly performed using fused silica (fused quartz) due to its uniform mechanical properties and generally high hardness and Young's modulus (Pharr 1998; Oyen and Cook 2009; Broitman 2017). It is a common practice to calibrate the area function using ∼100 indentations spanning the load thresholds of the machine, starting at high loads (as thermal drift is higher at the beginning of a test) and decreasing the load for each subsequent indent to measure the contact area at various indent depths. A validation test, using a simple nanoindentation grid on the same material, is conducted to ensure the instrument is producing accurate modulus and hardness measurements before testing the sample material.
Additional calibrations and factors that affect testing
There are several factors to keep in mind when conducting mechanical tests at such small scales, some of which are addressed by the indenter system or software. The microenvironment in the indenter is important because the physical environment of a biological hard material affects its material properties (Van Vliet 2019). To address this, many nanoindenter systems are enclosed to reduce microenvironmental fluctuations during testing. In some systems, it is possible to control the temperature and humidity within the chamber, though this capability is not universal. A calibration indentation in air should be performed to account for the microenvironment inside the tester. This calibration involves an indentation in the air of the microenvironment (the diamond tip does not make contact with the sample) to adjust for temperature, humidity, and other environmental factors.
Additionally, nanoindentation systems are equipped with drift correction features. This capability compensates for minor changes or fluctuations in tip movement due to factors such as mechanical creep and thermal expansion by measuring tip displacement at a constant load (Mayo and Nix 1988). Increased motor activity (i.e., moving the tip around the stage, moving from optic lens to indenter tip) leads to higher drift due to the heat generated by the movement of the transducer. To address this, the system re-measures the drift rate and implements correction between each indent.
Sample surface roughness, which indicates the deviation in height relative to a perfectly smooth surface, also significantly affects the measured material properties during nanoindentation (Sun et al. 2008). If the surface roughness is significant enough that the indenter tip cannot contact a relatively flat surface, the results of indent tests will not accurately reflect the material's properties. Therefore, a polishing regime like the one described above is essential. Additionally, the tip-to-optic calibration of the nanoindenter is crucial, particularly with heterogeneous materials, as not every area of the sample will be suitable for testing and must be carefully selected by the practitioner. It is critical that the tip lands precisely where the optical system indicates because the practitioner must locate appropriate locations for testing through the optic lens. Additionally, this calibration is crucial for one of the greatest advantages of small-scale testing—it allows for precise comparison of specific layers or regions within the biological sample itself. A tip-to-optic calibration is typically performed using a material with readily visible indents, such as aluminum. This process enables the creation of an indent pattern that allows the practitioner to precisely pinpoint the location of the indent and indicate that to the indenter.
Biological material hydration state
Many biological hard materials exist in some state of hydration in biological natural conditions. Natural hydration of the material is important to take into account when testing. For example, the water content of bone typically ranges from 10 to 20% (Oyen 2013). Because the properties of biological hard material vary with hydration levels, testing hydrated materials more accurately reflects biological conditions (Oyen 2013). However, preventing evaporation and maintaining a consistent biological hydration level during testing is challenging. Therefore, biological hard materials are often fully hydrated by soaking in liquid prior to testing as well as being tested while submerged. Studies have employed various techniques to test both wet and dry biological materials, primarily bone, including tensile testing, ultrasonic velocity testing, and nanoindentation (Evans and Lebow 1950; Currey 1988; Rho 1999; Swadener et al. 2001; Bembey, Oyen, et al. 2006). These studies reported a 15–24% increase in elastic modulus when bones are dehydrated (Swadener et al. 2001), though the magnitude of this increase can vary (Rho 1999). Saline (0.9%) is isotonic to the internal environment of mammals, and most organisms maintain a certain level of salinity in their bodies. Therefore, a saline solution is often the most biologically relevant medium for soaking biological hard materials that exist in a hydrated state in vivo. However, soaking and testing in saline can present challenges when using nanoindentation. As the indenter tip recedes from the sample and the liquid after an indent, the water on the tip evaporates quickly, potentially leaving salt crystals attached to the tip that affect subsequent indents. Many studies have hydrated and tested bone in deionized water (Evans and Lebow 1950; Bembey et al. 2006; Bembey, Oyen et al. 2006; Oyen et al. 2012), though a few studies performed successful indents using salt solutions (Bushby et al. 2004; Wolfram et al. 2010).
Liquid nanoindentation typically employs a setup similar to that of air indentation, though it may not be possible with all instruments and at all facilities. In liquid nanoindentation, the sample is positioned in a flat-bottomed petri or weighing dish, which is then placed on the stage of the nanoindenter. The choice of dish is critical; it must have a flat bottom to prevent movement or tipping during testing and must be sufficiently thin to allow the stage's magnet to secure the sample via the metal puck on the bottom of the embedding medium. Additionally, there is a specialized liquid indentation tip, distinguished primarily by its length. It is longer than a standard tip used for indentation in air to accommodate capillary action as the tip enters and recedes from the liquid. Additionally, the thickness of the liquid layer covering the sample in the dish can also affect the test. It should be fully submerged with a 2–3 mm layer on top, but the water layer should not be so large that capillary action interferes with the transducer. The primary challenge during the indentation itself is the presence of the surface layer of liquid over the sample. At such a small scale, the indenter tip may mistake the liquid surface as the sample surface because the liquid surface will exert a load on the tip when it is encountered. To address this issue, a preload setting is necessary. This preload ensures that the tip disregards any load encountered up to a specified threshold. After setting up, the required considerations for liquid indentation outlined above, and before commencing sample testing, the indenter must be calibrated to the specific conditions using a material with known properties. This material should be submerged in the dish to a depth of ∼2 mm, after which the standard calibration procedure should be executed.
Testing the artiodactyl dataset
Work was performed, in part, at the Center for Integrated Nanotechnologies (CINT), an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Los Alamos National Laboratory (Contract 89233218CNA000001) and Sandia National Laboratories (Contract DE-NA-0003525). The dataset included embedded bone cores from dried museum specimens of 10 artiodactyl species; Sus scrofa, Antilocapra americana, Pecari tajacu, Lama glama, Hippopotamus amphibius, Giraffa camelopardalis, Nanger granti, Odocoileus virginianus, Capra hircus, and Bos taurus. All samples were subjected to dry indentation testing in air, and two locations (occipital and posterior mandible) from each species were then tested in liquid to evaluate the effect of rehydration on the bone cores. The embedded samples were transported to the Center for Integrated Nanotechnologies at Sandia National Laboratories in Albuquerque, NM, where they were tested using a Bruker Hysitron Triboindenter (Fig. 6A). A metal puck was superglued to the bottom of the polished sample to facilitate connection to the magnetic indenter stage (Fig. 6A). A Berkovich tip was used in the Triboindenter, featuring a load-hold-unload trapezoidal function with a 3-s hold at maximum load before unloading. The maximum load applied to the samples was 7000 μN. Each test at each bone location involved a grid pattern ranging from 9 to 25 indents, depending on the need for repeated indents, available machine time, and suitable indenting areas on the sample (Fig. 7A). The grid locations on the bone core were selected using the optical lens of the indenter to ensure areas of low surface roughness. Large crevices and pores were avoided to ensure accurate results (Fig. 7A). After specimen extraction, they were categorized based on cortical and trabecular bone presence. However, the indentations did not target a specific bone type, as our goal was to extrapolate findings to the whole structure. Any associated variability was accounted for in the measurement averages. A tip to optic calibration was performed to ensure that the area seen in the optical lens was where the tip would land. Then, a calibration for the area function was performed. Immediately before each testing session of the bone cores, a calibration air indent was performed. Once the bone location was chosen and the test initiated, the indenter tip moved into position with a 60-s motor settle time followed by a 45-s piezo settle time. During this time, the drift rate was calculated prior to each indent in the grid. Each bone core was tested with a grid pattern at 2–3 different locations. The mean elastic modulus and hardness were calculated using Bruker TriboScan software and averaged from all bone locations, with specific outlier curves removed (see “Nanoindentation output”).
(A) 4 × 4 indent grid on a cattle (Bos taurus) posterior mandible bone core (B) a depiction of the load-displacement curves output for 10 individual indents with an example of an outlier, where the tip may have landed on the embedding medium or an area that was too rough.
The embedded posterior mandible and occipital specimens for each species were then soaked in distilled water in a weighing dish for 1–1.5 h prior to liquid indentation testing (Wolfram et al. 2010). For testing, the sample was submerged in the dish to a depth of 2 mm, and then loaded onto the stage of the nanoindenter, taking care that the magnet that was super-glued to the bottom of the sample was secured to the stage. The liquid Berkovich tip, a longer version of the air testing tip, was used to do the same testing regime as the dry sample testing: a load-hold-unload trapezoidal profile with a maximum load of 7000 µN. However, the preload for the test was set at 200 µN to ensure that the indenter did not mistake the surface of the liquid for the surface of the sample. The testing regime was the same as for dry indentation, with a 60-s motor settle time followed by a 45-s piezo settle time in between the tip movement and the subsequent indent in the grid.
To verify the effectiveness of the polishing and testing regime used in this study, a Hysitron Picoindenter was mounted inside an SEM. This allowed visualization of the test that is not possible using only nanoindentation instruments. This visualization ensured that the indenter tip was not erroneously measuring surface roughness or otherwise not producing an accurate test. Images from this trial show the indenter tip contacting the bone surface and then being retracted to reveal a triangular indentation (Fig. 8). This visualization verifies that the polishing regime decreases surface roughness enough for appropriate nanoindentation testing on the bone cores extracted from museum specimens.
Nanoindentation series inside an SEM for visualization; (A) the indenter tip in the top of the image is making contact with the bone core surface, (B) the indenter tip is being retracted and the indentation in the bone is beginning to come into view, and (C) the indenter tip is retracted further and the whole indent is seen and is deeper than the surface roughness observed at the sight.
To assess the effect of the number of indents per bone and per test on the resulting elastic modulus, we used a linear model implemented using the function lm() in the base statistics package in R. To explore the effect of indentation in air versus water, we conducted tests in both media for two bone elements—the posterior mandible and occipital bone. We used the lmer() function in the lme4 R package (Bates et al. 2015) to assess differences in modulus between the testing media, the bone locations, and the interaction between these variables, with a random effect of species. The linear relationship between the average modulus tested in air and the average modulus tested in deionized water was also estimated. To assess differences in bone elastic modulus between species that engage in head-to-head combat, phylogenetic analysis of variance (ANOVAs) were performed using the phylANOVA() function in the phytools package using a time-calibrated phylogeny of Cetartiodactyla (Zurano et al. 2019) pruned to match the species in this dataset. The phenogram() function in the R package phytools (Revell 2012) was used to plot the phylogeny onto the traitspace, where the elastic modulus is represented on the y-axis. All analyses were conducted in R version 4.2 (R Core Development Team 2020).
Nanoindentation output
Most nanoindentation systems output raw data of each indent in the grid including the three continuously monitored variables, load, displacement, and time. They will also output the variables that are important for the calculation of reduced modulus and hardness. These include contact displacement (hc), maximum load (Pmax), stiffness (S), contact area (A), and max displacement (hmax). The software that comes with the machine will use this data to calculate material properties and will also output the reduced elastic modulus (Er) and hardness (H) values along with drift for each indent. The reduced elastic modulus is defined as the series combination of the probe and sample material properties; however, for materials, far more compliant than the indenter tip materials (including most biological hard materials), this distinction from standard values of elastic modulus is negligible (Oyen 2013). The measurement of the variables above allows a force-displacement curve to be plotted for each indent, and the practitioner can assess its quality (Fig. 7B). For example, Fig. 7B illustrates the force-displacement curves for an indentation grid. Each curve corresponds to one indent. It is common in these tests for a specific indent to be uncharacteristic of the material because it hits a spot in the sample that moves, breaks, or has too high a surface roughness. Additionally, a profilometer can be used to locate and visually inspect the indentation grid for each testing regime, which would further assess the quality of an indent or grid. Software accompanying the nanoindentation system will fit the unloading curve for each indent based on the Oliver–Pharr method. It is then possible to identify outlier curves and remove them from the analysis, as they are often not characteristic of the biological material between the pores in the core. Each successful indent has its own reduced modulus value, which can be used to calculate an average reduced modulus for a given specimen.
Results and discussion
Effect of indent number on elastic modulus
A total of 1494 indentations were produced on the artiodactyl bone cores in this study. The number of indents conducted per bone core, including indents in all locations, did not affect the resulting reduced modulus value (P = 0.183) (Fig. 9B). Additionally, the number of indents conducted per test had no effect on the modulus value (P = 0.464) (Fig. 9A). In both linear models, the slope of the line is not distinguishable from 0, indicating that a very high number of indents or replicates, on a sample are not necessary to obtain a reliable reduced modulus value.
(A) Regression of the number of indents performed per test and the average reduced modulus (GPa), (B) regression of the number of indents performed per bone core and the average reduced modulus (GPa).
The monetary cost associated with using nanoindentation instruments is often based on the time spent using the indenter, making it important to optimize instrument efficiency. This also makes travel to facilities more cost-effective for scientists without access to an indenter at their institution. While the number of indents is often reported (Rho et al. 1997) or kept consistent throughout an experiment (Bushby et al. 2004; Bembey, Bushby, et al. 2006; Bruet et al. 2008), their specific impact on the evaluation of specimen properties has not been explicitly considered. This is significant, as it may not always be feasible to perform the same number of indents on a sample due to the unique characteristics of specimens or constraints on instrument time. These findings enhance the utility of nanoindentation for scientists with limited access to the necessary instruments.
Effect of testing medium on elastic modulus
The pairwise analysis of the effect of testing medium on two bone locations revealed that bone is more compliant when hydrated (P = 0.004) (Fig. 10A). This decrease in elastic modulus compared to dehydrated bones did not depend on bone location (P = 0.414) and the posterior mandible and occipital bone locations did not have statistically different modulus values (P = 0.161) (Fig. 10B). The regression of the elastic modulus of the posterior mandible and occipital tested dry versus rehydrated shows a significant positive correlation (slope 1.197, P = 0.017, R2 = 0.518) (Fig. 10C). The increase in the elastic modulus of the dehydrated bone is roughly 16.1%. There was notable variation in these patterns across our samples with some bone cores not showing any difference in the modulus when soaked in deionized water, but there were no consistent patterns of bone location or species associated with this variation.
The top two panels represent the same individual data points of elastic modulus measurements in air and deionized water. (A) Overall difference in elastic modulus between dry and hydrated bone, (B) represents pairwise comparison of reduced modulus for two bone types and each core from those types, (C) scatterplot of the regression of the reduced modulus (GPa) of the bone cores tested both dehydrated and rehydrated with deionized water. The blue line indicates the slope of the relationship, and the gray shaded area represents the 95% confidence interval (CI) of the linear model. The black line represents a slope of 1 with an intercept of zero.
The increase in elastic modulus in dehydrated bone in this study supports other studies that have investigated the effects of hydration, with the 16.1% increase falling within the range that has previously been reported (Swadener et al. 2001; Bushby et al. 2004; Bembey, Bushby, et al. 2006; Wolfram et al. 2010; Oyen et al. 2012). Most of these studies associated with hydration state were performed on human, bovine, or equine long bones (Reilly and Burstein 1975; Rho et al. 1997; Swadener et al. 2001; Wolfram et al. 2010). This study further confirms that skull bone hydration state significantly impacts mechanical properties with dehydrated bones exhibiting a higher modulus value across artiodactyl families regardless of bone location.
Many studies on the material properties of biological materials are focused on obtaining values of the properties that most accurately reflect the condition of the materials as they would be used by living organisms. In the case of nanoindentation, this would require liquid indentation of (re-)hydrated materials for specimens that are naturally hydrated, such as bones that were originally surrounded by living tissue. Such accuracy can be crucial for advancing understanding of how many biological materials function. However, achieving such accuracy often requires highly specialized techniques and instruments, as well as significant time, making the process challenging and limiting its accessibility. Nanoindentation measurements of dehydrated biological material can be useful for many contexts and questions. Comparing these measurements can give insights into relative differences in properties between species, bone type, or local differences in bone areas. Moreover, the relationship between the measurements in each medium could allow for the estimation of a range of hydrated elastic modulus values, which is valuable for investigating samples that cannot be rehydrated. If existing specimens from museums and other collections can reliably produce meaningful measurements in addition to fresh specimens, it opens the use of nanoindentation to rare or otherwise difficult to obtain specimens that could not be evaluated using other methods.
Elastic modulus across skull and artiodactyl species comparison
Elastic modulus varies between locations across the skull and mandible of artiodactyls (P < 0.01). The posterior bone locations (occipital and posterior mandible) had the highest elastic modulus values, with means of 17.6 and 18.4 GPa, respectively (Table 1). The anterior bones of the rostrum, the premaxilla, and nasal have lower elastic moduli, near 13 GPa. Taken together, these results indicate that there is an anterior–posterior pattern across artiodactyl skulls, from lower to higher stiffness (Fig. 11).
Elastic modulus (reduced modulus) values of five bone locations from all artiodactyl species in this study. All pairwise comparisons were conducted, the brackets at the top illustrate only the significant differences between bone location with the corresponding P-values.
Species, combat behavior, average elastic modulus, and standard deviation, along with indent count, for each bone location across species
| Species | Common name | ID# | Combat type | Bone location | Air Ind. # | Average elastic modulus air (GPa) | Elastic modulus standard deviation air | DI Ind. # | Average elastic modulus DI (GPa) | Elastic modulus standard deviation DI |
|---|---|---|---|---|---|---|---|---|---|---|
| Antilocapra americana | pronghorn | uncategorized | combat | premaxilla | 18 | 18.1 | 1.11 | |||
| nasal | 25 | 13.13 | 0.98 | |||||||
| occipital | 29 | 21.93 | 0.83 | 18 | 21.52 | 2.73 | ||||
| ant. mandible | 22 | 16.87 | 0.51 | |||||||
| post. mandible | 22 | 21.57 | 0.84 | 20 | 15.73 | 1.57 | ||||
| Bos taurus | cattle | uncategorized | combat | premaxilla | 28 | 10.48 | 1.1 | |||
| nasal | 28 | 10.6 | 1 | |||||||
| occipital | 24 | 11.74 | 1.47 | |||||||
| ant. mandible | 41 | 11.49 | 1.29 | |||||||
| post. mandible | 46 | 11.3 | 0.83 | |||||||
| Capra hircus | goat | CU4148 | combat | premaxilla | 24 | 17.32 | 0.78 | |||
| nasal | 23 | 11.8 | 1.22 | |||||||
| occipital | 17 | 16.07 | 0.53 | 20 | 11.08 | 0.58 | ||||
| ant. mandible | 31 | 17.64 | 0.72 | |||||||
| post. mandible | 24 | 17.35 | 1.09 | 18 | 17.37 | 0.99 | ||||
| Giraffa camelopardalis | giraffe | uncategorized | combat | premaxilla | 23 | 11.62 | 1.42 | |||
| nasal | 21 | 13.82 | 0.93 | |||||||
| occipital | 19 | 16.43 | 1.81 | 20 | 16.8 | 4.83 | ||||
| ant. mandible | 24 | 13.71 | 0.79 | |||||||
| post. mandible | 32 | 15.29 | 0.94 | 20 | 10.22 | 1.38 | ||||
| Hippopotamus amphibius | hippo | 003DBC | non-combat | premaxilla | 14 | 5.52 | 0.68 | |||
| nasal | 20 | 12.5 | 0.86 | |||||||
| occipital | 39 | 17.18 | 1.78 | 23 | 7.79 | 0.79 | ||||
| ant. mandible | 23 | 14.22 | 1.1 | |||||||
| post. mandible | 20 | 19.18 | 1.74 | 20 | 13.38 | 0.97 | ||||
| Lama glama | llama | CU3726 | non-combat | premaxilla | 15 | 16.20 | 1.38 | |||
| nasal | 25 | 18.03 | 0.86 | |||||||
| occipital | 24 | 18.00 | 1.81 | 19 | 10.61 | 1.18 | ||||
| ant. mandible | 24 | 21.34 | 0.86 | |||||||
| post. mandible | 44 | 21.54 | 1.52 | 16 | 18.10 | 1.57 | ||||
| Nanger granti | Grants gazelle | CU2057 | non-combat | premaxilla | 22 | 14.61 | 1.37 | |||
| nasal | 20 | 12.05 | 0.76 | |||||||
| occipital | 20 | 19.27 | 0.68 | 20 | 15.95 | 1.24 | ||||
| ant. mandible | 19 | 14.89 | 0.75 | |||||||
| post. mandible | 25 | 20.85 | 1.17 | 20 | 21.96 | 2.08 | ||||
| Odocoileus virginianus | White-tailed deer | 002DBC | combat | premaxilla | 25 | 11.40 | 0.83 | |||
| nasal | 31 | 13.15 | 2.73 | |||||||
| occipital | 18 | 18.58 | 0.89 | 20 | 18.21 | 1.22 | ||||
| ant. mandible | 24 | 11.63 | 0.55 | |||||||
| post. mandible | 33 | 15.05 | 1.37 | 19 | 17.35 | 2.79 | ||||
| Pecari tajacu | peccary | CU4264 | non-combat | premaxilla | 18 | 15.43 | 1.59 | |||
| nasal | 29 | 10.85 | 2.35 | |||||||
| occipital | 18 | 18.61 | 1.22 | 20 | 13.29 | 0.78 | ||||
| ant. mandible | 18 | 14.71 | 2.69 | |||||||
| post. mandible | 34 | 20.10 | 2.10 | 20 | 19.64 | 3.11 | ||||
| Sus scrofa | wild boar | 001DBC | non-combat | premaxilla | 18 | 15.04 | 0.85 | |||
| nasal | 16 | 18.13 | 0.96 | |||||||
| occipital | 18 | 18.12 | 0.95 | |||||||
| ant. mandible | 15 | 13.21 | 0.99 | |||||||
| post. mandible | 18 | 21.34 | 1.71 |
| Species | Common name | ID# | Combat type | Bone location | Air Ind. # | Average elastic modulus air (GPa) | Elastic modulus standard deviation air | DI Ind. # | Average elastic modulus DI (GPa) | Elastic modulus standard deviation DI |
|---|---|---|---|---|---|---|---|---|---|---|
| Antilocapra americana | pronghorn | uncategorized | combat | premaxilla | 18 | 18.1 | 1.11 | |||
| nasal | 25 | 13.13 | 0.98 | |||||||
| occipital | 29 | 21.93 | 0.83 | 18 | 21.52 | 2.73 | ||||
| ant. mandible | 22 | 16.87 | 0.51 | |||||||
| post. mandible | 22 | 21.57 | 0.84 | 20 | 15.73 | 1.57 | ||||
| Bos taurus | cattle | uncategorized | combat | premaxilla | 28 | 10.48 | 1.1 | |||
| nasal | 28 | 10.6 | 1 | |||||||
| occipital | 24 | 11.74 | 1.47 | |||||||
| ant. mandible | 41 | 11.49 | 1.29 | |||||||
| post. mandible | 46 | 11.3 | 0.83 | |||||||
| Capra hircus | goat | CU4148 | combat | premaxilla | 24 | 17.32 | 0.78 | |||
| nasal | 23 | 11.8 | 1.22 | |||||||
| occipital | 17 | 16.07 | 0.53 | 20 | 11.08 | 0.58 | ||||
| ant. mandible | 31 | 17.64 | 0.72 | |||||||
| post. mandible | 24 | 17.35 | 1.09 | 18 | 17.37 | 0.99 | ||||
| Giraffa camelopardalis | giraffe | uncategorized | combat | premaxilla | 23 | 11.62 | 1.42 | |||
| nasal | 21 | 13.82 | 0.93 | |||||||
| occipital | 19 | 16.43 | 1.81 | 20 | 16.8 | 4.83 | ||||
| ant. mandible | 24 | 13.71 | 0.79 | |||||||
| post. mandible | 32 | 15.29 | 0.94 | 20 | 10.22 | 1.38 | ||||
| Hippopotamus amphibius | hippo | 003DBC | non-combat | premaxilla | 14 | 5.52 | 0.68 | |||
| nasal | 20 | 12.5 | 0.86 | |||||||
| occipital | 39 | 17.18 | 1.78 | 23 | 7.79 | 0.79 | ||||
| ant. mandible | 23 | 14.22 | 1.1 | |||||||
| post. mandible | 20 | 19.18 | 1.74 | 20 | 13.38 | 0.97 | ||||
| Lama glama | llama | CU3726 | non-combat | premaxilla | 15 | 16.20 | 1.38 | |||
| nasal | 25 | 18.03 | 0.86 | |||||||
| occipital | 24 | 18.00 | 1.81 | 19 | 10.61 | 1.18 | ||||
| ant. mandible | 24 | 21.34 | 0.86 | |||||||
| post. mandible | 44 | 21.54 | 1.52 | 16 | 18.10 | 1.57 | ||||
| Nanger granti | Grants gazelle | CU2057 | non-combat | premaxilla | 22 | 14.61 | 1.37 | |||
| nasal | 20 | 12.05 | 0.76 | |||||||
| occipital | 20 | 19.27 | 0.68 | 20 | 15.95 | 1.24 | ||||
| ant. mandible | 19 | 14.89 | 0.75 | |||||||
| post. mandible | 25 | 20.85 | 1.17 | 20 | 21.96 | 2.08 | ||||
| Odocoileus virginianus | White-tailed deer | 002DBC | combat | premaxilla | 25 | 11.40 | 0.83 | |||
| nasal | 31 | 13.15 | 2.73 | |||||||
| occipital | 18 | 18.58 | 0.89 | 20 | 18.21 | 1.22 | ||||
| ant. mandible | 24 | 11.63 | 0.55 | |||||||
| post. mandible | 33 | 15.05 | 1.37 | 19 | 17.35 | 2.79 | ||||
| Pecari tajacu | peccary | CU4264 | non-combat | premaxilla | 18 | 15.43 | 1.59 | |||
| nasal | 29 | 10.85 | 2.35 | |||||||
| occipital | 18 | 18.61 | 1.22 | 20 | 13.29 | 0.78 | ||||
| ant. mandible | 18 | 14.71 | 2.69 | |||||||
| post. mandible | 34 | 20.10 | 2.10 | 20 | 19.64 | 3.11 | ||||
| Sus scrofa | wild boar | 001DBC | non-combat | premaxilla | 18 | 15.04 | 0.85 | |||
| nasal | 16 | 18.13 | 0.96 | |||||||
| occipital | 18 | 18.12 | 0.95 | |||||||
| ant. mandible | 15 | 13.21 | 0.99 | |||||||
| post. mandible | 18 | 21.34 | 1.71 |
Note: Average elastic modulus of the measurements taken in DI water for the posterior mandible and occipital bone locations.
Species, combat behavior, average elastic modulus, and standard deviation, along with indent count, for each bone location across species
| Species | Common name | ID# | Combat type | Bone location | Air Ind. # | Average elastic modulus air (GPa) | Elastic modulus standard deviation air | DI Ind. # | Average elastic modulus DI (GPa) | Elastic modulus standard deviation DI |
|---|---|---|---|---|---|---|---|---|---|---|
| Antilocapra americana | pronghorn | uncategorized | combat | premaxilla | 18 | 18.1 | 1.11 | |||
| nasal | 25 | 13.13 | 0.98 | |||||||
| occipital | 29 | 21.93 | 0.83 | 18 | 21.52 | 2.73 | ||||
| ant. mandible | 22 | 16.87 | 0.51 | |||||||
| post. mandible | 22 | 21.57 | 0.84 | 20 | 15.73 | 1.57 | ||||
| Bos taurus | cattle | uncategorized | combat | premaxilla | 28 | 10.48 | 1.1 | |||
| nasal | 28 | 10.6 | 1 | |||||||
| occipital | 24 | 11.74 | 1.47 | |||||||
| ant. mandible | 41 | 11.49 | 1.29 | |||||||
| post. mandible | 46 | 11.3 | 0.83 | |||||||
| Capra hircus | goat | CU4148 | combat | premaxilla | 24 | 17.32 | 0.78 | |||
| nasal | 23 | 11.8 | 1.22 | |||||||
| occipital | 17 | 16.07 | 0.53 | 20 | 11.08 | 0.58 | ||||
| ant. mandible | 31 | 17.64 | 0.72 | |||||||
| post. mandible | 24 | 17.35 | 1.09 | 18 | 17.37 | 0.99 | ||||
| Giraffa camelopardalis | giraffe | uncategorized | combat | premaxilla | 23 | 11.62 | 1.42 | |||
| nasal | 21 | 13.82 | 0.93 | |||||||
| occipital | 19 | 16.43 | 1.81 | 20 | 16.8 | 4.83 | ||||
| ant. mandible | 24 | 13.71 | 0.79 | |||||||
| post. mandible | 32 | 15.29 | 0.94 | 20 | 10.22 | 1.38 | ||||
| Hippopotamus amphibius | hippo | 003DBC | non-combat | premaxilla | 14 | 5.52 | 0.68 | |||
| nasal | 20 | 12.5 | 0.86 | |||||||
| occipital | 39 | 17.18 | 1.78 | 23 | 7.79 | 0.79 | ||||
| ant. mandible | 23 | 14.22 | 1.1 | |||||||
| post. mandible | 20 | 19.18 | 1.74 | 20 | 13.38 | 0.97 | ||||
| Lama glama | llama | CU3726 | non-combat | premaxilla | 15 | 16.20 | 1.38 | |||
| nasal | 25 | 18.03 | 0.86 | |||||||
| occipital | 24 | 18.00 | 1.81 | 19 | 10.61 | 1.18 | ||||
| ant. mandible | 24 | 21.34 | 0.86 | |||||||
| post. mandible | 44 | 21.54 | 1.52 | 16 | 18.10 | 1.57 | ||||
| Nanger granti | Grants gazelle | CU2057 | non-combat | premaxilla | 22 | 14.61 | 1.37 | |||
| nasal | 20 | 12.05 | 0.76 | |||||||
| occipital | 20 | 19.27 | 0.68 | 20 | 15.95 | 1.24 | ||||
| ant. mandible | 19 | 14.89 | 0.75 | |||||||
| post. mandible | 25 | 20.85 | 1.17 | 20 | 21.96 | 2.08 | ||||
| Odocoileus virginianus | White-tailed deer | 002DBC | combat | premaxilla | 25 | 11.40 | 0.83 | |||
| nasal | 31 | 13.15 | 2.73 | |||||||
| occipital | 18 | 18.58 | 0.89 | 20 | 18.21 | 1.22 | ||||
| ant. mandible | 24 | 11.63 | 0.55 | |||||||
| post. mandible | 33 | 15.05 | 1.37 | 19 | 17.35 | 2.79 | ||||
| Pecari tajacu | peccary | CU4264 | non-combat | premaxilla | 18 | 15.43 | 1.59 | |||
| nasal | 29 | 10.85 | 2.35 | |||||||
| occipital | 18 | 18.61 | 1.22 | 20 | 13.29 | 0.78 | ||||
| ant. mandible | 18 | 14.71 | 2.69 | |||||||
| post. mandible | 34 | 20.10 | 2.10 | 20 | 19.64 | 3.11 | ||||
| Sus scrofa | wild boar | 001DBC | non-combat | premaxilla | 18 | 15.04 | 0.85 | |||
| nasal | 16 | 18.13 | 0.96 | |||||||
| occipital | 18 | 18.12 | 0.95 | |||||||
| ant. mandible | 15 | 13.21 | 0.99 | |||||||
| post. mandible | 18 | 21.34 | 1.71 |
| Species | Common name | ID# | Combat type | Bone location | Air Ind. # | Average elastic modulus air (GPa) | Elastic modulus standard deviation air | DI Ind. # | Average elastic modulus DI (GPa) | Elastic modulus standard deviation DI |
|---|---|---|---|---|---|---|---|---|---|---|
| Antilocapra americana | pronghorn | uncategorized | combat | premaxilla | 18 | 18.1 | 1.11 | |||
| nasal | 25 | 13.13 | 0.98 | |||||||
| occipital | 29 | 21.93 | 0.83 | 18 | 21.52 | 2.73 | ||||
| ant. mandible | 22 | 16.87 | 0.51 | |||||||
| post. mandible | 22 | 21.57 | 0.84 | 20 | 15.73 | 1.57 | ||||
| Bos taurus | cattle | uncategorized | combat | premaxilla | 28 | 10.48 | 1.1 | |||
| nasal | 28 | 10.6 | 1 | |||||||
| occipital | 24 | 11.74 | 1.47 | |||||||
| ant. mandible | 41 | 11.49 | 1.29 | |||||||
| post. mandible | 46 | 11.3 | 0.83 | |||||||
| Capra hircus | goat | CU4148 | combat | premaxilla | 24 | 17.32 | 0.78 | |||
| nasal | 23 | 11.8 | 1.22 | |||||||
| occipital | 17 | 16.07 | 0.53 | 20 | 11.08 | 0.58 | ||||
| ant. mandible | 31 | 17.64 | 0.72 | |||||||
| post. mandible | 24 | 17.35 | 1.09 | 18 | 17.37 | 0.99 | ||||
| Giraffa camelopardalis | giraffe | uncategorized | combat | premaxilla | 23 | 11.62 | 1.42 | |||
| nasal | 21 | 13.82 | 0.93 | |||||||
| occipital | 19 | 16.43 | 1.81 | 20 | 16.8 | 4.83 | ||||
| ant. mandible | 24 | 13.71 | 0.79 | |||||||
| post. mandible | 32 | 15.29 | 0.94 | 20 | 10.22 | 1.38 | ||||
| Hippopotamus amphibius | hippo | 003DBC | non-combat | premaxilla | 14 | 5.52 | 0.68 | |||
| nasal | 20 | 12.5 | 0.86 | |||||||
| occipital | 39 | 17.18 | 1.78 | 23 | 7.79 | 0.79 | ||||
| ant. mandible | 23 | 14.22 | 1.1 | |||||||
| post. mandible | 20 | 19.18 | 1.74 | 20 | 13.38 | 0.97 | ||||
| Lama glama | llama | CU3726 | non-combat | premaxilla | 15 | 16.20 | 1.38 | |||
| nasal | 25 | 18.03 | 0.86 | |||||||
| occipital | 24 | 18.00 | 1.81 | 19 | 10.61 | 1.18 | ||||
| ant. mandible | 24 | 21.34 | 0.86 | |||||||
| post. mandible | 44 | 21.54 | 1.52 | 16 | 18.10 | 1.57 | ||||
| Nanger granti | Grants gazelle | CU2057 | non-combat | premaxilla | 22 | 14.61 | 1.37 | |||
| nasal | 20 | 12.05 | 0.76 | |||||||
| occipital | 20 | 19.27 | 0.68 | 20 | 15.95 | 1.24 | ||||
| ant. mandible | 19 | 14.89 | 0.75 | |||||||
| post. mandible | 25 | 20.85 | 1.17 | 20 | 21.96 | 2.08 | ||||
| Odocoileus virginianus | White-tailed deer | 002DBC | combat | premaxilla | 25 | 11.40 | 0.83 | |||
| nasal | 31 | 13.15 | 2.73 | |||||||
| occipital | 18 | 18.58 | 0.89 | 20 | 18.21 | 1.22 | ||||
| ant. mandible | 24 | 11.63 | 0.55 | |||||||
| post. mandible | 33 | 15.05 | 1.37 | 19 | 17.35 | 2.79 | ||||
| Pecari tajacu | peccary | CU4264 | non-combat | premaxilla | 18 | 15.43 | 1.59 | |||
| nasal | 29 | 10.85 | 2.35 | |||||||
| occipital | 18 | 18.61 | 1.22 | 20 | 13.29 | 0.78 | ||||
| ant. mandible | 18 | 14.71 | 2.69 | |||||||
| post. mandible | 34 | 20.10 | 2.10 | 20 | 19.64 | 3.11 | ||||
| Sus scrofa | wild boar | 001DBC | non-combat | premaxilla | 18 | 15.04 | 0.85 | |||
| nasal | 16 | 18.13 | 0.96 | |||||||
| occipital | 18 | 18.12 | 0.95 | |||||||
| ant. mandible | 15 | 13.21 | 0.99 | |||||||
| post. mandible | 18 | 21.34 | 1.71 |
Note: Average elastic modulus of the measurements taken in DI water for the posterior mandible and occipital bone locations.
Phylogenetic ANOVAs revealed that the posterior mandible elastic modulus differed between artiodactyls that engage in combat and those that do not (P = 0.05), with those exhibiting combat behaviors having a lower modulus. The other four bone locations (premaxilla, nasal, occipital, and anterior mandible) were not statistically different between species that use combat and those that do not (P > 0.10). However, the phenograms that plot the phylogeny onto the traitspace reveal patterns in the variation of modulus values. For example, the occipital bone shows higher variation in elastic modulus for species that engage in combat, whereas this group exhibits low elastic modulus variation in the nasal bone (Fig. 12).
Phenograms of the five bone locations with the phylogeny mapped onto the elastic modulus trait (y-axis). Tips labeled with species names and branches indicate the relatedness of the species. Species that engage in combat (orange) and those that do not (blue) have no significant differences in the majority of bones, except in the posterior mandible where species that engage in combat have lower moduli.
The gradient in bone material properties found in artiodactyl skulls can be interpreted in the context gradients of in vivo strain measurements recorded from a range of tetrapod species, where anterior skull bones experience higher strains and the neurocranium experiences lower strains (Hylander and Johnson 1997; Ross and Metzger 2004). A similar pattern is found within structures of the skull such as the zygomatic arch, with the anterior portion of the arch experiencing higher strains than the posterior portion (Hylander and Johnson 1997, 2002). The posterior bone locations in this study (occipital bone and posterior mandible) exhibited higher stiffness, which may be beneficial for transmitting forces to anterior skull regions that are directly engaged with functions, such as foraging and mastication. Taken with studies on antlers and long bone functional morphology (Espinoza 2000; Blob and LaBarbera 2001; Blob and Snelgrove 2006; Wilson et al. 2009), this suggests that selection for varying bone stiffness values may be driven by behavioral and ecological factors, underscoring the adaptive significance of bone properties in response to specific functional demands (Layton 1987; Biewener 1990; Blob et al. 2014; Willie et al. 2020).
The elastic modulus of bone cores in all species ranged from 6–22 GPa. There was little difference in modulus values for skull bones between species that engage in head-to-head combat and those that do not, with only the posterior mandible in combat artiodactyls showing lower values. However, combat species generally exhibit higher variation in elastic modulus for posterior bone locations (occipital and posterior mandible). This finding is noteworthy given the variation in combat types among species—such as head-on ramming, stabbing, fencing, and wrestling—that could impose different loads on the skull bones, potentially driving structural adaptations to these different strategies (Kitchener 1988; Blob and Snelgrove 2006; Farke 2008; Picavet and Balligand 2016). The elastic modulus of bones from the skulls of species that use combat is highly variable, despite these species belonging to younger clade (Fig. 12). Additionally, three of the four species that exhibit wrestling combat show high occipital stiffness, whereas the ramming (C. hircus) and necking (G. camelopardalis) species show a lower modulus, possibly indicating that type of combat is important for occipital stiffness. This further suggests that the evolutionary diversity of bone material properties may be influenced by ecological factors and is not strictly constrained by phylogeny. Interestingly, the hippopotamus, which has a semi-aquatic lifestyle and spends most of the day in a buoyant environment, exhibits similar elastic moduli across all bones except for the premaxilla, which shows a comparatively lower modulus. Future studies should compare bone material property patterns across the skull of the fully aquatic relatives of the artiodactyls (Cetaceans). Additionally, studies at broader phylogenetic scales (e.g., elastic modulus variation within and between artiodactyls and carnivores) could determine whether some categories of species exhibit variation, while others do not.
Conclusions
From a methodological perspective, our use of nanoindentation showed that consistent results can be achieved with varying number of indents per sample and that there is a predictable relationship for elastic modulus measurements between hydrated and dry specimens. This is crucial, as concerns about the impact of specimen hydration on test results have limited the use of nanoindentation for evolutionary and comparative biology. Although indentation while specimens are immersed in liquid likely provides the most accurate and natural testing environment for biological tissues, such approaches are technically challenging and may not be feasible with all instruments. They also may introduce additional complexities, such as required preloads and difficulties in identifying appropriate testing areas through the fluid. Nevertheless, the correlation between liquid and air nanoindentation measurements confirms that nanoindentation in air remains a valuable tool for the study of hard biological materials.
From the broader biological perspective, nanoindentation can generate material property data from novel ranges of biological specimens that, when considered in a comparative framework, can be applied to test innovative hypotheses about the evolution of hard biological tissues. Our measurements of Young's modulus (material stiffness) across skull and mandible regions of artiodactyl mammals sought to test associations between bone properties and the use of the skull for head-to-head combat. Nanoindentation enabled data collection from small bone samples that could be extracted with minimum impact from museum specimens. These data revealed unanticipated patterns in bone properties, including, (1) a general anterior–posterior pattern throughout the skull, with the posterior areas exhibiting higher general stiffness, and (2) species that engaged in combat generally showed higher variation in Young's modulus for the occipital and posterior mandible compared to non-combat species. Such insights into the heterogeneity of tetrapod skull material properties can offer clues about how these traits evolved over time. Nanoindentation also provides precise materials for theoretical models like FEA. These values will enhance future bone strain and bite force models.
Although widely used in other fields, nanoindentation should also be recognized to have broad utility in comparative and evolutionary biology, where rare specimens and limited sampling are common. Advancements in nanoindentation technology are improving testing speeds, reducing data collection time, and lowering costs. It is our hope that the practical recommendations presented in this paper help biologists overcome some of the barriers to collecting nanoindentation data and improve the standardization of testing approaches, enabling more direct comparisons of results across studies. Such opportunities should encourage an exciting new range of comparative and evolutionary analyses of organismal function.
Acknowledgments
The authors would like to thank Melissa Fuentes and the staff at Clemson's Bob and Betsey Campbell Natural History Museum for providing specimens and assistance with bone core extraction. They also thank N. Adam Smith and the staff of the Clemson Campbell Geology Museum for help with bone grinding and polishing methods. Work was performed, in part, at the Center for Integrated Nanotechnologies, an office of science user facility operated for the U.S. Department of Energy (DOE) Office of Science.
Funding
This research was based on work supported by the CINT User proposal 2022BC0131, the American Society of Mammologists Grant-in-Aid, the Grant ID is G20230315-5454, the Clemson University Biological Sciences Professional Development Course: Grants-in-Aid, and the Clemson Graduate Student Government travel grant.
Author Contributions
D.S.A conceived the study and developed the design with R.W.B and S.A.P. B.L.B advised on nanoindentation methodology and provided instrumentation. D.S.A., K.W.G, and B.K. conducted indentation tests and gathered data. D.E.H. advised on general materials science methodology. D.S.A analyzed the data with input from S.A.P and R.W.R and wrote the manuscript with contributions from all authors.
Conflict of Interest
The authors declare no conflict of interest.
Data Availability
The data underlying this article are available in the article tables.
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