Comparing and combining sliding semilandmarks and weighted spherical harmonics for shape analysis.

Quantifying morphological variation is critical for conducting anatomical research. Three-dimensional geometric morphometric (3D GM) landmark analyses quantify shape using homologous Cartesian coordinates (landmarks). Setting up a high-density landmark set and placing it on all specimens, however, can be a time-consuming task. Weighted spherical harmonics (SPHARM) provides an alternative method for analyzing the shape of such objects. Here we compare sliding semilandmark and SPHARM analyses of the calcaneus of Gorilla gorilla gorilla (n = 20), Pan troglodytes troglodytes (n = 20), and Homo sapiens (n = 20) to determine whether the SPHARM and sliding semilandmark analyses capture comparable levels of shape variation. We also compare both the sliding semilandmark and SPHARM analyses to a novel combination of the two methods, here termed SPHARM-sliding. In SPHARM-sliding, the vertices of the surface models produced from the SPHARM analysis (that are the same in number and relative location) are used as the starting landmark positions for a sliding semilandmark analysis. Calcaneal shape variation quantified by all three analyses was summarized using separate principal components analyses. Results were compared using the root mean square (RMS) and maximum distance between surface models of species averages scaled (up) to centroid size created from each analysis. The average RMS was 0.23 mm between sliding semilandmark and SPHARM average surface models, 0.19 mm between SPHARM and SPHARM sliding average surface models, and 0.22 mm between sliding semilandmark and SPHARM sliding average surface models. Although results indicate that all three analyses are comparable methods for 3D shape analysis, there are advantages and disadvantages to each. While the SPHARM analysis is less time-intensive, it is unable to capture the same level of detail around the sharp edges of articular facets on average surface models as the sliding semilandmark analysis. The SPHARM analysis also does not allow for individual articular facets to be analyzed in isolation. SPHARM-sliding, however, captures the same level of detail as the sliding semilandmark analysis, and (as in the sliding semilandmark analysis) allows for the evaluation of individual portions of bone. SPHARM is a comparable method to a 3D GM analysis for small, irregularly shaped bones, such as the calcaneus, and SPHARM-sliding allows for an expedited set up process for a sliding semilandmark analysis.

A new early hominin calcaneus from Kromdraai (South Africa).

The Kromdraai site in South Africa has yielded numerous early hominin fossils since 1938. As a part of recent excavations within Unit P, a largely complete early hominin calcaneus (KW 6302) was discovered. Due to its role in locomotion, the calcaneus has the potential to reveal important form/function relationships. Here, we describe KW 6302 and analyze its preserved morphology relative to human and nonhuman ape calcanei, as well as calcanei attributed to Australopithecus afarensis, Australopithecus africanus, Australopithecus sediba, Homo naledi, and the Omo calcaneus (either Paranthropus or early Homo). KW 6302 calcaneal morphology is assessed using numerous quantitative metrics including linear measures, calcaneal robusticity index, relative lateral plantar process position, Achilles tendon length reconstruction, and a three-dimensional geometric morphometric sliding semilandmark analysis. KW 6302 exhibits an overall calcaneal morphology that is intermediate between humans and nonhuman apes, although closer to modern humans. KW 6302 possesses many traits that indicate it was likely well-adapted for terrestrial bipedal locomotion, including a relatively flat posterior talar facet and a large lateral plantar process that is similarly positioned to modern humans. It also retains traits that indicate that climbing may have remained a part of its locomotor repertoire, such as a relatively gracile tuber and a large peroneal trochlea. Specimens from Kromdraai have been attributed to either Paranthropus robustus or early Homo; however, there are no definitively attributed calcanei for either genus, making it difficult to taxonomically assign this specimen. KW 6302 and the Omo calcaneus, however, fall outside the range of expected variation for an extant genus, indicating that if the Omo calcaneus was Paranthropus, then KW 6302 would likely be attributed to early Homo (or vice versa).

Calcaneal shape variation in humans, nonhuman primates, and early hominins.

The foot has played a prominent role in evaluating early hominin locomotion. The calcaneus, in particular, plays an important role in weight-bearing. Although the calcanei of early hominins have been previously scrutinized, a three-dimensional analysis of the entire calcaneal shape has not been conducted. Here, we investigate the relationship between external calcaneal shape and locomotion in modern Homo sapiens (n = 130), Gorilla (n = 86), Pan (n = 112), Pongo (n = 31), Papio (n = 28), and hylobatids (Hylobates, Symphalangus; n = 32). We use these results to place the calcanei attributed to Australopithecus sediba, A. africanus, A. afarensis, H. naledi, and Homo habilis/Paranthropus boisei into a locomotor context. Calcanei were scanned using either surface scanning or micro-CT and their external shape analyzed using a three-dimensional geometric morphometric sliding semilandmark analysis. Blomberg's K statistic was used to estimate phylogenetic signal in the shape data. Shape variation was summarized using a principal components analysis. Procrustes distances between all taxa as well as distances between each fossil and the average of each taxon were calculated. Blomberg's K statistic was small (K = 0.1651), indicating weak phylogenetic effects, suggesting variation is driven by factors other than phylogeny (e.g., locomotion or body size). Modern humans have a large calcaneus relative to body size and display a uniquely convex cuboid facet, facilitating a rigid midfoot for bipedalism. More arboreal great apes display relatively deeper cuboid facet pivot regions for increased midfoot mobility. Australopithecus afarensis demonstrates the most human-like calcaneus, consistent with obligate bipedalism. Homo naledi is primarily modern human-like, but with some intermediate traits, suggesting a different form of bipedalism than modern humans. Australopithecus africanus, A. sediba, and H. habilis/P. boisei calcanei all possess unique combinations of human and nonhuman ape-like morphologies, suggesting a combination of bipedal and arboreal behaviors.

Gorilla calcaneal morphological variation and ecological divergence.

OBJECTIVES: The primate foot has been extensively investigated because of its role in weight-bearing; however, the calcaneus has been relatively understudied. Here we examine entire gorilla calcaneal external shape to understand its relationship with locomotor behavior. MATERIALS AND METHODS: Calcanei of Gorilla gorilla gorilla (n = 43), Gorilla beringei graueri (n = 20), and Gorilla beringei beringei (n = 15) were surface or micro-CT scanned. External shape was analyzed through a three-dimensional geometric morphometric sliding semilandmark analysis. Semilandmarks were slid relative to an updated Procrustes average in order to minimize the bending energy of the thin plate spline interpolation function. Shape variation was summarized using principal components analysis of shape coordinates. Procrustes distances between taxa averages were calculated and resampling statistics run to test pairwise differences. Linear measures were collected and regressed against estimated body mass. RESULTS: All three taxa exhibit statistically different morphologies (p < .001 for pairwise comparisons). G. g. gorilla demonstrates an anteroposteriorly elongated calcaneus with a deeper cuboid pivot region and mediolaterally flatter posterior talar facet. G. b. beringei possesses the flattest cuboid and most medially-angled posterior talar facets. G. b. graueri demonstrates intermediate articular facet morphology, a medially-angled tuberosity, and an elongated peroneal trochlea. DISCUSSION: Articular facet differences separate gorillas along a locomotor gradient. G. g. gorilla is adapted for arboreality with greater joint mobility, while G. b. beringei is adapted for more stereotypical loads associated with terrestriality. G. b. graueri's unique posterolateral morphology may be due to a secondary transition to greater arboreality from a more terrestrial ancestor.

Long bone structural proportions and locomotor behavior in Cercopithecidae.

Limb bone articular and diaphyseal proportions have been shown to relate to locomotor behavior in broad comparisons across catarrhines, but comparisons among phylogenetically and functionally more closely related species may be particularly useful in investigating form-function relationships that can be applied to fossil taxa. Here we compare inter- and intra-limb proportions of diaphyseal strength and articular surface area and breadth of the femur and humerus with frequencies of leaping and vertical climbing behavior in 13 cercopithecid species. Leaping frequency is highly positively correlated with femoral/humeral diaphyseal strength, moderately positively correlated with femoral/humeral articular breadth, and less highly correlated with femoral/humeral articular surface area. These results are consistent with predicted higher bending loads as well as joint reaction forces on the femora of leapers. Surface areas may show a weaker association because they also directly impact joint excursion and are thus more influenced by other aspects of locomotion, including climbing. Climbing frequency is positively correlated with humeral head articular surface area/diaphyseal strength, but weakly negatively correlated with femoral head articular surface area/diaphyseal strength. These combined trends lead to a strong negative association between climbing and femoral/humeral head surface area. Femoral/humeral diaphyseal strength and distal articular breadth are not correlated with climbing frequency. The climbing results are consistent with greater shoulder mobility in more frequent vertical climbers. The lack of such a relationship in the femur among these taxa contrasts with earlier findings for catarrhines more generally, including hominoids, and may be a result of different climbing kinematics in cercopithecoids involving less hip abduction than in hominoids. Different use of the forelimb during climbing in cercopithecoids and hominoids may also explain the lack of association between femoral/humeral diaphyseal strength and climbing in the present study, in contrast to comparisons across catarrhines more generally.

Comparing lateral plantar process trabecular structure to other regions of the human calcaneus.

Investigating skeletal adaptations to bipedalism informs our understanding of form-function relationships. The calcaneus is an important skeletal element to study because it is a weight-bearing bone with a critical locomotor role. Although other calcaneal regions have been well studied, we lack a clear understanding of the functional role of the lateral plantar process (LPP). The LPP is a bony protuberance on the inferolateral portion of the calcaneus thought to aid the tuberosity in transmission of ground reaction forces during heel-strike. Here, we analyze LPP internal trabecular structure relative to other calcaneal regions to investigate its potential functional affinities. Human calcanei (n = 20) were micro-CT scanned, and weighted spherical harmonic analysis outputs were used to position 251 volumes of interest (VOI) within each bone. Trabecular thickness (Tb.Th), spacing (Tb.Sp), degree of anisotropy (DA), and bone volume fraction (BV/TV) were calculated for each VOI. Similarities in BV/TV and DA (p = 0.2741) between the LPP and inferior tuberosity support suggestions that the LPP is a weight-bearing structure that may transmit forces in a similar direction. The LPP significantly differs from the inferior tuberosity in Tb.Th and Tb.Sp (p < 0.05). Relatively thinner, more closely spaced trabeculae in the LPP may serve to increase internal surface area to compensate for its relatively small size compared to the tuberosity. Significant differences in all parameters between LPP and joint articular surfaces indicate that trabecular morphology is differently adapted for the transmission of forces associated with body mass through joints.

Trabecular bone variation in the gorilla calcaneus.

OBJECTIVES: Calcaneal external shape differs among nonhuman primates relative to locomotion. Such relationships between whole-bone calcaneal trabecular structure and locomotion, however, have yet to be studied. Here we analyze calcaneal trabecular architecture in Gorilla gorilla gorilla, Gorilla beringei beringei, and G. b. graueri to investigate general trends and fine-grained differences among gorilla taxa relative to locomotion. MATERIALS AND METHODS: Calcanei were micro-CT scanned. A three-dimensional geometric morphometric sliding semilandmark analysis was carried out and the final landmark configurations used to position 156 volumes of interest. Trabecular thickness (Tb.Th), trabecular spacing (Tb.Sp), and bone volume fraction (BV/TV) were calculated using the BoneJ plugin for ImageJ and MATLAB. Non-parametric MANOVAs were run to test for significant differences among taxa in parameter raw values and z-scores. Parameter distributions were visualized using color maps and summarized using principal components analysis. RESULTS: There are no significant differences in raw BV/TV or Tb.Th among gorillas, however G. b. beringei significantly differs in z-scores for both parameters (p = <0.0271). All three taxa exhibit relatively lower BV/TV and Tb.Th in the posterior half of the calcaneus. This gradation is exacerbated in G. b. beringei. G. b. graueri significantly differs from other taxa in Tb.Sp z-scores (p < 0.001) indicating a different spacing distribution. DISCUSSION: Relatively higher Tb.Th and BV/TV in the anterior calcaneus among gorillas likely reflects higher forces associated with body mass (transmitted through the subtalar joint) relative to forces transferred through the posterior calcaneus. The different Tb.Sp pattern in G. b. graueri may reflect proposed differences in foot positioning during locomotion.

A statistical analysis of human talar shape and bone density distribution.

The shape of the talus, its internal structure, and its mechanical properties are important in determining talar behavior during loading, which may be significant for the design of surgical tools and implants. Although recent studies using statistical shape modeling have described quantitative talar external shape variation, no similar quantitative study exists to describe the density distribution of internal talar structure. The goal of this study is to quantify statistical variation in talar shape and density to benefit the design of talar implants. To this end, weight-bearing computed tomography (CT) scans of the ankle were collected in neutral, bilateral standing posture, and three-dimensional models were generated for each talus. Local density derived from the Hounsfield unit of each CT voxel was extracted. A weighted spherical harmonic analysis was performed to quantify the talar external shape. One hundred and seventy-nine volumes of interest were placed in the same relative position within each talus to quantify the talar density. Additionally, a finite element analysis (FEA) was conducted on a talus with both heterogeneous and homogeneous material properties to observe the effect of these properties on the stress and strain response. Significant differences were found in the talar density in sex and age, as well as in the stress and strain response between homogeneous and heterogeneous FEA. These differences show the importance of considering heterogeneity when examining the load response of tarsal bones.

Morphological variation of the Pan talus relative to that of Gorilla.

OBJECTIVES: Differences in talar articular morphology relative to locomotion have recently been found within Pan and Gorilla. Whole-bone talar morphology within, and shared variation among, Pan and Gorilla (sub)species, however, has yet to be investigated. Here we separately analyze talar external shape within Pan (P. t. troglodytes, P. t. schweinfurthii, P. t. verus, P. paniscus) and Gorilla (G. g. gorilla, G. b. beringei, G. b. graueri) relative to degree of arboreality and body size. Pan and Gorilla are additionally analyzed together to determine if consistent shape differences exist within the genera. MATERIALS AND METHODS: Talar external shape was quantified using a weighted spherical harmonic analysis. Shape variation both within and among Pan and Gorilla was described using principal component analyses. Root mean square distances were calculated between taxon averages, and resampling statistics conducted to test for pairwise differences. RESULTS: P. t. verus (most arboreal Pan) talar shape significantly differs from other Pan taxa (p < 0.05 for pairwise comparisons) driven by more asymmetrical trochlear rims and a medially-set talar head. P. t. troglodytes, P. t. schweinfurthii, and P. paniscus do not significantly differ (p > 0.05 for pairwise comparisons). All gorilla taxa exhibit significantly different talar morphologies (p < 0.007 for pairwise comparisons). The more terrestrial subspecies of G. beringei and P. troglodytes exhibit a superoinferiorly taller talar head/neck complex. DISCUSSION: P. t. verus exhibits talar morphologies that have been previously related to more frequent arboreality. The adaptations in the more terrestrial G. beringei and P. troglodytes subspecies may serve to facilitate load transmission.

Scaling and relative size of the human, nonhuman ape, and baboon calcaneus.

Among human and nonhuman apes, calcaneal morphology exhibits significant variation that has been related to locomotor behavior. Due to its role in weight-bearing, however, both body size and locomotion may impact calcaneal morphology. Determining how calcaneal morphologies vary as a function of body size is thus vital to understanding calcaneal functional adaptation. Here, we study calcaneus allometry and relative size in humans (n = 120) and nonhuman primates (n = 278), analyzing these relationships in light of known locomotor behaviors. Twelve linear measures and three articular facet surface areas were collected on calcaneus surface models. Body mass was estimated using femoral head superoinferior breadth. Relationships between calcaneal dimensions and estimated body mass were analyzed across the sample using phylogenetic least squares regression analyses (PGLS). Differences between humans and pooled nonhuman primates were tested using RMA ANCOVAs. Among (and within) genera residual differences from both PGLS regressions and isometry were analyzed using ANOVAs with post hoc multiple comparison tests. The relationships between all but two calcaneus dimensions and estimated body mass exhibit phylogenetic signal at the smallest taxonomic scale. This signal disappears when reanalyzed at the genus level. Calcaneal morphology varies relative to both body size and locomotor behavior. Humans have larger calcanei for estimated body mass relative to nonhuman primates as a potential adaptation for bipedalism. More terrestrial taxa exhibit longer calcaneal tubers for body mass, increasing the triceps surae lever arm. Among nonhuman great apes, more arboreal taxa have larger cuboid facet surface areas for body mass, increasing calcaneocuboid mobility.

A novel method for quantifying femoral neck anteversion: A case study in extinct and extant sloths.

Extinct sloths represent a wide range of morphological, locomotor, and body size variation. Researchers have examined femoral neck angle in two dimensions to hypothesize locomotor behaviors in this group; however, this measure does not account for femoral neck anteversion. Here, we present a new method for quantifying femoral neck anteversion angle, in addition to femoral neck angle, to capture the 3D position of the femoral head/neck. Femora of extant (n = 21; Bradypus and Choloepus) and extinct (n = 49; Acratocnus, Megalocnus, Neocnus, and Parocnus) sloths were surface scanned and their surface models used to calculate three angles of femoral neck anteversion and femoral neck angle. Femoral neck anteversion was calculated as the angle between the femoral neck axis and the geometric axis of the femoral condyles (GA), the 35% cross section axis, and a trochanter axis. Femoral neck angle was calculated as the angle between the femoral neck and shaft axes. Genera were compared using ANOVAs with post hoc multiple comparisons for each angle. Femoral neck angle and femoral neck anteversion relative to the cross section were also analyzed. Significant differences among genera exist for all angles, (p < .001) but not all angles separate all genera. Femoral neck and anteversion angles typically yield different results, demonstrating the utility of analyzing both angles. The GA and cross section angles are highly correlated in sloths, with the exception of comparisons among Megalocnus, Parocnus, and Neocnus, suggesting morphological variation in the distal femur. While this method was applied to sloths, it has broad applicability to mammalian groups.

Effective Mechanical Advantage Allometry of Felid Elbow and Knee Extensors.

Larger terrestrial mammals have generally been found to use more extended limb postures, a mechanism which maintains muscular requirements at larger sizes by improving the effective mechanical advantage (EMA) of limb musculature. Felids, however, have been documented to maintain joint angles across body sizes. If felid morphology scales isometrically, it would mean larger felids have relatively weaker muscles, compromising locomotor activities. Here, we examine the allometric relationships between the EMA of the elbow and knee extensors and body mass, finding that the EMA of the triceps brachii and quadriceps muscles scale with positive allometry. When species-specific joint angles were used rather than felid-average joint angles, EMA scales to body mass with more positive allometry. When the scaling of the muscle and ground reaction force (GRF) lever arms were investigated individually the allometric signal was lost; however, the muscle lever arms generally have allometric slope coefficients that are consistent with positive allometry, while the GRF lever arms demonstrate negative allometric slope coefficients. This suggests there are subtle alterations to limb morphology allowing different felid species to achieve an increased EMA via distinctive mechanisms. The quadriceps EMA was found to scale with sufficient positive allometry to compensate for increases in size without alteration in muscular anatomy; however, this is not the case for the triceps brachii EMA. Anat Rec, 2018. © 2018 Wiley Periodicals, Inc. Anat Rec, 302:775-784, 2019. © 2018 Wiley Periodicals, Inc.