Paul O’Higgins

Combining geometric morphometrics and functional simulation: an emerging toolkit for virtual functional analyses

The development of virtual methods for anatomical reconstruction and functional simulation of skeletal structures offers great promise in evolutionary and ontogenetic investigations of form–function relationships. Key developments reviewed here include geometric morphometric methods for the analysis and visualization of variations in form (size and shape), finite element methods for the prediction of mechanical performance of skeletal structures under load and multibody dynamics methods for the simulation and prediction of musculoskeletal function. These techniques are all used in studies of form and function in biology, but only recently have they been combined in novel ways to facilitate biomechanical modelling that takes account of variations in form, can statistically compare performance, and relate performance to form and its covariates. Here we provide several examples that illustrate how these approaches can be combined and we highlight areas that require further investigation and development before we can claim a mature theory and toolkit for a statistical biomechanical framework that unites these methods.

The effects of the periodontal ligament on mandibular stiffness: a study combining finite element analysis and geometric morphometrics

It is generally accepted that the periodontal ligament (PDL) plays a crucial role in transferring occlusal forces from the teeth to the alveolar bone. Studies using finite element analysis (FEA) have helped to better understand this role and show that the stresses and strains in the alveolar bone are influenced by whether and how PDL is included in FE models. However, when the overall distribution of stresses and strains in crania and mandibles are of interest, PDL is often not included in FE models, although little is known about how this affects the results. Here we study the effect of representing PDL as a layer of solid material with isotropic homogeneous properties in an FE model of a human mandible using a novel application of geometric morphometrics. The results show that the modelling of the PDL affects the deformation and thus strain magnitudes not only of the alveolar bone around the biting tooth, but that the whole mandible deforms differently under load. As a result, the strain in the mandibular corpus is significantly increased when PDL is included, while the strain in the bone beneath the biting tooth is reduced. These results indicate the importance of the PDL in FE studies. Thus we recommend that the PDL should be included in FE models of the masticatory apparatus, with tests to assess the sensitivity of the results to changes in the Youngs modulus of the PDL material.

Discriminant function sexing of the mandible of Indigenous South Africans

South Africa currently has a high homicide rate. This results in a large number of unidentified bodies being recovered each year, many of which are referred to the forensic examiner. This situation has resulted in considerable growth of forensic anthropological research devoted to devising standards for specific application in South African medico-legal investigations. The standards suitable for Black South Africans now encompass a wide variety of skeletal elements (e.g. cranium, humerus, pelvis, femur, patella, talus, calcaneus), each with differing degrees of accuracy. Apart from a preliminary investigation of the Zulu local population, however, we note that there appears to be no established metric mandible discriminant function standards for sex determination in this population. The purpose of the present study is to undertake a comprehensive analysis of sexual dimorphism in the mandible of Black South Africans, incorporating individuals from a selection of the larger local population groupings; the primary aim is to produce a series of metrical standards for the determination of sex. The sample analyzed comprises 225 non-pathological mandibles of Black South African individuals drawn from the R.A. Dart Collection. Nine linear measurements, obtained from mathematically transformed three-dimensional landmark data, are analyzed using basic univariate statistics and discriminant function analyses. All of the measurements examined are found to be sexually dimorphic; the dimensions of the ramus and corpus lengths are most dimorphic. The sex classification accuracy of the discriminant functions ranged from 70.7 to 77.3% for the univariate method, 81.8% for the stepwise method, and 63.6 to 84% for the direct method. We conclude that the mandible is a very useful element for sex determination in this population.

Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry

Finite element analysis is a powerful tool for predicting the mechanical behaviour of complex biological structures like bones, but to be confident in the results of an analysis, the model should be validated against experimental data. In such validation experiments, the strains in the loaded bones are usually measured with strain gauges glued to the bone surface, but the use of strain gauges on bone can be difficult and provides only very limited data regarding surface strain distributions. This study applies the full-field strain measurement technique of digital speckle pattern interferometry to measure strains in a loaded human mandible and compares the results with the predictions of voxel-based finite element models of the same specimen. It is found that this novel strain measurement technique yields consistent, reliable measurements. Further, strains predicted by the finite element analysis correspond well with the experimental data. These results not only confirm the usefulness of this technique for future validation studies in the field of bone mechanics, but also show that the modelling approach used in this study is able to predict the experimental results very accurately.

Masticatory loadings and cranial deformation in Macaca fascicularis: a finite element analysis sensitivity study.

Biomechanical analyses are commonly conducted to investigate how craniofacial form relates to function, particularly in relation to dietary adaptations. However, in the absence of corresponding muscle activation patterns, incomplete muscle data recorded experimentally for different individuals during different feeding tasks are frequently substituted. This study uses finite element analysis (FEA) to examine the sensitivity of the mechanical response of a Macaca fascicularis cranium to varying muscle activation patterns predicted via multibody dynamic analysis. Relative to the effects of varying bite location, the consequences of simulated variations in muscle activation patterns and of the inclusion/exclusion of whole muscle groups were investigated. The resulting cranial deformations were compared using two approaches; strain maps and geometric morphometric analyses. The results indicate that, with bite force magnitude controlled, the variations among the mechanical responses of the cranium to bite location far outweigh those observed as a consequence of varying muscle activations. However, zygomatic deformation was an exception, with the activation levels of superficial masseter being most influential in this regard. The anterior portion of temporalis deforms the cranial vault, but the remaining muscles have less profound effects. This study for the first time systematically quantifies the sensitivity of an FEA model of a primate skull to widely varying masticatory muscle activations and finds that, with the exception of the zygomatic arch, reasonable variants of muscle loading for a second molar bite have considerably less effect on cranial deformation and the resulting strain map than does varying molar bite point. The implication is that FEA models of biting crania will generally produce acceptable estimates of deformation under load as long as muscle activations and forces are reasonably approximated. In any one FEA study, the biological significance of the error in applied muscle forces is best judged against the magnitude of the effect that is being investigated.

Rigid-body analysis of a lizard skull: Modelling the skull of Uromastyx hardwickii

Lizard skulls vary greatly in their detailed morphology. Theoretical models and practical studies have posited a definite relationship between skull morphology and bite performance, but this can be difficult to demonstrate in vivo. Computer modelling provides an alternative approach, as long as hard and soft tissue components can be integrated and the model can be validated. An anatomically accurate three-dimensional computer model of an Uromastyx hardwickii skull was developed for rigid-body dynamic analysis. The Uromastyx jaw was first opened under motion control, and then muscle forces were applied to produce biting simulations where bite forces and joint forces were calculated. Bite forces comparable to those reported in the literature were predicted, and detailed muscular force information was produced along with additional information on the stabilizing role of temporal ligaments in late jaw closing.

Differential Growth and Development of the Upper and Lower Human Thorax

The difficulties in quantifying the 3D form and spatial relationships of the skeletal components of the ribcage present a barrier to studies of the growth of the thoracic skeleton. Thus, most studies to date have relied on traditional measurements such as distances and indices from single or few ribs. It is currently known that adult-like thoracic shape is achieved early, by the end of the second postnatal year, with the circular cross-section of the newborn thorax transforming into the ovoid shape of adults; and that the ribs become inclined such that their anterior borders come to lie inferior to their posterior. Here we present a study that revisits growth changes using geometric morphometrics applied to extensive landmark data taken from the ribcage. We digitized 402 (semi) landmarks on 3D reconstructions to assess growth changes in 27 computed tomography-scanned modern humans representing newborns to adults of both sexes. Our analyses show a curved ontogenetic trajectory, resulting from different ontogenetic growth allometries of upper and lower thoracic units. Adult thoracic morphology is achieved later than predicted, by diverse modifications in different anatomical regions during different ontogenetic stages. Besides a marked increase in antero-posterior dimensions, there is an increase in medio-lateral dimensions of the upper thorax, relative to the lower thorax. This transforms the pyramidal infant thorax into the barrel-shaped one of adults. Rib descent is produced by complex changes in 3D curvature. Developmental differences between upper and lower thoracic regions relate to differential timings and rates of maturation of the respiratory and digestive systems, the spine and the locomotor system. Our findings are relevant to understanding how changes in the relative rates of growth of these systems and structures impacted on the development and evolution of modern human body shape.

RETRACTED: Modelling subcortical bone in finite element analyses: A validation and sensitivity study in the macaque mandible

Finite element analysis (FEA) is a fundamental method to study stresses and strains in complex structures, with the accuracy of an FEA being reliant on a number of variables, not least the precision and complexity of the models geometry. Techniques such as computed tomography (CT) allow general geometries to be derived relatively quickly; however, constraints on CT image resolution mean defining subcortical geometries can be problematic. In relation to the overall mechanical response of a complex structure during FEA, the consequence of variable subcortical modelling is not known. Here we test this sensitivity with a series of FE models of a macaque mandible with different subcortical geometries and comparing the FEA strain magnitudes and orientations. The validity of the FE models was tested by carrying out experimental strain measurements on the same mandible. These strain measurements matched the FE predictions, providing confidence that material properties and model geometry were suitably defined. Results of this study show that cortical bone alone is not as effective in resisting bending as it is when coupled with subcortical bone, and as such subcortical geometries must be modelled during an FEA. This study demonstrates that the fine detail of the mandibular subcortical structure can be adequately modelled as a solid when assigned an appropriate Youngs modulus value, in this case ranging from 1 to 2 GPa. This is an important and encouraging result for the creation of FE models of materials where CT image resolution or poor preservation prevent the accurate modelling of subcortical bone.

Comparison between in vivo and theoretical bite performance: using multi-body modelling to predict muscle and bite forces in a reptile skull.

In biomechanical investigations, geometrically accurate computer models of anatomical structures can be created readily using computed-tomography scan images. However, representation of soft tissue structures is more challenging, relying on approximations to predict the muscle loading conditions that are essential in detailed functional analyses. Here, using a sophisticated multi-body computer model of a reptile skull (the rhynchocephalian Sphenodon), we assess the accuracy of muscle force predictions by comparing predicted bite forces against in vivo data. The model predicts a bite force almost three times lower than that measured experimentally. Peak muscle force estimates are highly sensitive to fibre length, muscle stress, and pennation where the angle is large, and variation in these parameters can generate substantial differences in predicted bite forces. A review of theoretical bite predictions amongst lizards reveals that bite forces are consistently underestimated, possibly because of high levels of muscle pennation in these animals. To generate realistic bites during theoretical analyses in Sphenodon, lizards, and related groups we suggest that standard muscle force calculations should be multiplied by a factor of up to three. We show that bite forces increase and joint forces decrease as the bite point shifts posteriorly within the jaw, with the most posterior bite location generating a bite force almost double that of the most anterior bite. Unilateral and bilateral bites produced similar total bite forces; however, the pressure exerted by the teeth is double during unilateral biting as the tooth contact area is reduced by half.

The Head and Neck Anatomy of Sea Turtles (Cryptodira: Chelonioidea) and Skull Shape in Testudines

Background Sea turtles (Chelonoidea) are a charismatic group of marine reptiles that occupy a range of important ecological roles. However, the diversity and evolution of their feeding anatomy remain incompletely known. Methodology/Principal Findings Using computed tomography and classical comparative anatomy we describe the cranial anatomy in two sea turtles, the loggerhead (Caretta caretta) and Kemp’s ridley (Lepidochelys kempii), for a better understanding of sea turtle functional anatomy and morphological variation. In both taxa the temporal region of the skull is enclosed by bone and the jaw joint structure and muscle arrangement indicate that palinal jaw movement is possible. The tongue is relatively small, and the hyoid apparatus is not as conspicuous as in some freshwater aquatic turtles. We find several similarities between the muscles of C. caretta and L. kempii, but comparison with other turtles suggests only one of these characters may be derived: connection of the m. adductor mandibulae internus into the Pars intramandibularis via the Zwischensehne. The large fleshy origin of the m. adductor mandibulae externus Pars superficialis from the jugal seems to be a characteristic feature of sea turtles. Conclusions/Significance In C. caretta and L. kempii the ability to suction feed does not seem to be as well developed as that found in some freshwater aquatic turtles. Instead both have skulls suited to forceful biting. This is consistent with the observation that both taxa tend to feed on relatively slow moving but sometimes armoured prey. The broad fleshy origin of the m. adductor mandibulae externus Pars superficialis may be linked to thecheek region being almost fully enclosed in bone but the relationship is complex.