Predicting skull loading: applying multibody dynamics analysis to a macaque skull

Functional adaptation of the infant craniofacial system to mechanical loadings arising from masticatory forces

The morphology and biomechanics of infant crania undergo significant changes between the pre- and post-weaning phases due to increasing loading of the masticatory system. The aims of this study were to characterize the changes in muscle forces, bite forces and the pattern of mechanical strain and stress arising from the aforementioned forces across crania in the first 48 months of life using imaging and finite element methods. A total of 51 head computed tomography scans of normal individuals were collected and analysed from a larger database of 217 individuals. The estimated mean muscle forces of temporalis, masseter and medial pterygoid increase from 30.9 to 87.0 N, 25.6 to 69.6 N and 23.1 to 58.9 N, respectively (0-48 months). Maximum bite force increases from 90.5 to 184.2 N (3-48 months). There is a change in the pattern of strain and stress from the calvaria to the face during postnatal development. Overall, this study highlights the changes in the mechanics of the craniofacial system during normal development. It further raises questions as to how and what level of changes in the mechanical forces during the development can alter the morphology of the craniofacial system.

The role of cranial osteoderms on the mechanics of the skull in scincid lizards

Osteoderms (ODs) are calcified organs formed directly within the skin of most major extant tetrapod lineages. Lizards possibly show the greatest diversity in ODs morphology and distribution. ODs are commonly hypothesized to function as a defensive armor. Here we tested the hypothesis that cranial osteoderms also contribute to the mechanics of the skull during biting. A series of in vivo experiments were carried out on three specimens of Tiliqua gigas. Animals were induced to bite a force plate while a single cranial OD was strain gauged. A finite element (FE) model of a related species, Tiliqua scincoides, was developed and used to estimate the level of strain across the same OD as instrumented in the in vivo experiments. FE results were compared to the in vivo data and the FE model was modified to test two hypothetical scenarios in which all ODs were (i) removed from, and (ii) fused to, the skull. In vivo data demonstrated that the ODs were carrying load during biting. The hypothetical FE models showed that when cranial ODs were fused to the skull, the overall strain across the skull arising from biting was reduced. Removing the ODs showed an opposite effect. In summary, our findings suggest that cranial ODs contribute to the mechanics of the skull, even when they are loosely attached.

Masticatory biomechanics of red and grey squirrels (Sciurus vulgaris and Sciurus carolinensis) modelled with multibody dynamics analysis

The process of feeding in mammals is achieved by moving the mandible relative to the cranium to bring the teeth into and out of occlusion. This process is especially complex in rodents which have a highly specialized configuration of jaw adductor muscles. Here, we used the computational technique of multi-body dynamics analysis (MDA) to model feeding in the red (Sciurus vulgaris) and grey squirrel (Sciurus carolinensis) and determine the relative contribution of each jaw-closing muscle in the generation of bite forces. The MDA model simulated incisor biting at different gapes. A series of 'virtual ablation experiments' were performed at each gape, whereby the activation of each bilateral pair of muscles was set to zero. The maximum bite force was found to increase at wider gapes. As predicted, the superficial and anterior deep masseter were the largest contributors to bite force, but the temporalis had only a small contribution. Further analysis indicated that the temporalis may play a more important role in jaw stabilization than in the generation of bite force. This study demonstrated the ability of MDA to elucidate details of red and grey squirrel feeding biomechanics providing a complement to data gathered via in vivo experimentation.

Modeling tooth enamel in FEA comparisons of skulls: Comparing common simplifications with biologically realistic models

Palaeontologists often use finite element analyses, in which forces propagate through objects with specific material properties, to investigate feeding biomechanics. Teeth are usually modeled with uniform properties (all bone or all enamel). In reality, most teeth are composed of pulp, dentine, and enamel. We tested how simplified teeth compare to more realistic models using mandible models of three reptiles. For each, we created models representing enamel thicknesses found in extant taxa, as well as simplified models (bone, dentine or enamel). Our results suggest that general comparisons of stress distribution among distantly related taxa do not require representation of dental tissues, as there was no noticeable effect on heatmap representations of stress. However, we find that representation of dental tissues impacts bite force estimates, although magnitude of these effects may differ depending on constraints. Thus, as others have shown, the detail necessary in a biomechanical model relates to the questions being examined.

Regional Patterning in Tail Vertebral Form and Function in Chameleons (Chamaeleo calyptratus)

Previous studies have focused on documenting shape variation in the caudal vertebrae in chameleons underlying prehensile tail function. The goal of this study was to test the impact of this variation on tail function using multibody dynamic analysis (MDA). First, observations from dissections and 3D reconstructions generated from contrast-enhanced µCT scans were used to document regional variation in arrangement of the caudal muscles along the antero-posterior axis. Using MDA, we then tested the effect of vertebral shape geometry on biomechanical function. To address this question, four different MDA models were built: those with a distal vertebral shape and with either a distal or proximal musculature, and reciprocally the proximal vertebral shape with either the proximal or distal musculature. For each muscle configuration, we calculated the force required in each muscle group for the muscle force to balance an arbitrary external force applied to the model. The results showed that the models with a distal-type of musculature are the most efficient, regardless of vertebral shape. Our models also showed that the m. ilio-caudalis pars dorsalis is least efficient when combining the proximal vertebral shape and distal musculature, highlighting the importance of the length of the transverse process in combination with the lever-moment arm onto which muscle force is exerted. This initial model inevitably has a number of simplifications and assumptions, however its purpose is not to predict in vivo forces, but instead reveals the importance of vertebral shape and muscular arrangement on the total force the tail can generate, thus providing a better understanding of the biomechanical significance of the regional variations on tail grasping performance in chameleons.

"Simple" Biomechanical Model for Ants Reveals How Correlated Evolution among Body Segments Minimizes Variation in Center of Mass as Heads Get Larger

The field of comparative biomechanics strives to understand the diversity of the biological world through the lens of physics. To accomplish this, researchers apply a variety of modeling approaches to explore the evolution of form and function ranging from basic lever models to intricate computer simulations. While advances in technology have allowed for increasing model complexity, insight can still be gained through the use of low-parameter "simple" models. All models, regardless of complexity, are simplifications of reality and must make assumptions; "simple" models just make more assumptions than complex ones. However, "simple" models have several advantages. They allow individual parameters to be isolated and tested systematically, can be made applicable to a wide range of organisms and make good starting points for comparative studies, allowing for complexity to be added as needed. To illustrate these ideas, we perform a case study on body form and center of mass stability in ants. Ants show a wide diversity of body forms, particularly in terms of the relative size of the head, petiole(s), and gaster (the latter two make-up the segments of the abdomen not fused to thorax in hymenopterans). We use a "simple" model to explore whether balance issues pertaining to the center of mass influence patterns of segment expansion across major ant clades. Results from phylogenetic comparative methods imply that the location of the center of mass in an ant's body is under stabilizing selection, constraining the center of mass to the middle segment (thorax) over the legs. This is potentially maintained by correlated rates of evolution between the head and gaster on either end. While these patterns arise from a model that makes several assumptions/simplifications relating to shape and materials, they still offer intriguing insights into the body plan of ants across ∼68% of their diversity. The results from our case study illustrate how "simple," low-parameter models both highlight fundamental biomechanical trends and aid in crystalizing specific questions and hypotheses for more complex models to address.

A Procedure for Analyzing Mandible Roto-Translation Induced by Mandibular Advancement Devices

Background: Sleep-Related Breathing Disorders are characterized by repeated episodes of complete or partial obstruction of the upper airway during sleep. Mandibular advancement devices represent a non-invasive treatment in reducing the number of respiratory events and in decreasing symptoms. The advancement extent of these devices is responsible for the mandibular roto-translation and its effects on the temporomandibular joint. Methods: This study defined a systematic method to assess the mandible roto translation that is caused by MADs according to a scan-to-CAD approach. Starting from a closed mouth position and simulating the oral appliance at different settings it was possible to define a local reference system that is useful for the evaluation of the mandibular roto-translation. This latter was then applied to evaluate the movements of the condyle and the mandibular dental arch. Results: MAD1 resulted in a reduced mouth opening and protrusion, while MAD2 enabled a higher degree of motion of the mandible useful for patients who need an important protrusion. Conclusions: The two devices present different dynamics. Results that are achievable employing this method can be directly used by practitioners in comparing MADs, as well as by researchers in evaluating MADs effects.

Humerus osteology, myology, and finite element structure analysis of Cheloniidae

Adaptation of osteology and myology lead to the formation of hydrofoil foreflippers in Cheloniidae (all recent sea turtles except Dermochelys coriacea) which are used mainly for underwater flight. Recent research shows the biomechanical advantages of a complex system of agonistic and antagonistic tension chords that reduce bending stress in bones. Finite element structure analysis (FESA) of a cheloniid humerus is used to provide a better understanding of morphology and microanatomy and to link these with the main flipper function, underwater flight. Dissection of a Caretta caretta gave insights into lines of action, that is, the course that a muscle takes between its origin and insertion, of foreflipper musculature. Lines of action were determined by spanning physical threads on a skeleton of Chelonia mydas. The right humerus of this skeleton was micro-CT scanned. Based on the scans, a finite element (FE) model was built and muscle force vectors were entered. Muscle forces were iteratively approximated until a uniform compressive stress distribution was attained. Two load cases, downstroke and upstroke, were computed. We found that muscle wrappings (m. coracobrachialis magnus and brevis, several extensors, humeral head of m. triceps) are crucial in addition to axial loading to obtain homogenous compressive loading in all bone cross-sections. Detailed knowledge on muscle disposition leads to compressive stress distribution in the FE model which corresponds with the bone microstructure. The FE analysis of the cheloniid humerus shows that bone may be loaded mainly by compression if the bending moments are minimized.

Cell Mechanics of Craniosynostosis

Craniosynostosis is the premature fusion of the calvarial sutures that is associated with a number of physical and intellectual disabilities spanning from pediatric to adult years. Over the past two decades, techniques in molecular genetics and more recently, advances in high-throughput DNA sequencing have been used to examine the underlying pathogenesis of this disease. To date, mutations in 57 genes have been identified as causing craniosynostosis and the number of newly discovered genes is growing rapidly as a result of the advances in genomic technologies. While contributions from both genetic and environmental factors in this disease are increasingly apparent, there remains a gap in knowledge that bridges the clinical characteristics and genetic markers of craniosynostosis with their signaling pathways and mechanotransduction processes. By linking genotype to phenotype, outlining the role of cell mechanics may further uncover the specific mechanotransduction pathways underlying craniosynostosis. Here, we present a brief overview of the recent findings in craniofacial genetics and cell mechanics, discussing how this information together with animal models is advancing our understanding of craniofacial development.

Investigating the running abilities of Tyrannosaurus rex using stress-constrained multibody dynamic analysis

The running ability of Tyrannosaurus rex has been intensively studied due to its relevance to interpretations of feeding behaviour and the biomechanics of scaling in giant predatory dinosaurs. Different studies using differing methodologies have produced a very wide range of top speed estimates and there is therefore a need to develop techniques that can improve these predictions. Here we present a new approach that combines two separate biomechanical techniques (multibody dynamic analysis and skeletal stress analysis) to demonstrate that true running gaits would probably lead to unacceptably high skeletal loads in T. rex. Combining these two approaches reduces the high-level of uncertainty in previous predictions associated with unknown soft tissue parameters in dinosaurs, and demonstrates that the relatively long limb segments of T. rex—long argued to indicate competent running ability—would actually have mechanically limited this species to walking gaits. Being limited to walking speeds contradicts arguments of high-speed pursuit predation for the largest bipedal dinosaurs like T. rex, and demonstrates the power of multiphysics approaches for locomotor reconstructions of extinct animals.

Masticatory biomechanics in the rabbit: a multi-body dynamics analysis

Multi-body dynamics is a powerful engineering tool which is becoming increasingly popular for the simulation and analysis of skull biomechanics. This paper presents the first application of multi-body dynamics to analyse the biomechanics of the rabbit skull. A model has been constructed through the combination of manual dissection and three-dimensional imaging techniques (magnetic resonance imaging and micro-computed tomography). Individual muscles are represented with multiple layers, thus more accurately modelling muscle fibres with complex lines of action. Model validity was sought through comparing experimentally measured maximum incisor bite forces with those predicted by the model. Simulations of molar biting highlighted the ability of the masticatory system to alter recruitment of two muscle groups, in order to generate shearing or crushing movements. Molar shearing is capable of processing a food bolus in all three orthogonal directions, whereas molar crushing and incisor biting are predominately directed vertically. Simulations also show that the masticatory system is adapted to process foods through several cycles with low muscle activations, presumably in order to prevent rapidly fatiguing fast fibres during repeated chewing cycles. Our study demonstrates the usefulness of a validated multi-body dynamics model for investigating feeding biomechanics in the rabbit, and shows the potential for complementing and eventually reducing in vivo experiments.

The impact of simplifications on the performance of a finite element model of a Macaca fascicularis cranium

In recent years finite element analysis (FEA) has emerged as a useful tool for the analysis of skeletal form-function relationships. While this approach has obvious appeal for the study of fossil specimens, such material is often fragmentary with disrupted internal architecture and can contain matrix that leads to errors in accurate segmentation. Here we examine the effects of varying the detail of segmentation and material properties of teeth on the performance of a finite element model of a Macaca fascicularis cranium within a comparative functional framework. Cranial deformations were compared using strain maps to assess differences in strain contours and Procrustes size and shape analyses, from geometric morphometrics, were employed to compare large scale deformations. We show that a macaque model subjected to biting can be made solid, and teeth altered in material properties, with minimal impact on large scale modes of deformation. The models clustered tightly by bite point rather than by modeling simplification approach, and fell out as being distinct from another species. However localized fluctuations in predicted strain magnitudes were recorded with different modeling approaches, particularly over the alveolar region. This study indicates that, while any model simplification should be undertaken with care and attention to its effects, future applications of FEA to fossils with unknown internal architecture may produce reliable results with regard to general modes of deformation, even when detail of internal bone architecture cannot be reliably modeled.

Retrodeformation and muscular reconstruction of ornithomimosaurian dinosaur crania

Ornithomimosaur dinosaurs evolved lightweight, edentulous skulls that possessed keratinous rhamphothecae. Understanding the anatomy of these taxa allows for a greater understanding of “ostrich-mimic” dinosaurs and character change during theropod dinosaur evolution. However, taphonomic processes during fossilisation often distort fossil remains. Retrodeformation offers a means by which to recover a hypothesis of the original anatomy of the specimen, and 3D scanning technologies present a way to constrain and document the retrodeformation process. Using computed tomography (CT) scan data, specimen specific retrodeformations were performed on three-dimensionally preserved but taphonomically distorted skulls of the deinocheirid Garudimimus brevipesBarsbold, 1981 and the ornithomimids Struthiomimus altusLambe, 1902 and Ornithomimus edmontonicusSternberg, 1933. This allowed for a reconstruction of the adductor musculature, which was then mapped onto the crania, from which muscle mechanical advantage and bite forces were calculated pre- and post-retrodeformation. The extent of the rhamphotheca was varied in each taxon to represent morphologies found within modern Aves. Well constrained retrodeformation allows for increased confidence in anatomical and functional analysis of fossil specimens and offers an opportunity to more fully understand the soft tissue anatomy of extinct taxa.

A general-purpose framework to simulate musculoskeletal system of human body: using a motion tracking approach

Computation of muscle force patterns that produce specified movements of muscle-actuated dynamic models is an important and challenging problem. This problem is an undetermined one, and then a proper optimization is required to calculate muscle forces. The purpose of this paper is to develop a general model for calculating all muscle activation and force patterns in an arbitrary human body movement. For this aim, the equations of a multibody system forward dynamics, which is considered for skeletal system of the human body model, is derived using Lagrange-Euler formulation. Next, muscle contraction dynamics is added to this model and forward dynamics of an arbitrary musculoskeletal system is obtained. For optimization purpose, the obtained model is used in computed muscle control algorithm, and a closed-loop system for tracking desired motions is derived. Finally, a popular sport exercise, biceps curl, is simulated by using this algorithm and the validity of the obtained results is evaluated via EMG signals.

Modeling the biomechanics of swine mastication--an inverse dynamics approach

A novel reconstructive alternative for patients with severe facial structural deformity is Le Fort-based, face-jaw-teeth transplantation (FJTT). To date, however, only ten surgeries have included underlying skeletal and jaw-teeth components, all yielding sub-optimal results and a need for a subsequent revision surgery, due to size mismatch and lack of precise planning. Numerous studies have proven swine to be appropriate candidates for translational studies including pre-operative planning of transplantation. An important aspect of planning FJTT is determining the optimal muscle attachment sites on the recipient's jaw, which requires a clear understanding of mastication and bite mechanics in relation to the new donated upper and/or lower jaw. A segmented CT scan coupled with data taken from literature defined a biomechanical model of mandible and jaw muscles of a swine. The model was driven using tracked motion and external force data of one cycle of chewing published earlier, and predicted the muscle activation patterns as well as temporomandibular joint (TMJ) reaction forces and condylar motions. Two methods, polynomial and min/max optimization, were used for solving the muscle recruitment problem. Similar performances were observed between the two methods. On average, there was a mean absolute error (MAE) of <0.08 between the predicted and measured activation levels of all muscles, and an MAE of <7 N for TMJ reaction forces. Simulated activations qualitatively followed the same patterns as the reference data and there was very good agreement for simulated TMJ forces. The polynomial optimization produced a smoother output, suggesting that it is more suitable for studying such motions. Average MAE for condylar motion was 1.2mm, which reduced to 0.37 mm when the input incisor motion was scaled to reflect the possible size mismatch between the current and original swine models. Results support the hypothesis that the model can be used for planning of facial transplantation.

The morphology of the mouse masticatory musculature

The mouse has been the dominant model organism in studies on the development, genetics and evolution of the mammalian skull and associated soft-tissue for decades. There is the potential to take advantage of this well studied model and the range of mutant, knockin and knockout organisms with diverse craniofacial phenotypes to investigate the functional significance of variation and the role of mechanical forces on the development of the integrated craniofacial skeleton and musculature by using computational mechanical modelling methods (e.g. finite element and multibody dynamic modelling). Currently, there are no detailed published data of the mouse masticatory musculature available. Here, using a combination of micro-dissection and non-invasive segmentation of iodine-enhanced micro-computed tomography, we document the anatomy, architecture and proportions of the mouse masticatory muscles. We report on the superficial masseter (muscle, tendon and pars reflecta), deep masseter, zygomaticomandibularis (anterior, posterior, infraorbital and tendinous parts), temporalis (lateral and medial parts), external and internal pterygoid muscles. Additionally, we report a lateral expansion of the attachment of the temporalis onto the zygomatic arch, which may play a role in stabilising this bone during downwards loading. The data presented in this paper now provide a detailed reference for phenotypic comparison in mouse models and allow the mouse to be used as a model organism in biomechanical and functional modelling and simulation studies of the craniofacial skeleton and particularly the masticatory system.

Cranial sutures work collectively to distribute strain throughout the reptile skull

The skull is composed of many bones that come together at sutures. These sutures are important sites of growth, and as growth ceases some become fused while others remain patent. Their mechanical behaviour and how they interact with changing form and loadings to ensure balanced craniofacial development is still poorly understood. Early suture fusion often leads to disfiguring syndromes, thus is it imperative that we understand the function of sutures more clearly. By applying advanced engineering modelling techniques, we reveal for the first time that patent sutures generate a more widely distributed, high level of strain throughout the reptile skull. Without patent sutures, large regions of the skull are only subjected to infrequent low-level strains that could weaken the bone and result in abnormal development. Sutures are therefore not only sites of bone growth, but could also be essential for the modulation of strains necessary for normal growth and development in reptiles.

The importance of accurate muscle modelling for biomechanical analyses: a case study with a lizard skull

Computer-based simulation techniques such as multi-body dynamics analysis are becoming increasingly popular in the field of skull mechanics. Multi-body models can be used for studying the relationships between skull architecture, muscle morphology and feeding performance. However, to be confident in the modelling results, models need to be validated against experimental data, and the effects of uncertainties or inaccuracies in the chosen model attributes need to be assessed with sensitivity analyses. Here, we compare the bite forces predicted by a multi-body model of a lizard (Tupinambis merianae) with in vivo measurements, using anatomical data collected from the same specimen. This subject-specific model predicts bite forces that are very close to the in vivo measurements and also shows a consistent increase in bite force as the bite position is moved posteriorly on the jaw. However, the model is very sensitive to changes in muscle attributes such as fibre length, intrinsic muscle strength and force orientation, with bite force predictions varying considerably when these three variables are altered. We conclude that accurate muscle measurements are crucial to building realistic multi-body models and that subject-specific data should be used whenever possible.

A sensitivity analysis to the role of the fronto-parietal suture in Lacerta bilineata: a preliminary finite element study

Cranial sutures are sites of bone growth and development but micromovements at these sites may distribute the load across the skull more evenly. Computational studies have incorporated sutures into finite element (FE) models to assess various hypotheses related to their function. However, less attention has been paid to the sensitivity of the FE results to the shape, size, and stiffness of the modeled sutures. Here, we assessed the sensitivity of the strain predictions to the aforementioned parameters in several models of fronto-parietal (FP) suture in Lacerta bilineata. For the purpose of this study, simplifications were made in relation to modeling the bone properties and the skull loading. Results highlighted that modeling the FP as either an interdigitated suture or a simplified butt suture, did not reduce the strain distribution in the FP region. Sensitivity tests showed that similar patterns of strain distribution can be obtained regardless of the size of the suture, or assigned stiffness, yet the exact magnitudes of strains are highly sensitive to these parameters. This study raises the question whether the morphogenesis of epidermic scales in the FP region in the Lacertidae is related to high strain fields in this region, because of micromovement in the FP suture.

Cranial myology and bite force performance of Erlikosaurus andrewsi: a novel approach for digital muscle reconstructions

The estimation of bite force and bite performance in fossil and extinct animals is a challenging subject in palaeontology and is highly dependent on the reconstruction of the cranial myology. Furthermore, the morphology and arrangement of the adductor muscles considerably affect feeding processes and mastication and thus also have important dietary and ecological ramifications. However, in the past, the reconstruction of the (cranial) muscles was restricted to the identification of muscle attachment sites or simplified computer models. This study presents a detailed reconstruction of the adductor musculature of the Cretaceous therizinosaur Erlikosaurus andrewsi based on a stepwise and iterative approach. The detailed, three-dimensional models of the individual muscles allow for more accurate measurements of the muscle properties (length, cross-section, attachment angle and volume), from which muscle and bite force estimates are calculated. Bite force estimations are found to be the lowest at the tip of the snout (43-65 N) and respectively higher at the first (59-88 N) and last tooth (90-134 N) position. Nevertheless, bite forces are comparatively low for E. andrewsi, both in actual numbers as well as in comparison with other theropod dinosaurs. The results further indicate that the low bite performance was mainly used for leaf-stripping and plant cropping, rather than active mastication or chewing processes. Muscle and thus bite force in E. andrewsi (and most likely all therizinosaurs) is considerably constrained by the cranial anatomy and declines in derived taxa of this clade. This trend is reflected in the changes of dietary preferences from carnivory to herbivory in therizinosaurs.

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.

Developing a musculoskeletal model of the primate skull: predicting muscle activations, bite force, and joint reaction forces using multibody dynamics analysis and advanced optimisation methods

An accurate, dynamic, functional model of the skull that can be used to predict muscle forces, bite forces, and joint reaction forces would have many uses across a broad range of disciplines. One major issue however with musculoskeletal analyses is that of muscle activation pattern indeterminacy. A very large number of possible muscle force combinations will satisfy a particular functional task. This makes predicting physiological muscle recruitment patterns difficult. Here we describe in detail the process of development of a complex multibody computer model of a primate skull (Macaca fascicularis), that aims to predict muscle recruitment patterns during biting. Using optimisation criteria based on minimisation of muscle stress we predict working to balancing side muscle force ratios, peak bite forces, and joint reaction forces during unilateral biting. Validation of such models is problematic; however we have shown comparable working to balancing muscle activity and TMJ reaction ratios during biting to those observed in vivo and that peak predicted bite forces compare well to published experimental data. To our knowledge the complexity of the musculoskeletal model is greater than any previously reported for a primate. This complexity, when compared to more simple representations provides more nuanced insights into the functioning of masticatory muscles. Thus, we have shown muscle activity to vary throughout individual muscle groups, which enables them to function optimally during specific masticatory tasks. This model will be utilised in future studies into the functioning of the masticatory apparatus.

Shearing mechanics and the influence of a flexible symphysis during oral food processing in Sphenodon (Lepidosauria: Rhynchocephalia)

The New Zealand tuatara, Sphenodon, has a specialized feeding system in which the teeth of the lower jaw close between two upper tooth rows before sliding forward to slice food apart like a draw cut saw. This shearing action is unique amongst living amniotes but has been compared with the chewing power stroke of mammals. We investigated details of the jaw movement using multibody dynamics analysis of an anatomically accurate three-dimensional computer model constructed from computed tomography scans. The model predicts that a flexible symphysis is necessary for changes in the intermandibular angle that permits prooral movement. Models with the greatest symphysial flexibility allow the articulation surface of the articular to follow the quadrate cotyle with the least restriction, and suggest that shearing is accompanied by a long axis rotation of the lower jaws. This promotes precise point loading between the cutting edges of particular teeth, enhancing the effectiveness of the shearing action. Given that Sphenodon is a relatively inactive reptile, we suggest that the link between oral food processing and endothermy has been overstated. Food processing improves feeding efficiency, a consideration of particular importance when food availability is unpredictable. Although this feeding mechanism is today limited to Sphenodon, a survey of fossil rhynchocephalians suggests that it was once more widespread.

3D analysis of the forearm rotational efficiency variation in humans

Pronosupination is a component of the hominoid orthograde corporal plane that enables primates to execute efficient and sure locomotion in their habitat and is an essential movement for the development of manipulative capacities. We analyze human variability in the rotational efficiency of the pronator teres muscle by applying the biomechanical model created by Galtés et al. (Am J Phys Anthropol 2008; 135:293-300; Am J Phys Anthropol 2009a; 140:589-594) to skeletal remains of a human sample (N = 29) and three nonhuman hominoid specimens (chimpanzee, gorilla, and orangutan) by means of 3D technology. We aim to examine whether there is a distinctive human pattern of rotational efficiency and determine which structural features of the upper-limb bones have the greatest influence on the determination of rotational efficiency. Our results show that the human pattern differs from efficiencies observed in nonhuman hominoids, which may be interpreted in the light of morphofunctional adaptations. We identify medial epicondylar form as the key structure of the upper-limb bones for the determination of the rotational efficiency of the forearm. Results indicate that the more medially projected epicondyle of nonhuman hominoids relative to humans leads to higher values of maximum rotational efficiency. Moreover, the orientation of the medial epicondyle determines the pronounced differences in the position of the maximum efficiencies in the pronosupination range between humans and the studied nonhuman hominoids. Proximodistal orientation of the medial epicondyle is suggested to be a more appropriate feature for distinguishing between humans and nonhuman hominoids than anteroposterior orientation and, therefore, for inferring behavioral aspects from skeletal remains and fossils of primate upper-limb bones.

Functional relationship between skull form and feeding mechanics in Sphenodon, and implications for diapsid skull development

The vertebrate skull evolved to protect the brain and sense organs, but with the appearance of jaws and associated forces there was a remarkable structural diversification. This suggests that the evolution of skull form may be linked to these forces, but an important area of debate is whether bone in the skull is minimised with respect to these forces, or whether skulls are mechanically "over-designed" and constrained by phylogeny and development. Mechanical analysis of diapsid reptile skulls could shed light on this longstanding debate. Compared to those of mammals, the skulls of many extant and extinct diapsids comprise an open framework of fenestrae (window-like openings) separated by bony struts (e.g., lizards, tuatara, dinosaurs and crocodiles), a cranial form thought to be strongly linked to feeding forces. We investigated this link by utilising the powerful engineering approach of multibody dynamics analysis to predict the physiological forces acting on the skull of the diapsid reptile Sphenodon. We then ran a series of structural finite element analyses to assess the correlation between bone strain and skull form. With comprehensive loading we found that the distribution of peak von Mises strains was particularly uniform throughout the skull, although specific regions were dominated by tensile strains while others were dominated by compressive strains. Our analyses suggest that the frame-like skulls of diapsid reptiles are probably optimally formed (mechanically ideal: sufficient strength with the minimal amount of bone) with respect to functional forces; they are efficient in terms of having minimal bone volume, minimal weight, and also minimal energy demands in maintenance.

Sensitivity and ex vivo validation of finite element models of the domestic pig cranium

A finite element (FE) validation and sensitivity study was undertaken on a modern domestic pig cranium. Bone strain data were collected ex vivo from strain gauges, and compared with results from specimen-specific FE models. An isotropic, homogeneous model was created, then input parameters were altered to investigate model sensitivity. Heterogeneous, isotropic models investigated the effects of a constant-thickness, stiffer outer layer (representing cortical bone) atop a more compliant interior (representing cancellous bone). Loading direction and placement of strain gauges were also varied, and the use of 2D membrane elements at strain gauge locations as a method of projecting 3D model strains into the plane of the gauge was investigated. The models correctly estimate the loading conditions of the experiment, yet at some locations fail to reproduce correct principal strain magnitudes, and hence strain ratios. Principal strain orientations are predicted well. The initial model was too stiff by approximately an order of magnitude. Introducing a compliant interior reported strain magnitudes more similar to the ex vivo results without notably affecting strain orientations, ratios or contour patterns, suggesting that this simple heterogeneity was the equivalent of reducing the overall stiffness of the model. Models were generally insensitive to moderate changes in loading direction or strain gauge placement, except in the squamosal portion of the zygomatic arch. The use of membrane elements made negligible differences to the reported strains. The models therefore seem most sensitive to changes in material properties, and suggest that failure to model local heterogeneity in material properties and structure of the bone may be responsible for discrepancies between the experimental and model results. This is partially attributable to a lack of resolution in the CT scans from which the model was built, and partially due to an absence of detailed material properties data for pig cranial bone. Thus, caution is advised when using FE models to estimate absolute numerical values of breaking stress and bite force unless detailed input parameters are available. However, if the objective is to compare relative differences between models, the fact that the strain environment is replicated well means that such investigations can be robust.

Craniofacial biomechanics: an overview of recent multibody modelling studies

Multibody modelling is underutilised in craniofacial analyses, particularly when compared to other computational methods such as finite element analysis. However, there are many potential applications within this area, where bony movements, muscle forces, joint kinematics and bite forces can all be studied. This paper provides an overview of recent, three-dimensional, multibody modelling studies related to the analysis of skulls. The goal of this paper is not to offer a critical review of past studies, but instead intends to inform the reader of what has been achieved with multibody modelling.

In vivo bone strain and finite-element modeling of the craniofacial haft in catarrhine primates

Hypotheses regarding patterns of stress, strain and deformation in the craniofacial skeleton are central to adaptive explanations for the evolution of primate craniofacial form. The complexity of craniofacial skeletal morphology makes it difficult to evaluate these hypotheses with in vivo bone strain data. In this paper, new in vivo bone strain data from the intraorbital surfaces of the supraorbital torus, postorbital bar and postorbital septum, the anterior surface of the postorbital bar, and the anterior root of the zygoma are combined with published data from the supraorbital region and zygomatic arch to evaluate the validity of a finite-element model (FEM) of a macaque cranium during mastication. The behavior of this model is then used to test hypotheses regarding the overall deformation regime in the craniofacial haft of macaques. This FEM constitutes a hypothesis regarding deformation of the facial skeleton during mastication. A simplified verbal description of the deformation regime in the macaque FEM is as follows. Inferior bending and twisting of the zygomatic arches about a rostrocaudal axis exerts inferolaterally directed tensile forces on the lateral orbital wall, bending the wall and the supraorbital torus in frontal planes and bending and shearing the infraorbital region and anterior zygoma root in frontal planes. Similar deformation regimes also characterize the crania of Homo and Gorilla under in vitro loading conditions and may be shared among extant catarrhines. Relatively high strain magnitudes in the anterior root of the zygoma suggest that the morphology of this region may be important for resisting forces generated during feeding.

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.

Strain in the ostrich mandible during simulated pecking and validation of specimen-specific finite element models

Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in-vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen-specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in-vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups.

Current computational modelling trends in craniomandibular biomechanics and their clinical implications

Computational models of interactions in the craniomandibular apparatus are used with increasing frequency to study biomechanics in normal and abnormal masticatory systems. Methods and assumptions in these models can be difficult to assess by those unfamiliar with current practices in this field; health professionals are often faced with evaluating the appropriateness, validity and significance of models which are perhaps more familiar to the engineering community. This selective review offers a foundation for assessing the strength and implications of a craniomandibular modelling study. It explores different models used in general science and engineering and focuses on current best practices in biomechanics. The problem of validation is considered at some length, because this is not always fully realisable in living subjects. Rigid-body, finite element and combined approaches are discussed, with examples of their application to basic and clinically relevant problems. Some advanced software platforms currently available for modelling craniomandibular systems are mentioned. Recent studies of the face, masticatory muscles, tongue, craniomandibular skeleton, temporomandibular joint, dentition and dental implants are reviewed, and the significance of non-linear and non-isotropic material properties is emphasised. The unique challenges in clinical application are discussed, and the review concludes by posing some questions which one might reasonably expect to find answered in plausible modelling studies of the masticatory apparatus.

Predicting muscle activation patterns from motion and anatomy: modelling the skull of Sphenodon (Diapsida: Rhynchocephalia)

The relationship between skull shape and the forces generated during feeding is currently under widespread scrutiny and increasingly involves the use of computer simulations such as finite element analysis. The computer models used to represent skulls are often based on computed tomography data and thus are structurally accurate; however, correctly representing muscular loading during food reduction remains a major problem. Here, we present a novel approach for predicting the forces and activation patterns of muscles and muscle groups based on their known anatomical orientation (line of action). The work was carried out for the lizard-like reptile Sphenodon (Rhynchocephalia) using a sophisticated computer-based model and multi-body dynamics analysis. The model suggests that specific muscle groups control specific motions, and that during certain times in the bite cycle some muscles are highly active whereas others are inactive. The predictions of muscle activity closely correspond to data previously recorded from live Sphenodon using electromyography. Apparent exceptions can be explained by variations in food resistance, food size, food position and lower jaw motions. This approach shows considerable promise in advancing detailed functional models of food acquisition and reduction, and for use in other musculoskeletal systems where no experimental determination of muscle activity is possible, such as in rare, endangered or extinct species.

Biomechanical assessment of evolutionary changes in the lepidosaurian skull

The lepidosaurian skull has long been of interest to functional morphologists and evolutionary biologists. Patterns of bone loss and gain, particularly in relation to bars and fenestrae, have led to a variety of hypotheses concerning skull use and kinesis. Of these, one of the most enduring relates to the absence of the lower temporal bar in squamates and the acquisition of streptostyly. We performed a series of computer modeling studies on the skull of Uromastyx hardwickii, an akinetic herbivorous lizard. Multibody dynamic analysis (MDA) was conducted to predict the forces acting on the skull, and the results were transferred to a finite element analysis (FEA) to estimate the pattern of stress distribution. In the FEA, we applied the MDA result to a series of models based on the Uromastyx skull to represent different skull configurations within past and present members of the Lepidosauria. In this comparative study, we found that streptostyly can reduce the joint forces acting on the skull, but loss of the bony attachment between the quadrate and pterygoid decreases skull robusticity. Development of a lower temporal bar apparently provided additional support for an immobile quadrate that could become highly stressed during forceful biting.