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A review of Multibody Dynamic versus Finite Element Analyses applied in palaeoanthropology: what can we expect for the study of hominin postcranial remains?

Revue des Analyses Dynamiques Multicorps versus Eléments Finis appliquées en paléoanthropologie : que pouvons-nous en attendre pour l’étude des restes postcrâniens d’hominines ?
Alicia Blasi-Toccacceli, Guillaume Daver et Mathieu Domalain

Résumés

Les méthodes d’Analyse "Dynamique Multicorps" (MDA) et en "Eléments Finis" (FEA) sont utilisées pour étudier les sollicitations biomécaniques associées à un mouvement. En paléontologie, ces approches de simulation numérique "redonnent vie" aux espèces éteintes, et notamment les hominines. Ce travail propose une analyse de la littérature sur l’utilisation des méthodes MDA et FEA en paléoanthropologie postcrânienne. Les concepts de modélisation et de simulation appliqués au champ de la biomécanique sont tout d’abord introduits. Les bases théoriques et champs applicatifs des méthodes MDA et FEA sont présentés. Une synthèse de la littérature met ensuite en lumière les questionnements paléoanthropologiques, les variables manipulées, les conclusions tirées ainsi que les limites méthodologiques à retenir. De manière plus générale, ce travail vise à synthétiser un cadre conceptuel et quelques recommandations pour l’utilisation de telles approches numériques dans l’étude des relations forme- fonction dans un contexte évolutif.

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Notes de la rédaction

Cette note fait suite à une communication présentée lors des 1846es journées de la Société d’Anthropologie de Paris dans le cadre de la session "Humanité(s) : définition(s), diversités et limites"

Texte intégral

Introduction

1In palaeontology, the bulk of inferences bearing on behaviour, ecology and phylogeny are based on relationships between form and function (Witmer, 1995; Ward, 2002; Rayfield, 2019). Generally, these relationships are investigated by applying three distinct approaches: comparative anatomy, experiments and numerical simulations (Hutchinson and Gatesy, 2006; Benton, 2010). The comparative anatomy approach aims to describe and quantify morphological characters from a selection of extant and extinct taxa in order to assess their potential functions. Knowledge of the behavioural repertoire of extant species provides a baseline for making behavioural inferences from fossil specimens. However, no mechanical evidence is given on putative relationships, which sometimes leads to confusion between phylogenetic and functional signals (Lauder, 1995; Witmer, 1995; Ward, 2002). Conversely, experiments (in-vivo, ex-vivo) with extant analogues give insights into the mechanical processes that link morphologies to functions, but may require challenging protocols (e.g. ethics, difficulty of access to biological variables, numerous variables that make it hard to control the experimental framework) (Lauder, 1995; Shi et al., 2012). In addition, given that fossils generally display unique character combinations with no extant equivalent, the choice of analogues is potentially open to criticism (Susman, 1998; Hutchinson and Gatesy, 2006). Here, we focus on numerical simulations that complement both approaches by giving access to biological variables that are not experimentally accessible and by taking the particular morphology of fossils into account. In addition, "what-if" scenarios, meaning assessments of different hypothetical scenarios predicting an outcome, can put fossil bones in their anatomical context, including soft tissues and range of joint motion, which are critical to understanding form-function relationships (Preuschoft and Witzel, 2004; Hutchinson and Gatesy, 2006; Brassey et al., 2017; Bishop et al., 2021).

2The simulation approaches most frequently used in palaeontology, Multibody Dynamics Analysis (MDA) and Finite Element Analysis (FEA), arose from the field of engineering (Richmond et al., 2005; Ross, 2005; Bright, 2014; Brassey et al., 2017; Rayfield, 2019; Lautenschlager, 2020). MDA was initially used to address questions of hominin bipedalism (Crompton et al., 1998; Wang et al., 2004) and dinosaur locomotion (Hutchinson, 2004; Hutchinson et al., 2005; Bates et al., 2010). FEA has brought insights into hominin craniodental debates (Spears and Crompton, 1994; Strait et al., 2009) and the morphology of the face in extant H. sapiens (Ichim et al., 2006a ; 2006b; Gröning et al., 2011; Wroe et al., 2018).

3Previous reviews of FEA/MDA applied to palaeontological questions have addressed simulation principles (Benton, 2010; Hutchinson, 2012) and the theory behind the method (FEA: Richmond et al., 2005; Ross, 2005; Rayfield, 2019/MDA: Lautenschlager, 2020; Bishop et al., 2021) with sometimes an emphasis on sensitivity and validation (Rayfield, 2007; Panagiotopoulou, 2009; Bright, 2014; Brassey et al., 2017). This article sheds light on the use of MDA and FEA in postcranial palaeoanthropology through (1) a theoretical summary of MDA and FEA methods and (2) a review of studies using MDA and FEA in postcranial palaeoanthropology. More specifically, we aim to provide a mean to help determine whether, and which, numerical simulation may be relevant to address a given question, and what are the main steps of the process.

Biomechanical modelling and simulation

4The essence of modelling is the simplification of a complex question through a defined framework, which ensures that the model setup is valid in a given limited and controlled environment. Simulation then consists of executing the ensuing workflow. The modelling process may be divided into (1) understanding the initial question, i.e. defining research hypotheses and objectives, (2) identifying outputs, i.e. results of the simulation, (3) identifying inputs, i.e. variables of the experimental framework, (4) determining relationships between model components and assumptions and simplification compatible with the initial question, (5) creating the model and testing its validity (Robinson, 2008). Each of these steps is detailed below:

5- Outputs are the mechanical performance indicators that enable testing of the initial hypotheses at best. In biomechanics, mechanical performance is assessed via minimizing biological functions (e.g. metabolic energy, muscle forces, stress, strain) or maximizing other parameters, such as torque generation capacities or mechanical strength (figure 1). In other words, the mechanical performance of two structures can be compared in terms of which one is the most efficient or, for example, better distributes stress to avoid failure. The choice of the output determines whether the simulation process is appropriate, and which type of simulation should be used;

6- Inputs are the variables of the experimental framework. In biomechanics, inputs represent all variables that constitute the model (geometrical data, mass data, material properties), boundary conditions and the loading scenario or the motion data (figure 1). Inputs can be changeable (independent variables) or fixed (fixed coefficients that will remain the same in all the simulations);

7- Assumptions and simplifications define the model’s complexity. The greater the complexity, the better the representation of reality. However, beyond a certain level, increasing complexity will no longer increase either precision (repeatability) or accuracy (exactness relative to real value) and results in time wasted on model design and calculation (Robinson, 2008; Sargent, 2010; Hutchinson, 2012). In biomechanics, model complexity may be dictated by the need for accurate representation of morphology. As an example, Brassey et al. (2013) raised the question of the utility of considering the morphology of long bones instead of modelling them as beams;

8- Testing of model validity (distance between experimental values and model outputs) investigates the validity of the model outputs relative to reality while also testing its sensitivity (how much the analysis outputs depend on the fixed input value) and identifies the critical inputs that deserve to be quantified accurately (Hutchinson, 2012). These two approaches are complementary, but the validation step is not always achievable in palaeontology because of the lack of data (Sellers and Crompton, 2004). These missing fixed inputs therefore have to be estimated (e.g. with the extant phylogenetic bracket concept, which is based on biological homologies between the two closest extant outgroups to provide a bounded estimation of the missing data; Witmer, 1995); the sensitivity of the model outputs to these fixed inputs therefore needs to be tested (see Hicks et al., 2015; Rayfield, 2019 for extensive recommendations on how to conduct sensitivity and validation studies). Testing the model may lead to readjusting the model parameters and inputs (figure 1).

Figure 1

Figure 1

Schematic view of the FEA and MDA simulation process. The modelling process consists of defining research hypotheses and objectives, identifying outputs/inputs, determining relationships between elements and the assumptions/simplifications compatible with research hypotheses, and creating a model from the original fossil (Robinson, 2008). The digitization and numerical restoration of a fossil process are detailed by Sutton et al. (2016) and are beyond the scope of this article. Once the model is created, inputs must be applied and the analysis can be run (FEA or MDA). The simulation process then computes the outputs and the validation and sensitivity analysis must be done to validate the model. If the model shows poor congruence with the experimental data or is highly sensitive to the input data, then it needs to be adjusted |
Schéma des méthodes de simulation FEA et MDA. La modélisation consiste en la définition des hypothèses de recherche et des objectifs, en l’identification des paramètres de sortie et d’entrée, en la détermination des relations entre les éléments et des simplifications compatibles avec les hypothèses de recherche et la création du modèle à partir du fossile d’origine (Robinson, 2008). Les procédés de digitalisation et de restauration numérique des fossiles sont détaillés par Sutton et al. (2016) et dépassent le cadre de cet article. Une fois le modèle crée, les paramètres d’entrée doivent être appliqués et l’analyse peut être lancée (FEA ou MDA). Les paramètres de sortie sont alors calculés et les analyses de validation et de sensibilité doivent être faites pour valider le modèle. Si le modèle montre une congruence faible avec les données expérimentales ou s’il est trop sensible aux paramètres d’entrée, alors le modèle doit être ajusté

Multibody Dynamics Analysis (MDA)

9MDA is an engineering method used for the mechanical analysis of structures, including vertebrate skeletons. This method addresses animal motion and its biomechanical performance. Biological structures are modelled as kinematic chains, composed of non-deformable solids (bones) connected by joints (articulations). The external geometry (bone length, enthesis location), inertial parameters (mass, inertia, centre of gravity), joints (centre of rotation, range of motion) and muscle parameters (length, isometric maximal force, physiological cross-sectional area, etc.) contribute to the model. Motion data (from an in-vivo or simulated kinematics record or from muscle activation profiles) or a static scenario (substrate reaction force) may load the model to simulate a behaviour. Thus, bony elements experience loadings (gravity, substrate reaction forces, joint reaction forces, muscle forces, etc.) and musculotendon units that span articulations generate forces and move the structure (Brassey et al., 2017; Lautenschlager, 2020; Bishop et al., 2021; Sylvester et al., 2021) (figure 1). Outputs may be geometrical variables, such as muscle moment arm in relation to a joint, or dynamic variables such as joint moments, muscle moments, and muscle forces. Outputs are calculated based on Newtonian mechanics, with bones considered as non-deformable and musculotendon units modelled as viscoelastic and contractile components. Some analyses include an optimization process based on a physiological criterion in order to solve the indeterminate problem due to muscle redundancy, i.e. when a system of equations is unsolvable due to several possible combinations of muscle forces produced by muscles around a single joint resulting in the same joint moment (Prilutsky and Zatsiorsky, 2010). Despite these assumptions, the approach showed its relevance for the study of human biomechanics (Thelen et al., 2003; Prilutsky and Zatsiorsky, 2010; Rajagopal et al., 2016; Seth et al., 2019).

Finite Element Analysis (FEA)

10FEA is also a generalist engineering method used to simulate the behaviour of mechanical structures and fluids. FEA does not assume rigid bodies but includes the deformable aspect of structures, including bones and teeth, to determine stress or strain distribution within a structure with known internal material properties under a certain load. Material constitutive laws and elasticity equations are known for simple geometries (e.g. beam theory) but biological structures are often complex and FEA is better suited than beam theory to account for their external and internal morphologies (Brassey et al., 2013). FEA discretizes the structure into a finite number of simple volume elements for which equations are known. Strains and stresses are computed at each node and displacement and deformation are discretized in the overall structure (Ross, 2005; Rayfield, 2007; Brassey et al., 2013; Bright, 2014). The finite element model considers external geometry (external surface), internal geometry (cancellous, cortical bone), and material properties (Young’s modulus, Poisson’s ratio, homo- or heterogeneity, iso- or orthotropy). As inputs, a loading scenario is applied that represents all the forces exerted on the bone during a typical motion (reaction force applied to the structure, forces estimated with the help of physiological cross-sectional area of each muscle, electromyography or MDA, ligament force) (figure 1). FEA approximates the geometry by discretizing it into a finite number of elements, and the precision of results can be verified with a convergence test (Bright, 2014). The main limitations of this approach mentioned in the palaeontological literature are (1) the loading scenario representing a particular motion is often oversimplified (Shefelbine et al., 2002; Macho et al., 2010; Gröning et al., 2011; Bucchi et al., 2020; Stamos and Berthaume, 2021); and (2) material properties are assumed to be the same for all species studied (for interspecies comparisons) (Püschel et al., 2020; Stamos and Berthaume, 2021).

Comparison between MDA and FEA

11Because MDA and FEA require different inputs and compute different outputs, their aims and application are different. With regard to the fossil record, MDA is particularly relevant for considering variations in proportions, including relative bone length, enthesis location and range of joint motion, in order to compare gross external morphology and kinematic chain variations. In other words, the bone shape is not as important as their general dimensions that affect joints and kinematic chains (Wang et al., 2004). FEA studies microvariations in morphology because the stress and strain results depend on the external and internal morphologies of the fossil. In other words, the exact shape of the bone is critical here.

12Both MDA and FEA can generate a chimeric model derived from an existing one to test the significance of morphological characters in fossil species. For example, Richmond (2007) used FEA to study the role of phalangeal curvature in arboreal locomotion: they compared a naturally curved gibbon’s phalanx with an artificially straight gibbon phalanx morphology in stress distribution and resistance to failure.

13The two methods are complementary. MDA uses rigid solids to represent the appendicular skeleton, while adding a criterion based on FEA of hyperelastic structures (such as ligaments) that estimates their deformation, internal stress and strength to failure, helping to resolve the effect of this deformation on the overall motion of the rigid skeleton (Halloran et al., 2010). A difficulty in FEA is the estimation of the loading scenario i.e. stresses generated by muscles, ligaments, joints and external forces such as body weight. MDA can provide a detailed estimation of muscle and joint reaction forces given the external loading (Marcé-Nogué et al., 2015; Dutel et al., 2021; Watson et al., 2021).

Application to hominin postcranial remains

14In palaeoanthropology, most simulations have addressed craniodental functions such as feeding (Spears and Macho, 1998; Preuschoft and Witzel, 2004; Strait et al., 2009; 2010; Berthaume et al., 2010; Macho et al., 2010; DeSantis et al., 2020; Marcé-Nogué et al., 2020; Cook et al., 2021;) or language (Ichim et al., 2006a; 2007; D’Anastasio et al., 2013). Appendix 1 focuses on postcranial studies that address the origin of bipedalism, the degree of arboreality of early hominins and their ancestors, the obstetrical dilemma and stone tool use and making. Bipedalism has drawn the most attention. In particular, while morphological comparisons of the Australopithecus afarensis postcranial skeleton could not agree on the type of bipedalism performed by this species, "bent-hip, bent-knee" or "erect" human-like gait, simulation studies have given support to the "erect" gait hypothesis: A. afarensis did not display anatomical incapacities (Kramer, 1999; Kramer and Eck, 2000), did not have a high energy cost of locomotion (Wang et al., 2004) and could perform the "erect" gait more efficiently than the "bent-hip, bent-knee" gait (Crompton et al., 1998).

15Appendix 1 shows that despite increasing model complexity with the evolution of computing power, MDA outputs have tended to become simpler. The earliest studies using MDA, in bipedalism especially, computed energy cost (Kramer, 1999; Sellers et al., 2003; Nagano et al., 2005), whereas some recent studies have relied on simpler and more controllable outputs such as muscle moment arm, muscle forces or muscle moment capacities (Domalain et al., 2017; Bardo et al., 2018; Karakostis et al., 2021). Extensive research on dinosaur locomotion has shown that although the muscle moment arm provides the first interpretation of muscle effectiveness (Hutchinson et al., 2005; Molnar et al., 2021), it is not necessarily optimized by the musculoskeletal system: a muscle may be at its optimal length for force production with a non-optimal muscle moment arm (Hutchinson et al., 2015). Therefore, dynamic factors such as muscle forces are deemed to be more appropriate for locomotor optimization (Hutchinson et al., 2015).

16The main limitation of these studies is that both MDA and FEA need information on soft tissues as input data, and this is unavailable in the fossil record. Some general concepts such as the extant phylogenetic bracket (Witmer, 1995) may be applied to overcome this limitation. Rayfield (2019) provides advice for performing sensitivity analyses. One possibility is to limit inputs by using a range of variables taken from extant species (phylogenetically close to the fossil specimen) that represent plausible scenarios, so that outputs are within the range of plausible results. As an example, Domalain et al. (2017) ran simulations of an australopithecine’s hand alternatively with human and chimpanzee muscle parameters and demonstrated that their model outputs were not sensitive to muscle parameters, so that either chimpanzee or human muscle values could be used to draw the same conclusions.

17The FEA studies listed in Appendix 1 were all performed with a static loading scenario. Although dynamic loading helps to make a better assessment of strain and stress magnitude distribution in the structure considered (Kayabaşı et al., 2006; Geramizadeh et al., 2016), FEA studies rarely perform dynamic analysis except for crash testing and modal analysis in bone fracture prediction (Gupta and Tse, 2013), mainly because of the considerable increase in complexity of the resulting equations. When applied to palaeoanthropology, it could be useful to take a dynamic loading scenario into consideration to better represent a behaviour. However, the absolute magnitude of stress and strain are often mis-estimated due to material properties or internal geometry issues, so that adding dynamic loading may not improve the accuracy.

18Palaeoanthropology would benefit from methodological advances in other fields such as human sport and medicine. In MDA, for example, some advances have been made in muscle force estimation by coupling in-vivo electromyographic data with the resolution of muscle redundancy equations (Vigouroux et al., 2007; Assila et al., 2020; Sarshari et al., 2020) or in joint stability compliance (Dickerson et al., 2007; Blache et al., 2017a; 2017b Akhavanfar et al., 2019). Both aspects are crucial for an accurate solution of muscle redundancy issues and to compute muscle forces in humans, and, therefore, by extension, to apply it to the hominin fossil record (Blasi-Toccacceli et al., 2020). As another example, FEA may complement bone functional remodelling laws, since bone morphological adaptation occurs in response to mechanical loading (Ruff et al., 2006). FEA can predict the strain experienced by the bone before computing bone morphological modifications (Hambli, 2014). The overall approach is quite similar to the theory behind studies of the diaphyseal cross-section as bones change under the influence of locomotor constraints (Carlson et al., 2006; Sládek et al., 2016; Ruff et al., 2020). Here, FEA and functional bone remodelling laws simulate how the bone changes under constraint, with a possible application to the hominin fossil record (Shefelbine et al., 2002).

Conclusion

19To sum up, although MDA and FEA are used to investigate different types of questions, i.e. MDA to explore the influence of variations in proportions among fossils and FEA to test the mechanical strength of their morphology under loads, both encompass the use of "what-if" scenarios and are complementary to some extent. We have summarised some of the general advice and good practices highlighted in the literature. The “simpler is better” principle should be kept in mind, but the challenge is to find the right balance between the model’s complexity/precision/accuracy and its simplicity. Sensitivity tests are also widely recommended, as well as validation whenever possible. Finally, this review highlights a lack of FEA application in hominin postcranial morphology. Although they are time-consuming, these approaches allow evolutionary issues to be investigated directly and in a different way to the usual practice in morpho-functional analyses. With MDA and FEA, the role of morphological features of primary evolutionary interest can be tested, validated and then prioritized in their functional context. These perspectives are promising because the MDA and FEA approaches could lead to the identification of suites of morphological characters that are possibly functionally related, which represents a major issue in palaeoanthropology (and more generally in palaeontology) in our understanding of form-function relationships.

Acknowledgments: We are grateful to the editors who invited us to take part of the Special Issue "Humankind(s) definitions, diversity and limits" and the editor-in-chief S. Kacki. We thank also the two anonymous reviewers and the translator I. Bossanyi whose helpful comments improved this manuscript. This work was supported by La Région Nouvelle Aquitaine ("LocHoSiM: Locomotion of fossil hominines using musculoskeletal simulation of the forelimbs", grant no. AAPR2020-2020-8624210).

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Table des illustrations

Titre Figure 1
Légende Schematic view of the FEA and MDA simulation process. The modelling process consists of defining research hypotheses and objectives, identifying outputs/inputs, determining relationships between elements and the assumptions/simplifications compatible with research hypotheses, and creating a model from the original fossil (Robinson, 2008). The digitization and numerical restoration of a fossil process are detailed by Sutton et al. (2016) and are beyond the scope of this article. Once the model is created, inputs must be applied and the analysis can be run (FEA or MDA). The simulation process then computes the outputs and the validation and sensitivity analysis must be done to validate the model. If the model shows poor congruence with the experimental data or is highly sensitive to the input data, then it needs to be adjusted |Schéma des méthodes de simulation FEA et MDA. La modélisation consiste en la définition des hypothèses de recherche et des objectifs, en l’identification des paramètres de sortie et d’entrée, en la détermination des relations entre les éléments et des simplifications compatibles avec les hypothèses de recherche et la création du modèle à partir du fossile d’origine (Robinson, 2008). Les procédés de digitalisation et de restauration numérique des fossiles sont détaillés par Sutton et al. (2016) et dépassent le cadre de cet article. Une fois le modèle crée, les paramètres d’entrée doivent être appliqués et l’analyse peut être lancée (FEA ou MDA). Les paramètres de sortie sont alors calculés et les analyses de validation et de sensibilité doivent être faites pour valider le modèle. Si le modèle montre une congruence faible avec les données expérimentales ou s’il est trop sensible aux paramètres d’entrée, alors le modèle doit être ajusté
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Alicia Blasi-Toccacceli, Guillaume Daver et Mathieu Domalain, « A review of Multibody Dynamic versus Finite Element Analyses applied in palaeoanthropology: what can we expect for the study of hominin postcranial remains? »Bulletins et mémoires de la Société d’Anthropologie de Paris [En ligne], 34 (2) | 2022, mis en ligne le 31 juillet 2022, consulté le 01 octobre 2022. URL : http://journals.openedition.org/bmsap/9914 ; DOI : https://doi.org/10.4000/bmsap.9914

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Alicia Blasi-Toccacceli

PALEVOPRIM, CNRS – Université de Poitiers, UMR 7262, Poitiers, France ; Institut Pprime, CNRS – Université de Poitiers – ENSMA, UPR 3346, Poitiers, France ; alicia.blasi.toccacceli@univ-poitiers.fr

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Guillaume Daver

PALEVOPRIM, CNRS – Université de Poitiers, UMR 7262, Poitiers, France

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Mathieu Domalain

Institut Pprime, CNRS – Université de Poitiers – ENSMA, UPR 3346, Poitiers, France

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