On the inference of function from structure using biomechanical modelling and simulation of
extinct organisms
Electronic Supplementary Material (ESM)
John R. Hutchinson
Structure and Motion Laboratory, Department of Veterinary Basic Sciences, The Royal Veterinary
College, Hawkshead Lane, Hatfield AL9 7TA, UK
jrhutch@rvc.ac.uk
Models and Simulations: Basic Definitions
I follow general practice [1,2] in defining a “model” (i.e., a theoretical construct) as an abstraction of
reality that may take any form, ranging from a mathematical equation to a static diagram [e.g.,2-5]
or even an anatomically realistic and complex 3D representation [e.g., 6-10]. A common feature of
biomechanical models is that they use some input data to produce output predictions/estimates
that are quite straightforward and can be replicated by following the same steps. A “simulation,”
then, uses a model to answer a more open-ended question such as run as quickly as possible (11,12),
generally employing optimization criteria [13] to filter solutions toward one or more final result(s).
Because the phenomenon being simulated may be extremely complex, simulation results are not
easily predicted a priori and may be quite different (e.g., finding solutions at different local optima)
when processed using slightly different techniques [11,12].
Static vs. dynamic and inverse vs. forward dynamic models
When embarking on a study using computer modelling and simulation one must ask why it is
necessary, and then what types of methods are most appropriate to the question being asked.
Static (or quasi-static; modelling a dynamic motion as a static one using inverse dynamics) models
ignore any potential history-dependent effects, such as the prior lengthening or need for future
shortening of a muscle at any point in time. They thus treat a functional situation as a motionless
snapshot frozen in time, even in some simpler models requiring static equilibrium (all moments and
forces must balance to sum as zero). Dynamic simulations (e.g., forward dynamics; “multi-body
dynamic models” [e.g.,14,15]) consider not only continuous periods of time but also the changing
nature of musculoskeletal mechanics due to events that did/must take place, such as the storage
and subsequent release of elastic strain energy. Static approaches have been extensively used for
many decades in comparative biomechanics [16,17]. More dynamic approaches are a recent
phenomenon because they are limited by computer technology, especially processing demands.
A key question is then, how different are inverse/static and forward/dynamic models of
musculoskeletal function? The answer to this will vary with the behaviour being modelled, and sadly
there are too few comparative studies of these methods being applied to the same system. One
such study, focused on human walking [18], showed these approaches actually gave comparable
results. Furthermore inverse dynamic estimates of musculoskeletal forces, stresses and strains have
frequently been compared with direct experimental measurements in vivo, with generally
encouraging matches between theoretical and empirical values [19-22]. Granted, some ideal
examples of the unpredictability of function from structure [23] are from quite rapid movements in
small animals for which small changes in the timing of muscle activity are still relatively sizeable
proportions of the function’s duration and hence quite influential. Contrastingly, more quasi-static,
slower functions might be expected to be more predictable. Particularly for behaviours that involve
near-static situations, such as midstance of locomotion or static biting, one would expect this match
to exist, but likewise the accuracy of static approaches should decrease in much more dynamic
motions such as early/late in the stance phase of locomotion or very rapid “snapping” bites.
Unfortunately, again there are too few studies like this to assess this prediction. Similarly, other
studies have shown that 2D and 3D approaches may give relatively similar results at least for some
joints [24].
Finite Element Analysis: Limitations
The limits of determining structure-function relationships in extinct organisms are nicely illustrated
by the use of finite element analysis (FEA) of bone stresses and strains. This approach lies at the
other end of the spectrum of simplicity vs. complexity from a popular alternative, beam theory or
“strength indicators” [e.g., 3]. Both methods may seem elementary to apply to fossil taxa because
they focus on bone mechanics and skeletal material is typically the best preserved fossil evidence.
Beam theory may seem too simple in its typical focus on bone loads generated by external forces
(rather than by muscles) and difficulty in quantifying localized stresses or strains for complex 3D
structures. But where do the limits of FEA lie? For extinct taxa FEA performs poorly at estimating
specific values of output results [6,25,26]; therefore although FEA is a quantitative method it is best
suited for qualitative comparisons between taxa or alternative functional hypotheses. Thus
calculations of bone failure, including safety factors, or comparisons of specific quantitative results
probably are beyond the resolution of FEA of extinct organisms. This argument becomes particularly
persuasive when one considers that bones are primarily stressed by soft tissue loads and hence FEA
must somehow incorporate those structures and their mechanics, such as fusing FEA and dynamic
modelling [15]. The problem of missing soft tissues in fossils cannot at present be sidestepped even
though FEA focuses on skeletal mechanics. Furthermore, those mechanics have their own
ambiguities. A recent methodological study [27] found that assumptions about bone material
properties alone (heterogeneous vs. homogenous) for an elephant femur typically influenced
regional stresses by ~60%. Considering that material properties are unknown for fossils and vary
throughout a bone in extant taxa, the high sensitivity of FEA to material properties poses serious
problems for the reliability of FEA, especially in providing specific quantitative estimates for extinct
organisms. However, wide recognition of this limitation could inspire considerable progress in
advancing the quality of methods and evidence used in FEA, so the future is not necessarily bleak.
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