On the inference of function from structure using biomechanical

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recognized. How can such reconstructions be done
scientifically, given that the organisms and most structural, physiological and behavioural data are missing?
Computer modelling and simulation can address this
problem with unique clarity. To explain this process
here, I use examples from my and others’ research on
locomotion in dinosaurs such as tyrannosaurs (but
similar methods have been applied to many extinct
organisms). I concentrate on methodological and philosophical issues because other issues are dealt with in
other reviews [2,3]. Some basic definitions of methodological approaches are in the electronic
supplementary material, with special consideration of
inverse versus forward dynamic models as well as
finite-element analysis.
Regardless of the modelling approach used, models
can be essential simply because musculoskeletal function is typically complex. Indeed, Lauder [1] might
have under-emphasized this complexity, because the
complex dynamics of biomechanical systems are
involved in a feedback loop with motor control and
musculoskeletal structure. Segment inertial and gravitational properties as well as interactions between linked
segments, let alone environmental interactions such as
limb–substrate or fluid dynamics [4], can cause muscles
with similar structure or motor control to have different
functions. Indeed, a compelling review [5] explained
how dynamic coupling can cause muscles to influence
the motions of joints they do not cross. Thus, even
experimental studies or simple models of musculoskeletal systems, particularly those dichotomizing muscles
into uni- versus bi-articular groups, may reach conclusions that more dynamic simulations would show
to be mechanically inaccurate or even unreliable. One
might then ask, how reliable is not doing computational
analysis of musculoskeletal function? This is especially a
tricky question for palaeontology, where most of these
complex strata of data are missing.
However, just because models capture structural or
mechanical complexity does not mean they are accurate
or reliable. Care must be taken to avoid a dangerous
attitude that, because the theoretical basis of a model
may seem sound and realistic, modelling may be accurate or at least reliable. The danger lies in the
assumption that we understand reality enough to
model its complexity, including all the critical theoretical ingredients with no missing interactions between
components that could cause surprising errors. For
example, experimental and modelling studies of
locomotor mechanics have provided a basic understanding of walking and running [6], but there is very
little known about many of the detailed principles of
these gaits (e.g. Why gait transitions occur? Why different footfall patterns are used? or How important passive
forces are?). As a result, a wide diversity of often contradictory theoretical models now exist [7]. Hence models
must be carefully matched to the current state of biomechanical understanding. Where omissions are made,
their implications for the results must be carefully and
explicitly gauged. Here lies a trade-off, and investigator
judgement call, between model reductionism and realism. Models must be complex enough but not too
complex, yet where does one draw the line?
Two critical tools at the disposal of those using
models to relate structure to function are ‘validation’
Biol. Lett. (2012) 8, 115–118
doi:10.1098/rsbl.2011.0399
Published online 10 June 2011
Palaeontology
Opinion piece
On the inference of
function from structure
using biomechanical
modelling and simulation
of extinct organisms
Biomechanical modelling and simulation techniques offer some hope for unravelling the
complex inter-relationships of structure and
function perhaps even for extinct organisms, but
have their limitations owing to this complexity
and the many unknown parameters for fossil
taxa. Validation and sensitivity analysis are two
indispensable approaches for quantifying the accuracy and reliability of such models or simulations.
But there are other subtleties in biomechanical
modelling that include investigator judgements
about the level of simplicity versus complexity in
model design or how uncertainty and subjectivity
are dealt with. Furthermore, investigator attitudes
toward models encompass a broad spectrum
between extreme credulity and nihilism, influencing how modelling is conducted and perceived.
Fundamentally, more data and more testing of
methodology are required for the field to mature
and build confidence in its inferences.
Keywords: musculoskeletal system; dinosaur;
computer modelling; simulation; palaeontology;
biomechanics
In an influential review, Lauder [1] outlined the hierarchical levels within organisms that obfuscate the
relationship between structure and function. Neural
control of muscles was adduced as one critical level
that could give even anatomically similar muscles
quite different functions. Lauder then cautioned that,
while very general and very specific predictions about
function using the structure of extinct taxa as primary evidence might sometimes be reliable, the more common
predictions of intermediate specificity were the most
problematic. His major points include that a structure–
function relationship is a hypothesis that is better tested
than presumed correct and that the inference of such
relationships is more challenging for extinct taxa.
Here, I focus on one approach to testing/inferring
the relationship between structure and function that
was nascent earlier [1] but has since seen a burst of
innovation enabled by improvements in computer
technology. Biomechanical modelling and simulation
are useful for inferring function from structure in
extinct animals, although their limitations must be
Electronic supplementary material is available at http://dx.doi.org/
10.1098/rsbl.2011.0399 or via http://rsbl.royalsocietypublishing.org.
One contribution of 12 to a Special Feature on ‘Models in palaeontology’.
Received 11 April 2011
Accepted 19 May 2011
115
This journal is q 2011 The Royal Society
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116 J. R. Hutchinson
Opinion piece. Biomechanical models in palaeontology
and ‘sensitivity analysis’. A model’s ‘validity’, or match
to some form of empirical data (the higher the quality
of those data, the better), must be checked. For
example, computational models used to estimate
body mass for extinct animals have been compared
with estimates [8,9] and direct specimen-specific
measurements [10] for extant animals. Those validation tests suggest approximately 50 per cent errors.
Other studies [11,12] applied static modelling techniques to extant taxa to test if animals known to be
proficient or poor bipedal runners would be predicted
as such and found good qualitative support. However,
it is a mistake to expect that the results of a validation
test will match reality extremely well, because models
only approximate reality, which is noisy, resulting in
non-zero errors. Conversely, to approach a validation
test with the bias that it cannot fail or that the purpose
of validation is to prove a method is correct (to what
standard of accuracy?) is just as naive. A healthier
approach to both of these extremes is that the purpose
of validation is to quantify how far an estimated value
may deviate from empirical measurements. Or in
other words, to find just how wrong the results of a
model might be, given that all models are wrong to
some degree. Thus, the term ‘validation’ is somewhat
misleading [13]—the goal is to quantify just how
much a model fails to replicate reality.
One reaction to this responsibility to validate models
might be that palaeontologists are often not equipped in
terms of tools or expertise to conduct validation tests,
especially experiments with live animals. Is this an excuse
from doing validation? This question is the cause for introspection—Are modelling approaches done for the right
reasons if their quality is not assessed? How can those
not doing validation studies determine if their models
had some critical flaws? I contend that modelling alone is
not enough. In structure–function analyses, one cannot
dwell in the theoretical realm alone [1]. Performing validation is a win–win situation, because the process helps
researchers contribute data, understand and improve
methodological limits, break out-of-disciplinary pigeonholes and potentially develop new collaborations with
those with the resources to conduct strong validation
tests. Our models cannot be more reliable than the empirical, biological understanding that supports them.
Adherence to this principle ultimately should lead to a
reduction in ambiguity in modelling and greater scientific
confidence in palaeobiology. The value of contributing
methods and evidence with more lasting influence also
should not be overlooked as a source of satisfaction—not
to mention historical responsibility.
Yet, model validation alone is not enough. The level
of error suggested by a validation test usually is the
‘best-case’ situation, in which more parameters are
known than are known for models of extinct taxa.
Because any model incorporates assumptions about
unknown parameters, those assumptions need to be
explicitly stated and their influences on model predictions need to be quantified in a sensitivity analysis [14].
This process addresses how sensitive the model’s quantitative results, and thus the study’s qualitative
conclusions, are to the input parameters and which
of those parameters are most critical to precisely quantify. In many models, this can be determined by
Biol. Lett. (2012)
varying one parameter at a time between minimal
and maximal values (e.g. crouched and columnar
limb poses) and evaluating the changes in model
output (e.g. required leg muscle mass [11,12]). This
task should be disconcerting because some subjective
decisions (ideally backed up with reference to variation
in extant taxa) are needed to circumscribe a plausible
range of values. One such judgement is whether to
be maximally inclusive (e.g. varying muscle maximal
isometric stress 100 – 1000 kN m22); potentially sacrificing plausibility and accuracy; or to favour a
best-supported ‘consensus’ value (e.g. maximal stress
of 200 – 300 kN m22 [15]). But not only does good
modelling practice require sensitivity analysis, it is
also a positive driver of later research because it identifies where future studies should focus their efforts in
trying to reduce uncertainty. Again, this is a win – win
situation.
Studies have shown the utility of palaeobiological
sensitivity analysis [11,12] in identifying how some parameters were critical for determining running potential
in large bipeds such as tyrannosaurs (figure 1). As a
result, later studies developed techniques to better estimate muscle moment arms [17], centre of mass [18]
and posture [16]. These studies also found that other
parameters such as body mass and muscle fascicle
pennation angle were relatively unimportant for those
models. Muscle fascicle length remains a vexing
unknown; the approach of estimating fascicle length
from necessary joint range of motion [19] is one promising avenue. Such critical parameters were quite
straightforward to identify in simple models [11,12].
As model complexity increases (e.g. highly dynamic
models of whole stride cycles), there is a similar increase
in unknowns, but this problem is not impossible to deal
with using broad sensitivity analyses [20].
A useful distinction in palaeobiological modelling is to
separate the issue of accuracy (how closely estimates
match reality) from reliability (how robust qualitative
conclusions are despite the unknown parameters are in
a model used to formulate those conclusions). Ideally,
validation tests quantify model accuracy through the
use of statistical tests and address the repeatability of
methods. Sensitivity analyses then can circumscribe the
more slippery nature of reliability—which is less amenable to statistical analyses for palaeontological data
because many parameters are unknowable—by bounding a range of possibility through exclusion of the
impossible or at least implausible [16]. By making this
distinction between accuracy and reliability, a tension
becomes evident, which lies between the quantitative
uncertainty that we have about palaeobiological data
and the qualitative understanding we minimally seek to
establish. One might argue that such uncertainty does
not matter much—perhaps, theoretical models are
simply phenomenological and thus do not need to be
accurate to be reliable. This argument, however, is worrisome in its lack of inquisitiveness. We simply do not
know how much uncertainty matters until we peer over
the ledge of the known and survey the landscape of the
unknown. The alternative is to blindly step across that
chasm and hope for serendipitous results.
In structure– function analyses of extinct organisms,
a course must be steered between excessive credulity
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Opinion piece. Biomechanical models in palaeontology J. R. Hutchinson
1
2
3
117
4
5
*
2.0
5
GRF (BW)
slow run
12
1.5
4
3
*
5
walk
1.0
2.1
5
2.5
2.9
hip height (m)
3.3
*
Figure 1. Tyrannosaurus right hindlimb in five poses (nos 1 –5); asterisks identify joints near their limits of muscle strength
(modified from Gatesy et al. [16]). The graph shows those five poses and the ground reaction forces (GRFs; in body weights,
BW) that limb muscles could sustain at different hip heights. Limb pose no. 5 (on right) shows three centre of mass (CoM)
positions that the foot could be placed under (shaded vertical bars). The graph also shows variation in sustainable GRFs
corresponding to the CoM positions (shaded curves). This sensitivity analysis reveals how limb pose and CoM influence
walking/running ability.
(overlooking the uncertainties in palaeontological
methods and evidence) and nihilism (retreating to
the defeatist view that the uncertainties are too
daunting to make progress). Both extremes dance precariously on a precipice of unambition and antiscience.
A major point of this review is that progress will be
most sustainable where studies are particularly explicit
when methods are difficult to reproduce objectively or
evidence is ambiguous. In modelling and simulation,
quantitative approaches maximize the benefits of explicitness. Although uncertainty and subjectivity may or
may not matter, their extent and influence can be
characterized with model validation and sensitivity
analysis. We all can do better in maximizing the accuracy and reliability of palaeobiological models and
simulations. The way forward is clear—first, contribute
more data to shore up the foundations of evidence;
second, be explicit and cautious with the tools used
to analyse that evidence, thereby improving the quality
of methods and assumptions.
This work was supported by a grant from the NERC (NE/
G00711X/1) to J.R.H. It benefited from discussions with
colleagues in the Structure and Motion Laboratory as well
as Steve Gatesy, Emily Rayfield, Bill Sellers and Karl Bates.
Julia Molnar assisted with figure 1.
John R. Hutchinson*
Structure and Motion Laboratory, Department of
Veterinary Basic Sciences, The Royal Veterinary
College, Hawkshead Lane, Hatfield AL9 7TA, UK
*[email protected]
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