REVIEW
Modern three-dimensional digital methods for studying locomotor
biomechanics in tetrapods
Oliver E. Demuth1,*, Eva Herbst2,*, Delyle T. Polet3,*, Ashleigh L. A. Wiseman4,* and John R. Hutchinson3,‡
ABSTRACT
Here, we review the modern interface of three-dimensional (3D)
empirical (e.g. motion capture) and theoretical (e.g. modelling and
simulation) approaches to the study of terrestrial locomotion using
appendages in tetrapod vertebrates. These tools span a spectrum
frommore empirical approaches such as XROMM, to potentially more
intermediate approaches such as finite element analysis, to more
theoretical approaches such as dynamicmusculoskeletal simulations
or conceptual models. Thesemethods havemuch in common beyond
the importance of 3D digital technologies, and are powerfully
synergistic when integrated, opening a wide range of hypotheses
that can be tested. We discuss the pitfalls and challenges of these 3D
methods, leading to consideration of the problems and potential in
their current and future usage. The tools (hardware and software) and
approaches (e.g. methods for using hardware and software) in the 3D
analysis of tetrapod locomotion have matured to the point where now
we can use this integration to answer questions we could never have
tackled 20 years ago, and apply insights gleaned from them to other
fields.
KEY WORDS: Animation, Bone, Dynamics, Gait, Muscle,
Optimization
Introduction
Scientists studying organismal biomechanics at the musculoskeletal
level (and neural control thereof ) today are working in a new age of
modern methods at the interface of empirical and theoretical
approaches to movement, which were unavailable or very immature
even 20 years ago. Examples of the former include XROMM (X-ray
reconstruction of moving morphology; see Glossary; Brainerd et al.,
2010) and the latter includes predictive simulation (see Glossary;
e.g. Falisse et al., 2019). These techniques have much in common,
particularly the importance of three-dimensional (3D) digital
technologies and the ability to test hypotheses about comparative
locomotor biomechanics in unprecedented spatial and temporal
resolution. By ‘digital’ here, we refer to the central importance of
software for processing those complex 3D data. Computational
power and software sophistication are central in these digital
technologies because they enable analyses that could not
realistically be done manually in a real-world setting.
Furthermore, these 3D digital methods are visual in nature,
producing valuable data on, and compelling visualisations of, 3D
locomotor dynamics. Because of this digital nature that these
approaches share, they can be powerful together, giving major
insights into the kinematics, kinetics and control of locomotion.
One might ask, why bother using 3D digital methods at all? The
simple answer is that they can more objectively handle complex
computational problems whilst visualising organismal morphology
and motion in realistic detail. That detail allows answering
biological questions about how organisms locomote (using
mechanisms that may be complex) in the real, 3D world; and how
real, 3D (often complex) morphology plays a role in locomotor
behaviours. However, 3D approaches (and more complex varieties
of 3D methods) need not be used simply because they exist. The
benefits should be weighed considering their ability to answer
research questions, and their cost in terms of time, accuracy and
other challenges (e.g. Hicks et al., 2015). As an example, if the
research question is about how a muscle functions in one plane, a
more 2D approach might provide sufficient fidelity, although this
would introduce assumptions that dynamics in other planes are of
negligible importance. Yet a 3D approach might not provide such
outstanding benefits that they justify the effort, or might be
impractical in terms of experimental data collection. The answer to
this conundrum may, admittedly, lie in researcher preferences and
traditions– not just purely practical issues – and thus there may be no
one ‘correct’ answer for a given research question.
Here, we focus on how the biomechanical application of 3D
digital approaches enables more powerful tests of how tetrapod
vertebrates use their appendages to locomote (both support and
motion) on land. We do not cover feeding, breathing, vertebral
motions, flight and swimming, etc., although these behaviours have
ideas in common with (and sources of inspiration for) our topic.
Despite its high relevance, space constraints prevent us from truly
covering the huge amount of research on human locomotion. We
also do not review biorobotics in depth. There is tremendous
relevance of research on arthropod locomotion, but again we cannot
adequately review that field here. Nor do we cover limbless
locomotion or the role of the axial column in tetrapod movement.
We briefly address sensitivity analysis (see Glossary), and
especially ‘validation’ (Hutchinson, 2012; Hicks et al., 2015) or
model evaluation. We also discuss how comparative, evolutionary
and palaeobiological studies have benefitted, and reciprocally
moved the state of the art forwards, for the methods we focus on.
We begin by considering 3D digital tools such as XROMM and
musculoskeletal modelling; such tools may be used in empirical
contexts to address questions about locomotor or appendicular
dynamics. We then explore the spectrum (explained below) of ways
that researchers in biomechanics can use digital methods to
understand locomotor mechanisms, such as finite element
1Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ,
UK. 2Palaeontological Institute and Museum, University of Zurich, 8006 Zürich,
Switzerland. 3Structure and Motion Laboratory, Department of Comparative
Biomedical Sciences, Royal Veterinary College, North Mymms, AL9 7TA, UK.
4McDonald Institute for Archaeological Research, University of Cambridge,
Cambridge, CB2 3ER, UK.
*In alphabetical order.
‡Author for correspondence ( jhutchinson@rvc.ac.uk)
O.E.D., 0000-0003-4876-1311; E.H., 0000-0003-3640-9695; D.T.P., 0000-0002-
8299-3434; A.L.A.W., 0000-0002-9575-4387; J.R.H., 0000-0002-6767-7038
This is an Open Access article distributed under the terms of the Creative Commons Attribution
License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use,
distribution and reproduction in any medium provided that the original work is properly attributed.
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© 2023. Published by The Company of Biologists Ltd | Journal of Experimental Biology (2023) 226, jeb245132. doi:10.1242/jeb.245132
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analysis (FEA; see Glossary) and dynamic simulation. This
spectrum proceeds from more empirical toward more theoretical
analyses, but all analyses here considered arguably involve a
form of ‘model’ (see Glossary) that their digital methods
visually represent. Next, we investigate how integration of digital
tools across this spectrum achieves novel, exciting understanding
of motion. Finally, we explore the pitfalls and challenges involved
in these approaches; and current frontiers at the cutting edge of
using 3D digital tools and methods in tetrapod locomotor
biomechanics. Our review demonstrates how tools have matured
to the point where now we can use them in isolation or integration to
answer fundamental questions we never could have tackled two
decades ago.
Digital tools for empirical data
Dynamic assessment of 3D skeletal motion is key to the
understanding of how animals move and how their movement
might be affected as a result of injury or disease. Such kinematic
data can be obtained with high precision using biplanar fluoroscopy
(in vivo and/or ex vivo X-ray videos) combined with 3D bone
geometry (XROMM); or motion capture. A researcher must first
capture kinematic data and collect high quality 3D data [e.g. from
computed tomography (CT) or magnetic resonance imaging (MRI)
scans] of that specimen either before or after experimentation. These
scans provide 3D bone geometries and the locations of any
implanted markers to be tracked. Fluoromicrometry offers an
analogue to XROMM for studying soft tissue kinematics, and
empirical data from anatomy and kinematics may be used for
building and analysing musculoskeletal models. Together, realistic
3D kinematic data produced by these tools also can be inputs
that improve the accuracy of more theoretical models and
simulations, or that can be used to evaluate how accuracy and any
uncertainties impact the ability to answer a research question (see
further below).
XROMM
In one version of XROMM (Fig. 1), small beads are implanted into
bones (Tashman and Anderst, 2003), which are then automatically
tracked, and the bones’ 3D positions are linked to the beads’
positions by skeletal morphological data (Brainerd et al., 2010).
Alternatively, XROMMdata can be manually or semi-automatically
rotoscoped by matching bones to their respective X-ray shadows
using a hierarchical joint marionette (‘scientific rotoscoping’;
Gatesy et al., 2010) when no or too few implanted markers are
present. In this case, the proximal or distal segments/joint positions
and orientations drive the positions and orientations of the
connected upstream or downstream segments in the hierarchy
(forward kinematics or inverse kinematics; see Glossary), and
respective segments can be further refined based on this ‘initial
guess’ (e.g. Fischer et al., 2010; Nyakatura and Demuth, 2019;
Turner et al., 2020; Turner and Gatesy, 2021; Zwafing et al., 2021;
Herbst et al., 2022a;Wiseman et al., 2022a). There is a rich literature
on the usage of 3D digital kinematic data such as XROMM for
studying terrestrial legged locomotion in tetrapods in vivo (e.g.
Nyakatura and Fischer, 2010; Baier and Gatesy, 2013; Nyakatura
et al., 2014; Bonnan et al., 2016; Heers et al., 2016; Mayerl et al.,
2016; Kambic et al., 2017; Lin et al., 2019; Turner and Gatesy,
2021), which we cannot adequately cover here. XROMMdata allow
the calculation of joint kinematics using anatomically relevant
coordinate systems which define the joint centres (e.g. Kambic
et al., 2014; Gatesy et al., 2022). We consider XROMM data as a
form of ‘model’ (but more on the empirical end of the spectrum,
away from pure theory), because they are an abstraction of the
empirical (X-ray video and 3D scan) data. The assumptions and
simplifications of XROMM include matching jointed marionettes to
biplanar 2D images, 3D bone segmentation and meshing, the
fundamental assumption that bones are perfectly rigid objects, and
Glossary
Conceptual model
An abstraction of an organism to a small number of parameters to
investigate fundamental functional principles.
Data overfitting
When a model is adjusted to match its training or validation set too
closely, and is thus unable to generalise to new datasets.
Degree(s) of freedom (DOF)
The number of parameters that can vary in a system (e.g. axes of joint
motion).
Finite element analysis (FEA)
Estimating stress or strain using smaller components subjected to
load(s).
Forward dynamic simulation
Simulation that solves a differential equation of a system’s physics over
incremental timesteps.
Forward kinematics
Using joint angles to estimate end (e.g. foot) positions.
Inverse dynamic/static simulation
Simulation that solves joint moments (and potentially muscle forces and
activations) from input kinematics and kinetics. In the static case, static
equilibrium is assumed.
Inverse kinematics
Using an endpoint of a series of segments (e.g. foot) to estimate joint
angles.
Multi-body dynamics analysis (MDA)
Rigid body mechanics.
Model
A representation of reality, used to understand reality.
Model evaluation
‘Validation’, i.e. testing how well theoretical predictions match empirical
data.
Moment arm
Leverage of a force around a rotational centre.
Musculoskeletal model
A skeletal framework around which the geometry of muscle–tendon units
is positioned.
Optimal control
A set of methods to find inputs to a time-dependent system that
minimises an objective function.
Precision
The reproducibility, or repeated variation, of a given measurement.
Predictive simulation
Estimating system outputs using only inputs of optimisation criteria and
constraints.
Robustness
How changes in model inputs influence output fidelity to empirical data.
Sensitivity analysis
Varying model/simulation input parameters or assumptions to quantify
variation of the output data.
Synergistic approach
Combination of empirical and dynamic simulation data, enhanced by the
benefits of both.
Tracking simulation
Conducting a simulation with an objective to best match input empirical
data.
Verification
Testing the mathematical validity of the design of a model or simulation.
XROMM
X-ray reconstruction of moving morphology: animation of a 3D skeletal
marionette using biplanar X-ray video data.
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REVIEW Journal of Experimental Biology (2023) 226, jeb245132. doi:10.1242/jeb.245132
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the frequent simplification of joint degrees of freedom (DOF; see
Glossary); or the number of joints connecting segments.
Motion capture
Motion capture uses special cameras to digitally capture the 3D
positions of markers on a subject. Software then reconstructs the 3D
motions of the markers and the segments they are placed on. Motion
capture may also be markerless (e.g. Mathis et al., 2018; Moore
et al., 2022). Whilst the positional marker data are truly empirical,
the resulting kinematic data for segments are a form of ‘model’, for
reasons similar to those for XROMM. However, motion
capture also involves the assumption that skin-attached markers
accurately reflect underlying skeletal 3D positions – at best only
somewhat true – and this is one reason why XROMM typically is
considered more accurate (Cerveri et al., 2005; Shultz et al., 2011;
Moore et al., 2022). However, motion capture has the benefits
that it can be readily available (and more affordable than XROMM),
is easily used in most laboratory settings, tends to provide
much larger capture volumes, and involves no radiation dosage,
along with being less invasive. For ex vivo experiments where soft
tissue is removed (e.g. Arnold et al., 2014), motion capture
avoids the issues of movement between skin/markers and skeleton.
Markers can be attached to the bones or, for small specimens, can
be attached elsewhere and the 3D data transformed to a joint-
centric motion (e.g. Stowers et al., 2017; Manafzadeh, 2020;
Herbst et al., 2022a). There have been a tremendous number of 3D
motion capture studies in the field, which we cannot do justice
to here.
Ex vivo and virtual experiments
Whilst XROMM facilitates a direct observation of the skeletal
kinematics of an animal, it is inherently limited to the capture
volume and the behaviour an animal exhibits within it (Fig. 1A).
Motion experiments involving cadavers allow measurement of the
passive 3D mobility repertoire (Arnold et al., 2014; Stowers et al.,
2017; Manafzadeh, 2020; Regnault et al., 2021). Digital animation
tools permit the manipulation of a skeleton via its joint marionette,
where the user has full control over the position and orientation of
individual body segments. This allows one to produce any behaviour
imaginable, ranging from behavioural reconstructions that are
informed by motion data (Lee et al., 2020) to excluding extreme
and unlikely (Nyakatura et al., 2019; Zwafing et al., 2021), or even
implausible and impossible bone orientations (Manafzadeh and
Padian, 2018; Fig. 1B). Such virtual experiments can, therefore,
examine functional limits constrained solely by skeletal morphology,
and generate new and novel skeletal movements that cannot be
otherwise observed. These experiments can be performed using
inverse kinematics animation tools such as inverse kinematics solvers
(e.g. Nyakatura et al., 2019; Wiseman et al., 2021; Fig. 1C) whereby
the proximal and distal limb elements are manually positioned and the
orientations of remaining elements are interpolated (Wiseman et al.,
2022a; Fig. 1D). Alternatively, forward kinematics animations can be
created to systematically sample joint poses to estimate the overall
mobility of a joint (e.g. Manafzadeh and Padian, 2018), which could
otherwise not be practically observed in vivo. Additional constraints
can be incorporated into such animations to force joint articulation
(Lee et al., 2020; Jones et al., 2021; Bishop et al., 2022).
Capturing motion
Fo
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XROMM and scientific rotoscoping Range of motion simulations
IK animation and rotoscoping
Adjustment of body posture 
and interpolation of motion
A B
C D
In
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Generating motion
Capture 
volume
Red camera 
projection
Blue camera 
projection
Long-axis
rotation
Flexion/extension Abduction/
adduction
Change in
hip height
Foot 
controller
Pelvis 
controller
Knee pole
 vector control
IK handle
Automatic adjustment 
of limb posture
Fig. 1. The capture and generation
of motion. Skeletal motion can be
captured through matching the bones
to X-ray shadows using XROMM (A)
or inverse kinematic (IK) animation
tools (C). Motion can be quantified
either through forward kinematic
simulations (B) or alternatively,
through adjustment of individual
parameters, such as hip height, new
hypothetical motion can be generated
in inverse kinematic setups (D).
Additionally, inverse kinematic tools
can be used to interpolate motion that
could not be directly captured, e.g. if
the specimen leaves the capture
volume. Nile crocodile bone models
(A–C) and X-ray data (A,C) from
Wiseman et al. (2021); Caiman
model (D) from Nyakatura and
Demuth (2019).
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Fluoromicrometry
Like XROMM, biplanar fluoroscopy with 3D anatomical data can
reveal the roles of soft tissues during locomotion (i.e.
‘fluoromicrometry’; Camp et al., 2016; see also Regnault et al.,
2021). Tsai et al. (2019) applied XROMM to walking alligators to
obtain skeletal kinematics, but then combined these 3D data with
3D morphology of articular cartilage, ligaments and other tissues
around the hip joint to estimate deformations of those tissues and
their roles in joint motion. Astley and Roberts (2012) used XROMM
to obtain skeletal kinematics and tendon strain during hopping in
frogs, revealing how the plantaris muscle–tendon unit (MTU) acted
as a catapult mechanism around the ankle joint. Similarly, Arellano
et al. (2019) integrated XROMM skeletal kinematics with changes
of M. gastrocnemius lateralis fibre length and aponeurosis length
and width in wild turkeys during landing and jumping, showing that
aponeurosis width had negative effects on aponeurosis stiffness in
the longitudinal direction, and thereby how springlike the
MTU was. Konow et al. (2020) used fluoromicrometry of the
M. gastrocnemius medialis in rats to show that, as slope and gait
change during locomotion, muscle fibre and tendon lengths and
muscle width increase, whilst muscle thickness decreases.
XROMM with soft tissue implantations has also been used in
veterinary contexts, such as the superficial digital flexor tendons in
the forelimbs of ponies, revealing up to ∼6% strain in vivo during
trotting (Wagner et al., 2021). Whereas Allen et al. (2017)
principally measured skeletal kinematics in vivo via XROMM in
the guineafowl hindlimb, they used these data to infer the
mechanical leverage of the patellar sesamoid and thereby its
influence on knee extensor muscle actions. Regnault et al. (2017)
conducted similar inquiries with the ostrich knee joint and its
‘double patella’ system ex vivo.
Musculoskeletal modelling: a more empirical basis
3D digital tools can give new understanding of musculotendinous
(henceforth ‘muscle’) function during locomotion in extant
tetrapods, typically beginning with a 3D skeletal marionette as in
XROMM, but then adding soft tissues (Fig. 2). These
musculoskeletal models (see Glossary) normally are grounded in
empirical data such as dissections or 3D imaging of soft tissue
morphology (e.g. Brown et al., 2003; Nagano et al., 2005; Zarucco
et al., 2006; Hutchinson et al., 2015; Charles et al., 2016; Regnault
and Pierce, 2018; Sullivan et al., 2019; Bishop et al., 2021b;
Wiseman et al., 2021; Collings et al., 2022), or a 3D polygonal
modelling approach (Demuth et al., 2022a; Herbst et al., 2022b),
and are sometimes placed within a phylogenetic context
(Brocklehurst et al., 2022; Löffler et al., 2022). Musculature must
be reconstructed if the research question pertains to the moment
arms (see Glossary), moment-generating capacity and/or activation
of specific muscles/muscle groups. Muscle architectural data (e.g.
fibre length, pennation angle, tendon slack length) can be obtained
from dissection data, or simplified into whole MTUs (e.g. Bishop
et al., 2021a). Such muscle data enable the creation of subject-
specific theoretical musculoskeletal models (see below).
Muscle modelling tools, often combined with data from or
estimates of joint mobility, can be used to test how muscle moment
arms depend on limb orientation ( joint angles/kinematics).
Empirical data from experimental measurements of muscle
moment arms via ‘tendon travel’ (An et al., 1984; Lieber, 1997;
Cox et al., 2019), fluoromicrometry, or other methods, including
more theoretical ones (e.g. Alexander and Dimery, 1985; Sherman
et al., 2013; Allen et al., 2017; Regnault et al., 2017; Young et al.,
2019), are highly valuable in conjunction with these studies, to
evaluate their accuracy. These studies of muscle leverage versus
limb orientation often address a fundamental principle of great
relevance to locomotor biomechanics: how closely matched are
‘optimal’ moment arms to limb orientation such as during maximal
ground reaction forces (e.g. Fujiwara, 2018)? Empirically based 3D
studies on this topic tend to have fairly mixed or nuanced results and
conclusions (Kargo and Rome, 2002; Hutchinson et al., 2015; Cox
et al., 2019; Wiseman et al., 2021). Hence, assumptions that
maximal muscle moment arms indicate ‘optimal posture’ remain on
somewhat shaky ground. However, quantification of how moment
arms and limb orientation covary is still valuable, giving insight into
muscle function.
Spectrum of digital modelling methods: toward theoretical
approaches
Empirical-to-theoretical spectrum
Fig. 3 shows how 3D modelling approaches fall on a spectrum from
empirical methods (discussed above) to purely theoretical models.
In a more empirical example, XROMM was used to reconstruct a
tinamou during running (Bishop et al., 2021b). Biplanar X-ray and
bone geometries formed the input, with 3D kinematics being an
output. A ‘synergistic’ approach (see Glossary) used by Bishop
et al. (2021b) combined XROMM data with abstracted muscle
architecture and optimisation techniques to explore joint moments,
muscle activations and fibre length changes during locomotion.
Synergistic models combine empirical and theoretical approaches to
generate rich datasets that allow researchers to infer unmeasurable
data, thereby more holistically testing hypotheses on locomotor
biomechanics or control. More theoretical models enable
researchers to (1) infer data that are difficult to collect empirically,
which (2) tests the effects of morphology on locomotor
mechanisms. Methods for such models and simulations include
musculoskeletal modelling (Fig. 2; e.g. of muscle moment arms as
per extant taxa above; but based on minimal empirical data), finite
element analysis, inverse and forward dynamic simulation, soft
body dynamics, dynamic simulation of particles, and combinations
of the above. In some cases, more theoretical, even conceptual
models (see Glossary) can be far-removed from the organism; the
tinamou might be abstracted as a simple volume connected to two-
joint legs (Fig. 3). Such a model can be explored with theoretical
techniques to test control strategies that can be compared (usually in
qualitative terms) with organismal behaviour.
Conceptual models
Conceptual – or theoretical (Fig. 3) –models, which greatly abstract
the organism to salient features of interest, are commonplace in
studies of organismal control of movement (e.g. Alexander, 1989;
Blickhan, 1989; Farley et al., 1993; Seipel et al., 2017). Most
examples are 2D; because of the mostly parasagittal nature of avian
and mammalian legged locomotion, the vast majority of conceptual
models abstract the organism to motion in the sagittal plane (with a
smaller number focusing solely on motion in other planes). The
parasagittal approximation is an obvious and natural level of
abstraction, but it has the potential to hide important dynamic effects
(e.g. Kambic et al., 2014, 2017), and cannot address several
important open questions in locomotor biomechanics – such as the
distribution of diagonal sequence gaits (Cartmill et al., 2002), or the
functional significance of pacing (Janis et al., 2002).
While comparatively rare, other conceptual studies explore the
3D nature of locomotion. Usherwood and Davies (2017) explored
work-minimising slow quadrupedal walking with a point mass 3D
model. The model had only a few input parameters: duty factor (tied
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to speed), phase and three parameters affecting ground reaction
force shape. Yet, a common pattern of increasing phase with
increased speed emerged from the model, implying the perceived
change in control reduced the cost of locomotion. Usherwood and
Smith (2018) applied a 3D geometric model to explain the phase
sequences of slow grazing gaits, with a tentative explanation for
diagonal sequence gaits in primates. They later developed a robot
based on the concept (Smith and Usherwood, 2020).
Passive dynamic conceptual models ignore muscular actuation
and instead focus on the dynamics of locomotion under the
influence of gravity. Remy et al. (2010) produced a passive dynamic
quadrupedal 3D model with 1 DOF rigid legs. Whilst they found no
difference in economy or stability between lateral and diagonal
sequence gaits, they found that increased leg spacing stabilised the
gaits and affected limb phase, at the expense of economy. Other
studies have focused on recovery from disturbance at a conceptual
level, where the spring-loaded inverted pendulum (SLIP) model is a
common conceptual basis. Whilst many 2D studies have examined
perturbation rejection in animals using SLIP models (e.g. Blum
et al., 2014), and 3D SLIP-based model control has been applied to
human running (e.g. Peuker et al., 2012) and to quadrupedal robots
(e.g. Han et al., 2022), only one study to our knowledge has
examined the stability of a 3D SLIP model in a non-human tetrapod
(a kangaroo-inspired hopper; Seipel and Holmes, 2006). The usage
of 3D SLIP models to test hypotheses about 3D locomotor control
and stability is an area ripe for exploration.
Musculoskeletal modelling: a more theoretical basis
Theoretical models can also be used to probe questions that are
experimentally difficult or impossible to undertake. Because more
empirical approaches are impossible for extinct tetrapods, these
models have been very popular for estimating locomotor function in
palaeobiology, and thereby there has been much progress in using
the methods themselves. Modelling 3D muscle moment arms (and
possibly maximal moment-generating capacity) has become
popular for understanding locomotor function in extinct taxa,
especially dinosaurs and other archosaurs (e.g. Hutchinson et al.,
2005; Bates et al., 2015; Brassey et al., 2017; Otero et al., 2017; Cuff
et al., 2022) but also in other extinct tetrapods (e.g. Molnar et al.,
2021). Here, the core input empirical data tends to be 3D skeletal
morphology via scanning, which, if not well preserved, can be
scaled and composited into one individual (e.g. Demuth et al., 2020;
Molnar et al., 2021), or represented as an idealised model of a
species (Demuth et al., 2022b). Soft tissue anatomy is inferred
somewhat directly from ‘muscle scars’ on bones that are
osteological correlates of soft tissue attachments or (more
indirectly) relative positions in extant relatives; this inferential
approach uses the ‘extant phylogenetic bracket’ (Witmer, 1995; also
see Bishop et al., 2021a) or analogues (Demuth et al., 2022a). These
methods can answer how 3D muscle function evolved across vast
macroevolutionary scales and key morphological transitions (e.g.
Bates et al., 2015; Allen et al., 2021; Molnar et al., 2021;
Brocklehurst et al., 2022; Cuff et al., 2022).
Joint mobility constrains the range of axial and/or appendicular
kinematics. Quantifying these kinematic limits is important for
deciphering evolutionary patterns in major transformations of axial
and/or limb function. Digital tools enable the quantification of 3D
joint mobility (Fig. 1B) not only in extant taxa but also in extinct
ones (Pierce et al., 2012; Nyakatura et al., 2015; Manafzadeh and
Padian, 2018; Demuth et al., 2020; Richards et al., 2021; Herbst
et al., 2022c; Wiseman et al., 2022b) where, unlike in extant
animals, the joint movement cannot directly be observed or
otherwise estimated. The osteological range of motion (ROM) is
influenced by the thickness of articular cartilage (permitting more
SU
IS
Hip
Knee
Ankle
z
x
IE
II
PY
CR
GL
IFB
IL
CI
IFM
SM
AM
GR
IE
II
SA
OE
AL
CR
GL
A B C Fig. 2. Sample musculoskeletal model
of the hindlimbs of a red-legged frog,
Kassina. The model is shown in dorsal
(A,B) and ventral (C) views (from
Collings et al., 2022). Limbs are in a
straightened reference pose. (A) Joints:
SU, sacrourostylic; IS, iliosacral, with axes
shown (x, flexion/extension; z, long-axis
rotation). (B,C) Muscles: AL, M. adductor
longus; AM, M. adductor magnus; CI,
M. coccygeoiliacus; CR, M. cruralis; GL,
M. gluteus maximus; GR, M. gracilis major;
IE, M. iliacus externus; IFB, M. iliofibularis;
IFM, M. ilofemoralis; II, M. iliacus internus;
IL, M. iliolumbaris; OE, M. obturator
externus; PY, M. pyriformis; SA,
M. sartorius; SM, M. semimembranosus.
Creative Commons Attribution CC-BY
license.
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or less motion depending on joint spacing), and by the accuracy of
the joint centre position estimation (Demuth et al., 2020; Herbst
et al., 2022c; Wiseman et al., 2022b). Because of the complex
interplay of different DOF during motion (Kambic et al., 2014;
2017), single-axis estimates have been deemed unreliable and
multi-axis mobility needs to be assessed (Manafzadeh and
Padian, 2018). However, considering all rotational DOF together
might even be insufficient as a result of translational movement
present in the joints of extant taxa (Manafzadeh and Gatesy, 2021,
2022) or uncertainties in the joint centre position of extinct taxa
(Wiseman et al., 2022b). Although the inclusion of translations
allows studies to capture all 3D mobility present in a joint,
these simulations can overestimate the true mobility that would
otherwise be restricted by soft tissues (Arnold et al., 2014). Recent
advances in simulating ligaments and other soft tissue constraints
(Manafzadeh and Padian, 2018; Lee et al., 2020; Jones et al., 2021;
Griffin et al., 2022; Bishop et al., 2022) can narrow down the
osteological joint mobility to more accurately estimate true mobility.
Joint mobility estimates can be combined with musculoskeletal
models to compute muscle moment arms across the whole set
of viable limb postures and draw evolutionary inferences
(Brocklehurst et al., 2022).
Finite element analysis
Finite element analysis allows investigation of stress and strain
distributions when forces are applied to an object. FEA can act as a
bridge between studying various aspects of bone structure
(microstructure, material properties and overall bone shape) and
kinetics (Fig. 4). It can be used to examine the effects of bone and
joint morphologies and loading environment on stress distributions,
for example, to investigate functional implications of certain bone
shapes. FEA involves dividing the object into polygonal elements
and assigning material properties to the object to model its physical
behaviour (Richmond et al., 2005; Rayfield, 2007; Bright, 2014;
Blasi-Toccacceli et al., 2022). Keeffe and Blackburn (2022) used
FEA to investigate the mechanical implications of radioulnar fusion
in frogs, concluding that the semi-fused condition present in frogs is
associated with smaller von Mises stress and higher bending
resistance than in unfused or completely fused conditions. FEA of
the carpal bones of a chimpanzee revealed that scaphoid–centrale
fusion has lower stresses in knuckle walking than lack of fusion,
supporting this fusion’s role in that behaviour and its evolution
(Püschel et al., 2020). FEA of trabecular bone across a range of
loadings in the proximal femur of two primate species showed
similar stress and strain distributions, revealing how bone strength
can be preserved despite differences in 3D trabecular morphology
(Ryan and van Rietbergen, 2005).
FEA can also be used to address developmental questions
including the evolution of joint or bone shapes, because bony
morphology reflects loading regime. Carter et al. (1987) proposed
that hydrostatic compression decelerates and intermittent high shear
stress accelerates endochondral growth and ossification. Using an
Animation TheoreticalSynergistic
Inputs:
Outputs: • Kinematics
• Bi-planar X-ray
• Bone geometries
• Bone geometries
• Muscle architecture
• (Kinematics, GRFs)
• Kinematics
• GRFs
• Joint moments
• Muscle activation
• Fibre length change
• Approximate morphology
• Kinematics
• GRFs
• Joint moments
Fig. 3. Digital tools lie on a spectrum, from more empirical animation methods to theoretical and conceptual models. Left: animation methods, such
as XROMM, put measured data into a 3D visualisation, where component interaction can be observed. Shown here is a kinematic tinamou model, described
by Bishop et al. (2021b), where the positions of limb bones were derived from XROMM. For animation methods, the required inputs tend to be large
compared to the outputs. Right: theoretical methods can involve high levels of abstraction, generating many outputs with few empirical measurements. For
example, the tinamou may be modelled as a simple sphere with two-joint legs (here, ‘hips’ and ‘knees’). Such a model can be integrated with predictive
simulation to study control, stability, economy or other aspects of locomotion from a broad (if not precise) perspective. Middle: synergistic methods combine
empirical data with theoretical models to produce rich datasets. Bishop et al. (2021b) combined XROMM data with measured ground reaction forces (GRFs),
and modelled the line of action of various muscles. Using inverse tracking simulations (see Glossary), they could predict muscle fibre length changes and
activations, which could not be measured experimentally. While synergistic methods require more empirical inputs, they have the potential to generate much
more (unobservable) data by integrating these inputs though model-based analyses.
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FEAmodel subjected to such mechanistic stresses as well as growth
and remodelling, Stevens et al. (1999) were able to create a model of
endochondral growth that reflected key prenatal and postnatal
developmental mechanisms. Chadwick et al. (2014, 2015)
combined 3D ex vivo morphology obtained via CT and MRI scans
with FEA to test howmechanobiological loading environments might
relate to patellar sesamoid development and function in adult
ostriches, finding that high shear stresses around the distal femur
may help explain why two patellar sesamoids form there.
Application of FEA to soft tissue biomechanics
FEA is also used for studying soft tissue biomechanics in the
context of locomotor function. Insights that are gained from FEA of
muscles can be highly compatible with those from experimentally
based fluoromicrometry, in terms of discovering how soft tissues
function in locomotion. Micromechanical finite element models can
inform upon the 3D or quasi-3D biomechanics of muscles. An
analysis of the M. rectus femoris and M. soleus in rabbits indicated
that, unlike fibre-based muscles, fascicle-based ones have extremely
different shear moduli and transversely anisotropic deformations
(Sharafi and Blemker, 2010). Another study focused on three
forearmmuscles in mice, testing the model against histological data,
and discovered that the endomysium around fibres resists active
muscle forces, passively regulating strain in the terminal ends of
fibres and thus potentially playing a protective role (Sharafi et al.,
2011).
Realistic 3D models of muscle can give deeper insights into the
dynamics of, and interactions between, muscles during various
tasks or with different geometries (Fig. 4). In many musculoskeletal
models, muscles are represented as simple 3D lines of action,
especially in earlier musculoskeletal modelling (i.e. Nagano et al.,
2005; Hutchinson et al., 2005), sometimes including some
wrapping behaviour. Recent methods, predominantly focused on
humans, have enabled more complex modelling of muscle lines of
actions during locomotion. For example, muscles can be modelled
as finite element meshes in musculoskeletal dynamic simulations
(e.g. Elyasi et al., 2022, who investigated human patellar
movements). Blemker and Delp (2005) developed a finite element
model incorporating muscle fibres: ‘fibre geometry templates’ were
transformed to a volumetric muscle mesh to create muscle-specific
geometries. Changes in muscle shapes as a result of joint rotation
were accurately predicted by the 3D muscle fibre models in
comparison to empirical MRI data (see also Blemker et al., 2007).
Fibre-based FEA muscles have been integrated with
musculoskeletal dynamic simulation (Lloyd et al., 2012; Stavness
et al., 2012). Kohout and Kukačka (2014) and Modenese and
Kohout (2020) developed a similar approach using fibre templates
to generate curved fusiform muscles in a model. The muscle fibre
displacements during movement were calculated by linking the
transformations of each fibre point to the two closest bones, with the
influence of each bone’s position diminishing with increasing
distance.
Biomechanical models and simulations of neuromuscular dynamics
during legged locomotion
Modelling and simulating terrestrial locomotion are powerful ways
to test locomotor mechanisms. These methods involve a choice
between simpler, inverse dynamic (typically static; see Glossary)
approaches and more forward dynamic (even predictive; see
Glossary) ones. These approaches are often somewhat
misleadingly labelled ‘multibody dynamic analysis’ (MDA; see
Glossary; Fig. 5) but MDA purely involves rigid body dynamics,
not necessitating any biological data (e.g. vehicular crashes), unlike
musculoskeletal models and simulations, the terms we use here
(e.g. Seth et al., 2018). The inverse dynamic approach requires the
following input data: external forces, body inertial properties, joints,
muscles and kinematics – the latter may be motion data captured by
XROMM as discussed above. Kinematics and kinetics may be
assumed (e.g. where unknown, such as for an extinct taxon; e.g.
Bishop et al., 2021c), or track specific experimental data. This
approach produces a rigid body mechanical framework (i.e. MDA)
towhich muscle models are appended (e.g. Millard et al., 2013), and
joint moments and muscle activations are extracted. Forward
dynamic simulations have a different setup, in which external forces
and kinematics are not used as input data (Fig. 5). Rather, only
inertial properties, joints and muscles are used to create a
musculoskeletal model. Control targets and cost functions may
define an optimal control (see Glossary) problem to produce
optimal muscle activations, simulated forces (via MDA) and
simulated kinematics. For example, a predictive simulation (see
Glossary) seeking to ascertain the maximal jumping height of an
animal (e.g. Bishop et al., 2021d) would first dictate constraints on
the task (e.g. bounds on joint angles), a time to accomplish the task
(e.g. 1.5 s), and a target to be optimised (e.g. jumping as high as
possible). Further constraints/cost functions can also be appended,
such as minimisation of muscle activation.
Predictive simulations in palaeontology
Studies have used optimal control methods in predictive simulations
of locomotion in extinct taxa to answer questions about locomotor
behaviour, which is important as experimental data are entirely
absent for fossils. These methods are best evaluated by first
simulating movement in an extant species (more so if ex vivo or in
vivo data are available) and then extrapolating the approach to an
A B C Fig. 4. Different methods for muscle modelling and
usage in finite element modelling. (A) 3D muscles
were reconstructed for the right hindlimb of Triassic
reptile Euparkeria (bone images from Demuth et al.,
2020). (B) Muscles can be decomposed into curved
strands (black lines) or even as a 3D finite element
mesh with these lines as embedded fibres to model
lines of actions and deformations during movement.
(C) Finite element analysis (FEA) can estimate the
stresses or strains in bones (heat map indicates
stresses; the low-to-high stress colour spectrum is
cool/blue to hot/red). Muscle strands were created
using the plugin of J. Hereš (https://doi.org/10.5281/
zenodo.7100418), based on Kohout and Kukačka
(2014) and Modenese and Kohout (2020).
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extinct analogous species. For example, Bishop et al. (2021c) used a
musculoskeletal model of a tinamou, formulating an optimal control
problem of generating a gait cycle which was solved by constraining
a target forward speed. This produced a minimal walking speed and
a maximal running speed, which formed the baseline for simulating
the maximum running speed in the extinct dinosaur Coelophysis –
and further highlighted the important 3D dynamic contribution of
the tail to regulating angular momentum during movement.
More theoretical biomechanical simulations can predict or
otherwise test locomotor behaviours that are not directly observed.
Studies by Sellers and colleagues have used evolutionary algorithms
(solving an optimisation problem by applying concepts of biological
evolution to ‘generations’ of potential solutions) to predict locomotor
dynamics in a variety of species, such as suggesting that diagonal
footfall patterns are not chosen based on simple optimisation criteria
in quadrupedal chimpanzees but rather are likely to be a compromise
between energetic efficiency and lateral stability (Sellers and
Hirasaki, 2018). Sellers et al. (2022) generated plausible
neuromechanical simulations (i.e. incorporating neural control) of
non-steady locomotion such as stopping and turning. Simulations of
dinosaur locomotion have given insights into their maximal
locomotor performance and gait dynamics, such as slow walking
and low joint mobility for a giant sauropod (Sellers et al., 2013); and a
relatively slow ‘grounded running’ gait for Tyrannosaurus (Sellers
et al., 2017). Surprisingly fast bipedal and quadrupedal gaits for the
fairly large ornithopod dinosaur Edmontosaurus intimated that
unrepresented constraints might be causing overestimation of
locomotor performance (Sellers et al., 2009).
Synergistic integration of empirical and theoretical methods
The combination of empirical and theoretical approaches
(‘synergistic’; Fig. 3) can address research questions that are
difficult to answer with either approach on its own (Fig. 6). This
combination can be achieved using empirical data as per above, or
using robotics or fluid dynamics approaches. A variety of studies
have combined empirical data with simulations to study 3D
locomotor dynamics – including prediction of jumping
performance in frogs (Kargo et al., 2002; Porro et al., 2017;
Richards et al., 2018; see also Collings et al., 2022), joint reaction
forces and soft tissue strains as well as substrate dynamics in horse
forelimbs (e.g. Swanstrom et al., 2005; Becker et al., 2019, 2020;
Harrison et al., 2010; Symons et al., 2016, 2017), neuromuscular
control in rats and mice (e.g. Johnson et al., 2011; Yeo et al., 2011;
Charles et al., 2018), muscle activations in dog forelimbs (Stark
et al., 2021), and relative postural leverage or ‘effective mechanical
advantage’ across the evolution of giraffids (Basu and Hutchinson,
2022). Neuromechanical analyses of walking in cats have benefitted
from integration of empirical- and simulation-based data for the
hindlimbs. Simulations have shown how feline hindlimbs produce
forces in postural control mechanisms that resist perturbations
(McKay et al., 2007), how muscles are activated to couple joint
dynamics proximodistally in limbs (van Antwerp et al., 2007) and
how the muscular anatomy influences constraints on the
coordination of limb endpoint forces (Bunderson et al., 2010),
demonstrating that inverse simulations produce reasonable matches
to experimental in vivo data from electromyography (EMG), MTU
lengths and tendon force–buckle measurements (Karabulut et al.,
2020). Quite a few of the above examples are more inverse dynamic
approaches than forward dynamic, whereas truly predictive (without
much empirical data, but still realistic/synergistic rather than
conceptual) simulations remain rarer.
Digital empirical and theoretical approaches can also be
integrated with, or tested against, digital and physical robotics
approaches (Karakasiliotis et al., 2016), even including
Controllers
Neural
command
Musculotendon
dynamics
Multibody
dynamics
Musculoskeletal
geometry
Excitations Muscle forces Moments Accelerations
Velocities
Angles
Movement
Fig. 5. Typical workflow in a 3D forward dynamic musculoskeletal simulation. Workflow taken from Seth et al. (2018; https://doi.org/10.1371/journal.
pcbi.1006223.g001 CC BY 4.0 license). Input data are controllers (optimisation criteria, constraints, etc.), assumed musculotendinous model (e.g. Hill; Millard
et al., 2013) used for computing dynamics, and musculoskeletal geometry. Orange boxes emphasise the start and end points of the simulation; dark grey
boxes are the intermediate steps. Running the simulation solves for the controls (neural commands) leading to muscle excitations and activations and
thereby forces, generating joint moments that produce (via rigid body dynamics; multibody dynamics analysis or MDA) accelerations and other kinematics of
locomotion. Outputs can then give insight into the underlying controllers, and across a stride(s) the changing movements will result in different initial
conditions for computing the dynamics over the next time step.
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palaeontological and evolutionary inferences. Building on prior 3D
bio-inspired robotics studies by Ijspeert et al. (2007), Nyakatura
et al. (2019) investigated how the early amniote tetrapod Orobates
walked by combining (1) experimental XROMM and ground
reaction force (GRF) data from four extant tetrapods used to
constrain a kinematic simulation of Orobates, (2) both dynamic
simulation and robotic representations of Orobates, and (3) a
‘sprawling gait space’ of 3D kinematic solutions that would fit the
actual fossil trackways of Orobates. Together, these analyses
pointed toward a derived, somewhat erect (more crocodile-like than
salamander-like) limb posture for Orobates (Fig. 7). There are
relatively few studies that have conducted such 3D integration of
rigorous morphology-based experimental kinematics (and kinetics)
with simulations and robotics. As Nyakatura et al. (2019) showed,
there is great similarity between physical (hardware) robotics
approaches and digital models and simulations (‘virtual robotics’) –
including those used by roboticists – and these two methods have
great synergy in biomechanics despite their differences (e.g.
theoretical simulations produce data not obtainable by physical
robot experiments; the latter generate actual locomotion in the real
world). Together, those data can test hypotheses about what
behaviours or performance could be generated by certain
morphologies, or how those are controlled.
Integration of biomechanical experiments and models and
simulations with digital fluid dynamics analysis has seldom been
conducted in studies of tetrapod terrestrial legged locomotion, but is
powerful for addressing the mechanistic influences of rigid body
and fluid dynamics. Kinematics of the wings fromXROMM, force
platforms (hindlimb GRFs) and aerodynamic forces from ex vivo
propeller experiments were tracked by Heers et al. (2018) in
inverse simulations. These simulations predicted wing muscle
forces and activities, with reasonable matches to empirical muscle
excitations, for three ontogenetic stages of chukar birds while they
conducted wing-assisted incline running. However, no studies to
date have fully integrated 3D digital fluid dynamics (e.g.
computational fluid dynamics) into such analyses. Regardless,
there is exciting potential shown by studies such as that by
Falkingham and Gatesy (2014), where 3D discrete element
method simulations of substrate deformation in ‘sediments’
represented by poppy seeds (and rigid substrates) were
compared (and integrated) with XROMM data for walking
guinea fowl birds, and their real tracks. These particle-based
analyses (building upon the groundbreaking 3D kinematic study
of Gatesy et al., 1999; also see Falkingham et al., 2020) not only
demonstrated how 3D footprint shapes were produced during a
complex mechanism that is otherwise invisible but also showed
homologous traits of track formation via comparisons with
fossilised theropod dinosaur tracks.
Combination of musculoskeletal simulations and FEA
Integrating musculoskeletal models with FEA enables investigation
of how bones mechanically respond to locomotor loads primarily
imposed by muscles, and how bony or muscular morphology affects
this mechanical response (Fig. 4). Historically, musculoskeletal
simulation and FEA have been combined by running simulations,
then using resulting muscle forces or joint reaction forces as inputs
for FEA simulations in separate programs, but more recent
developments conduct the two analyses in the same model (e.g.
Lloyd et al., 2012). As an unusual example of integration of
musculoskeletal simulation and FE models, Goetz et al. (2008a,b)
built a 3Dmodel of an emu hindlimb and used the simulation results
in a thermal finite element model of the femoral head to simulate
loading-induced bone necrosis. Shahar et al. (2003) applied loads
informed by experimental GRF and kinematic data and a
musculoskeletal model to a 3D finite element model of a canine
femur to estimate stresses and strains, showing that joint reaction
forces alone overestimated these values and that, if muscle forces
were included, peak values in the diaphysis were medial
(compression) and lateral (tension), indicating bending. A variety
of studies have applied FEA to horse limbs, especially feet, along
with 3D empirical data (e.g. XROMM) and musculoskeletal
simulations (e.g. Harrison et al., 2014; Panagiotopoulou et al.,
2016), generally aiming at more veterinary clinical applications.
Bishop et al. (2018) devised a different kind of integration, whereby
a musculoskeletal simulation of a chicken hindlimb was used to
calculate muscle forces for application to a finite element model,
testing how the principal stress trajectories compared with actual
cancellous bone architecture. They discovered a good
correspondence, supporting the usage of cancellous bone structure
to infer general hindlimb orientation in theropod dinosaur hindlimb
bones, and the evolution of limb poses. A 3D musculoskeletal
model of a rat hindlimb using XROMMkinematic data in an inverse
simulation of locomotion produced data that compared favourably
with in vivo experimental EMG data and bone strains in the femur
(Wehner et al., 2010).
How does an organism move?
An organism moves by...
Inverse
approach/
static
Forward
approach/
dynamic
Musculoskeletal,
FE model?
Empirical data, e.g.
kinematics, kinetics
Tracking simulation
Muscle
activations, 
forces, etc.
Constraints,
optimisation criteria
Predictive simulation
Motion
+ muscle
dynamics, etc.
Model
evaluation
METHODS
OUTPUT DATA
INPUT DATA
QUESTION
ANSWER
Fig. 6. Generalised workflow for study design and conclusion using
various integrative 3D digital simulation methods. Choices arise
between more inverse or forward dynamic methods, then what kinds of
tissue models are used [finite element (FE) and/or musculoskeletal], and
how much empirical/theoretical data are integrated, leading to analyses via,
for example, tracking/predictive simulation that produce data used in model
evaluation, and then ultimately an answer to the study’s question(s).
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Pitfalls and challenges
Uncertainty in models and simulations often complicates the testing
of hypotheses about locomotion. These uncertainties arise from
many aspects of design and implementation: imprecision or
inaccuracy in empirical inputs; oversimplification hiding
important effects; errors in computational implementation; or the
inappropriate mathematical or computational implementation to the
problem of interest. In making inferences, there must always be a
‘leap of faith’. If we could directly measure the phenomenon of
interest, or knew the ‘answer’ to the question already, we would not
need a model. However, we can increase trust and credibility in a
modelling framework through verification (see Glossary) and
‘validation’ (a misleading term as this implies rendering a model
infallible or 100% accurate, when all models are ‘wrong’). As
covered in detail by Hicks et al. (2015), model evaluation (Fig. 6;
see Glossary) begins from the formulation of the research question –
asking whether the model can answer the research question of
interest, and whether the modeller understands the assumptions
being made. It continues with comparing the model and simulation
with well-established results, either from empirical data or from
other models. Robustness and precision (see Glossary) can be
evaluated through sensitivity analyses – examining how input
parameter changes affect outputs (Hutchinson, 2012). Finally, the
careful documentation and dissemination of methods, data and
software used allows peers to test, evaluate and expand models
beyond the life of a single publication.
Model evaluation can be difficult with high-dimensional models
and data, which are more common in 3D digital methods. The
problem is exacerbated when increasing biological fidelity is
sought. As an example, if the research question was about a limb’s
3D dynamic mechanisms in locomotion, then wewould first need to
model an adequate amount of DOF andmuscles. However, for every
dimension that is added, there is in turn an increasing number of
possible solutions. Challenges from additional joint DOF (many
dozen in one real limb; e.g. Manafzadeh et al., 2021) are
compounded by adding muscles, which would number several
dozen in one limb. Excessive dimensions inevitably will
significantly increase simulation time and could make a
Forward kinematics of analogous
extant species’ limbs OroBOT = physical robot and
digital model
IK results = gait constraints
for OroBOT
Predictive simulations of OroBOT
IK of limbs and backbone =
kinematic ‘sprawling gait space’
Also GRF data
Dynamic simulation of kinematics 
and GRFs for evaluating potential 
locomotor patterns
Compared with IK results
OroBOT produced sprawling gait
matching trackways (including stride
length, width, etc.)
Model evaluation:
Using kinematics from extant species and trackways:
OroBOT data nested well
Locomotor dynamics:
Mechanical power, GRFs, stability, etc., quantified
Unlikely sprawling-type gaits excluded
Orobates had a more erect (i.e. less sprawling) posture than earlier tetrapods, thus representing advanced amniote gaits
METHODS
GENERATED DATA
THE ANSWER
3D skeletal model of Orobates, trackway gait constraints
for predictive simulations
INPUT DATA
How did the extinct stem-amniote
Orobates move?
THE QUESTION
In vivo XROMM
TASK
Fig. 7. Example integrative 3D digital research study workflow. Workflow adapted from Nyakatura et al. (2019). Images used with permission, courtesy of
(clockwise from top left): Thomas Martens; Jonas Lauströer, Amir Andikfar and John Nyakatura; Konstantinos Karakasiliotis; John Nyakatura.
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simulation computationally infeasible as a result of the exponential
growth of variables – the so-called ‘curse of dimensionality’ (e.g.
Halilaj et al., 2018). Rather, it is necessary to reduce the number of
input variables to generate results, whilst maintaining sufficient
realism to answer the research question, i.e. finding a suitable
balance. The reduction of dimensions introduces a level of
abstraction to models and simulations whose consequences can be
difficult to evaluate (Hicks et al., 2015). Simulation data can of
course be compared with existing data, such as simulated muscle
excitations in comparison to EMG data (Bishop et al., 2021a,b,d),
but existing data can be limited and challenging to obtain.
Sensitivity analysis of the effects of model complexity on
simulations are extremely valuable. For example, Kargo et al.
(2002) conducted a sensitivity analysis of a frog hindlimb to find the
minimal DOF required to adequately simulate jumping
performance.
Another challenge is data overfitting (see Glossary), which can
give the researcher the false security of inflated model accuracy (see
Ferber et al., 2016). Two possible scenarios can be envisaged. First,
results may become too similar, reducing a realistic range of data
present within the variable, and errors may become harder to spot.
Second, if numerous models and/or conditions are modelled via
overfitting, the researcher may inadvertently fail to acknowledge
errors which would otherwise be easily spotted without overfitted
data. Human biomechanists have attempted to solve such issues via
developing trained neural networks (Smirnov et al., 2021) and
machine learning tools (Halilaj et al., 2018; Song et al., 2021), but as
yet such developments have not been implemented for models of
many other animals. These issues will be present in simulations
using trained data as feedback loops, but evaluation of the results
should minimise the risk of overfitted data in such circumstances
(Hicks et al., 2015).
3D analysis: caution and potential
Returning to an issue raised in the Introduction, future studies
should continue to ask themselves during study design and perhaps
explicitly within their publication: why is a 3D approach required,
and why is the level of complexity therein required, to answer the
research question (Figs 3 and 6)? As computational power
inevitably increases (e.g. Mack, 2011) and 3D tools become more
sophisticated, more complex 3D questions can be answered – but is
that necessary? Weighing necessity versus sufficiency remains
important, and is not so often explicitly addressed in 2D or 3D
studies. Real organisms have complex 3D morphology and move
in (very) complex 3D environments, but most studies may not
need to maximise complexity. Furthermore, some added
complexity might not even be biologically accurate, or remains
debatable. An example is the practice of breaking single line-of-
action muscles into numerous strands (described above). Whilst
this is geometrically more realistic in 3D, and might provide better
finite element results, a question remains how to activate these
strands in a biologically realistic way – should the activation of
separate fibres be homogeneous or heterogeneous? This remains a
frontier in which answering its fundamental questions will require
more integration with neuroscience. More generally, weworry that
the attitude of ‘more complex and realistic is always better’ is very
dangerous (see also ‘Pitfalls and challenges’ above, especially the
‘curse of dimensionality’). Researchers might be seduced by the
attractiveness of 3D approaches, but gradually these approaches
may provide more and more incremental answers as they are
applied to the same or similar question(s). This danger could be
especially risky for early career researchers, who should be
appropriately mentored in choosing and wielding these complex
tools.
On the more positive side, there is a vast vista of unanswered,
exciting questions in this field that could benefit from the
application of these 3D approaches, and innovations of them, as
the techniques rapidly mature. New discoveries, beyond science’s
capacity less than 20 years ago, could thereby be made regarding
how locomotion functions in particular species and evolutionary
lineages, as well as the fundamental mechanisms, constraints and
principles underlying this locomotion. Empirical approaches will
always have great value in measuring important parameters, but
we can never measure everything. Theoretical approaches have
their well-known limits, but can estimate that unmeasurable
information – or they can predict things we might not have
expected. Together, these approaches have much synergy for testing
major hypotheses (Figs 3, 6 and 7). Furthermore, these approaches
not only can answer how individual organisms or species move but
also can influence other fields, particularly fields close to
comparative biomechanics such as physiology, engineering/
robotics and evolution/palaeobiology, but also fields that overlap
with these, such as ecology (e.g. the role that 3D locomotion plays
in ecosystems) and environmental sciences (e.g. the role that 3D
environments play in locomotion).
Acknowledgements
We thank the two peer reviewers and the editors for their very helpful comments on
prior drafts of this paper, and we thank other members of the DAWNDINOS team
specifically, and John R. Hutchinson's team generally, for their influential
discussions over the years.
Competing interests
The authors declare no competing or financial interests.
Funding
This study was supported by funding from an ERC Horizon 2020 Advanced
Investigator Grant (695517) to J.R.H. Open Access funding provided by The Royal
Veterinary College. Deposited in PMC for immediate release.
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