View Full Version : Computer Simulation of Horse Locomotion

Herman J. Woltring
11-22-1989, 06:24 AM
Dear Biomch-L readers,

Yesterday, I received a copy of Ton van den Bogert's PhD-thesis which he
hopes to defend in public (as is the Dutch tradition) on 7 December 1989
at 12.45 h:

A.J. van den Bogert
Computer Simulation of Locomotion in the Horse
Dissertation Utrecht State University, Faculty of Veterinary Medicine
ISBN 90-9003176-6, SISO 593 UDC 681.3:[531.1:599.72](043.3), 1989

It is a great pleasure to announce this thesis, typeset by the author using
LaTeX and published under his own steam (still the custom in most Dutch
science faculties) in a limited number of copies. The 160-page booklet con-
tains an unusual but most appropriate, 5.25 inch "Horse Animation Diskette for
IBM PC and compatible computers" which I had the pleasure to see demonstrated
by a colleague on the list to-day.

Before reproducing his Chapter 8, I'd like to copy his quotation from one of
the Founding Fathers of Biomechanics and Movement Science, at the beginning
of his thesis:

E Gregi`e in hac parte allucinantur,
nedum vulgares homines, set aetiam praeclari Philosophi, & anatomici;
qui potius false opinioni per manus traditae,
qu`am propriis oculis fidem praestare volunt.

A large amount of nonsense has been said about this subject,
not only by ordinary people but even by excellent scientists and anatomists;
who prefer to pass on incorrect second-hand theories,
rather than trust their own observations.

-- GIOVANNI ALFONSO BORELLI, De Motu Animalium (1680)
(recently replublished by Springer in English)

With such an audacious claim, Ton is bound to have a interesting time while
being questioned about his four-year work on the moving horse. Those of you
interested in a copy of his thesis know how to reach him electronically. His
chapters 2 - 6 have been published or are currently being reviewed for pub-



This thesis deals with modelling and simulation of the equine locomotor system.
Its main constituents are: introduction (chapter 1), theory (chapters 2 and 3),
data acquisition (chapters 4, 5 and 6), and applications (chapter 7).

Chapter 1 presents a short overview of the state of the art in equine
locomotion research, divided into experimental methods and biomechanical
modelling. This overview is followed by a classification of existing
methods for simulation of movement using rigid body dynamics, illustrated
by examples from human biomechanics. Finally, the aims of the study
presented in this thesis are defined and the subjects of the individual
chapters are briefly introduced, according to a stepwise strategy to
achieve these goals.

The equations of motion for a hinged rigid-body system are formulated in
chapter 2, and a numerical solution method for simulation of movement is
developed. The solution method allows for driving parts of the model on
the basis of kinematical data, while the movements in other parts are
caused by the muscular forces in that area. This technique was used to
simulate movement in a twodimensional (2D) model having 20 rigid segments
connected by 19 hinge joints. The ground reaction forces in this model
are generated by a visco-elastic model of hoof-ground interaction, and
muscles are represented by one total moment of force between a pair of
adjacent body segments. Such moments, controlled by linear feedback, are
used in 11 joints; in the remaining 8 joints the relative movement between
the two segments is prescribed. The simulated ground reaction forces, and
the movements of the total body centre of gravity, were found to be in
agreement with in vivo measurements. This indicates that a model combining
muscle properties (in this case represented by the feedback control system)
with kinematic input, is suitable for simulation of certain aspects of
locomotion under realistic conditions. However, due to the reduction of
individual muscles and tendons to net joint moments, this model could not
provide useful information concerning the internal forces.

A method to incorporate individual musculotendinous structures in a rigid
body model is described in chapter 3. The tensile force of a muscle is
assumed to act along the shortest path connecting the origin and insertion
points. This path is generally not a straight line, because retinacula and
bone surfaces may change a tendon's line of action. In this calculation,
these structures are represented by pulleys along which the tendon can slide.
An algorithm to calculate the forces and moments acting on the individual
body segments, based on the principle of virtual work, was implemented in the
DADS multibody simulation package (CADSI, 1988). This package was then used
to simulate movements and forces in a vertically loaded isolated hindlimb of
a horse. Despite the rough estimates of the mechanical properties of muscles
and tendons, the behaviour of the model was very realistic. This model not
only produced estimates of tendon forces and joint contact forces during static
equilibrium, but also provided a fundamental explanation for oscillations
within the limbs that have been observed in kinematics and ground reaction
forces during faster gaits. A simulated contraction of the deep digital
flexor muscle showed a rather complex functional role of this muscle, depending
on the loading regime of the limb as well as on the mechanical properties of
other passive structures in the lower limb.

The force development in active muscles is studied in chapter 4, using in
vivo measurements on the deep digital flexor muscle in the hindlimb. Similar
to previous work in human biomechanics, a mathematical model was developed
relating muscle force to the activation of the contractile machinery
(represented by the electromyogram), instantaneous muscle length and
contraction velocity. It was concluded that such a model can describe force
development with sufficient accuracy for use in simulation of locomotion.
However, application of this muscle model is restricted to a limited range of
operating conditions, because parameter estimation and validation were only
possible during two types of walking.

Chapter 5 presents post mortem measurements of the inertial parameters (mass,
moment of inertia and centre of mass) of all 25 body segments --- head and
hooves now being considered separately --- in five ponies. Estimation methods
based on these data were developed for determining the inertial parameters in
an arbitrary living pony. These results are indispensable ingredients for any
(forward or inverse) dynamic analysis of equine locomotion and form the basis
for development of the simulation model in chapter 7.

Because of the lack of existing data concerning the properties and function
of flexors and extensors in the lower forelimb, measurements of kinematics,
muscle activation and tendon strain were carried out in the same group of five
ponies (chapter 6). Activation of the deep and superficial digital flexors
was observed during the swing phase and the early stance phase. All flexor
tendons were strained during the stance phase only, showing slightly larger
amplitudes than previously measured in the hindlimb. The combination of
kinematics and tendon strain data led to the conclusion that, similar to the
situation in the hindlimb, flexor muscle forces were mainly determined by the
passive elastic properties of the structures, and that muscle activity is of
minor importance during walking.

In chapter 7 all previously collected data and theory are combined into a
model for simulation of a walking pony. Movement and forces in the lower
part of all four limbs are simulated using the activity and elastic properties
of 18 muscles and tendons. The joints proximal to the metacarpus and
metatarsus are driven using kinematic data, as in the model of chapter 2.
Simulations with this model, using the DADS package, required several hundred
times more processor time for solving the equations of motion than the
numerical method of chapter 2. This discrepancy is partially due to the
increased complexity of the model, but predominantly by the more general
character and more strict error control of the numerical solution method in
DADS. Simulated movements, ground reaction forces and tendon loading patterns
were similar to in vivo measurements. This model was successfully used to
obtain insight into the changes in load distribution caused by altered ground
properties, hoof shape and tendon properties. The effect of a tendon rupture
was also simulated.

This research project has led to the following conclusions :

o The mathematical techniques and numerical solution methods that have
been developed (chapters 2 and 3) are adequate for simulation of equine
locomotion. The combination of dynamic driving by muscles and tendons,
and kinematic driving by prescribed joint angle patterns, allows
stepwise refinement of the existing model by gradually adding muscles
and removing the corresponding kinematic input data from the model.
This strategy allows the development of new applications of the model,
without the necessity to incorporate all muscles responsible for
locomotion at once.

Future developments include partially threedimensional (3D) models with
additional muscles, where the existing 2D geometrical models for the
curved line of action of lower limb muscles can be retained. The 3D
kinematic data of equine locomotion required for such models can
conveniently be obtained with the recently developed automated CODA-3
system (Lammertink et al., 1989). The rotation of the pelvis with
respect to the thorax, as well as rotation and adduction-abduction
movements originating in the hip and shoulder joints will be considered
in the next model generation.

o It was found that only the mechanical properties of tendons and
contraction patterns of the muscles have to be incorporated in the
muscle model to be able to simulate force distribution in the lower limb
area during walking (chapter 7). When other gaits are studied or more
muscles are added, a more physiologically oriented muscle model as
described in chapter 4 will be required. In the horse however, the
parameters of such a muscle model are quite difficult to obtain from
in vivo measurements of EMG, muscle force and kinematics. The
origin of this problem is that, contrary to similar experiments with
humans, it is not possible to explore many kinds of muscular
contraction; the maximum attainable is a variation of the type of gait.
A promising alternative is the use of muscle architectural parameters
for estimation of muscle properties (Woittiez et al., 1983).

o The development of a locomotion model requires many complex animal
experiments (chapter 5 and 6). However, as soon as a working model is
available, it can be used to perform simulation experiments and thus
save on laboratory animals. This possibility to `play' with a model
also significantly enhances the understanding of the locomotor system.
Experimentation with a computer model has the advantage that results are
perfectly repeatable, and cannot be obscured by uncontrollable
biological variations.

In chapter 7 several examples of such applications of computer
simulation have been given. The reliability of the results, which
in this stage of development should only be interpreted qualitatively,
will have to be further tested by parameter sensitivity analysis.
Additionally, the simulated changes in kinematics and ground reaction
forces should be compared to results of parameter variations in (non-
invasive) in vivo studies corresponding to the simulation experiments.
Using the material and methods presented in this thesis, a model capable
of reliable quantitative predictions is certainly feasible.


CADSI (1988) DADS users manual, version 5.0. Computer Aided Design Software
Inc., Oakdale, Iowa.

Lammertink, J.L.M.A., Markies, H. and Bogert, A.J. van den (1989) The CODA-3
machine revised. Modifications of the original concept in order to produce a
highly accurate and reliable 3-D kinematic analysis system. Manuscript in

Woittiez, R.D., Huijing, P.A. and Rozendal, R.H. (1983) Influence of muscle
architecture on the length-force diagram. Pfl"ugers Arch. 397, 73--74.


As a loose leaflet, the traditional "propositions" have been included. Some of
these should relate materially to the subject of the study, some should have a
more general scope, and some may be `fun' propositions. I'll confine myself
to only a few, and especially those with a Biomch-L bias:

4. Excentric muscle contractions are not at all excentric.

6. An inverse dynamical analysis is not suited for obtaining insight into,
and for predicting the functioning of the musculoskeletal system.

7. A model should not be more detailed than is necessary for its application.

10. In practical applications of automated movement analysis, preferably the
human brain should be used for pattern recognition.

13. Replacing the medium FAX by publicly acces-
sible `electronic mail' and `electronic publishing' will lead to more ef-
ficient communication and larger savings in paper.

The last proposition reminds me of an other one (the author's name I have for-
gotten, unfortunately) recently defended at, I believe, Nijmegen University in
The Netherlands:

Facsimile is not only an efficient and user-friendly means of communication,
it even has something human: the longer ago it was transmitted, the more its
contents fade away.

Actually, these tho propositions ignore the upcoming trend of combining FAX and
MODEM in single PC-connected units. Thus, one might transmit manuscripts in
ASCII form, and the concomitant illustrations in pixel-by-pixel format by FAX.
In this fashion, the advantages of both communication protocols are optimally
combined (even though LaTeX allows some picture definitions in alphanumerical

Herman J. Woltring, Eindhoven, The Netherlands.