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Computer Simulation of Horse Locomotion

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  • Computer Simulation of Horse Locomotion

    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.