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First published online May 21, 2007
Journal of Experimental Biology 210, 1885-1896 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02774
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Validation of vertical ground reaction forces on individual limbs calculated from kinematics of horse locomotion

Maarten F. Bobbert1,*, Constanza B. Gómez Álvarez2, P. René van Weeren2, Lars Roepstorff3 and Michael A. Weishaupt4

1 Institute for Fundamental and Clinical Human Movement Sciences, Vrije Universiteit, van der Boechorstraat 9, NL-1081 BT Amsterdam, The Netherlands
2 Department of Equine Sciences, Faculty of Veterinary Medicine Utrecht University, Yalelaan 12, NL-3584 CM Utrecht, The Netherlands
3 Department of Equine Studies, Swedish University of Agricultural Sciences, 750 05 Uppsala, Sweden
4 Equine Hospital, Vetsuisse Faculty, University of Zurich, Winterthurerstrasse 260, CH-8057 Zurich, Switzerland


Figure 1
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  		Fig. 1. Location of markers and explanation of the GRF distribution method. Retroreflective markers (small circles) were placed bilaterally on the skin overlying bony landmarks of the forelimb (tuber of spina scapulae, greater tubercle of humerus, a point midway between the two, lateral epicondyle of humerus, carpal joint, fetlock joint, lateral side of the hoof at the level of the coffin joint), hindlimb (tuber coxae, greater trochanter of femur, lateral epicondyle of femur, tarsal joint, fetlock joint, lateral side of the hoof at the level of the coffin joint), and on the head and neck (crista facialis, zygomatic arc, wing of atlas, transverse process of vertebra C7). Furthermore, spherical markers were placed on the trunk (spinous processes of vertebrae T6, T10, T13, T17, L1, L3, L5, S3, S5 and C2). Left limbs are indicated with dotted lines, markers on hoofs in contact with the ground have been filled. The GRF distribution method involved the following steps. The acceleration of the centre of mass (CM) of the horse was calculated from the marker position–time histories using a segmental model. The acceleration of CM, combined with the acceleration due to gravity, provided the magnitude and direction of the calculated total ground reaction force vector FR,total. The product of the ground reaction force and its moment arm relative to CM (aR) equals the rate of change of angular momentum. The latter was also calculated from marker position–time histories, so aR could be calculated. This then fully defined the line of action of the calculated FR,total, and therewith the point P where it passed between the hoofs of the limbs in contact with the ground. When only one forelimb and one hindlimb were in contact with the ground, the relative contribution of the forelimb to the calculated FR,total was taken to be equal to ah/(af+ah) and that of the hindlimb was taken to be equal to af/(af+ah). The situation shown in the diagram occurred at the instant that the vertical component of FR,total (FRy,total) reached its peak at trot (for illustrative purposes a trial was selected in which the angular momentum and horizontal component of FR,total were exceptionally large at the instant that FRy,total attained its peak).

 

Figure 2
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  		Fig. 2. Time histories of the measured and calculated total vertical ground reaction force (FRy,total), as well as of the measured and calculated vertical ground reaction force on each of the limbs (FRy,i), of three horses at trot. Calculated FRy,i(t) were obtained from distal limb lengths, using the force–length relationships of the distal limbs determined with the help of calculated values of FRy,i and limb lengths at trot. Dotted horizontal lines indicate half the peak value of FRy,total. FL, left forelimb; FR, right forelimb; HL, left hindlimb; HR, right hindlimb.

 

Figure 3
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  		Fig. 3. Time histories of the measured and calculated total vertical ground reaction force (FRy,total), as well as of the measured and calculated vertical ground reaction force on each of the limbs (FRy,i), of three horses at walk. Calculated FRy,i(t) were obtained from distal limb lengths, using the force–length relationships of the distal limbs determined with the help of calculated values of FRy,i and limb lengths at trot. Dotted horizontal lines indicate half the peak value of FRy,total. FL, left forelimb; FR, right forelimb; HL, left hindlimb; HR, right hindlimb. Thin dotted curves in diagrams of horse 2 represent FRy,i calculated according to the GRF distribution method for the two phases in each half-cycle in which only two limbs were in contact with the ground (insets in lowermost diagram of horse 3; see legend to Fig. 1 for explanation of information provided in insets), one in which the body is supported by a forelimb and the ipsilateral hindlimb (phase I, grey bars below time axes), and the other in which it is supported by this forelimb and the contralateral hindlimb (phase C, open bars below time axes). Floating dots are values for FRy,i extracted from these curves at fixed points during these phases (at 50% of phase I and phase C for the forelimb, at 20% of phase C for the hindlimb and at 80% of phase I for the hindlimb).

 

Figure 4
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  		Fig. 4. Mean peak values of the measured and calculated total vertical ground reaction force (FRy,total) at walk and trot. Each point is the average of the peak values of FRy,total obtained in several individual stance phases of one horse (15 at trot, nine at walk). Left forelimb stance phases were processed separately from right forelimb stance phases, hence each horse contributed two points at walk and two at trot. The dotted line is the line of identity.

 

Figure 5
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  		Fig. 5. Peak values of the measured and calculated total vertical ground reaction force (FRy,total) of the individual stance phases of one horse at trot. Left diagonal stance phases (FL–HR) were processed separately from right diagonal stance phases (FR–HL). The dotted line is the line of identity.

 

Figure 6
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  		Fig. 6. Mean relative load on the forelimb at the instant that FRy,total reached its peak at trot. Left diagonal stance phases (FL–HR) were processed separately from right diagonal stance phases (FR–HL), hence each horse contributed two points. The dotted line is the line of identity.

 

Figure 7
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  		Fig. 7. Mean peak values of the measured and calculated vertical ground reaction forces on the individual limbs (FRy,i) at trot and at walk. Calculated results were obtained using the GRF distribution method; at trot we used the peak value of FRy,i, at walk we took the largest one from the two values selected during each stance phase (see Fig. 3). The dotted line is the line of identity.

 

Figure 8
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  		Fig. 8. Mean peak values of the measured and calculated vertical ground reaction forces on the individual limbs (FRy,i) at trot and at walk. Calculated results were obtained using Eqn 1, with duty factors determined from the measured ground reaction forces. The dotted line is the line of identity.

 

Figure 9
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  		Fig. 9. Mean peak values over the stance phase of the measured and calculated vertical ground reaction forces on the individual limbs (FRy,i) at trot and at walk. Calculated results were obtained from distal limb lengths, using the force–length relationships of the distal limbs determined with the help of calculated values of FRy,i and limb lengths at trot. For each horse there are four data points, but some of these are hidden by others. The dotted line is the line of identity.

 

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© The Company of Biologists Ltd 2007