The Journl of Experimentl Biology 7, 339-38 Pulished y The Compny of Biologists doi:1.1/je.118 339 Determintion of pek verticl ground rection force from duty fctor in the horse (Equus cllus) T. H. Witte 1, K. Knill 1 nd A. M. Wilson 1,, * 1 Structure nd Motion L, The Royl Veterinry College, Hwkshed Lne, Htfield, Hertfordshire, AL9 7TA, UK nd Structure nd Motion L, University College London, Royl Ntionl Orthopedic Hospitl, Brockley Hill, Stnmore, Middlesex, HA7 LP, UK *Author for correspondence (e-mil: wilson@rvc.c.uk) Accepted 13 July Mesurement of pek verticl ground rection force (GRFz) from multiple lims simultneously during highspeed, over-ground locomotion would enhnce our understnding of the locomotor mechnics of cursoril nimls. Here, we evlute the ccurcy of predicting pek GRFz from duty fctor (the proportion of the stride for which the lim is in contct with the ground). Footmounted unixil ccelerometers, comined with UHF FM telemetry, re shown to e prcticl nd ccurte for the field mesurement of stride timing vriles, including duty fctor. Direct comprison with the force plte produces men error of.3 ms nd 3.5 ms for the timing of foot on nd foot off, respectively, cross ll gits. Predictions of pek GRFz from duty fctor show men Summry errors (with positive vlues indicting n overestimte) of.8±. N kg 1 (13%; N=; men ± S.E.M.) t wlk,.3±. N kg 1 (3%; N=75) t trot,.3±.7 N kg 1 (1%; N=18) for the non-led lim t cnter nd +.1±.7 N kg 1 (19%; N=9) for the led lim t cnter. The sustntil over- nd underestimte seen t cnter, in the led nd non-led lims, respectively, is ttriuted to the different functions performed y the two lims in the symmetricl gits. The difference in lod experienced y the led nd non-led lims decresed with incresing speed. Key words: ground rection force, field locomotion, ccelerometer, duty fctor, horse. Introduction The mximum verticl ground rection force (pek GRFz) experienced y n individul lim during ground contct hs een shown to constrin mximum running speed in humns nd hs een proposed s trigger for git trnsition in oth ipeds nd qudrupeds (Weynd et l., 1; Frley nd Tylor, 1991; Hreljc, 1993; Nilsson nd Thorstensson, 1989; Wickler et l., 3). Lim force lso determines the lod experienced y musculoskeletl structures, the sfety fctors involved in high-speed locomotion nd the cost of locomotion (Biewener, 199; Krm nd Tylor, 199). Pek GRFz lso determines the risk of frctures nd other musculoskeletl injuries in horses nd hs een used in the ssessment of lmeness (Merkens nd Schmhrdt, 1988,). In ddition, the mgnitude nd time course of forces experienced y the lims re importnt in eliciting positive, or negtive, one remodelling response. Force is routinely mesured with high precision nd ccurcy in the lortory environment using force plte (Elftmn, 1938; Cvgn et l., 19; Prtt nd O Connor, 197). Force pltes, however, hve numer of drwcks. They re expensive, need to e mounted in purpose-uilt runwy nd rely on the suject hitting the plte with exctly one leg. More recently, force pltforms hve een incorported into tredmills, offering dvntges over stndrd instlltions, ut studies re still limited to the lortory environment. We re prticulrly interested in the horse (Equus cllus) s model system for the study of locomotion. The horse hs evolved highly specilised musculoskeletl system nd is cple of short ursts of high-speed locomotion s well s more sustined exercise t lower speeds. Pressure-sensitive insoles re commonly used in humn iomechnics; however, their ppliction in horses is limited s the technology is expensive nd frgile, nd solute clirtion vlues re poor (Hennig et l., 198; Cvngh et l., 1983). A numer of groups hve developed instrumented horseshoes nd hve chieved incresing levels of ccurcy (Mrey, 188; Björk, 1958; Frederick nd Henderson, 197; Hügelshofer, 198; Ki et l., ; Rtzlff et l., 1985, 199; Roepstorff nd Drevemo, 1993). However, it is still difficult to record the entire force trnsmitted y the foot while mintining the requirements for grip, ll in thin construct of miniml mss. Even smll chnges in digitl mss my hve significnt effects on kinemtics due to the rpid ccelertions experienced during the git cycle (Bck et l., 1995). Lim force hs een predicted from kinemtic dt, lthough this is difficult. We hve demonstrted tht, in horses,
3 T. H. Witte, K. Knill nd A. M. Wilson there is git-independent liner reltionship (r =.95.99) etween the pek extension ngle (the posterior ngle sutended y the xis of the third metcrpl one nd the xis of the phlnges) of the metcrpophlngel (MCP) joint nd lim force (McGuign nd Wilson, 3). The joint ngle force reltionship cn e clirted t low speed using force plte, nd susequently lim force cn e predicted from kinemtics t higher speeds. The method is, however, limited to the horse nd requires the collection of kinemtic dt, which is difficult outdoors. Cine film hs een used to estimte lim force in glloping ufflo (Syncerus cffer) nd mling elephnt (Loxodont fricn) y pplying the principle of conservtion of momentum (Alexnder et l., 1979). In stedy-stte locomotion, the totl verticl impulse (the integrl of force with respect to time) pplied to the centre of mss during stride must equl the product of ody weight nd the stride durtion. There is, therefore, n inverse reltionship etween stnce time nd pek verticl force if lim genertes certin impulse. Tht frction of the stride time for which the lim trnsmits force to the ground (i.e. the lim is in the stnce phse) is known s the duty fctor. Alexnder nd co-workers used these concepts, nd the oservtion tht the GRF time curve in spring-like or running git is pproximtely sinusoidl in shpe, to generte the following eqution: Fz mx = πpmg/β, (1) where Fz mx is pek verticl ground rection force (N), p is the proportion of the mss of the niml crried y the pir of legs in question (conventionlly. nd. for the front nd rer pirs, respectively), m is the mss of the niml (kg), g is the grvittionl constnt (9.81 m s ) nd β is the duty fctor. The ccurcy of this clcultion relies on three ssumptions nd/or constnts: (1) The shpe of the GRF curve. In iology, the shpe of the GRF curve is not the result of simple oscillting spring mss system. Geometric compression of the leg spring due to forwrd motion of the trunk over the plnted foot nd ntomicl design cuses the resultnt curve to differ from pure sine wve (Frley et l., 1993). This shpe effect hs een demonstrted in kngroos (Mcropus rufus), where it resulted in 3% underestimtion of GRFz predicted using eqution 1 (Krm nd Dwson, 1998). The shpe of the GRF curve in the horse, where there is n pprently simpler lever system, hs not een compred to pure sine wve. () The proportion of the ody mss supported y the front nd hind legs. This is trditionlly stted to e % or more on the forelims (Hoyt et l., ). The exct origin of this figure is hrd to trce (Stshk, ); however, the figure cn e derived for other qudrupeds from the dt of Cvgn et l. (1977) nd others. In our momentum-sed clcultion, the proportion ssigned should relte to the reltive impulse generted y the front nd hind legs rther thn simply the pek lim force. (3) The symmetry of lim GRF curves etween pirs of legs in symmetricl gits. Bipedl skipping nd qudrupedl cnter nd gllop re termed symmetricl gits ecuse the foot strikes of contr-lterl lims re not evenly spced in time (Gmryn, 197; Hildernd, 1989). In contrst to humn ipedl skipping, where pek lim force hs een shown to e the sme in oth lims of the pir (Minetti, 1998), the lims of horse performing n symmetricl git experience mrkedly different pek GRFz (Biewener et l., 1983; Merkens et l., 1993; McGuign nd Wilson, 3). The first lim to contct the ground fter the eril phse is known s the non-led leg, nd the lim tht leds into the eril phse is known s the led leg. The non-led lim experiences 5% greter pek force thn the led lim t slow cnter (Merkens et l., 1993), nd similr difference hs een predicted t higher speeds (McGuign nd Wilson, 3). However, the stnce durtion nd duty fctor re very similr etween the led nd non-led lim (Bck et l., 1997). In fct, using the dt of Bck et l. (1997), eqution 1 would predict only 3% difference in lim force etween the forelims. It therefore ppers tht n offset or correction fctor is required in order to give n ccurte prediction of lim force from duty fctor t symmetricl gits. Appliction of the ove technique for the prediction of pek GRFz requires tht stnce time e ccurtely determined. Direct GRF mesurement, ccelerometer dt nd kinemtic methods hve een compred for the ojective determintion of the timing of foot on nd foot off (Schmhrdt nd Merkens, 199). Force plte dt re extremely ccurte for oth initil ground contct time nd the time of foot off. Kinemtic nlysis lone, on the other hnd, ws reported to e insufficiently ccurte for the determintion of either prmeter. Anlysis of digitl ccelertion offers n lterntive nd hs een used to develop tool for the estimtion of eroic power during wlking nd running in humns (Weynd et l., 1). This method, however, lso hs potentil disdvntges. In the lte stnce phse, the foot pivots out the toe (n event known s heel off) prior to the foot completely leving the ground (Fig. 1; Schmhrdt nd Merkens, 199). The error in stnce time determintion ws % in study of humns, which ws ttriuted to the inility to differentite foot rottion from ctul foot off (Weynd et l., 1). We propose tht, in the horse, toe off cn e ccurtely detected nd differentited from heel off using n ppropritely mounted ccelerometer due to the chnges in the direction of foot ccelertion. The ility to ccurtely determine the verticl force experienced y ll four lims of lrge cursoril nimls during high-speed locomotion in the field would contriute gretly to our understnding of the thletic ility of these nimls, since pek lim force hs een identified s limiting to running speed. In order to pply the technique descried y Alexnder et l. (1979), we must first vlidte method for determining the stride timing vriles used to clculte duty fctor. Susequently, the ssumptions tht eqution 1 relies on must e vlidted. It would therefore e useful to compre the ctul GRF curves to sine wve of the sme se nd re nd to determine whether this method provides good estimte of GRF throughout the stride or only t the pek vlue.
Pek verticl GRF from duty fctor 31 The gol of this study ws first to evlute the ccurcy of system of lim-mounted ccelerometers for detecting foot on nd foot off in the horse. Second, foot on nd foot off dt would e used to test the hypothesis tht pek GRFz cn e predicted from duty fctor. Specificlly, experiments were designed to nswer the following questions: (1) cn the timing of foot on nd foot off e determined using dt from footmounted ccelerometers during locomotion on oth hrd nd soft surfces; () wht is the rtio of front hind impulses s function of speed nd git nd (3) cn the pproch of Alexnder et l. (eqution 1) e pplied to wlking nd symmetricl gits? Mterils nd methods Two experiments were performed. First, the timings of foot on nd foot off events were determined simultneously y force plte nd ccelerometry during led wlk, trot nd cnter. Pek lim force ws determined y force plte mesurement nd clculted from duty fctor using eqution 1. Second, mximum MCP joint extension ngle ws mesured for the led nd non-led forelims during high-speed tredmill locomotion in order to quntify pek lim force symmetry t higher speeds. Determintion of foot on nd foot off nd pek lim force t wlk, trot nd cnter on hrd surfce Six Wrmlood-type riding horses (mss 573 75 kg; men 3 kg) were used for the wlk nd trot experiment, nd four fit Thoroughred horses (mss 53 51 kg; men 88 kg) were used for the cntering. All sujects were ssessed s eing free of lmeness y veterinry exmintion prior to ech experiment. Foot ccelertion ws mesured using solid-stte cpcitive ccelerometers with dynmic rnge of ±5 g (ADXL15, Anlog Devices, Norwood, MA, USA; sensitivity 38 mv g 1 ). These were protected y enclosure in epoxyimpregnted Kevlr fires (totl mss g) nd mounted on the dorsl midline of the hoof, with the sensitive xis orientted in proximo-distl direction, using hot melt glue from hot glue gun (Bostik Findley Inc., Stfford, UK). The optimum position nd rnge of the ccelerometer ws first determined y experimenttion with oth ±5 g nd ±5 g ccelerometers nd with mounting on the lterl spect of the third metcrpl/ mettrsl one (MC/MT), the lterl nd dorsl spects of the proximl phlnx nd vrious positions on the foot during locomotion on oth hrd nd soft surfces. Output signls were telemetered vi progrmmle nrrow-nd nlogue FM rdio telemetry devices operting t 58 MHz (ST/SR5; Wood nd Dougls Ltd, Tdley, Hmpshire, UK) nd logged vi 1-it A/D converter nd PCMCIA crd (DAQcrd7; Ntionl Instruments, Newury, Berkshire, UK) into lptop computer running custom softwre in LView (Ntionl Instruments). The telemetry trnsmitter, s wve whip ntenn nd NiCd ttery were mounted in custom-designed exercise ndge on the lterl spect of the MC/MT (mss of telemetry unit 73 g nd ttery 88 g; totl mss of ndge with telemetry unit, 37 g). A short, ftigue-resistnt cle ws constructed of multi-strnd copper wire coiled round flexile mmdimeter core of mountineering cord nd coted in silicon ruer (Wilson nd Goodship, 199). This highly flexile cle rn long the lterl spect of the digit nd linked the telemetry unit to the ccelerometer (Fig. ). Horses were led y n experienced hndler long n 8-m dirt nd concrete runwy in which force plte ws emedded Antenn Third metcrpl Rdio trnsmitter MCP joint Proximl phlnx c d e f g h Fig. 1. The orienttion of the equine digit during foot on nd foot off. The ccelerometer is mounted xilly on the dorsl hoof wll with the sensitive xis orientted disto-proximlly. Criticlly, the foot ccelertion vector (indicted y the red rrows) is orientted long the sensitive xis of the ccelerometer t foot on (d) nd t foot off (g). However, during roll over (f), when the heel of the foot (the most rerwrd point of the ground-ering surfce) hs left the ground nd the foot is rotting round the toe (the most forwrd point of the ground-ering surfce), the vector is orientted orthogonl to the sensitive xis. Fig.. An ccelerometer nd telemetry unit in plce on the distl lim of horse. The telemetry unit nd ttery re contined within the exercise ndge nd mounted on the lterl spect of the third metcrpl one. The ccelerometer is encsed in epoxy nd Kevlr fires, mounted on the dorsl surfce of the hoof nd protected from rsion y the exercise surfce with electricl insultion tpe.
3 T. H. Witte, K. Knill nd A. M. Wilson (Kistler 987BA; Kistler Instruments Ltd, Alton, Hmpshire, UK). Both force plte nd runwy were covered in commercil conveyor elt mtting. Force dt were mplified y integrl chrge mplifiers, filtered through low-pss filter ( db octve 1 from 5 Hz) nd collected simultneously with ccelerometer dt in LView (Ntionl Instruments). All dt were logged t 1 Hz. The time of foot plcement (foot on) ws tken s the first frme in which the verticl force rose ove 5 N, nd foot off ws defined s eing the first frme in which the verticl force (GRFz) fell elow 5 N (Clyton et l., 1999). In the horse, the well-defined increse nd decrese in GRFz, which occur t foot on nd foot off, respectively, men tht 5 N threshold ccurtely identified the timing of these events. These times were used to visully ssess the ccelerometer dt nd define the ccelertion fetures tht corresponded to foot on nd foot off. The opertor ws then linded to the force dt for the reminder of the nlysis. The times of foot on nd foot off were mnully extrcted from the ccelerometer trces using trnscription freewre (http://www.etc.fr/cta/gip/projets/ Trnscrier). For ech stride, the times of foot on nd foot off, s determined using the force plte, were sutrcted from those determined using the ccelerometer such tht n error vlue ws otined tht ws negtive if the ccelerometer time ws erly nd positive if it ws lte. From the ccelerometer dt, totl stride period ws defined s the difference etween two sequentil foot on events, nd stnce period s the time etween foot on nd the susequent foot off. Duty fctor ws then clculted s the rtio of stnce period to stride period nd ws used to clculte Fz mx using eqution 1. Force plte dt were used to clculte rtios of front to hind pek verticl force nd front to hind verticl impulse, lthough for cnter dt this ws only possile for non-led lims. Pek verticl force ws determined for ech lim strike nd compred with the predicted force. Mesurement of MCP joint ngle during high-speed tredmill locomotion Flt, circulr retro-reflective mrkers (Scotchlite 885; 3M, Brcknell, Berkshire, UK), mm in dimeter, were plced t the following skeletl lndmrks on the lterl spect of the left forelims nd the medil spect of the right forelims of the sme four Thoroughred horses used in experiment 1: (1) proximl end of the fourth metcrpl; () proximl ttchment of the lterl/medil collterl ligment of the MCP joint to the distl third metcrpl one (centre of rottion of the MCP joint) nd (3) lterl/medil hoof wll pproximtely over the centre of rottion of the distl inter-phlngel (DIP) joint. The horses hd een hituted to locomotion on highspeed tredmill (Stö, Knivst, Sweden; Buchner et l., 199). During the experiment, they wore neoprene rushing oots nd over-rech oots to void interference injuries while glloping. After wrm-up period, the horses were exercised t increments of speed etween m s 1 nd 1 m s 1. During cnter locomotion it ws recorded whether the left forelim or the right forelim ws the led leg. Mrker loction in the sgittl plne ws recorded from the horses left side (ProReflex; Qulisys AB, Gothenurg, Sweden). At ech speed increment, the horse ws llowed s to settle into stedy git pttern prior to the collection of 1 s of dt. MCP joint extension ngle ws clculted s the posterior ngle sutended y the xes of the third metcrpl one nd proximl phlnx. The pek ngle ws determined for ech stride of ech file, nd the men pek MCP ngle ws determined for oth front legs t ech speed increment. Results The fetures ttriuted to foot on nd foot off re presented long with the corresponding verticl force trces in Fig. 3. A high-frequency, high-mplitude ccelertion signl ws seen t Force (kn) 3 1 A 5 3 1 B 5 C 3 1 1 1 18 8 1 1 1 Time (ms) 13 135 1 15 15 Fig. 3. Representtive grphs of simultneous pek verticl ground rection force (GRFz) nd ccelerometer dt collected during wlk (A), trot (B) nd cnter (C) locomotion. For wlk nd trot trils, force plte dt were collected for oth front lims (red roken line) nd hind lims (green roken line) during the sme tril. Beneth the force outputs, the corresponding ccelerometer trces re shown. Verticl roken lines indicte the timing of foot on () nd foot off (). The red solid line indictes the output from the forelim ccelerometer, nd the green solid line the hind lim ccelerometer dt. Note the precipitous rise in force t foot on nd the rpid drop in force t foot off, which llow the ccurte determintion of foot on nd foot off from verticl force dt lone. Also note the sence of fetures in the ccelerometer trce during the stnce phses, except minor undultion shortly prior to foot off, corresponding to heel off nd foot rottion. The utomtic gin control in the telemetry link mens tht whilst the ccelerometer signl mplitude is the sme in ll three plots, the ctul ccelertion will differ.
Pek verticl GRF from duty fctor 33 the time of foot on. This ws followed y short urst of high frequency oscilltions nd then plteu while the foot ws in stnce. Susequently, lower frequency pek ws seen to coincide with foot off, feture tht ws esily distinguishle from the heel lift nd foot rottion tht occurred prior to foot off. Heel lift nd foot rottion were prominent if the ccelerometer ws mounted on the proximl phlnx, especilly on soft surfce, ut were only evident s very minor low-frequency oscilltion with hoof mounting (see Fig. ). These fetures were consistent on oth hrd nd soft surfces, cross the gits nd etween individuls. The fetures were most ovious nd distinctive when the ccelerometer ws positioned on the dorsl hoof wll, orientted with the sensitive xis long the midline of the lim (Fig. ). Initil experiments with the ccelerometer mounted on the lterl spect of the proximl phlnx resulted in stisfctory ccelertion fetures corresponding to the foot on event; however, foot off ecme difficult to detect relily, especilly on soft surfce. In the first experiment, totl of 17 stnce phses were collected ( t wlk, 75 t trot nd t cnter). Men solute error for foot on time ws. ms t wlk (medin error ms, inter-qurtile rnge to 1 ms), ms t trot (medin 1 ms, IQR to +1 ms),. ms (medin ms, IQR +1 to + ms) for the non-led lim nd 3. ms (medin.5 ms, IQR + to +3 ms) for the led lim t cnter. Men solute error for foot off time ws 3. ms t wlk (medin ms, IQR 5 to +1 ms),. ms t trot (medin 1 ms, IQR to ms), 5. ms for the non-led lim (medin ms, IQR 1 to +9 ms) nd.8 ms for the led lim (medin ms, IQR 7 to 1 ms) t cnter. In order to test the vlidity of the ssumption tht GRFz follows sinusoidl curve s required y eqution 1, we superimposed sine wves of the sme se nd re on ech GRFz curve generted in experiment one. The mplitude of the sine wve generted ws sutrcted from the pek GRFz mesured in ech cse. This produced n error vlue, which ws positive if the pek GRFz ws overestimted nd negtive if it ws underestimted. Fig. 5 shows men (± S.D.) GRFz curves cross ll strides recorded for front nd hind lims t wlk nd trot nd led nd non-led forelims t cnter. The superimposed sine wves lie within 1 S.D. of the men force for etween % nd 7% of the stride for oth front nd hind lims t trot nd cnter. The men vlue of the mplitude error ws.3 N kg 1 (% of pek GRFz; N=7; rnge 1.1 to +1.3 N kg 1 ) t wlk,.8 N kg 1 (7% of pek GRFz; N=19; rnge.1 to.7 N kg 1 ) t trot,. N kg 1 (5% of pek GRFz; N=3; rnge 1.1 to.3 N kg 1 ) for the non-led lim t cnter nd. N kg 1 (3% of pek GRFz; N=7; rnge. to. N kg 1 ) for the led lim t cnter (Fig. ). The rtios of front to hind pek verticl force nd front to hind verticl impulse were clculted nd re expressed s percentges nd plotted ginst pek GRFz for ll strides in Fig. 7. Liner regression of front:hind force rtio ginst solute forelim force showed tht the force rtio ws git dependent (y=198.358x, r =.7, P<.1). The Output voltge (V) 1. 1. 1. 1. 1. 1. 1. Hrd surfce MCP Soft surfce Time (ms) A MCP B Prox. phlnx C Prox. phlnx D Prox. phlnx E Prox. phlnx F Prox. phlnx Fig.. Comprison of different ccelerometer mounting positions y simultneous collection of dt from severl ccelerometer loctions. The output for the hoof-mounted ccelerometer is lwys shown in green, nd the comprison loction in red. The output during locomotion on hrd surfce of n ccelerometer mounted on the lterl spect of the third metcrpl one (MCP) t wlk (A) nd trot (B), nd the output of n ccelerometer mounted on the proximl phlnx (prox. phlnx) during wlk (C) nd trot (D) re shown. The output during soft surfce locomotion of n ccelerometer mounted on the proximl phlnx during wlk (E), trot (F) nd cnter (G) is lso shown. Verticl roken lines indicte the time of foot on () nd foot off (). Accelerometer output in volts cnnot e converted to ms due to utomtic gin control within the nlogue telemetry system used. G
3 T. H. Witte, K. Knill nd A. M. Wilson Force (N kg 1 ) 8 1 5 15 8 38% 13% Forelim Trot 5% % C 1 5 Forelim Cnter 5% 15 71% A E Hindlim Hindlim B D F Fig. 5. Men (± S.D.; roken lines) verticl ground rection force (lue) reltive to percentge of stnce durtion for the forelim nd hind lim t wlk (A,B) nd trot (C,D), nd led nd non-led forelims t cnter (E,F). A sine wve of equl se nd re is superimposed in red over the ground rection force. Vlues in the upper left corner of ech grph indicte the percentge of the stnce time for which the sine wve lies within 1 S.D. of the men force. 1 1 5 5 Non-led forelim Led forelim 8 1 8 1 % Stnce 1 A Wlk B Trot 1 8 % Totl oservtions 5 C 1 1 8 1 8 1 8 3 Non-led lim t cnter D 8 1 1 8 1 8 Led lim t cnter 3 1 1 8 Error (% of ctul pek force) 8 Fig.. Histogrms showing the distriution of errors in pek lim force prediction for individul stnce phses using sine wve of sme se nd re t wlk (A) nd trot (B) nd for the non-led (C) nd led lims (D) t cnter.
Pek verticl GRF from duty fctor 35 Front:hind verticl GRF rtio :3 :3 :38 : 58: 5: 5: 5:8 5:5 A Wlk Trot Non-led cnter 8:5 8 1 1 1 Front:hind verticl impulse rtio :3 :38 : 58: 5: 5: 5:8 5:5 B 8:5 8 1 1 1 Pek verticl GRF (N kg 1 ) Fig. 7. (A) Plot of front:hind rtio of pek verticl ground rection force (GRFz) versus pek forelim GRFz, expressed s percentges. Dt re shown for wlk (red dimonds), trot (green tringles) nd cnter non-led leg (filled lue circles). The liner regression line is fitted to ll dt (y=198.358x, r =.7, P<.). (B) Plot of front:hind verticl impulse rtio versus pek GRFz, expressed s percentges. Symols re s for A. The horizontl red solid line shows the men rtio cross ll speeds (1.33). The red roken lines indicte ± S.D., nd the lue roken lines indicte the inter-qurtile rnge. men front:hind force rtio (± S.D.) ws 1.±.1 (N=1) t wlk, 1.3±.9 (N=18) t trot nd 1.18±.17 (N=3) for the non-led lims t cnter. The rtio of verticl impulse, however, ws minimlly ffected y speed nd git (y=1.37.x, r =.18, P=.81). The verge front:hind verticl impulse rtio ws 1.33±.11 (men ± S.D.). This equtes to percentge verticl impulse distriution (front:hind) of 57%:3%. This impulse distriution ws used Predicted pek GRFz (N kg 1 ) 18 1 1 1 1 8 Wlk Trot Non-led lim t cnter Led lim t cnter Led/non-led men 8 1 1 1 1 18 Actul pek GRFz (N kg 1 ) Fig. 8. Sctter plot of predicted pek verticl ground rection force (GRFz) versus ctul pek GRFz. Both re normlised to ody mss. Dt re shown for wlk (red dimonds), trot (green tringles), nonled leg t cnter (lue circles) nd led leg t cnter (lck squres). The red line indictes the function y=x. The red str shows the position of the men of the verge led nd non-led lim dt. in the susequent clcultions of predicted pek GRFz from duty fctor. A sctter plot of predicted pek GRFz versus ctul pek GRFz for ll strides is shown in Fig. 8. This shows tht the prediction is slight overestimte for ll wlk strides, good for ll trot strides ut underestimtes the non-led leg pek force nd overestimtes the led leg pek force t cnter. Error ws negtive if the prediction underestimted the ctul vlue. The men error ws.8 N kg 1 (13% of pek GRFz; rnge.3 N kg 1 ) t wlk,.3 N kg 1 (3% of pek GRFz; rnge to 1. N kg 1 ) t trot,.3 N kg 1 (17% of pek GRFz; rnge 5. to.3 N kg 1 ) for the non-led lim t cnter nd.1 N kg 1 (19% of pek GRFz; rnge 3.7 N kg 1 ) for the led lim t cnter. When the mens of the led nd non-led lims re plotted on the sme grph, the point is very close to the line of normlity. Fig. 9 shows the difference in pek MCP joint ngle etween the forelims plotted ginst speed for four horses. Becuse solute ngle vlues could differ due to differences in mrker plcement etween the left nd right lims, the dt hve een normlised to ensure symmetry t trot speed of 3 m s 1. At cnter, the men difference in pek MCP ngle etween the two lims decresed y fctor of three from 7. t the lowest speed (7 m s 1 ) to. t the highest speed exmined (1 m s 1 ). Discussion Determintion of the timing of foot off with ccelerometers is difficult. Previous studies hve mounted the ccelerometer perpendiculr with the ground surfce, wheres here we mounted it long the dorsl hoof wll with the sensitive xis prllel to the long xis of the lim (Fig. ; Schmhrdt nd Merkens, 199). This mens tht during foot rottion prior to
3 T. H. Witte, K. Knill nd A. M. Wilson MCP ngle difference (deg.) 1 1 8 8 1 1 1 Speed (m s 1 ) Fig. 9. Difference in metcrpophlngel (MCP) joint extension ngle etween left nd right forelims during tredmill locomotion t rnge of speeds nd gits for four horses. Colours indicte individul horses. foot off, no component of the ccelertion is trnsduced (Fig. 1). At foot off, however, the ccelertion vector is ligned with the long xis of the lim, nd hence the sensitive xis of the ccelerometer, nd the mjority of the ccelertion is detected. mounting therefore provided cler nd repetle fetures during oth hrd surfce nd soft surfce locomotion t ll gits nd represented the optimum site of ccelerometer plcement, lthough this loction is less convenient thn higher up the leg. Due to its low mss nd smll size, ttchment of the ccelerometer to the dorsl hoof wll ws strightforwrd nd rrely filed. The Kevlr nd epoxy csing ensured tht the electronic components remined sfe even when the ttchment filed. The connecting cle ws found to e the wekest point, prompting the design of strong, ftigue-resistnt, yet highly flexile cle. The mss of the equine metcrpus nd digit is 3 g (Buchner et l., 1997). Horses commonly wer rushing oots (mss g) to prevent injury from interference etween lims during trining nd rcing. The comined mss of the ccelerometer, telemetry unit, ttery nd exercise ndge (37 g) is within the mss rnge of commercil rushing oots nd is therefore unlikely to interfere with norml kinemtics. In one study, ttching 88 g weights to the toes of Stndrdred trotters hd miniml effect on stride length, stride durtion nd the reltive durtion of stnce nd swing phses s percentge of the stride (Willemen et l., 199). Our equipment is mounted further proximl on the lim, where the effect on kinemtics will e even less. In ddition, the equipment could e mde lighter y reducing the ttery size (currently 88 g) or y using smller, nd lower power, telemetry trnsmitter. The four-lim telemetry system presented some technicl difficulties during design. The effect of four trnsmitters in close proximity to one nother nd the rerditing nd/or shielding effect of the horse ws expected to significntly reduce the rnge from the mnufcturers climed line of sight rnges of up to km. However, during the series of experiments descried here, undertken t rnges of up to 3 m, signl reception nd strength ws never prolem. Anlogue telemetry links use utomtic gin control to ensure tht the dynmic rnge of the system is used. The output voltge is therefore proportionl to ccelertion through the stride, ut ctul ccelertion vlues cnnot e otined. This is seen in Figs 3,, where input mplitude will vry ut the output mplitude remins the sme. Eqution 1 relies on the sinusoidl nture of the GRFz time curve. This ssumption holds true for the running gits, where the lim compresses nd extends during the stnce phse to store nd return elstic energy. In comprison, wlking gits re trditionlly modelled s n inverted pendulum with the trunk vulting over reltively incompressile lim, resulting in imodl GRF time curve. It is interesting, therefore, tht the technique presented still provides resonle estimte of lim force t wlk. Indeed, the predictions for wlking re more ccurte thn those for slow cntering (Fig. 8). In the horse, wlking still hs spring-like properties lthough with less leg compression nd reduced trunk lift t mid-stnce. During trot locomotion, the prediction of force from duty fctor ws shown to e ccurte. However, during cnter locomotion, eqution 1 provided n underestimte for the nonled lim nd n overestimte for the led lim. A considerle symmetry therefore exists in the impulse pplied y the two forelims since sine wve ssumption ws similr (Figs 5, ). Eqution 1 requires knowledge of the distriution of the mss of the niml etween the front nd hind lims. This should consider the rtio of the verticl impulses rther thn simply the pek force since the eqution is sed upon momentum. This study shows tht lthough the front:hind impulse distriution nd the front:hind force distriution re oth similr t 57:3, the front:hind pek force rtio did decrese with git from wlk to trot nd cnter. The reson for this chnge is unknown. The impulse distriution ws shown not to chnge within the speed rnge studied nd it is therefore pproprite to use the sme rtio for ll gits in the clcultion of pek force. During this study, horses were exmined on tredmill t rnge of cnter speeds. As speed incresed, the difference in MCP joint extension ngle (linerly relted to verticl lim force) etween the led nd non-led legs decresed. Using the previously pulished popultion regression of lim force ginst MCP joint ngle of McGuign nd Wilson (3), this equtes to reduction in led non-led force difference from N kg 1 to.5 N kg 1. This indictes tht s speed increses, lim function ecomes more symmetricl. At mximum rcehorse running speed (18 m s 1 ), therefore, the error in pek
Pek verticl GRF from duty fctor 37 GRFz prediction my e gretly reduced. On the sctter plot of predicted versus ctul force, the men of led nd non-led lims lies very close to the line of normlity (Fig. 8). This confirms tht the GRFz trce is inherently sinusoidl in nture nd tht the non-led leg simply genertes lrger impulse. It lso suggests tht the distinct til of the cnter GRFz trce (Fig. 5) does not contriute to prediction inccurcy. It my e possile to generte speed-dependent correction fctor to increse the ccurcy of the force prediction during symmetricl gits; however, the led non-led difference in solute pek lim force is vrile etween individuls (Fig. 9). The reduction in pek ngle symmetry seen t higher speeds suggests tht such correction my e unnecessry for studies of mximum speed locomotion. The pek ngle symmetry seen here t high speed is generlly less thn we found previously (7.7 ), where only one leg per horse ws nlysed (McGuign nd Wilson, 3). The superimposed sine wve of the sme se nd re did hve similr shpe to the GRFz curve t oth trot nd cnter. This demonstrted tht the method cn lso e used to estimte GRFz with resonle ccurcy throughout stnce t these gits nd not just t mid stnce. The system of lim-mounted ccelerometers descried in this pper proved to e prcticl for use in field conditions, mking it possile to estimte the mechnicl environment of the skeleton in individul horses nd consider the fctors tht limit gllop speed in horses under different environmentl conditions. In the future, it my e possile to utomte the detection of the fetures in the ccelerometer output in order to reduce the time required for dt nlysis. Conclusions It is possile to ccurtely predict pek GRFz from duty fctor in the horse. For symmetricl gits, correction fctor is required to compenste for the difference etween the led nd non-led lims of pir. Men pek lim force cn, however, e ccurtely determined for symmetricl gits. 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