1. Bwrrrr&nu, Vol. 24. No. IL pp. 1095.1105. 1991. Rntcd 10 Great Bnlu~ CALCULATION OF VERTICAL GROUND REACTION FORCE ESTIMATES DURING RUNNING FROM POSITIONAL DATA MAARTEN F. BOBBERT. HENK C. SCHAMHARDT and BENNO M. NICK? Human Performance Laboratory. Faculty of Physical Education. University of Calgary, Canada Abstract-The purpose of this study was to calculate. as a function of time, segmental contributions to the vertical ground reaction force F, from positional data for the landing phase in running. In order to evaluate the accuracy of the method, time histories of the sum of the segmental contributions were compared to F,(t) measured directly by a force plate. The human body was modeled as a system of seven rigid segments. During running the positions ol markers defining these segments were monitored using a video analysis system operating at 200 Hz. Special care was taken to minimize marker movement relative to the mass centers of segments, and low-pass cutoff frequencies of50 Hz(markers defining leg segments) and IS-20 Hz (markers defining upper body) were used in filtering the position time histories so as to ensure that high signal frquencies were preserved. The magnitude of the high-frequency peak in F,.. also known as ���impact force peat���. was estimated with errors 10%. while the time of occurrence of the peak was estimated with errors 5 ms. It would appear that the positional data were sufficiently accurate to be used for calculation of intersegmental forces and moments during the landing phase in running. Analysis of the segmental contribu!ions to F,(t) revealed that the first peak in I , has its origin in the contribution of support leg segments, while its magnitude is determined primarily by the contribution of the rest of the body. These contributions could be varied independently by changing running style. It follows that if the possible relationship between ���impact force peaks���and injuries is to be investigated, or if the egects of running shoe and surface construction on these force peaks are to be evaluated. the calculation of segmental contributions to F,(t) is a more suitable approach than measuring only F,(t). INTRODUCTION A large portion of today���s population is aware of the bcncfits to be gained from being physically lit, and numerous individuals rely on running as a means to acquire and retain their fitness. Because of the increase in the number of runners and the mileage covered, clinicians nowadays are frequently facing patients with running injuries. Unfortunately, as the etiology of many injuries is unknown, the development of pre- vention and treatment modahties is severely ham- pered. It seems reasonable to assume that at least some running injuries are associated with the landing phase where the body, so to speak, collides with the ground. In this phase the muscles which control the movement are forcibly lengthened, which could cause them to develop large forces and high internal stresses. Large muscular forces may also cause high stresses in the tendons which transmit these forces and in their bony attachments. The landing phase is also the phase where runners who strike the ground first with their rtarfoot produce the so-called ���impact force peaks���: high-frequency force peaks in the time histories of the vertical ground reaction force F, occurring in the Iirst Received in$naf&rm 30 May 1991. Address lor correspondence: Maartcn F. Bobbert. Vrije Universiteit. Vakgroep Functionele Anatomic, Faculteit der Bewegingwetenschappen. v.d. Boechorststraat 9. 1081 BT Amsterdw The Netherlands. 50 ms of ground contact (Cavanagh and Lafortunc, 1980 Frederick et al.. 1981 Dickinson et ol., 1985 Nigg cf (II.. 1987). If the joints of animals arc regularly submitted to such high-frequency force peaks, dcgcn- erativc chanps take place in articular cartilage and subchondral bone (Dekel and Wcissman, 1978 Radin et ul., 1973, 1978 Serink er al., 1977). Based on these findings. several authors have speculated that impact transients on heel strike in walking may lead to degeneration of articular cartilage, osteoarthritis and low back pain (Light et ul., 1980 Wosk and Voloshin, 1981 Voloshin and Wosk, 1982). Analogously, it has been speculated that ���impact force peaks��� play a role in the development of pain and injuries in runners (e.g. James et 01.. 1978 Clement et al.. 1981). If we assume that phenomena occurring during the landing phase in running are involved in the etiology of injuries, a mechanical analysis of this phase, includ- ing estimates of intersegmental forces and moments, becomes desirable. In order to make such an analysis, estimates are required of inertial and gravitational force contributions. This necessitates the assessment of mass distribution in the body segments under consideration, as well as estimation of translational and rotational displacements and accelerations. In biomechanical studies, the latter accelerations are usu- ally obtained by double differentiation of positional data in the time domain, and it would be very conveni- ent if the same procedure could be followed for the landing phase in running. However, the high-frc- quency peaks in F,(r) reflect high-frequency peaks in 1095

1096 M. F. BOBBERT et al. the time histories of accelerations of body segments, and the reconstruction of such peaks is only possible if a high signal-to-noise ratio exists in the positional data. Thus. the question arises whether it is possible to obtain positional data of sufficient accuracy for a mechanical analysis of the landing phase. The present study is a first step towards providing a mechanical description of the landing phase in run- ning. The purpose of the study is to calculate as a function of time the segmental contributions to F, using accelerations estimated from positional data. In order to evaluate the accuracy of the method, time histories of the sum of the segmental contributions, henceforth referred to as calculated F,(t), were com- pared to F,(t) measured directly by a force plate. A few of the results of this study were published earlier (Bobbert and Schamhardt, 1989). METHODS Ourline o/ wlup und prowdures Using Newton���s second law of motion for a single, rigid body. it may be derived that: f, = m,(&,, -R). (1) whcrc F, is the vertical component of the ground reaction force vector (forces directed upward are de- lined as positive). tn,, is the body mass, R is the accclcration due to gravity (-9.81 ms-���), and i,,, is the vertical component of the acceleration of the body���s mass center (upward accelerations arc defined as positive). If the body is subdivided into n rigid segments, equation (I) may be written as: F,= i m,(?,-R), (2) 1-1 where M, is the mass of the ith segment and i, is the vertical acceleration of the ith segment. In this study, seven body segments were delined the two feet, the two lower legs, the two upper legs, and a segment comprising head, arms and trunk (HAT). The segment locations were derived from the three-dimensional positions of retroflective spheres. monitored using four video cameras and a high-speed video-analysis system. Landmark position time histories were smoothed and differentiated twice to obtain acceler- ations. The latter were used in combination with literature data on magnitudes and locations of seg- mental masses (Clauser cr ul.. 1969) to calculate F, according to equation (2). The calculated F,(t) curves were compared to F,(t) curves measured using a force PliItc. The comparison between calculated and measured F,(r) curves was made for three male subjects (masses of 65.69 and 77 kg), each of whom performed several running trials wearing personal shoes. Running speed and running style were varied across trials so as to obtain a broad spectrum of ground reaction force time histories. Details on methods and procedures are provided below. Collection of force data Ground reaction forces were recorded using a KISTLER type 9287 force plate (Kistler Instrumente AG, Winterthur, Switzerland), which was installed according to the manufacturer���s specifications. The force plate was connected to an electronic amplifier unit (KISTLER type 9861A. Kistler Instrumente AG, Winterthur, Switzerland), and the eight output signals of this unit were sampled at 1000 Hz using a data acquisition board (DT2821-F-16SE. Data Trans- lation Inc., Marlborough, MA) and a personal com- puter (COMPAQ Portable III, Compaq Computer Corp., Houston, TX). The analog F, output of the amplifier was fed to a circuit including a light emitting diode (LED) in view of one of the video cameras. The threshold in the circuit was such that the LED came on when F, exceeded 20 N. Collection 01 video data Video data were collected using a VP310 video- recorder (Motion Analysis Corporation, Santa Rosa. CA) and four electronically shuttered cameras (NAC MOS V-14 Camera 60/220 F/S) equipped with 12-120 mm zoom lenses (Anglnicux, Paris, France). Camera positions arc shown schematically in Fig. I. A 1000 W lamp was placed directly behind each camera. The cameras were zoomed in as far a possible to a volume of 2 m in x (fore-aft axis), I m in y (medio- lateral axis) and 2 m in z (vertical axis), with the center of the base arca corresponding to the center of the force plate. This volume was subJequcntly calibrated using 16 control points and Expert Vision thrce- dimensional software. ,.fl _. :. _..��� _..��� 67 :. ,..��� ,_.��� r .: ,... .��� _..��� \ : ,c....-��� I% X .- direcfi0ll of ruming - ��� forte ��� plate ....., *. *. *. X. .... *.a. .... .... 1 . *:, ���... ���b J!?L Fig. 1. Positions of cameras used for collecting positional data. Arrows indicate the comers of the base of the calibrated volume.