Spot check of the calibrated force platform location

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systems and force platforms must share one absolute reference frame that allows ... email: [email protected] ... mass and to the two extremities.
Spot check of the calibrated force platform location M. Rabuffetti1

M. Ferrarin1

F. Benvenuti2

1

Centro di Bioingegneria, Fondazione Don Gnocchi ONLUS IRCCS, Politecnico di Milano, Milan, Italy Laboratorio di Fisiopatologia e Riabilitazione del Movimento, Geriatric Department, ‘‘I Fraticini’’ INRCA IRCCS, Florence, Italy

2

Abstract—In a movement analysis laboratory, stereophotogrammetric motion capture systems and force platforms must share one absolute reference frame that allows the computation of joint moments and powers. The correct calibration of the platform location identifies the transformation between force plate and absolute reference systems, which determines the spatial coherence among the equipments’ measurements. The aim of this study was to develop and test a spot check for the assessment of platform location calibration. Platform location calibration was assessed by comparing the measured outcome of an experiment performed with a pointed rigid rod bearing a set of markers with the corresponding expected results, computed with a model. A set of indices was then proposed to define a confidence volume in which the true ground reaction force is expected to be. The spot check was applied to a real laboratory setup and the effects of simulated platform mislocations were analysed. It was verified that the hip joint moment may be equally affected by a single marker misplacement of about 20 mm during platform location calibration, an occurrence that was clearly identified by the spot check, and by a hip centre location inaccuracy of 30 mm. Keywords—Motion analysis, Force platform, Calibration, Accreditation, Laboratory management, Spot check, Rehabilitation outcome assessment Med. Biol. Eng. Comput., 2001, 39, 638–643

1 Introduction A MULTIFACTOR motion analysis basically integrates the measurements from a stereophotogrammetric system (detecting the trajectories of markers) and from a dynamometric platform (measuring the ground reaction) (FRIGO et al., 1998; RABUFFETTI and BARONI, 1999; RIENER et al., 1999). These measurements, originally related to their own relative time– space reference systems, must be transformed into one global absolute time–space reference system. The transformation parameters have already been obtained from a specific calibration procedure. Platform location calibration is the procedure that identifies the rigid transformation between the platform reference frame and the stereophotogrammetric system reference frame (assumed to be the absolute reference): it practically consists of measuring the absolute positions of markers, at least three, located onto well-defined points, whose co-ordinates in the platform frame are known. Despite reliable calibrations of the stand-alone stereophotogrammetric system and force platform, several errors may affect the platform location calibration: one or more markers may be misplaced by the operator; local non-linearity or distortion may

Correspondence should be addressed to Dr M. Rabuffetti; email: [email protected] Paper received 12 December 2000 and in final form 20 September 2001

MBEC online number: 20013623 # IFMBE: 2001

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affect the stereophotogrammetric system (EHARA et al., 1995); markers may show altered reflective efficacy; non-optimal algorithms may be applied to raw data processing (RABUFFETTI and FRIGO, 2001). These possible occurrences determine an error in the estimated rigid transformation between the two reference frames. This error results in a nonlinear distortion of the biomechanical variables, the joint moments and powers, which rely upon the spatial coherence between the platform and stereophotogrammetric system reference frames: a small error in the calibrated platform location distorts the amplitude and phase of the computed joint moments (MCCAW and DEVITA, 1995; HOLDEN and STANHOPE, 1998; STAGNI et al., 2000). Although the calibration and accuracy of each individual measuring instrument are often considered, either the force platform (BOBBERT and SCHAMHARDT, 1990; HALL et al., 1996; G ILL andO’C ONNOR ,1997; MIDDLETON et al., 1999; FAIRBURN et al., 2000) or the stereophotogrammetric system (EHARA et al., 1995; DELLA CROCE and CAPPOZZO, 2000), the accuracy of the spatial coherence between the reference frames of the stereophotogrammetric system and the force platform are seldom addressed (MASIELLO et al., 1994; STANHOPE, 1994; RABUFFETTI et al., 1997). In the literature, only one full paper (MIYAZAKI, 1992) and two congress abstracts (BAKER, 1997; HOLDEN et al., 2000) concerning the assessment of platform location calibration can be found: in the first two approaches this assessment is performed by comparing the same moment of force computed on experimental measures and on the corresponding expected value of the measures, as obtained by a mechanical model of the experiment. In the third approach the assessment is made by comparing the measured and expected position of the Medical & Biological Engineering & Computing 2001, Vol. 39

centre of pressure and orientation of a testing rod. The two congress abstracts propose a method that shares many features with the already cited stereophotogrammetric spot check (DELLA CROCE and CAPPOZZO, 2000), thus enforcing the hypothesis of a single experiment to perform both spot checks. The present paper describes a method, for laboratories equipped with a stereophotogrammetric system and a dynamometric platform, consisting of an experimental protocol and a mechanical model for the quantification of indices related to the spatial coherence between the reference frames as determined by the current platform location calibration. The rationale of the indices is explained and guidelines are provided to use their values to assess the reliability of experimental data obtained in that calibrated setup. The relevance of the present paper lies in the necessity for accurate computation of joint dynamics in motion analysis: functional diagnosis, treatment planning and assessment of rehabilitative outcome are greatly affected by platform location calibration inaccuracies. 2 Methods 2.1 Test object The test object consists of a rigid pointed rod, bearing a set of reflective markers in known positions with respect to its centre of mass and to the two extremities. Two hard metal plates are crafted to seat both rod extremities in predefined hemispherical frictionless sockets: one plate is firmly placed onto the platform, while the second plate is handled by the operator (Fig. 1). The system composed of the plates, the rod and the platform can be modelled as a couple of ideal spherical hinges (one characterised by a fixed position relative to the platform) connected by a rigid structure.

2.2. Spot check experimental procedure The experimental procedure requires an operator, standing outside the platform to keep the rod almost vertical and to push it for 10 seconds by means of the handled plate against the inferior plate positioned onto the platform. Although the test spot check does not require a specific level of force, it is recommended that a force be applied of the same order of magnitude as the expected load in the current use of the platform. This procedure is repeated, pointing the rod at the platform centre and symmetrically in the corner areas and the resulting measures are merged into one single data set. The experiment is simultaneously recorded by the stereophotogrammetric system, providing the rod position (particularly the position of the two extremities P1 and P2, expressed in the absolute reference frame), and by the force platform, providing the ground reaction (particularly the reaction force direction fM and module F, and the application point position PM, expressed in the platform relative reference frame as denoted by the subscript M). The calibration procedures, and in particular platform location calibration, have previously been performed using standard procedures (as described by the instrument manufacturers) and provide the six parameters of the rigid transformation T between the platform relative reference frame and the absolute reference frame. 2.3 The model The proposed mechanical model (Fig. 2) analyses the experimental outcome to estimate the absolute components of the application point P and of the unit direction vector f of the ground reaction. The parameters of the model are: l: rod length w: rod weight (applied at the rod mid-point) h: plate height The inputs to the model, referred to the single time sample, are the following variables: P1, P2: the rod extremities co-ordinates as recorded by the stereophotogrammetric system; F: the module of the reaction force F (a platform measurement which is invariant with respect to any spatial transformation).

β

θ α

P2

W

P1 h P

F

Fig. 1 Test object consisting of a marked rod whose two pointed extremities constitute two frictionless hinges connected to two metal plates: the lower one is firmly placed onto the platform, the upper plate is handheld by the operator Medical & Biological Engineering & Computing 2001, Vol. 39

Fig. 2 Model of the experimental setup includes the rod (P1 and P2 are the rod extremities and W is the weight), the plate (h is the plate height) and the expected ground reaction (F vector applied at the point P). The graphical representation shows the plane identified by the rod and by the reaction force, including also the Y-axis gravity line. The angular variables describe the orientation of the rod and the reaction force. The angular variable g quantifying the spatial angle between the represented plane and the reference absolute XY plane is not shown 639

A set of variables are then computed by obvious operations: a: angle between the rod and reaction force direction (note that the rod, the reaction force and the gravity line identify one single plane); b: angle between the rod and the vertical Y axis (gravity line); g: angle between the plane identified by the rod and by the vertical Y axis, and the absolute XY plane. The first equation of the model describes the static equilibrium with respect to P2, the upper rod extremity: Fl sinðaÞ 

l w sinðbÞ ¼ 0 2

and determines the intermediate variable as follows:   w sinðbÞ a ¼ arcsin 2F

ð1Þ

ð2Þ

ð3Þ

the unit vector f fY

f ¼ ½ fX

fZ 

ð4Þ

is defined by its components fX ¼ sinðWÞ  sinðgÞ

ð5Þ

fY ¼ cosðWÞ

ð6Þ

fZ ¼ sinðWÞ  cosðgÞ

ð7Þ

The application point P of the ground reaction force is determined by extrapolating from the point P1, the rod extremity, along the direction f to the platform surface. The vector equation follows: P ¼ P1 

h f cosðWÞ

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u   2 N uP jðf i  f Ti Þ  Ef j2 u arccos 1  t 2 ð11Þ sf ¼ i¼1 N With reference to the ground reaction application point P, the mean vector error N P

After defining the difference angle W¼ba

is applied to the definition of two scalar (expressed in angular units) indices: the Carnot theorem has been applied to quantify, respectively, the mean error and the data scatter:   jEf j2 ð10Þ mf ¼ arccos 1  2

ð8Þ

EP ¼ i¼1

ðPi  PTi Þ

ð12Þ N allows one to define two scalar indices, expressed in length units, respectively describing the mean and the standard deviation of the error: mP ¼ jEP j vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uN uP u jðPi  PTi Þ  EP j2 t sP ¼ i¼1 N

ð13Þ

ð14Þ

The proposed indices may be graphically represented to describe the current platform calibration. Given the current measure of the ground reaction, properly transformed to the absolute reference frame according to the calibrated platform location, a geometric object, eventually shaped like a ‘badminton shuttlecock’, may represent the confidence volume where the true ground reaction is expected to be (Fig. 3).

3 Results The method described has been applied in the movement analysis laboratory of the hospital ‘‘I Fraticini’’ (INRCA, Florence, Italy) (BENVENUTI et al., 1999) equipped with a 6TVC optoelectronic system (ELITE, BTS, Milan, Italy) and a force platform (Type 9281B, Kistler Instrumente A.G., Winterthur, Switzerland). Calibration of the whole system has

2.4 The indices The measurements of P and f, as obtained by the force platform and expressed in its relative frame, can be transformed to the absolute reference frame by the co-ordinate transformation T determined by the platform location calibration. The transformed measured quantities (subscript T), respectively fT ¼ T(fM) and PT ¼ T(PM), are expected to coincide with the corresponding model-derived quantities (see eqns 4–8) for the whole duration of the experiment. A set of scalar indices, computed on the whole data set (numerosity N), are defined to quantify the congruence, or the incongruence, between the ground reaction as estimated by the model and the ground reaction as measured by the platform and successively transformed by T. With reference to the ground reaction force direction f, the mean vector error N P

Ef ¼ i¼1 640

ðf i  f Ti Þ N

ð9Þ

Fig. 3

The current measurement of ground reaction force transformed by the parameters derived from the platform location calibration is depicted as the unit vector fT applied in PT . The same entities estimated by the model are represented as f and P. The related spot check indices graphically represent a confidence volume, in the shape of a ‘badminton’ shuttle: mP and mf , quantify the offsets in the application point and in the direction of the vector, sP quantifies the radius of the sphere, sf determines the angle of the conical part

Medical & Biological Engineering & Computing 2001, Vol. 39

been performed according to the manufacturer’s guidelines, and the platform location was calibrated by placing four markers on the four platform vertices. The latter procedure was repeated ten times. Each platform calibration data set was averaged and the resulting mean values assumed to be the current platform location. The repositioning of the markers was very precise and test–retest reliable: the largest difference observed among any co-ordinate of any marker, across the ten repetitions, was 1.3 mm, and, most of the times, it was below 1 mm. These numbers indicate that the marking of well-defined physical points, such as the platform vertices, is about one order of magnitude more precise than marking anatomical landmarks (DELLA CROCE et al., 1999). The spot check was performed as described in the method section, at a sampling frequency of 50 Hz and neither kinematic data nor platform data were filtered. The indices were computed for the experimental outcome of the spot check, considering the ten alternative calibrated platform locations. A statistical summary of the indices derived from the experiments is provided in Table 1. It can be noted that all four indices, particularly the s-indices, are characterised by repeatable values. The m-indices obtained show a variability demonstrating how the spot check provides indices that are highly sensitive to any small variability of platform location. Nonetheless, the m-indices show smaller values than the s-indices: this means that the offsets affecting the transformed reaction force application point and the direction of the reaction force are significantly smaller than the scatter in the observed values, thus confirming that all platform location calibrations have been performed correctly. Additionally, a simulation was performed by virtually misplacing (in all three main directions) the position of one vertex as originally measured, thus simulating a platform mislocation. The misplacements were set at 5, 10, 20 and 30 mm. The spot check was then applied to the corrupted platform locations and the results are reported in Table 2.

It can be noted that platform mislocation basically affects only the m-indices, while the s-indices are only slightly modified by large errors in platform location. 4 Discussion and conclusions

The test method presented consisting of an experimental protocol with a test object and a mechanical model providing numerical indices, checks the spatial coherence between the reference system of the stereophotogrammetric system and the reference system of the dynamometric platform as quantified by the current platform location calibration. The present method shares the same approach as previous work (MIYAZAKI, 1992; BAKER, 1997; HOLDEN et al., 2000): the measured outcomes of a spot check experiment are compared with a model-based estimate of the same quantities. The innovative aspects of the present method concern the modality of the spot check experiment, the characteristics of the model and the definitions of the indices. The experimental protocol does not require the rod to be moved in a conical pattern (BAKER, 1997; HOLDEN et al., 2000); the rod has only to be set at different platform areas, thus allowing the adoption of a quasi static model, which eliminates problems due to the numerical differentiation of noisy kinematic data and to approximations in the estimation of the rod inertial properties. The 3D features of the model overcome the limitations of 2D approaches (MIYAZAKI, 1992), while the inclusion of the inferior plate in the model avoids the approximation of assuming coincidence between the rod tip and the centre of pressure (HOLDEN et al., 2000). Finally, the proposed indices are characterised by innovative definitions: the m-indices consist of the mean differences between the model estimations of the reaction force direction and application point, and the same geometrical entities as measured by the force platform and then transformed according to the current platform location calibration; the s-indices quantify the scatter in the differences previously identified. Such definitions relate the indices to specific measurement error sources: the s-indices are mainly related to the individual Table 1 Values of the indices obtained from one spot check applied to calibrations of the two measuring instruments, and the m-indices ten repeated platform location calibrations are mainly derived from the platform location calibration. The outcome indices allow for classification of the considered sP, mm mf, deg sf, deg N ¼ 10 mP, mm calibrated platform location. First of all, reliable platform Mean 1.9 7.9 0.30 0.59 location is characterised by m-indices with smaller values than STD 0.2 0.0 0.05 0.00 the corresponding s-indices (Fig. 4a), and, in particular, an ideal Min 1.6 7.9 0.19 0.58 calibration implies null values for all indices. In contrast, a value Max 2.4 8.0 0.37 0.59 of mP larger than the value of sP implies the occurrence of an offset in the arm of the reaction force (Fig. 4b), thus distorting all the computed joint moments and powers. Alternatively, if mf is larger than sf, larger offsets affect the proximal joints, these Table 2 Values of the indices obtained from one spot check applied to being furthest from the platform (Fig. 4c). The worst situation is a set of platform locations affected by simulated misplacements. The when offsets affect both the application point and the direction of first data row is the reference data without simulated misplacement. the reaction force (Fig. 4d). The following rows report the applied marker misplacement characThe results presented (Table 1) for the spot check applied to terised by the component (‘H’ for horizontal, ‘V’ for vertical) and by ten repeated calibrated platform locations classify all calibrathe magnitude (in millimetres) tions as acceptable. Nonetheless, the m-indices, particularly, Misplacement show high sensitivity to even small differences in platform (component, mm) mP, mm sP, mm mf, deg sf, deg locations. In contrast, repeated platform location calibrations do not substantially modify the s-indices, thus confirming the 0 2.1 8.1 0.30 0.59 hypothesis that they are mainly determined by the quality of the H5 3.3 8.1 0.30 0.59 individual instrument calibrations. H 10 4.5 8.1 0.30 0.59 A set of simulations of one marker misplacement, resulting in H 20 7.0 8.1 0.31 0.59 a platform mislocation, was performed and showed the possible H 30 9.4 8.1 0.30 0.59 occurrence of large indices: a marker horizontal misplacement V5 2.8 8.2 0.73 0.59 negatively affects the spot check (according to the case depicted V 10 3.7 8.4 1.16 0.59 in Fig. 4b) when larger than 20 mm, while a much smaller verV 20 6.0 9.0 2.02 0.59 tical misplacement, inducing a virtual platform rotation, might V 30 8.4 9.9 2.88 0.60 affect the indices (according to the case depicted in Fig. 4c). Medical & Biological Engineering & Computing 2001, Vol. 39

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µ σf

µ σf

c

Fig. 4

d

Paradigmatic spot check outcomes in simplified 2D representation: relevance of the m-indices. Case A represents an acceptable condition: the model derived ground reaction (solid tip arrow) is close to the one measured by the platform and then transformed (thin tip arrow). Cases B and C reveal linear and rotational offsets respectively. Case D shows both a displacement and a rotation in the platform location. The computation of joint dynamics is reliable in case A, because the offsets are within the noise levels, and is affected by errors in all other cases, depending on the magnitudes of the offsets

These simulated miscalibrations, which are well identified by the spot check indices, would have affected the computed joint moments and powers by erroneously changing the ground reaction arm of force relative to the joint centres. It is possible to estimate that a mf value of about 1.7 (a value comparable to those obtained in the simulations) might cause an error of about 30 mm in the ground reaction force arm relative to the hip joint, which has been demonstrated to largely distort the joint moment and power (STAGNI et al., 2000). According to this example, it is demonstrated that a single marker vertical misplacement of 20 mm during platform location calibration: (1) is clearly identified by the spot check; and (2) causes the same error in the hip joint moment as that of a 30 mm inaccuracy in hip centre location. The independence of the s-indices from the platform location is confirmed by their substantially constant values. But the only acceptable condition previously identified (s-indices larger than m-indices) requires some more comment because large values of s-indices may hide an existing offset (Fig. 5). The values of the s-indices may be attributed to two causes:

µPA=µPB σPA>σPB

a

Fig. 5

642

µfA=µfB σfA>σfB

b

Paradigmatic spot check outcomes in simplified 2D representation: relevance of the s-indices. Both cases presented are characterised by equal m-indices, which imply constant offsets between the model-derived reaction force (solid tip arrow) and the measured and transformed one (thin tip arrow), and by different s-indices. The occurrence of large s-indices in case A hides the relevance of the offsets, thus possibly misleading one to accept the current calibration. In case B, small s-indices enable the tester to correctly identify insufficient spatial coherence and an unreliable platform location calibration

a white noise, whose characteristics are constant with reference to time and position, affecting the measurements;

a non-linear distortion component affecting either the stereophotogrammetric or the force platform measurements, or both.

While the first component is always expected and must show constant characteristics across repeated spot checks, the second component may occur when one of the measurement systems has not been correctly calibrated or is affected by non-linearity. Consequently, to correctly interpret the results of the proposed spot check, a threshold value for the s-indices has to be identified: because it is not possible to provide a unique reference value for the first contribution (it depends on the current laboratory setup), a practical guideline is that any laboratory should perform a series of spot checks, eventually recalibrating the whole setup each time, collecting the resulting s-indices values. The smallest value observed in the series of spot checks may be assumed to be determined by noise only, and therefore can be used to define a threshold value for s-indices. In conclusion the proposed spot check provides indices that, when they are globally ‘sufficiently’ small and, in particular, the m-indices are smaller than the s-indices, certify that all the measuring systems are singularly well calibrated and correctly integrated into one reference frame. When the m-indices are larger than the s-indices, the calibrated platform location is not correct and should be repeated. When the s-indices show excessively large values, thus possibly hiding large values of m-indices, the indication is to individually check the accuracy of the stereophotogrammetric system and the force platform with specific spot checks (DELLA CROCE and CAPPOZZO, 2000; FAIRBURN et al., 2000). No threshold values of the indices are provided to certify the reliability of the current platform calibration because they are specific to the current laboratory setup and, moreover, they depend on the required level of accuracy, the type of movement considered (gait, posture, running) and the anatomical segments analysed (a platform location miscalibration may distort the hip moment, while not producing a significant effect at ankle level). The future perspectives of the present work are the definition of an optimised procedure to calibrate the force platform location and the definition of a single spot check to assess the calibration of each equipment composing a motion analysis laboratory and their spatial coherence. Acknowledgment—The authors would like to acknowledge the contribution of Paolo Mazzoleni in the experimental activity. The anonymous reviewers are thanked for their useful comments.

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EHARA, Y., FUJIMOTO, H., MIYAZAKI, S., TANAKA, S., and YAMAMOTO, S. (1995): ‘Comparison of the performance of 3D camera systems’, Gait Posture, 3, pp. 166–169 FAIRBURN, P. S., PALMER, R., WHYBROW, J., FIELDEN, S., and JONES, S. (2000): ‘A prototype system for testing force platform dynamic performance’, Gait Posture, 12, pp. 25–33 FRIGO, C., RABUFFETTI, M., KERRIGAN, D. C., DEMING, L. C., and PEDOTTI, A. (1998): ‘Functionally oriented and clinically feasible quantitative gait analysis method’, Med. Biol. Eng. Comput., 36, 179–185 GILL, H. S., and O’CONNOR, J. J. (1997): ‘A new testing rig for force platform calibration and accuracy tests’, Gait Posture, 5, pp. 228–232 HALL, M. G., FLEMING, H. E., DOLAN, M. J., MILLBANK, S. F., and PAUL, J. P. (1996): ‘Static in situ calibration of force plates’, J. Biomech., 29, pp. 659–665 HOLDEN, J. P., SELBIE, S., and STANHOPE, S. J. (2000): ‘A proposed test for clinical movement analysis laboratory accreditation’, Gait Posture, 11, pp. 131 HOLDEN, J. P., and STANHOPE, S. J. (1998): ‘The effect of variation in knee center location estimates on net knee joint moments’, Gait Posture, 7, pp. 1–6 MASIELLO, G. H., STANHOPE, S. J., VAUGHAN, C. L., and PAYNE, P. A. (1994): ‘The first step towards standardization for three gait laboratory’, Gait Posture, 2, p. 54 MCCAW, S. T., and DEVITA, P. (1995): ‘Errors in alignment of center of pressure and foot coordinates affect predicted lower extremity torques’, J. Biomech., 28, pp. 985–988 MIDDLETON, J., SINCLAIR, P., and PATTON, R. (1999): ‘Accuracy of centre of pressure measurement using a piezoelectric force platform’, Clin. Biomech., 14, pp. 357–360 MIYAZAKI, S. (1992): ‘A simple and practical method for evaluating overall measurement error of joint moments obtained by a force platform and a position sensing device’, Front. Med. Biol. Eng., 4, pp. 257–270 RABUFFETTI, M., BENVENUTI, F., MECACCI, R., NICOLODI, S., and STANHOPE, S. (1997): ‘Quality assessment of the performance of a motion analysis laboratory’. Proc. XVIth ISB Congress, Tokyo, Japan RABUFFETTI, M., and BARONI, G. (1999): ‘Validation protocol of models for centre of mass estimation’, J. Biomech., 32, pp. 609–613

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RABUFFETTI, M., and FRIGO, C. (2001): ‘Ground reaction: intrinsic and extrinsic variability assessment and related method for artefact treatment’, J. Biomech., 34, pp. 363–370 RIENER, R., RABUFFETTI, M., FRIGO, C., QUINTERN, J., and SCHMIDT, G. (1999): ‘Instrumented staircase for ground reaction measurement’, Med. Biol. Eng. Comput., 37, pp. 526–529 STAGNI, R., LEARDINI, A., CAPPOZZO, A., BENEDETTI, M. G., and CAPPELLO, A. (2000): ‘Effects of hip joint centre mislocation on gait analysis results’, J. Biomech., 33, 1479–1487 STANHOPE, S. J. (1994): ‘A procedure for evaluating gait analysis system performance’, Gait Posture, 2, p. 54

Authors’ biographies MARCO RABUFFETTI received his MSc in Electronic Engineering from the Polytechnic of Milan in 1991. He is a researcher at the Bioengineering Centre (Fnd. Don Carlo Gnocchi and Polytechnic of Milan), where he is responsible for the Laboratory of Experimental Neuropsychology. His main research interests include experimental methodology and mathematical analysis, biomechanics and neuropsychology. MAURIZIO FERRARIN received his MSc in Electronic Engineering and PhD in Bioengineering from the Polytechnic of Milan in 1989 and 1993, respectively. He is a researcher at the Bioengineering Centre, Milan, where he is responsible for the Laboratory for the Study of Motor Recovery (LarMo). He is also temporary Professor of Rehabilitation Robotics at the Polytechnic of Milan. His main research interests include functional electrical stimulation and innovative orthoses, clinical gait analysis, visuo-spatial co-ordination, and wheelchair ergonomics. FRANCESCO BENVENUTI was born in Pisa, in 1952. He received his MSc in Medicine in 1977, from the University of Florence. He is a specialist in geriatric medicine (1980) and neurophysiology (1988). Since 1979 he has been a medical doctor in the Dipartimento di Geriatria of the INRCA, Florence (Italian Nationa Research Institute on Ageing), and is presently director of the Laboratorio di Fisiopatologia e Riabilitazione del Movimento. His research interests include incontinence and gait and balance disorders as markers of frailty in the elderly.

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