Human movement analysis using stereophotogrammetry

Gait and Posture 21 (2005) 212–225

Review

Human movement analysis using stereophotogrammetry Part 3. Soft tissue artifact assessment and compensation Alberto Leardinia,∗ , Lorenzo Chiarib , Ugo Della Crocec , Aurelio Cappozzod a

Laboratorio di Analisi del Movimento, Centro di Ricerca Codivilla-Putti, Istituti Ortopedici Rizzoli, Via di Barbiano 1/10, 40136 Bologna, Italy b Dipartimento di Elettronica, Informatica e Sistemistica, Universit` a degli Studi di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy c Dipartimento di Scienze Biomediche, Universit` a degli Studi di Sassari, Viale San Pietro 43c, 07100 Sassari, Italy d Istituto Universitario di Scienze Motorie, Piazza Lauro de Bosis 15, 00194 Roma, Italy Received 10 May 2004; accepted 19 May 2004

Abstract When using optoelectronic stereophotogrammetry, skin deformation and displacement causes marker movement with respect to the underlying bone. This movement represents an artifact, which affects the estimation of the skeletal system kinematics, and is regarded as the most critical source of error in human movement analysis. A comprehensive review of the state-of-the-art for assessment, minimization and compensation of the soft tissue artifact (STA) is provided. It has been shown that STA is greater than the instrumental error associated with stereophotogrammetry, has a frequency content similar to the actual bone movement, is task dependent and not reproducible among subjects and, of lower limb segments, is greatest at the thigh. It has been shown that in in vivo experiments only motion about the flexion/extension axis of the hip, knees and ankles can be determined reliably. Motion about other axes at those joints should be regarded with much more caution as this artifact produces spurious effects with magnitudes comparable to the amount of motion actually occurring in those joints. Techniques designed to minimize the contribution of and compensate for the effects of this artifact can be divided up into those which model the skin surface and those which include joint motion constraints. Despite the numerous solutions proposed, the objective of reliable estimation of 3D skeletal system kinematics using skin markers has not yet been satisfactorily achieved and greatly limits the contribution of human movement analysis to clinical practice and biomechanical research. For STA to be compensated for effectively, it is here suggested that either its subject-specific pattern is assessed by ad hoc exercises or it is characterized from a large series of measurements on different subject populations. Alternatively, inclusion of joint constraints into a more general STA minimization approach may provide an acceptable solution. © 2004 Elsevier B.V. All rights reserved. Keywords: Human movement analysis; Experiments; Soft tissue artifacts; Minimization; Compensation

1. Introduction The fundamental role of human movement analysis in the advancement of the understanding of musculo-skeletal system physiopathology is well established [1], and the utilization of this technique continues to flourish. However, there are limitations due to limited awareness of the methodological fundamentals and experimental inaccuracies associated with the instrumentation examining a biological system. The present paper is the third in a series of articles ∗

Corresponding author. Tel.: +39 051 6366522; fax: +39 051 6366561. E-mail address: [email protected] (A. Leardini).

0966-6362/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2004.05.002

addressing the major issues concerning the reconstruction of human skeletal system 3D kinematics when analyzed using optoelectronic stereophotogrammetry, by far the most widespread technique used. The series is aimed at enhancing the comprehension of the fundamentals of human movement analysis techniques and its concomitant problems. The first article in this series [2] provided the necessary theoretical bases for the description of human movement, and suggestions for appropriate terminology. The second [3] reported on the instrumental errors associated with any stereophotogrammetric system and on the analytical and technical procedures necessary to cope with this source of inaccuracy. In this article, where rigidity of the body

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segments was assumed and only the stereophotogrammetric error was dealt with, it was shown that the reliability with which joint degrees of freedom (DOF) with limited range of motion are reconstructed is very low. It is an unfortunate reality that, apart from a few special in vivo tests [4], routine in vivo movement analysis experiments must deal with deformable tissues. This introduces methodological problems that are recognized to be the primary limitation to further advancements of human movement analysis [1]. Two different sources of error originate at the interface between the stereophotogrammetric system and the bony segment under analysis: anatomical landmark (AL) misplacement [5] and soft tissue artifact (STA). The present paper addresses the latter source of error, the nature of which resides in the relative movement between the markers and the underlying bone. This is associated with the specific marker set and experimental protocol adopted. Inertial effects, skin deformation and sliding, which occur mainly in areas closer to the joints [6], and deformation caused by muscle contractions, contribute independently to STA. Because of its nature, the artifact has a frequency content similar to the actual bone movement and it is therefore very difficult to distinguish between the two by means of any filtering technique. A comprehensive review of the studies aimed at assessing STA and at devising methods for the minimization of its effects on the description of the musculo-skeletal function is presented first. Pelvic and lower limb segments are dealt with, as these are of great interest in human movement analysis. Proposed techniques designed to minimize these effects are also reported, as divided into those analyzing skin surface motion and deformation and those including joint motion constraints. The main purpose is to facilitate the rapid identification of the most critical issues and the retrieval from the literature of the most salient solutions.

2. Soft tissue artifact assessment A ‘soft tissue shifting’ effect of body surface markers that is very critical particularly when precise analyses of joint motion are needed, was already presumed a long time ago [7]. Since then, a remarkable number of studies that describe patterns and magnitudes of STA have been reported. The most relevant works are reported here, organized according to the technique used, namely intra-cortical pins, external fixators, percutaneous skeletal trackers and Roentgen photogrammetry. 2.1. Techniques based on intra-cortical pins A few pioneering studies [8,9] were conducted using intra-cortical pins to analyze skeletal motion during walking that were reported more extensively only recently. In 1991, Lafortune and Lake [10] described the use of X-ray videofluoroscopy and intra-cortical pins to quantify STA magnitude. In a preliminary experiment using fluoroscopy, three

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cycles of unloaded flexion-extension of the knee were analyzed. A marker placed on the proximal tibia exhibited a 21 mm distal and a 23 mm posterior displacement, found to be linearly related to knee flexion. In a second experiment, the STA magnitude was analyzed at heel strike during running. Data were obtained from a marker attached to a cortical pin inserted into the tibia and from a marker stuck on the skin of a volunteer over the lateral tibial condyle. The magnitude of the relative movement between these two markers reached 10 mm, and was also dependent also upon the type of impact. A later study by the same authors [11] reported actual tibiofemoral 3D kinematics during walking using target clusters fixed directly into the bones, but no information was provided for describing patterns of STA. Karlsson and Lundberg [12] used external marker devices each consisting of a bone screw and an aluminum tripod instrumented with three reflective spherical markers. Two of these devices were anchored on the distal femur and on the proximal tibia. Three skin markers were also stuck on the distal thigh and on the proximal shank. Two volunteers were asked to perform hip internal-external rotation with the knee in extension while standing. Comparison between knee joint rotations obtained with bone-anchored and skin-attached markers showed a large discrepancy. Internalexternal rotation of the knee when measured with the former cluster of markers revealed a range of about 20◦ , which was observed to be about 50◦ when measured with the latter skin cluster. The skin displacement tracked by shank markers was found to be smaller than that by thigh markers. Reinschmidt et al. [13] assessed STA contribution both in the knee (tibiofemoral) and ankle (tibiocalcaneal) motion during walking. Intra-cortical Hofmann pins with triads of reflective markers were inserted into the lateral femoral condyle, the lateral tibial condyle and the postero-lateral aspect of the calcaneus in three volunteers. Six skin markers were also stuck on the thigh, six on the shank and six on the shoe, covering the entire lateral and anterior aspects. Three-dimensional rotations of the knee and ankle joint were described using standard conventions [14,15]. The root mean square and maximal difference between bone- and skin-marker based rotations are reported in Table 1 for these two joints and for each anatomical plane. It was confirmed through segmental error analysis (the average difference between the bone- and skin marker-based motion) that most of knee rotation errors are due to STA at the thigh. It was concluded that skin markers can only be used to reliably determine flexion/extension (FL/EX) at the tibiofemoral joint, whereas for the knee abduction/adduction (AB/AD) and internal/external rotations (IN/EX), the error introduced by the STA can almost be as high in magnitude as the real joint motion. The same authors [16] used a similar technique to also determine the effect of STA on 3D joint rotations in the stance phase of five running trials. The knee motion was expressed, as in the previous work, in terms of Cardan angles calculated from both the external and skeletal markers. Good

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Table 1 Root mean square differences (RMS Diff.) and maximal differences (Max Diff.) between bone- and skin-marker based for knee and ankle complex rotations in the three anatomical planes during the stance phase of walking for three healthy subjects Anatomical planes

Variable

Knee rotations

Ankle complex rotations

Subject 1

Subject 2

Subject 1

Subject 2

Subject 3

Frontal

RMS Diff. Max Diff.

2.1 3.1

2.4 4.0

2.8 6.0

4.4 6.4

3.6 5.6

2.9 4.2

Transverse

RMS Diff. Max Diff.

4.2 7.6

2.1 7.3

5.3 10.3

4.3 5.7

2.0 5.0

3.2 4.5

Sagittal

RMS Diff. Max Diff.

1.5 2.6

1.7 4.6

3.2 5.8

3.1 4.9

4.4 8.1

2.5 4.6

Subject 3

All measurements are in degrees (reprinted from [13] with permission from Elsevier).

agreement was found between skin- and bone-based knee patterns of FL/EX. For AB/AD and IN/EX, the difference between skeletal and external motion was large compared to the amplitude of the corresponding physiological motion. Errors relative to the full range of motion were 21% for FL/EX, 64% for IN/EX and 70% for AB/AD when averaged across the three subjects analyzed. It was also shown that skin markers lead to an overestimation of joint motion. The single segment error analysis showed that the STA at the shank did not exceed 5◦ for all subjects and all rotations. At the thigh, STA was more significant and reached values higher than 10◦ in IN/EX. As expected, the skin movement errors were higher in running than in walking. Fuller et al. [17] instrumented a leg with two arrays of six markers inserted directly into the tibial tubercle and the greater trochanter. Twenty markers were also stuck all over the thigh and shank segments. Several different motor tasks were analyzed from a single volunteer. It was shown that skinmounted markers could exhibit displacements with respect to the underlying bone of up to 20 mm. Furthermore, STA was found to be task-dependent, i.e. the pattern of errors differed from task to task. Using a power spectrum analysis, it was observed that any attempt to remove STA through traditional filtering techniques can result in loss of information or in introduction of spurious motion patterns. It was concluded that the skin-mounted marker position data are not appropriate for representing motion of the underlying bones, particularly of the femur. While testing a new femoral tracking device, Yack et al. [18] reported skin/femur relative motion in the transverse plane in a preliminary study on two volunteers. Intra-cortical pins, instrumented with four infrared light emitting diodes, were inserted into the proximo-lateral aspect of the right femur and tibia. Three surface markers were attached along the crest of the tibia. The femoral tracking device was clamped over the femoral condyles with two diodes attached to its lateral extension, and a third diode was placed on the skin just distal to the greater trochanter. Walking and running at freely selected speed were analyzed. The authors claimed a ‘reasonable validity’ (rotation errors within a few degrees) of the new device over 85% of the stance phase of gait, based on the observation that real transverse knee

motion based on bone pins was reproduced with a 20% error in amplitude. In the following relevant paper [19], a 10 mm root mean square (RMS) was also reported as erroneous tibiofemoral displacement. In addition, the performance of the femoral tracking device was reported when compared with the traditional Helen Hayes marker set in 13 healthy subjects. Results showed a large decrease of knee rotations and translations in the transverse plane, considered as an important advancement toward the tracking of knee real motion. It was admitted in both reports, however, that the errors increased substantially in terminal stance and during the swing phase, which is when substantial knee flexion occurs. In the most recent study, Westblad et al. [20] assessed the difference in ankle complex motion during the stance phase of walking as measured by skin- and bone-anchored markers in three volunteers. Three markers were attached laterally on each shank, heel, and forefoot. Skin marker position data were collected during a barefoot walking trial. Hoffman pins were inserted into the tibia, fibula, talus and calcaneus. Four markers were attached to each pin and further walking trials were performed. Their results showed that the mean maximal differences between the skin- and bone-based joint rotations were less than 5◦ . The smallest absolute difference was found for plantar/dorsiflexion. This finding was in contrast to a previous report [13] where AB/AD was shown to exhibit the smallest difference. This may be explained by the fact that subjects assessed in the latter study wore shoes. 2.2. Techniques based on external fixators Angeloni et al. [21] first made use of patients wearing external devices for fracture fixation at either the femur or the tibia to analyze STA. These devices allowed, through adequate marker mounting, the definition of a set of axes rigidly associated with the underlying bone (Fig. 1). Markers were placed on the skin surface over four ALs: greater trochanter (GT), lateral epicondyle (LE), head of the fibula (HF), lateral malleolus (LM). Additional markers were placed on rigid plates strapped to the proximal half of the thigh and the shank using large elastic bands and Velcro fasteners. The range of displacement of these skin- and plate-mounted markers with respect to the corresponding underlying bones during

A. Leardini et al. / Gait and Posture 21 (2005) 212–225

Fig. 1. Example of a femur fracture fixation device. An external metallic frame is rigidly attached to the bone by means of several intracortical bone screws. The three markers (full circles) on the fixator are depicted. The set of axes rigidly associated to the femur (xf , yf , zf ) can then be described in a laboratory frame (X, Y, Z) (reprinted from [6] with permission from Elsevier).

walking is reported in Table 2. Similar results were obtained using a semi-quantitative video-fluoroscopic analysis. It was shown that skin mounted markers are subjected to larger STA than the markers mounted on the rigid plates. More detailed results were reported in a later paper by the same authors [6] using the same technique. Anatomical frames (AF) associated with skin- and fixator-marker cluster technical frames (CTF) were defined using calibrated ALs. Markers on the fixator were assumed to provide instantaneous positions and orientations, hereinafter referred to as poses, of the corresponding rigidly associated bone. Markers were also located where visible to the cameras above the bony prominences typically used in gait analysis: GT, LE, HF, LM. Additional skin markers were stuck on other locations of the lateral aspect of the body segment compatible with the presence of the fixator and camera visibility. Several motor tasks were analyzed: level walking at a natural speed, cycling on an exercise bike, flexion of the lower limb Table 2 Directional displacement (X, Y, Z) of the skin (greater trochanter: GT, lateral epicondyle: LE, head of the fibula: HF, lateral malleolus: LM) and plate-mounted markers strapped to the thigh (T1, T2, T3, T4) and on the shank (S1, S2, S3, S4) during walking X

Y

Z

Femur GT LE T1 T2 T3 T4

5 6 7 12 5 4

14 16 3 4 5 4

8 9 8 9 6 8

5 6 3 4 3 3

Tibia HF LM S1 S2 S3 S4

11 18 8 7 6 9

10 13 11 12 7 10

7 8 10 6 6 6

5 7 6 4 3 4

RMS

These are expressed in the corresponding anatomical reference fixator-based frame (reprinted from [21]). Root mean square (RMS) values of the distance between the mean location of the markers and their instantaneous location in this frame over one walking cycle, are also reported. All values are in millimeters.

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while standing, repetitive isometric muscular contraction, and hip external rotation while standing with the knee in hyperextension. Typical local trajectories of the GT, LE, HF and LM skin markers in the relevant fixator-based AF during a walking stride are reported in Fig. 2. The marker position errors associated with STA showed remarkable magnitudes (up to 40 mm), as much as an order of magnitude larger than stereophotogrammetric errors. In general, the value of the STA associated with the GT, LE, HF and LM markers was found to be related to the relevant joint angle, irrespective of the motor task performed. The extent to which joint rotations were affected by these skin marker position errors is reported in Table 3. STA caused a peak-to-peak error in bone orientation between 6◦ and 20◦ in the femur, and between 4◦ and 10◦ in the tibia. During a 45◦ hip IN/EX excursion, the artifact in femoral orientation reached magnitudes ranging from 6◦ to 28◦ . It was concluded that the estimation of knee joint kinematics might be affected by inaccuracies that for FL/EX, AB/AD, and IN/EX can be respectively as large as 10, 20, and 100% of the relevant expected range of motion. 2.3. Techniques based on percutaneous trackers Another set of studies has been performed recently using percutaneous skeletal trackers. These were metal devices rigidly attached to bony segments by using a number of halo pins inserted into the periosteum on opposite sides, instrumented with a rigid array of four retroreflective markers. Holden et al. [22] simultaneously tracked the motion of the shank during self-selected speed walking using two sets of targets. Skeletal fixation of a bone-mounted target was accomplished using a tracker device mounted on the distal tibia and fibula. Additional markers were attached to Table 3 Root mean square (RMS) values of the effect of soft tissue artifact (STA) on bone orientation Clusters

Walking

m1–m4–m5 m2–m4–m5 GT–m4–m5 m3–m4–m5 m1–m4–m2 m2–m4–m1 m1–m5–m3 m2–m5–m3 m5–m4–m1 m5–m4–m3 m1–m2–m4 m1–m2–m3 m6–m7–LM m6–m7–HF HF–LM–m7 HF–LM–m6

– – – – – – – – – – – – 1.5 1.5 1.0 3.5

– – – – – – – – – – – – 2.5 2.0 3.0 2.5

Cycling – – – – – – – – – – – – 1.5 3.0 2.5 2.5

1.5 1.5 1.5 2.0 2.5 1.5 3.0 2.5 3.0 3.5 3.5 4.5 – – – –

1.5 2.0 1.5 2.0 1.5 3.0 2.5 2.5 2.0 3.0 4.0 3.0 – – – –

Hip rotation 2.0 2.5 2.5 2.0 2.5 2.5 2.0 2.5 2.5 2.0 4.0 5.5 – – – –

2.0 1.0 3.0 5.0 5.5 2.5 7.0 6.0 3.0 2.5 1.5 3.0 – – – –

3.0 3.0 3.0 1.5 4.5 5.0 7.0 6.5 3.0 3.0 6.5 7.0 – – – –

1.5 2.0 1.5 4.0 4.0 5.0 7.0 7.0 2.5 5.5 2.0 3.0 – – – –

The three scalar components along the antero-posterior, longitudinal and medio-lateral axes are reported for each of the analyzed motor tasks and for several combinations of skin markers (m1, m2, m3, m4, m5 on the thigh and m6, m7 on the shank). All measurements are in degrees (reprinted from [6] with permission from Elsevier).

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Fig. 2. Frontal (a and c) and sagittal (b and d) plane projections of the trajectories of great trochanter (GT), lateral epicondyle (LE), head of the fibula (HF) and lateral malleolus (LM) skin markers during a walking cycle at natural cadence (reprinted from [6] with permission from Elsevier).

shells mounted on the lateral surface of the mid-shank and on the dorsal aspect of the mid-foot. A static anatomical calibration trial was used to establish an AF associated with both the skeletal and surface arrays. The relative 3D difference between the skeletal- and the surface-based AFs was calculated and considered as a measure of the STA. The first internal rotation error peak, at 8% of gait cycle, had a mean value of 4◦ over the three subjects analyzed. Additional rotation errors occurred during the terminal stance and most of the swing phase, with a magnitude that reached 8◦ in one subject. The largest relative rotations about the medio-lateral and antero-posterior axes were less than 3◦ . Maximum absolute displacements of the skin-based AF were less than 6.0 mm in the transverse plane but reached 10.5 mm longitudinally. Reproducibility of the relative displacement between skin markers and underlying bone was good within subjects, but poor among subjects. The effect of STA on knee moments in the three subjects analyzed was considered relatively small, as the largest difference between the trackerand surface-based estimations was only 9 N m. Another study [23], although aimed at determining an optimal marker set for the spatial tracking of the tibia, indirectly provided information on the STA. A single tracker was clamped to the two malleoli and AFs were defined for the foot, shank and thigh using markers located over ALs. Three subjects performed several walking trials for each of the eleven different configurations of markers stuck on the shank, obtained by combining geometry, location (proximal/distal) and attachment (underwrap/overwrap) factors for the array. The best performance was observed for an underwrapped rigid shell with four markers located distally, as far as possible. Generally better estimates of the tibial rotations were obtained by placing the array more distally over the lateral aspect of the shank. Larger errors were observed during the first and last thirds of the stance phase, probably associated respectively to inertial effects at heel-strike, and to muscle contraction for ankle push-off. Rotational errors about the medio-lateral and antero-posterior axes were similar in magnitude (1–2◦ ), ranging respectively between 2 and 3% and 10 and 25% when expressed in percentage of the relevant range of motion. The maximum rotational errors were observed about the longitudinal axis (7–8◦ ). The same authors

later reported [24] on the effect of STA on knee moments in level walking, by comparing relevant calculations obtained using the same tracking targets and the surface cluster ranked the best in the former study. On the six subjects analyzed, the largest difference was 3 N m, but probably not enough to affect relevant clinical interpretation. 2.4. Techniques based on Roentgen photogrammetry Maslen and Ackland [25] first used 2D Roentgen photogrammetry to investigate STA at the foot and ankle during rear foot inversion/eversion maneuvers. Small steel markers were stuck over the two malleoli, the navicular tuberosity, the sustentaculum tali and the base of the fifth metatarsal. Lateral view radiographs from ten volunteers were collected and analyzed, including compensation for X-ray magnification. Mean displacement between the skin markers and the silhouette of underlying bones varied from 2.7 to 14.9 mm, with the two malleoli markers showing the largest artifact. Tranberg and Karlsson [26] performed a similar study on six healthy volunteers, but they analyzed neutral, 20◦ of ankle dorsiflexion and 30◦ of ankle plantarflexion. Spherical lead markers were stuck on the skin over the medial malleolus, the navicular, the medial calcaneus, and the base of the first and fifth metatarsal heads. The largest STA was found for the proximal markers (up to 4 mm), i.e. the ones closest to the medial malleolus and to the calcaneus. This was explained by the largest angular motion exhibited by the talocrural joint implying the largest skin sliding. The smallest STA was found for the metatarsal bones (less than 1.8 mm). This technique, however, can provide estimation of the STA only in the sagittal plane. Sati et al. [27] first performed a study to assess quantitatively the relative movement between skin and underlying bone at the knee using standard fluoroscopy. Small metallic markers were individually taped on the medial and lateral aspects of the distal thigh. Fluoroscopic images were collected during approximately 65◦ of active knee flexion from upright posture in three male subjects. Effects of image distortion and 3D femur movements were removed with a mathematical model. RMS values of lateral marker movements varied from 2.5 to 16.8 mm, with a 42.5

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and 20.6 mm maximum peak-to-peak respectively along the antero-posterior and vertical directions. Medial marker movements varied from 2.1 to 17.1 mm RMS, with a 31.0 and 39.2 mm peak-to-peak. This skin-to-bone movement varied considerably with marker location. In particular, the largest skin displacement was observed for markers located closest to the joint line. These results provide valuable information for marker placement in routine movement analysis. A biplanar radiographic system was also used to characterize STA at the knee [28]. For the first time, impact movement was analyzed (one-legged forward hopping), although only two skin markers mounted over the medial and lateral epicondyles were tracked. Reference femur and tibia motion was tracked in two patients after implantation of three 1.6 mm diameter tantalum beads at the time of knee surgery. The peak-to-peak magnitude of the STA after foot impact ranged from 5 to 31 mm. The time from impact to peak displacement, the dominant frequency and the magnitude of the transient component of the displacement were dependent on subject, marker and direction. The extent to which this marker displacement was generated by inertial effects and by knee flexion was not shown. Characterization of the STA was also recently obtained by means of a technique combining stereophotogrammetry and 3D fluoroscopy performed on a total knee replacement patient [29,30]. Sit-to-stand and stair climbing motor tasks were analyzed. Nineteen reflective markers were uniformly attached on the thigh and ten on the shank, covering the entire lateral aspect. One reflective and radiopaque marker on the patella and three in the fluoroscope field of view were used to obtain time synchronization and spatial registration respectively. The 3D pose of the prosthesis components was reconstructed from each 2D fluoroscopic projection with an iterative procedure using a shape matching technique based on corresponding CAD models. The skin marker trajectories from the stereophotogrammetric system were reported in the relevant prosthesis component reference frames. Markers on the thigh, particularly those located more postero-proximally, exhibited a much larger STA than those on the shank, particularly in sit-to-stand. The maximum amount of this STA was 40.0, 51.5, and 55.3 mm along the antero/posterior, medio/lateral and vertical directions, respectively. Tibio/femoral rotations, as reconstructed from several different sub-clusters of thigh skin markers, were also assessed. The AB/AD rotations were the least accurate, RMS of the error ranging from 250% (most distal cluster) to 360% (most proximal) in sit-to-stand, and from 135% (most distal) to 185% (most proximal) in stair climbing.

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tremities. The discrepancies between the values reported by different authors may be justified by the different techniques used, by the large variability in the subjects analyzed and in the tasks performed, but mainly by the different locations of the skin-mounted markers. However, the following general conclusions can be drawn: (a) errors introduced by the STA are much larger than stereophotogrammetric errors; (b) the pattern of the artifact is task dependent; (c) STA is reproducible within, but not among, subjects; (d) STA introduces systematic as well as random errors; (e) the STA associated with the thigh is greater any other lower limb segment. Skin markers can therefore be used to determine reliably joint FL/EX, whereas AB/AD and IN/EX rotations should be regarded much more skeptically as the STA produces spurious rotational effects that have magnitudes comparable with the relevant joint rotations during movement. As far as the technique used is concerned, external fixator devices [6,21] have enabled the accurate and simultaneous assessment of STA at several different areas of the thigh and shank, including the typical locations for skin marker placements (GT, LE, HF, LM) which are closer to the joints. Drawbacks are associated with the state of the soft tissues in these patients and to the likely non-physiological pattern of locomotion caused by the wearing of the device. On the other hand, percutaneous skeletal trackers [22–24] clamped to epiphyses can allow assessment of STA in healthy subjects, though encumbrance is similar to the external fixators. Assessment of STA in patients with external fixators and in volunteers with percutaneous pins is limited by the skin sliding restrictions imposed by the pins, typically mounted in traditional skin marker locations (epicondyles and malleoli). Several complications using bone anchored pins have been recently discussed, and the likely critical deformation of these has been pointed out by considering data collected in tests simulating in vivo experiments of direct skeletal motion tracking [31]. The use of intra-cortical and percutaneous pins on normal volunteers should be limited also for ethical reasons. Roentgen photogrammetric techniques, based on single X-rays [25,26], are invasive as well and provide only 2D information. The techniques based on fluoroscopy [27–30] are minimally invasive, provide a complete 3D measurement of the STA, and enable analyses of a larger number of skin markers, although this is limited to a single joint at time and extensive image data processing is necessary. When combined with traditional stereophotogrammetry [29,30], these techniques enable assessment of the STA over the entire lateral aspect of the lower limb segments with no skin sliding constraints.

2.5. Discussion 3. Soft tissue artifact minimization and compensation A summary of the studies on STA assessment is provided in Table 4, ordered by location of the skin markers along the lower limb, from proximal to distal. The studies reported provide a large quantity of data for describing the amount and the effects of STA at the lower ex-

STA strongly affects AL trajectories and, consequently, relevant segment AFs and finally joint kinematics and kinetics. Techniques for minimizing its contribution and compensating for the relevant effects are fundamental in

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Table 4 Summary table of the studies reporting soft tissue artifact (STA) measurements, ordered by anatomical location along the lower limb, from most proximal to most distal Anatomical locations of skin markers

Motor tasks

Technique

Full thigh Full thigh Full thigh Full thigh GT, LE, mid thigh (plate and skin) Distal thigh Distal thigh Distal thigh Distal thigh (clamp) Full shank Full shank Full shank Full shank Proximal shank Proximal shank HF, LM, mid shank (plate and skin) Mid shank (plate) Mid shank (several different clusters) Distal shank LM, medial malleolus Medial malleolus Full foot (shoe) Heel Rear foot Rear foot Forefoot

Walking Stance of running Leg swing; walking; cycling; squat Stair climbing; sit-to-stand/stand-to-sit Walking; cycling; active flexion; hip rotation

Intracortical pins Intracortical pins Intracortical pins 3D fluoroscopy External fixators

Hip IN/EX rotation Active knee flexion One-legged forward hopping Walking; running; leg swing Walking Stance of running Leg swing; walking; cycling; squat Stair climbing; sit-to-stand/stand-to-sit Active flexion, impact phase of running Hip IN/EX rotation Walking; cycling; active flexion; hip rotation

Reference

Year

3 3 1 1 2

13 16 17 29, 30 21, 6

1997 1997 1997 2002 1992, 1996

Intracortical pins Roentgen photogrammetry Biplane radiographic system Intracortical pins Intracortical pins Intracortical pins Intracortical pins 3D fluoroscopy Intracortical pins Intracortical pins External fixators

2 3 2 2 3 3 1 1 1 2 5

12 27 28 18, 19 13 16 17 29, 30 10 12 21, 6

1994 1996 2002 2000, 2004 1997 1997 1997 2002 1991 1994 1992, 1996

Walking Walking

Percutaneous trackers Percutaneous trackers

3 7

22 23

1997 2000

Stance of walking Ankle complex inversion/eversion Ankle complex dorsi/plantarflexion Walking Stance of walking Ankle complex inversion/eversion Ankle complex dorsi/plantarflexion Stance of walking

Intracortical pins Roentgen photogrammetry Roentgen photogrammetry Intracortical pins Intracortical pins Roentgen photogrammetry Roentgen photogrammetry Intracortical pins

3 10 6 3 3 10 6 3

20 25 26 13 20 25 26 20

2000 1994 1998 1997 2000 1994 1998 2000

human movement analysis. Several methods have been proposed and they are described in the present section. Before reporting on the analytical methods, a brief mention of the clusters of markers, which are usually employed, is necessary. There is still a debate on the optimal non-invasive marker set for tracking motion of human body segments [23]. Deformation of these clusters, that is, inter-marker distance changes, is always observed in the collected data due to stereophotogrammetric errors [3] and also due to STA when skin surface clusters are used. A CTF associated with a cluster of markers also moves rigidly with respect to the underlying bone due almost exclusively to STA. The displacement of the cluster with respect to the bone can thus be interpreted as the summation of an internal deformation plus a rigid displacement. The internal deformation may be reduced by the use of rigid supports [18,19,22,23,32–34]. These devices, however, do not guarantee a more rigid linkage to the bone and they may even introduce systematic rigid artifacts associated with their own inertial effects. The rigid displacement of the cluster due to STA is such that the pose of the relevant CTF differs substantially from that of the real bone. The use of minimization and compensation techniques can be effective in reducing the propagation of deformation and rigid motion of the cluster to bone kinematics. In this section, methods for the enhancement of CTF pose estimation from a cluster

Subjects

of both rigidly or non-rigidly supported external markers are discussed. 3.1. The “solidification” procedure A so-called “solidification” procedure was proposed [35] to address only the cluster deformation effect. This was aimed at defining marker trajectories consistent with the rigid body assumption. Since three non-collinear markers are sufficient to determine segment pose, the first step consists of the identification of the subset of three markers that defines the leastperturbed triangle throughout the entire motion. Then, the corresponding ‘solid’ shape which best fits this time-varying triangle is defined from the measured triangles using an iterative procedure which calculates the mean value for each vertex angle and eliminates step-by-step the most deformed frame, until 75% of the frames are retained. The best fit of the solid to each measured triangle is then determined by choosing appropriate points on the triangle and by using the standard Single Value Decomposition (SVD) algorithm [36] to solve a least-squares positioning problem. To validate this method, nominal trajectories of markers rigidly assembled in two clusters associated with the shank and thigh respectively were generated using experimental data obtained during the swing phase of gait. Artificial noise

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representing typical artifacts during gait was introduced to obtain perturbed marker trajectories. The ability of the method to recover nominal knee kinematics was evaluated. Results revealed that the proposed procedure works just as well as the least-squares method in reducing kinematic errors. The authors explicitly claimed that the only advantages of the proposed technique were its ability to identify erroneous frames and the use of unambiguous rigid body theory while maintaining the kinematic accuracy of the least-squares method. 3.2. Multiple anatomical landmark calibration The Calibrated Anatomical System Technique (CAST) was proposed for a more rational determination of AFs [37]. This technique entails a single static calibration of a number of ALs for the identification of their local coordinates in the relevant CTF. A pointer mounting two markers in known positions is used to identify accurately these ALs. An enhancement of this technique was proposed later, aimed at compensating for the skin sliding associated with joint flexion during the execution of the target motor task [38]. This technique overcomes the previous constraint of rigidity between the CTF and the ALs and recommends a double calibration of these, at the two extremes of the expected range of joint motion. The hypothesis, based on a previous experimental study [6], is that the AL local coordinates in the relevant CTF change consistently over the flexion cycle of the relevant joint and therefore interpolation between two known positions at the extremes of the range of flexion can be performed. To validate the new procedure, a cycling exercise was analyzed on a patient wearing a femoral external fixator. The femur ALs traditionally used in gait analysis (GT, LE and medial epicondyle: ME) were calibrated both at maximum hip/knee extension (E, pedal down, Fig. 3a) and flexion (F, pedal up, Fig. 3b). In each of the two calibrations, the CTF pose and the AL global positions were first determined. The optimal rigid transformation between the CTF poses in lower limb positions E and F was then estimated with

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the standard SVD technique [35]. This transformation was then also applied to the global coordinates of the ALs. Two geometrical configurations of the cluster and anatomical markers were therefore obtained, both expressed in the E position reference frame, providing information on cluster shape variation and AL displacements when passing from F to E. A time-varying overall model, including calibration parameters, was obtained through linear interpolation between these two configurations, assuming time as the independent variable. Femoral motion was finally estimated from the marker trajectories collected during cycling, using the FL/EX angle as the registering variable with the model. With respect to the original single-calibration procedure, the RMS reconstruction error for GT decreased from more than 15 mm to less than 10 mm, while the RMS of femur orientation and position decreased respectively from approximately 5◦ and 7 mm to less than 4◦ and 4.5 mm. Compensation methods based on multiple AL calibrations should be designed specifically for the motor task under analysis, according to the expected range of joint rotations. The preliminary implementation proposed for cycling, with two extreme positions and only a linear interpolation in between, has provided encouraging results. This technique can certainly be enhanced with more sophisticated methods for characterizing skin deformation and sliding throughout the joint flexion range (a larger number of joint positions analyzed, non-linear interpolation models, etc.). This enhancement should however be constrained in any specific application by limiting the corresponding number of necessary additional calibrations of the ALs. 3.3. Pliant surface modeling Another study [39] compared traditional rigid body modeling (RBM), which assumes body segment and surface rigidity and 6 DOF, with a novel non-rigid, 12 DOF method, also referred to as pliant surface modeling (PSM). The latter provided for simultaneous quantification of rigid rotations and translations, plus ‘pliant’ (scales and shears) motion accounting for deformation of the marker cluster associated with skin

Fig. 3. Diagrammatic representation of the double-calibration compensation method [38]. Skin and pointer markers (empty circles) and anatomical landmarks (grey circles) in the extension (a) and flexion (b) calibration procedures in cycling. Skin and anatomical landmark configurations in both flexion (F) and extension (E) postures when expressed in the same extension reference frame are depicted in (c) (reprinted from [38] with permission from Elsevier).

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stretching, muscle activity and inertial phenomena. Numerical methods traditionally used to modify the shape of virtual objects were taken from computer graphics to model nonrigid motion of the segment surface. In particular deformations were described with affine deformation matrices made up of rotation, scaling, shearing and translation. To assess the performance of the PSM method compared with traditional RBM techniques, experimental data were collected on three able-bodied subjects. Pins were inserted into the femur and tibia of each subject over the GT and Gerdy’s tubercle, and a circular cluster of markers was placed on the top of each pin to obtain real bone movements. Clusters of markers were also stuck on the thigh and on the shank external surfaces. The subjects were asked to walk on a treadmill at three different speeds and position data of the markers were collected. The errors in reconstructing real femur and tibia segment position with RBM technique were found to be 4.8 and 3.8 mm respectively, reduced by 45 and 56%, respectively by the PSM technique. The improvement in segment orientation was less than 0.5◦ , which is minimal. No significant differences in segment pose errors were noted between the two methods for different gait velocities, whereas, within the models, higher speeds produced only slightly higher errors. Of course, the new method cannot account for rigid cluster displacement with respect to the underlying bone. 3.4. Dynamic calibration Another combined experimental and analytical procedure to be included in routine movement analysis [40] was proposed for subject- and task-specific assessment of STA and for its compensation by means of a dynamic model of the CTF-to-AL relationship. Four markers were affixed to the pelvis by a rigid plate on a Milwaukee orthoses. Further, five markers were stuck directly on the skin of the thigh, and four on the skin of the shank. A standard CTF was associated with the pelvis, thigh, and shank segments, and another one to the ‘thigh-shank’ segment. Marker position data were collected in upright posture and during level walking at natural cadence. Then further tasks were performed with the knee locked in hyperextension with voluntary muscle contraction: (a) a hip FL/EX followed by AB/AD, (b) a lower limb pendulum swing, and (c) hip and pelvis 3D rotation simulating as much as possible the swing phase of walking (starting from an extended position, and coupled with an anti-clockwise rotation of the pelvis on the transverse plane). Calibration of traditional ALs was also performed and the hip joint centre was estimated using the functional approach [41]. Positions of the medial and lateral epicondyle were estimated on the basis of a rigid thigh-shank CTF defined by markers on the shank, which are supposed to be more reliable than the thigh CTF in a knee-locked leg, in both upright posture and gait-simulated hip rotation. Using this posture as a reference, the displacement of these ALs in the thigh CTF and the relevant relation to hip FL/EX, AB/AD and IN/EX were computed and stored in a ‘table of the artifact’.

Approximate values of hip rotations were first estimated using the traditional joint kinematics techniques to compensate for STA when the walking task was analyzed. For each of these 3D rotational positions, the corresponding least distant values in the artifact table were sought and the corresponding artifact vector extracted for each thigh-shank based AL of the femur. The final local positions of these ALs were thus corrected by subtracting the corresponding artifact component. The new ALs were the basis for the corrected AF and from this AF compensated knee translations and rotations were computed. A quantitative validation of this method was performed with a patient wearing a single DOF knee prosthesis (Kotz Modular Femur and Tibia Reconstruction System, Howmedica GmbH, Kiel, Germany). When femur and tibia poses were determined using a traditional least-squares optimal estimator, the knee joint translations and rotations were found to be affected by RMS errors up to 14 mm and 6◦ , respectively. Using the proposed technique, these errors were reduced to less than 4 mm and 3◦ , respectively. It is interesting to compare these error reductions due to those obtained by cluster optimization as reported in Table 3 of the previous paper in this series [3]. With this technique, the original strong correlation between STA and hip rotations was successfully removed. Further validation was obtained by comparing knee kinematics estimated through two different thigh clusters on a normal subject. The variables that undergo moderate variations during walking (frontal and transverse plane rotations) showed significantly different patterns for the two clusters when no compensation was applied. On the contrary, when compensation was applied, the two estimates were much more similar. It was deduced that this dynamic calibration significantly contributed to the compensation of STA. The effectiveness of this procedure was tested initially when considering knee joint kinematics only, at thigh markers affected only by hip motion related STA, and during gait analysis only. The method can be extended to other joints and other motor tasks, and the relevant effectiveness reconsidered. The technique is based on the confidence that STA during the dynamic target activity can be well reproduced during simulated trials of dynamic artifact assessment movements. 3.5. Point cluster technique A further technique [42] approached lower limb segment pose estimation by considering a cluster of a large number of markers uniformly distributed on the body segment under analysis, each with an assigned arbitrary mass, which can be varied from sample to sample. The centre of mass and the inertia tensor of the cluster are calculated at each time frame. The eigenvalues and eigenvectors of the inertia tensor are the principal moments of inertia and the principal axes of the ‘point cluster’. The basic idea is to adjust the mass of each marker at each step to minimize eigenvalue changes. In this way, the cluster has a time-invariant distribution matrix similar to that for rigid bodies. The variation in the mass

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distribution results in the estimated position of the centre of mass and, through the eigenvectors, in the orientation of the reference system. In turn, this reflects on translation and rotation components at the joint level. The method was tested in a simulation model where systematic and random errors were introduced into a fixed cluster of points. The simulation demonstrated that the error due to non-rigid body movement could be substantially reduced. The method was also applied in a group of ten normal subjects during walking. The results for knee rotation and translation obtained from the point cluster method compared well with results previously obtained from normal subjects with intra-cortical pins inserted into the femur and tibia [11]. This method was extended [43] to more general cases, providing transformation equations from assumed activitydependent deformation models. This further method was tested in 50 simulated trials for an eight-marker cluster set, and in vivo on a patient wearing an Ilizarov external fixation device on the shank that offered a coordinate system truly embedded into bone. In the latter single trial test, the reduction of the error for overall pose was 33 and 25%, respectively, though skin motion was likely to have been restricted by the numerous pins of the fixator. Techniques for characterizing general cases of segment deformation have also been recently proposed [44]. The original and the developed ‘point cluster’ techniques do not require the collection of a further specific motor task, but do require a significant number of additional markers on each body segment, with associated time-consuming marker placement and tracking. The techniques cannot cope with the rigid displacement of the array with respect to the underlying bone, and are also limited by the critical knowledge of the skin deformation models. It has also been suggested [28] that these techniques should be applied with caution for motion studies involving rapid movement and substantial impact. Furthermore, a recent assessment of the performance of this method [45] based on experimentally-obtained marker trajectories and relevant bone pose data [29,30] has shown that the estimated skeletal kinematics are strongly dependent on the modeling form assumed for the marker displacement in the bone frame. Estimation of bone position was also found to be much more critical than bone orientation.

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is performed. The hypothesis was that the consideration of joint constraints and global error minimization can significantly reduce the effects of STA on segment pose estimation, particularly on the critical IN/EX and AB/AD rotations. The optimization process was defined by minimizing the weighted sum of squared distances between simulated and model-determined marker positions, with the additional constraint, that data refers to a n-link chain model, where joints are taken as all perfect ball-and-sockets. A weighting matrix accounted for different segmental residual errors but assumed that all markers of a segment are equally affected by STA. A different weighting factor reflecting its average degree of STA was given to each segment. The method was tested on 20 simulated gait trials where artificial noise was added into each 3D marker coordinate as in Ch`eze et al. [35]. The validation was performed in terms of known joint angles and joint centre positions. Fig. 4 reports results from four techniques, including the proposed ‘global optimization’, employed in a typical simulated trial.

3.6. Global optimization The common limitation of all the above techniques is that each body segment is treated separately, without any imposition of known constraints at the joints. It was previously observed [46] that STA can result in apparent non-physiological joint translation or even dislocation, in addition to unreliable joint kinematics and kinetics. An innovative technique [47,48] was based on a global minimization, in a traditional least-squares sense, of the overall measurement errors when a simultaneous determination of the segment poses of a multi-link model of the locomotor musculo-skeletal system

Fig. 4. Results of the ‘global optimization’ technique [47] from a typical simulated trial. Calculated angles in degrees at the hip (a–c) and knee (d–f) joints by using original true values (thick solid lines), a basic direct linking method (dotted lines), a traditional segment-based optimization method (dashed lines), and the proposed global optimization method (thin solid lines) (reprinted from [47] with permission from Elsevier).

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With the non-optimized technique based on simple definition of vectors by direct linking of external markers (direct method), average hip and knee joint dislocations were 3.88 and 3.24 cm, respectively. With standard segment-based optimization techniques, the corresponding values were 1.33 and 0.69 cm. These figures should be compared with those of no dislocation as imposed on these two joints by the global optimization method. Moreover, the errors in joint rotations were found to be significantly reduced by the use of the proposed method with respect to the traditional one. It was also noted that the inclusion of the weighting matrix in the optimization provides a more effective STA minimization. The selection of different weighting factors according to the expected magnitude of STA at different body segments enables better estimation of relevant poses by stronger consideration of the more reliable of these segments. Spherical constraint at the hip, knee and ankle joints were also imposed on the Helen Hayes gait model for improving reliability of the gait measurements [49–51]. The bony segment poses and the functional joint centres and axes are estimated in the same general iterative procedure also by utilizing specifically designed optimization and filtering techniques. Repeatability of these was tested on a single healthy subject by analyzing approximately 100 gait cycles obtained from three physiotherapists [51]. The significant lower standard deviations obtained in inter-marker distance, bone segment dimensions and clinical output variables compared with the original gait model was considered as an important enhancement of gait analysis. Reduction of STA effects was claimed also by a similar technique [52,53] originally designed to compute joint linear and angular displacements and relevant derivatives able to cope in real time with severe cases of false identification and occlusion of markers. Joint kinematics were resolved by integrated marker trajectory tracking, segment pose reconstruction, joint angle determination, and derivative computation using the collected original image points on the CCD cameras and a multi-linkage ball-and-socket joint model parameterized specifically to the subject. Estimation was based on Kalman filters and on minimization of the summation of the distances on the 2D image plane between the measured marker traces and the corresponding back-projected markers of the 3D model. Although the robustness of the technique against missing and phantom marker configurations was demonstrated, the ability to cope also with STA effects needs to be assessed further. Global optimization that is capable of incorporating body segment pose data and joint motion constraints has been pursued by other workers. A complete optimization process and more physiological equations of joint motion, based on in vitro measurements of knee and ankle passive motion for a more realistic representation of motion of the locomotor apparatus have been reported recently [54]. Previously obtained in vitro single joint kinematics were synchronized to in vivo gait analysis by using FL/EX angles. One DOF mechanism equations were imposed at the knee and ankle joints,

and fine-tune adjustment of these equations was performed to match best estimated and in vivo measured segment poses. Global optimal estimation was performed also to simply identify model geometrical parameters of the human joints when these are assumed as simple kinematic pairs [55]. The application of these methods is limited by the controversial assumption of the ball-and-socket model for the lower limb joints, by the very complex analysis when more sophisticated joint models are included, and by the difficulty in applying these to patients with substantial joint instability or deformity. However, the inclusion of joint constraints into the overall estimation of the bony segment poses is fully appropriate and sensible. 3.7. Discussion Techniques based on minimization of a general error function, either defined locally to the single body segment [35,36,39,42–44] or globally to the entire lower limb [47–55], and on compensation of an assessed measurement of STA [38,40] have been proposed in the literature to optimize bone pose estimation. These techniques can also be differentiated by those modeling the external segment surface alone [35,39,42–44] and those addressing also segment relative motion [38,40,47–55]. The former enhances the traditional methods of segment pose optimal estimation [36,56] by explicitly addressing the random and systematic effects of STA and considers absolute and relative motion of the skin markers in a purely geometric view, irrespective of the physiological event generating the STA and irrespective of joint motion and constraints. The latter include in the analysis considerations about physiological joint motion, though very simple, for a more reliable final association between CTF and AF. However, two studies of this latter method [38,40] involve the performance of an additional task necessary for subject-specific STA calibration that is critical clinically. Each of these different techniques has both advantages and disadvantages, and should be chosen according to the specific application. It is the recommendation of the authors that no a priori selection should be pursued among these techniques unless a general validation is carried out based on a single set of consistent and realistic data. It should also be concluded that the overall reliability obtained by addressing explicitly STA effects exceeds that obtained using traditional filtering and smoothing algorithms of single position data and other optimization techniques as reported in the previous paper of this series [3]. One of the studies mentioned here [40] is exemplary in this respect, reporting the root mean square of the estimates of five DOFs at the knee joint, known to be zero. These values, therefore representing errors for the corresponding DOFs, were found to decrease very differently when non-optimal, optimal and STA compensation techniques were applied: in AB/AD these were 5.5◦ , 2.4◦ and 2.5◦ , respectively, in IN/EX 5.5◦ , 4.1◦ and 2.4◦ , in antero-posterior displacement 12.5, 11.9 and 3.6 mm, in vertical displacement 7.0, 6.7 and 4.5 mm, in medio-lateral

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displacement 13.5, 13.0 and 2.9 mm. Corresponding timehistories were reported in a recent paper [57]. Great improvements in bone pose estimation techniques are expected from a general and complete characterization of STA in the lower limb. This can be obtained in the future either by thoroughly modeling the three independent contributions (inertia, skin sliding near to the joints and segment deformation due to muscle contraction) or experimentally, based on a large series of measurements from several different populations of subjects. A preliminary attempt at the former approach was proposed recently [58,59], aimed at designing general dynamic models of body segments, including simulations of inertia and damping and ability to predict the complex motion of the soft tissues over the bony segments by using finite element techniques. Full validation will be necessary, though parameterization of the model to the specific subject and the sliding of those skin markers located closely to the joints are expected to be critical limitations. The latter approach, however, would likely require extensive investigations based on the simultaneous knowledge of external cluster and internal bone pose by means of invasive techniques. Besides ethically-related concerns, this approach is limited by the observation that these STA measurements are likely to be altered in case of the presence of external devices. Imaging techniques are less invasive, and may be exploited further in the future to simultaneously track both external markers and internal bony landmarks.

4. Conclusions It has been recognized that STA is the most significant source of error in human movement analysis [1,60]. Any future investigation aimed at reliably estimating in vivo human joint motion on a six-DOF-base certainly requires sophisticated techniques to cope with STA. The inaccuracies resulting from this source of error are critical not only in joint mechanics investigations and in virtual reality applications, but also in routine clinical movement analysis. The interpretation of relevant results and the associated clinical decision-making process should therefore include awareness of this critical phenomenon and its effects. Despite the numerous solutions proposed, the objective of a reliable estimation of skeletal motion in in vivo experiments of human movement has not yet been achieved satisfactorily. The minimization approach certainly would benefit from the introduction of more sophisticated joint models, but computational issues will certainly constrain these developments. For an effective compensation of the STA, it is here suggested that either ad hoc exercises be carried out to collect relevant subject-specific information, or a systematic general characterization of the artifact be made available. From this literature review, it is clear that this characterization is not only far from being completed but also far from being practicable, because large differences among subjects have been reported. It would, therefore, be desirable to identify structural models

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of the STA and to devise experiments that would allow for their calibration, i.e. model parameter determination, to be applicable to the specific subject and motor task under analysis.

Acknowledgments This work was initially supported by the project Vakhum (Virtual Animation of the Kinematics of the Human for Industrial, Educational and Research Purposes), funded by the Information Society Technologies Programme of the European Commission (IST-1999-10954).

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