- Journal of Biomechanics: Editorial Human movement analysis: The soft tissue artefact issue
- STAPAG (Soft-Tissue-Artifact-Propagation Attenuation Group) École polytechnique fédérale de Lausanne (EPFL) - Switzerland (CH)
"This Special Issue of the Journal of Biomechanics reports an overview of the innovative research being conducted on a problem which every researcher reporting on the movement of humans and animals must cope with. The problem is rooted in our inability to directly observe the bones of our participants during the activities of interest and it represents a critical challenge since it is the motion of these underlying bones that is generally the nexus of our research. We are most often forced to reconstruct the motion of bones using the recorded trajectories of markers placed on the skin, which, due to the interposed soft tissues, are not rigidly fixed to the underlying bones. The local mobility of these markers (now commonly referred to as soft tissue artefact, or STA) leads to errors that, in some cases, are of the same order of magnitude as the motions at the joints being investigated. This problem therefore puts at risk the validity of a significant body of research in the basic, clinical and applied sciences. It is also a problem that, until recently, has been neither fully understood nor considered, arguably overlooked, by many of us whose research is affected by it. With this Special Issue, we hope this scenario will change."
Laboratory of Movement Analysis and Measurement (LMAM)
STAPAG (Soft-Tissue-Artifact-Propagation Attenuation Group) is a consortium to share data and ideas, identify, implement and test the potentially most effective solutions to solve the soft tissue artefact (STA) issue and disseminate relevant results.
A-H
- A linear soft tissue artefact model for human movement analysis A linear soft tissue artefact model for human movement analysis:
- Analysis of skeletal motion kinematics for a knee movement cycle "This study estimated the skeletal motion for a knee motion cycle. The surface markers on the thigh and the shank showed the computed displacement during in vivo motion analysis. This error was minimized using optimization procedure. The displacement was generally greater on the thigh than the shank. The minimization of error produced by this procedure was more successful on the thigh than the shank. The purpose of his study was to require high value motion data. These results provide the basis to calculate the instantaneous knee axis of rotation in a follow up study."
- Bone orientation and position estimation errors using Cosserat point elements Bone orientation and position estimation errors using Cosserat point elements and least squares methods: Application to gait "The aim of this study was to analyze the accuracy of bone pose estimation based on sub-clusters of three skin-markers characterized by triangular Cosserat point elements (TCPEs) and to evaluate the capability of four instantaneous physical parameters, which can be measured non-invasively in vivo, to identify the most accurate TCPEs. Moreover, TCPE pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers, using rigid body (RBLS) and homogeneous deformation (HDLS) assumptions. Analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold-standard bone pose by bi-plane fluoroscopy tracking the subjects’ knee prosthesis and a stereophotogrammetric system tracking skinmarkers affected by soft tissue artifact."
- Can hip and knee kinematics be improved by eliminating thigh markers? "This study presents a comparison of hip and knee kinematics as calculated by five concurrently worn tracking marker sets during eight different tasks. The first three marker sets were based on Helen Hayes but used (1) proximal thigh wands, (2) distal thigh wands, and (3) patellar markers instead of thigh wands. The remaining two marker sets used rigid clusters on the (4) thighs and shanks and (5) only shanks. Pelvis and foot segments were shared by all marker sets."
- Comparison of kinematic and kinetic parameters calculated using a cluster based model Comparison of kinematic and kinetic parameters calculated using a cluster based model and Vicon’s plug-in gait "Gait analysis is an important clinical tool. A variety of models are used for gait analysis, each yielding different results. Errors in model outputs can occur due to inaccurate marker placement and skin motion artefacts, which may be reduced using a cluster-based model. We aimed to compare a custom-made cluster model (ClusBB) with Vicon's plug-in gait. A total of 21 healthy subjects wore marker sets for the ClusBB and plug-in gait models simultaneously while walking on a 6-m walkway".
- Comparison of surface mounted markers Comparison of surface mounted markers and atachment methods in estimating tibial rotations during walking: an in vivo study "The overall goal of this work was to determine an optimal surface-tracking marker set for tracking motion of the tibia during natural cadence walking. Eleven different marker sets were evaluated. The marker sets differed in the location they were attached to the shank, the method used to attach the marker sets to the segment and the physical characteristics of the marker sets. Angular position during stance for each marker set was expressed relative to the orientation of the tibia as measured using bone anchored markers. A marker set consisting of four markers attached to a rigid shell positioned over the distal lateral shank and attached to the leg using an underwrap attachment yielded the best estimate of tibial rotation. Rotational deviations of +/-2 degrees about the medio-lateral and antero-posterior axes, and +/-4 degrees about the longitudinal axis did occur even when using the optimal set of markers."
- Effect of Tibia Marker Placement on Kinematics in Pathological Gait "This study aimed to determine the effect of tibia marker placement on walking kinematics in children with pathological gait. Three-dimensional lower extremity gait data were collected using both a traditional tibia wand (protruding laterally from the distal shank) and a tibia crest marker on 25 children with pathological gait. Kinematic variables during walking and quiet standing were calculated using each marker and the "Plug-in Gait" implementation of the conventional gait model."
Proof of concept using in vivo data
"We investigated the accuracy of a linear soft tissue artefact (STA) model in human movement analysis. Simultaneously recorded bone-mounted pin and skin marker data for the thigh and shank during walking, cutting and hopping were used to measure and model the motion of the skin marker clusters within anatomical reference frames (ARFs)."
I-N
- In Vivo Knee Kinematics during Gait In Vivo Knee Kinematics during Gait Reveals New Rotation Profiles and Smaller Translations
- Influence of thigh cluster configuration on the estimation of hip axial rotation "The non-invasive estimation of hip axial rotation is prone to error. Most of this is likely to originate from soft tissue artefact (STA) at the thigh. The purpose of this study was to evaluate the relative performance of four different thigh cluster configurations. Three were novel configurations whilst one represented the Helen Hayes convention."
- Joint Center Estimation Using Single-Frame Optimization: Part 1: Numerical Simulation "The biomechanical models used to refine and stabilize motion capture processes are almost invariably driven by joint center estimates, and any errors in joint center calculation carry over and can be compounded when calculating joint kinematics. Unfortunately, accurate determination of joint centers is a complex task, primarily due to measurements being contaminated by soft-tissue artifact (STA). This paper proposes a novel approach to joint center estimation implemented via sequential application of single-frame optimization (SFO). First, the method minimizes the variance of individual time frames' joint center estimations via the developed variance minimization method to obtain accurate overall initial conditions. These initial conditions are used to stabilize an optimization-based linearization of human motion that determines a time-varying joint center estimation. In this manner, the complex and nonlinear behavior of human motion contaminated by STA can be captured as a continuous series of unique rigid-body realizations without requiring a complex analytical model to describe the behavior of STA. This article intends to offer proof of concept, and the presented method must be further developed before it can be reasonably applied to human motion."
- Knee moment profiles during walking Knee moment profiles during walking: errors due to soft tissue movement of the shank and the influence of the reference coordinate system
- Non-invasive assessment of soft-tissue artifact Non-invasive assessment of soft-tissue artifact and its effect on knee joint kinematics during functional activity
"In order to identify abnormal or pathological motions associated with clinically relevant questions such as injury mechanisms or factors leading to joint degeneration, it is essential to determine the range of normal tibiofemoral motion of the healthy knee. In this study we measured in vivo 3D tibiofemoral motion of the knee during gait and characterized the nonsagittal plane rotations and translations in a group of six healthy young adults."
"The soft-tissue interface between skin-mounted markers and the underlying bones poses a major limitation to accurate, non-invasive measurement of joint kinematics. The aim of this study was twofold: first, to quantify lower limb soft-tissue artifact in young healthy subjects during functional activity; and second, to determine the effect of soft-tissue artifact on the calculation of knee joint kinematics."
O-S
- On the influence of soft tissue coverage On the influence of soft tissue coverage in the determination of bone kinematics using skin markers
- Quantification of soft tissue artifact in lower limb human motion analysis: A systematic review "This systematic review critically evaluates the quantification of soft tissue artifact (STA) in lower limb human motion analysis. It has a specific focus on assessing the quality of previous studies and comparing quantitative results."
- Soft tissue artifact assessment and compensation Human movement analysis using stereophotogrammetry
- Soft tissue artifact causes significant errors in the calculation of joint angles Soft tissue artifact causes significant errors in the calculation of joint angles and range of motion at the hip "Soft tissue movement between reflective skin markers and underlying bone induces errors in gait analysis. These errors are known as soft tissue artifact (STA). Prior studies have not examined how STA affects hip joint angles and range of motion (ROM) during dynamic activities. Herein, we: 1) measured STA of skin markers on the pelvis and thigh during walking, hip abduction and hip rotation, 2) quantified errors in tracking the thigh, pelvis and hip joint angles/ROM, and 3) determined whether model constraints on hip joint degrees of freedom mitigated errors."
- Strategy for minimising soft tissue artefact at the tibia "The aim of this study is to identify a subset of markers on the tibia showing the least amount of movement with respect to each other."
"Accurate measurement of underlying bone positions is important for the understanding of normal movement and function, as well as for addressing clinical musculoskeletal or post-injury problems. Non-invasive measurement techniques are limited by the analysis technique and movement of peripheral soft tissues that can introduce significant measurement errors in reproducing the kinematics of the underlying bones when using external skin markers. Reflective markers, skeletally mounted to the right hind limb of three Merino-mix sheep were measured simultaneously with markers attached to the skin of each segment, during repetitions of gait trials. The movement of the skin markers relative to the underlying bone positions was then assessed using the Point Cluster Technique (PCT), raw averaging and the Optimal Common Shape Technique (OCST), a new approach presented in this manuscript."
Part 3. Soft tissue artifact assessment and compensation
T-Z
- The impact of thigh and shank marker quantity on lower extremity kinematics (open access) The impact of thigh and shank marker quantity on lower extremity kinematics using a constrained model "Background: Musculoskeletal models are commonly used to quantify joint motions and loads during human motion. Constraining joint kinematics simplifies these models but the implications of the placement and quantity of markers used during data acquisition remains unclear. The purpose of this study was to establish the effects of marker placement and quantity on lower extremity kinematics calculated using a constrained-kinematic model. We hypothesized that a constrained-kinematic model would produce lower-extremity kinematics errors that correlated with the number of tracking markers removed from the thigh and shank. Methods: Healthy-young adults (N = 10) walked on a treadmill at slow, moderate, and fast speeds while skin-mounted markers were tracked using motion capture. Lower extremity kinematics were calculated for 256 combinations of leg and shank markers to establish the implications of marker placement and quantity on joint kinematics."
- Tibiofemoral and tibiocalcaneal motion during walking: external vs. skeletal markers "The purpose of this study was to determine the errors in knee (tibiofemoral) and ankle joint complex (AJC; tibiocalcaneal) rotations caused by the skin movement artefact. Intracortical bone pins were inserted into the femur, tibia, and calcaneus of five subjects. Marker triads were attached to these pins, and additionally, six skin markers to the thigh, six to the shank, and three to the shoe. For each subject three walking trials were filmed with three synchronized LOCAM cameras (50 Hz). Flexion/extension, ab/adduction, and longitudinal rotation at the tibiofemoral joint as well as plantar-/dorsiflexion, ab/adduction, and in/eversion at the AJC were calculated from both skin and bone markers during the stance phase of walking. The results showed that the errors in knee rotations were mainly caused by the thigh markers."
- Towards a no-thigh markers protocol of gait analysis "An attempt to reduce the need for markers on the thigh is being carried out by modelling the knee joint constraints. By using MRI and fluoroscopy, the relative movements of femur, tibia and patella were captured in vivo during knee flexion. The length and orientation of cruciate ligaments were identified all along the range of movement. This information was then used in a four-bar, variablelength linkage model of the tibio-femoral connection. By knowing the location of the hip joint centre (fixed within the pelvis) and the shank in space, the rotation of the thigh can be determined from geometrical relationships. Preliminary results show that knee joint kinematic estimation errors are less than those due to markers being affected by skin artefacts."
Skin Deformation Measurements:
- Capturing and Animating Skin Deformation in Human Motion "During dynamic activities, the surface of the human body moves in many subtle but visually significant ways: bending, bulging, jiggling, and stretching. We present a technique for capturing and animating those motions using a commercial motion capture system and approximately 350 markers."
- Continuous Capture of Skin Deformation "We describe a method for the acquisition of deformable human geometry from silhouettes. Our technique uses a commercial tracking system to determine the motion of the skeleton, then estimates geometry for each bone using constraints provided by the silhouettes from one or more cameras."
- Estimating joint kinematics from skin motion observation: modelling and validation "Modelling of soft tissue motion is required in many areas, such as computer animation, surgical simulation, 3D motion analysis and gait analysis. In this paper, we will focus on the use of modelling of skin deformation during 3D motion analysis."
- Influence of soft tissue artifacts "Influence of soft tissue artifacts on the calculated kinematics and kinetics of total knee replacements during sit-to-stand
- Quantification of soft tissue artefact in motion analysis Quantification of soft tissue artefact in motion analysis by combining 3D fluoroscopy and stereophotogrammetry: a study on two subjects
- Soft tissue motion measurement Soft tissue motion measurement on shank and thigh with MRI
- Visualization of Local Movements for optimal Marker Positioning "In this paper we exploit a local fitting tool to visualize the influence of skin deformation on marker movements. Such a knowledge can in turn improve the layout of optical markers. We illustrate our viewpoint on motions of the upper-torso."
The current study aimed to quantify the soft tissue artifacts of selected markers on the thigh and shank, and their effects on the calculated joint center translations, angles and moments of the knee during sitto-stand. Ten patients with total knee replacements rose from a chair under simultaneous surveillance of a motion capture system, a force-plate and a fluoroscopy system."
"Two subjects, treated by total knee replacement, underwent data acquisition simultaneously with fluoroscopy and stereophotogrammetry during stair climbing, step up/down, sit-to-stand/stand-to-sit, and extension against gravity. The reference 3D kinematics of the femur and tibia was reconstructed from fluoroscopy-based tracking of the relevant prosthesis components. Soft tissue artefact was quantified as the motion of a grid of retro-reflecting makers attached to the thigh and shank with respect to the underlying bones, tracked by optoelectronic stereophotogrammetry. The propagation of soft tissue artefact to knee rotations was also calculated."
Patella Marker:
- Comparison of a thigh wand versus a patella marker "The effect of static standing posture on dynamic walking kinematics: Comparison of a thigh wand versus a patella marker A thigh wand affixed to the lateral and distal parts of the thigh has typically been used as part of the 3-D computerized gait analysis marker set andmodel to assess hip rotation in walking. A marker placed on the patella has been proposed as an alternative. The purpose of this study was two-fold. First, determine if the static standing hip posture affected kinematic gait data of hip rotation. Second, determine which marker within the configuration, (a thigh wand or patella marker) performedmore consistentlywith the variation in static hip position."
- Improved tracking of hip rotation using a patella marker "A marker placed on the patella allows for more accurate measurement of hip rotations than traditional thigh wands. In controlled trials of isolated hip internal-external rotation, the patella marker detected 97% of the actual range of motion, compared with 59% for a distal thigh wand and 41% for a proximal thigh wand."
- Use of a patella marker to improve traking of dynamic hip rotation range of motion "This study investigated effectiveness of a patella marker in tracking hip rotation range of motion in comparison with traditional thigh wands. In controlled trials of isolated hip internal–external rotation, the patella marker detected 98 +/- 8% of the actual range of motion, compared with 53 +/- 10% for a distal thigh wand and 43 +/- 13% for a proximal thigh wand. The patella marker produced the smoothest hip rotation curves and the smallest hip rotation range in walking, and results from the patella marker did not depend on walking speed."
Pelve - Pelvis:
- A joint kinematics driven model of the pelvic soft tissue artefact "When skin-markers trajectories are used in human movement analysis, compensating for their relative movement with respect to the underlying bone (soft tissue artefact, STA) is essential for accurate bone-pose estimation; information about the artefact is required in the form of a mathematical model. Such model, not available for pelvic artefacts, could allow pelvic STA compensation in routine gait analysis by embedding it in skeletal kinematics estimators and developing ad-hoc optimization problems for the estimate of subject-specific model parameters. It was developed as driven by adjacent body segment kinematics."
- Quantification of pelvic soft tissue artifact in multiple static positions "Soft tissue artifact (STA) has been identified as the most critical source of error in clinical gait analysis. Multiple calibration is a technique to reduce the impact of STA on kinematic data, which involves several static calibrations through the range of motion of the joint of interest. This study investigated how skin markers at the pelvis were displaced in relation to anatomical body landmarks in multiple static calibration positions."
- Soft tissue displacement over pelvic anatomical landmarks during 3-D hip movements "The position, in a pelvis-embedded anatomical coordinate system, of skin points located over the following anatomical landmarks (AL) was determined while the hip assumed different spatial postures: right and left anterior superior and posterior superior iliac spines, and the sacrum. Postures were selected as occurring during walking and during a flexion–extension and circumduction movement, as used to determine the hip joint centre position (star-arc movement). Five volunteers, characterised by a wide range of body mass indices (22–37), were investigated. Subject-specific MRI pelvis digital bone models were obtained. For each posture, the pose of the pelvis-embedded anatomical coordinate system was determined by registering this bone model with points digitised over bony prominences of the pelvis, using a wand carrying a marker-cluster and stereophotogrammetry."
Biomech-L forum:
- Marker set to minimize Soft-Tissue Artifact (12-12-2018), Dr. Allan Carman "What lower limb marker set would I want to use to minimize the effect of Soft-Tissue Artifact?"
"Re: Marker set to minimize Soft-Tissue Artifact
It is not just soft tissue artifact (STA) and it is not just the marker set that determines 3DMA validity and reliability of joint angle data. If you interested in measuring STA or correcting errors in joint angle data then there are larger sources of error that need to be addressed first before STA can be considered. 3DMA involves a series of processes, each should be based on a sound understanding of the sources of errors involved and with checks in place to assess and reduce these errors at each step in the process.
The major influences on validity and reliability of joint angle data during gait can be groups as: 1. 3D system (cameras, calibration, volume and reconstruction of 3D marker coordinates) 2. Post processing (tracking, identification, smoothing and gap filling) 3. Defining segment axes location and orientation (functional, regression, optimization) 4. Analytical methods (least squares, multi segment, joint DoF) 5. Skin movement artefact (marker placement, RFD).
Also see link to 3DMA error flow chart: Google drive folder: 3DMA Flow Chart.jpg
I have presented data previously comparing the 3DMA reliability literature of traditional minimalist marker based (PiG, HelenHayes, Kit Vaughan, T3Gait), KAD, Optimization methods and rigid fixation devices with and without functional joint centres. The unpublished gait reliability data from the University of Otago is included and is essentially using the guidelines mentioned below.
A summary can be found at: Google drive folder: Summary 3D Reliability.pdf and Results Table Systematic Review brief.xls
I have also presented data previously on normal gait and the widely varying, inconsistent and often unrealistic joint angle data that has been presented in the literature, including marker based, bone pins and radiographic. Google drive folder: Normal gait, axes misalignment.docx and nonlinear error.xls
All studies suffer greatly from axes misalignment errors. The examples demonstrate the influence and correction of axes misalignment and non-linear errors on joint angle data. The examples also show the close agreement in gait joint angle data (that seemed unrelated) that can be obtained by post hoc correction of axes misalignment. Where systematic errors in thigh axes alignment about the longitudinal axes of -12 to +22 degrees were observed across the studies. The examples also shows the relatively small and repeatable influence of soft tissue artefact (STA) makes on gait joint kinematics in marker based studies.
This is the first time that I am aware of that normal gait joint angles have been demonstrated.
From the 3DMA cluster design file, here are some basic guidelines used when placing markers: - At least four markers per segment [1,4,5], however six to ten markers has been recommended [6]. These may be real or virtual joint centers, defined relative to adjacent segments. - Markers are well distribution along at least two axes [7]. - Markers avoid areas of high skin movement artefact (proximal 1/3 thigh, Greater trochanter [8, 9], calf musculature [9], anterior forearm, and other large muscle bellies. - Do not place rigid fixation devices (RFD) containing fixed markers over large muscle bellies, such as anterior-lateral thigh. You are interested in the movement of the segment underneath and the RFD will only exacerbate skin movement artefact. - Placing markers at varying locations so individual markers contain varying motion due to skin movement artefact within the cluster [6]. This may involve placing markers on the anterior, lateral and posterior aspects, placing markers lateral to joints as well as on the body of the segment, and including virtual joint centers.
And some methodological guides: - Do not smooth 3D data. It will introduce distortions in 3D trajectories around sudden de- accelerations, particularly foot strike, hitting or striking. In the case of foot strike producing large errors between the foot segment and COP from force platforms. Which in turn produce large oscillations in resultant joint moments and forces immediately prior to and after foot strike. - Do not gap fill. The best way to reconstruct a 3D path if required is to reconstruct the segment location from all available markers and use the segment location to fill the missing frames. - Use a least squares method [4,5,6] even when using the minimum three markers [4]. The most stable and preferred least square method is that of Veldpaus (1988) [5]. Direct methods and inertial (principal axes) methods that are based purely only on the global marker coordinates are poor by comparison and should not be used to define segment axes location [4-5]. - Use 6 degrees of freedom joints. However, do include virtual joint centers from proximal and/or distal segments in the least square approach. - Do not use a multi-segment least squares or optimization approach with constrained joints (3 DoF). It is the least reliable of 3DMA methods as the model cannot accommodate unavoidable errors in 3D marker location, joint centers and skin movement artefact. Joint translations and changes in joint center of rotation will also adversely affect the model. - RMS Errors in reconstructed 3D markers as well as 3D segment location should be assess and reported as part of routine 3DMA. Marker and segment tracking errors are commonly step discontinuities which can be readily identified and corrected using RMS errors on a frame by frame basis. Allowing the identification of the marker in error on a 3D segment or 2D camera coordinate in error comprising a 3D marker location. Do not smooth raw 3D marker data as this will prevent routine identification and correction of errors in 3D markers and least squares reconstruction of segment locations. - Assess and correct axes misalignment in the subject calibration procedure by collecting and analyzing joint angle data from a controlled and repeatable movement pattern (squat or gait). This can be used to refine segment axes alignment by reducing non-linear error (cross talk) in non-sagital joint rotations and checking validity of rotations before the analysis of the trials of interest. - Do not add or subtract offsets directly from joint angle data. This ignores the source of the error (axes misalignment) and interdependency of joint angle data. Instead correct the segment axes miss-alignment within the subject calibration procedure. This will correct the nonlinear errors propagated through the Cardan rotations of both the proximal and distal joints of the segment. - Collect and analyze a controlled and repeatable movement pattern (squat or gait) both pre and post trials of each session. This can be used to assess consistency of methods, axes alignment and calculated joint angle data against known or expected joint rotations. Of interest is a special issue in the Journal of Biomechanics (Vol 62, 2017) on multi body kinematics optimisation methods (MBO or MKO) with soft tissue artefact (STA) compensation. What is evident in this issue is the lack of awareness of the multiple factors and their importance in influencing axes misalignment between modelled and underlying segment and on the validity and reliability of joint angle. Misconceptions and poor understandings are evident, including; assuming STA is the dominant source of error in axes misalignment; use of a model that introduces additional errors into the reconstruction of segment locations, is known to lack validity and reliability in joint angle data and is highly dependent on joint DoF, markers used and movement pattern; that bone pins give criterion joint angle data, and; a STA compensation approach that uses a predictive function based on derived joint angle data. Despite the extensive efforts presented in this special issue and in the wider literature related to the MBO model with STA compensation, the method has been unsuccessful and has yet to describe normal gait joint angles, has produced no improvement in validity of knee joint kinematics, and is yet to describe the relatively small and repeatable STA present in gait, which has been perceived as large, varied and inconsistent. A review can be found here. Google drive folder: JBiomech STA Vol62.pdf There is a lot of information contained in the links, let me know if you have difficulty accessing the files. This may well raise more questions than answers. Allan [1] Miller, N.R., Shapiro, R., McLauchlan, T.M. (1980), A technique for obtaining spatial kinematic parameters of segment of biomechanical systems from cinematographic data. JBiomechanics, 13, 535-547. [2] Veldpaus, F.E., Woltring, H.J., Dortmans, L.j.M.G. (1988) A least squares algorithm for the equiform transformation from spatial marker co-ordinates. J. Biomechanics, 21, 45-54. [3] Challis, J.H. (1995) A procedure for determining rigid body transformation parameters. J. Biomechanics, 28, 733-737. [4] Cappozzo, A, Cappello, A, Della Croce, U, Pensalfini, F (1997) Surface marker cluster design criteria for 3-D bone movement reconstruction, IEEE Trans. Biom. Eng., 44, 1165-1174. [5] Carman, AB, Milburn, PD (2006) Determining rigid body transformation parameters from ill-conditioned spatial marker coordinates. J. Biomechanics, 39, 1778-1786. [6] Miller, N.R., Shapiro, R., and McLaughlin, T.M. (1980) A technique for obtaining spatial kinematic parameters of segments of biomechanical systems from cinematographic data. Journal of Biomechanics, 13(7), 535-548. [7] Solderkvist, I, and Wedin, PA (1993) Determining the movement of the skeleton using well-configured markers, J. Biomechanics, 26, 1473-1477. [8] Cappozzo, A, Catani, F, Leardini, A, Benedetti, MG, Della Croce, U (1996) Position and orientation in space of bones during movement: experimental artifacts, Clinical Biomechancis, 11, 90-100. [9] Stagni, R, Fantozzi, S, Cappello, A, Leardini, A (2005) Quantification of soft tissue artifact in motion analysis by combining 3D fluoroscopy and sterophotogrammetry: a study on two subjects. Clinical Biomechanics, 20, 320-329.