Technical Brief

Model of Soft Tissue Artifact Propagation to Joint Angles in Human Movement Analysis

[+] Author and Article Information
Álvaro Page

CIBER de Bioingeniería,
Biomateriales y Nanomedicina (CIBER-BBN),
Barcelona, Spain
e-mail: afpage@ibv.upv.es

Helios de Rosario

Instituto de Biomecánica de Valencia,
CIBER de Bioingeniería,
Biomateriales y Nanomedicina (CIBER-BBN),
Barcelona, Spain
e-mail: helios.derosario@ibv.upv.es

Vicente Mata

D. Ingeniería Mecánica y de Materiales,
Universitat Politècnica de València,
Camino de Vera s/n,
Valencia E46022, Spain
e-mail: vmata@mcm.upv.es

Antonio Besa

D. Ingeniería Mecánica y de Materiales,
Universitat Politècnica de València,
Camino de Vera s/n,
Valencia E46022, Spain
e-mail: abesa@mcm.upv.es

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received April 12, 2013; final manuscript received November 26, 2013; accepted manuscript posted December 12, 2013; published online February 13, 2014. Assoc. Editor: Zong-Ming Li.

J Biomech Eng 136(3), 034502 (Feb 13, 2014) (7 pages) Paper No: BIO-13-1186; doi: 10.1115/1.4026226 History: Received April 12, 2013; Revised November 26, 2013; Accepted December 12, 2013

This work describes the kinematic laws that govern the transmission of soft tissue artifact errors to kinematic variables in the analysis of human movements. Artifacts are described as relative translations and rotations of the marker cluster over the bone, and a set of explicit expressions is defined to account for the effect of that relative motion on different representations of rotations: the rotation around the screw axis, or rotation vector, and three Euler angle sequences (XY′Z, YX′Y″, ZX′Y″). Although the error transmission is nonlinear in all cases, the effect of artifacts is greater on Euler sequences than on the rotation vector. Specifically, there are crosstalk effects in Euler sequences that amplify the errors near singular configurations. This fact is an additional source of variability in studies that describe artifacts by comparing the Euler angles obtained from skin markers, with the angles of an artifact-free gold standard. The transmission of errors to rotation vector coordinates is less variable or dependent on the type of motion. This model has been tested in an experiment with a deformable mechanical model with a spherical joint.

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Grahic Jump Location
Fig. 1

B0 represents the location of bone in the reference position. It moves to a given position B, {Θ;G0G1} being the associated finite displacement. MC0 represents the cluster of markers attached to the skin, at reference position (points Pi0). When B0 moves to B, MC0 goes to MC (points Pi) by means of the finite displacement {ΘMC;G0G}. STA are expressed in a bone-embedded reference frame by the displacements Pi0Pi2 of the individual markers with respect to the bone. Pi2 are obtained from the observed positions of the markers at MC, Pi, after applying the finite displacement {-Θ;-G0G1}, opposite to the real motion of the bone. The associated rotation dq represents the relative rotation of the whole cluster with respect to the bone.

Grahic Jump Location
Fig. 2

Experimental device to simulate a deformable marker set that moves relative to the bone

Grahic Jump Location
Fig. 3

RV and EA components of the bar and foam observed rotations. For the YX′Y″ sequence, the curve labeled as “Z” corresponds to the third angle (Y″).

Grahic Jump Location
Fig. 4

Components of the rotation artifact dq (relative motion of the foam with respect to the bar). Note that dq has not zero values at t = 0. This is because the reference position does not coincide with the initial position of the measured motion.

Grahic Jump Location
Fig. 5

Estimated and measured RV errors. (a) Coordinates of RV errors in the reference system {u,n,u × n}. (b) Module and orientation error of the RV.

Grahic Jump Location
Fig. 6

Components of the errors in RV and EA versus artifact dq. EA errors are permutated and related to the X-Y-Z axes as in Table 1.




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