Surface marker cluster translation, rotation, scaling and deformation: Their contribution to soft tissue artefact and impact on knee joint kinematics

Abstract

When recording human movement with stereophotogrammetry, skin deformation and displacement (soft tissue artefact; STA) inhibits surface markers’ ability to validly represent the movement of the underlying bone. To resolve this issue, the components of marker motions which contribute to STA must be understood. The purpose of this study is to describe and quantify which components of this marker motion (cluster translation, rotation, scaling and deformation) contribute to STA during the stance phase of walking, a cutting manoeuvre, and one-legged hops. In vivo bone pin-based tibio-femoral kinematics of six healthy subjects were used to study skin marker-based STA. To quantify how total cluster translation, rotation, scaling and deformation contribute to STA, a resizable and deformable cluster model was constructed. STA was found to be greater in the thigh than the shank during all three movements. We found that the non-rigid (i.e. scaling and deformation) movements contribute very little to the overall amount of error, rendering surface marker optimisation methods aimed at minimising this component superfluous. The results of the current study indicate that procedures designed to account for cluster translation and rotation during human movement are required to correctly represent the motion of body segments, however reducing marker cluster scaling and deformation will have little effect on STA.

Introduction

Tibiofemoral kinematics have been extensively investigated using reflective markers attached to the surrounding soft tissue of the shank and thigh to document general movement patterns, pathologies or sports related motions. However, the ability to perform motion analysis is limited by two principal sources of error: systematic and random errors with which markers are reconstructed (photogrammetric errors) and errors due to relative movement between surface markers and underlying bone. The latter is associated with the interposition of both active and passive soft tissues commonly referred to as soft tissue artefact (STA). High frequency photogrammetric errors may be resolved by smoothing the raw data using various digital filtering techniques (Cappello et al., 1996, Winter, 2004), while STA represents actual marker migration and must be treated differently. The relative motion between skin markers and the underlying bone is task- and subject-dependent, while introducing errors of up to 40 mm at the thigh and 15 mm at the shank (Benoit et al., 2006, Cappozzo et al., 1996, Fuller et al., 1997, Leardini et al., 2005, Lucchetti et al., 1998, Peters et al., 2010, Reinschmidt et al., 1997). These translate into average rotational errors of up to 4.48 and 13.18 and translational errors of up to 13.0 and 16.1 mm for the walk and cut, respectively. Furthermore, the direction of the reported motions may not represent those occurring in vivo, for example the skin markers may indicate a shift towards knee abduction during the initial contact and loading response of the cut while the pin markers over the same range (−10 to −40%) indicates and increase in adduction (Benoit et al., 2006, Fig. 4). Over this same period the skin markers indicated a lateral tibial position whereas the pin markers indicate a medial one (using the same segment origins derived simultaneously). Therefore, tibio-femoral displacements, abduction/adduction and internal/external rotations about the knee may not be accurately represented using skin-mounted markers (Cappozzo et al., 1996) and should be reported within the context of the measurement error to be expected for those motions (Benoit et al., 2006).

To determine the three-dimensional orientation of the shank and thigh in space, at least three markers are required to form a marker cluster applied to each limb segment. Skin marker clusters are frequently assumed to be rigidly attached to the underlying bone although the addition of STA violates this assumption. Spoor and Veldpaus (1980) used a least squares technique to minimise non-rigid movements between each measurement time interval to effectively ‘solidify’ the body formed by the cluster of three or more markers. Additional variations of the least-squares technique have also been proposed (Challis, 1995, Soderkvist and Wedin, 1993) and are commonly used to reduce movements caused by non-rigid cluster movements (Andriacchi and Alexander, 2000). Various surface marker optimisation methods have also been proposed to correct for STA through the application of marker clusters or solidification of marker groups (Andriacchi et al., 1998, Cheze et al., 1995, Lucchetti et al., 1998). The results of these techniques are encouraging, in particular the conventional singular value decomposition method along with additional redundant surface markers (Cereatti et al., 2006, Dumas and Cheze, 2009), with improvements of up to 33% accuracy based on the reduction of simulated STA.

Based on Procrustes analysis (a statistical shape analysis), STA can be viewed as a result of four independent geometrical transformations: translation, rotation, change in size (i.e. cluster scaling) and change in shape (i.e. cluster deformation) (Grimpampi et al., 2014). Additionally, the STA components are also sometimes referred to as the rigid body movements (both translation and rotation) and non-rigid movements (both cluster scaling and deformation). Recent studies of STA of the thigh and shank have found that STA is dominated by rigid body movements for treadmill walking of total knee arthroplasty patients (Barre et al., 2013) and vertical vibration of the leg (de Rosario et al., 2012). Additionally, using a principal component analysis (PCA), we recently found an indication of rigid body movements dominating STA during walking, one-legged jumping and cutting motions (Andersen et al., 2012). However, the results of that study only showed that each of the first five principle components had larger rigid body compared to non-rigid body components, but did not quantify the ratio of the two of the total STA. Additionally, it has not previously been quantified how each of the rigid body translations, rotations, scaling and deformation components contribute to the joint angle and displacement errors during overground walking, cutting and hopping.

The purpose of the investigation is therefore to study the components of the cluster marker transformations (translation, rotation, scaling and deformation), to quantify how they contribute to the thigh and shank soft tissue artefact, and to quantify their impact on knee joint kinematics.