Human Trunk Multi-segment Kinematics: Sensitivity to Experimental Errors
by
Sara Ayatollahzadeh
A thesis submitted in conformity with the requirements for the degree of Master of Applied Sciences Electrical and Computer Engineering Department University of Toronto
© Copyright by Sara Ayatollahzadeh 2014
ii
Human Trunk Multi-segment Kinematics: Sensitivity to Experimental Errors Sara Ayatollahzadeh Master of Applied Science Electrical and Computer Engineering 2014
Abstract Human trunk motion analysis, using optoelectronic stereophotogrammetry with skin-mounted markers, has been used as a standard practice to evaluate trunk motion. The challenge with this method is the inherent measurement errors: instrumentation error, marker misplacement error and skin movement artifact. These errors propagate into kinematic and, further, to kinetic analysis. This thesis provides the first comprehensive assessment of the impact of these errors on the accuracy of 3D kinematic analysis of the seven-segmental trunk model in able-bodied individuals during seated bending. The findings suggest that for certain movements the marker misplacement and skin movement artifact can have a profound impact on the estimation of the trunk’s 3D inter-segmental joint angles, to the extent that some measurements cannot be used to derive reliable assessments. A guideline is provided that determines which kinematic data across the trunk can be used to derive meaningful judgment and which data should be used with caution.
ii
iii
Acknowledgments I would like to express my sincere gratitude to my supervisor, Dr. Milos Popovic, for providing me with the opportunity to work on this project. I feel fortunate to have worked with him, have benefited from his knowledge and wisdom, and have been inspired by his attitude.
I would like to thank every member of the Rehabilitation Engineering Laboratory, who I consider my second family; all of them who were patient and fun subjects for my experiment and others who made the lab a warm and friendly environment. I would like to particularly express my gratitude to Naaz Desai who brought her expertise and helped with the experiment. Special thanks to Dr. Hossein Rouhani for suggesting this line of study and his useful insights and advice which helped me to carry out the research.
My deepest gratitude to my parents whom everything I am today I owe to them; to Maysam AsadiLari and all my family who have been extremely supportive throughout the process, and to Azadeh Yadollahi, a one of a kind friend.
iii
iv
Contents Acknowledgments.......................................................................................................................... iii List of Tables ................................................................................................................................ vii List of Figures ................................................................................................................................ ix List of Appendices ........................................................................................................................ xii 1 Introduction .................................................................................................................................1 1.1 Problem Statement and Motivation for the Study................................................................1 1.2 Outline of the Thesis ............................................................................................................4 2 Background .................................................................................................................................5 2.1 The Biomechanics of Human Movement ............................................................................5 2.2 Trunk Kinematic Model .......................................................................................................6 2.2.1
Anatomy of the Vertebral Column and Sacrum ......................................................6
2.2.2
Whole Trunk Models ...............................................................................................7
2.2.3
Multi-Segment Model of the Trunk .........................................................................8
2.3 Rigid Body Mechanics .......................................................................................................10 2.3.1
Global and Local Frames .......................................................................................10
2.3.2
Coordinate Transformation ....................................................................................12
2.4 Kinematic Description .......................................................................................................13 2.4.1
Fundamental Definitions ........................................................................................13
2.4.2
Joint Coordinate System ........................................................................................15
2.4.3
Calculating 3D Angles based on Joint Coordinate System ...................................16
2.5 Experimental Errors in Human Motion Analysis ..............................................................17 2.5.1
Instrumentation Errors ...........................................................................................17
2.5.2
Marker Misplacement Errors .................................................................................18
iv
v
2.5.3
Skin Movement Artifacts .......................................................................................20
2.6 Summary ............................................................................................................................24 3 Study Objectives .......................................................................................................................25 4 Methods .....................................................................................................................................26 4.1 The Kinematic Model of the Trunk ...................................................................................27 4.2 Data Acquisition ................................................................................................................29 4.3 Experimental Task .............................................................................................................31 4.4 Kinematic Evaluation.........................................................................................................32 4.4.1
Inter-segmental Joint Angles .................................................................................33
4.4.2
Angular Range of Motion of Inter-segmental Joints .............................................34
4.5 Sensitivity Analysis ...........................................................................................................35 4.5.1
Simulation of the instrumentation error .................................................................35
4.5.2
Simulation of the Marker Misplacement Induced Error ........................................36
4.5.3
Simulation of the Skin Movement Artifacts ..........................................................38
4.5.4
Calculating Noisy Angles ......................................................................................43
4.5.5
The Relative Error in ROMs ..................................................................................43
4.6 Summary ............................................................................................................................43 5 Results .......................................................................................................................................45 5.1 Subjects ..............................................................................................................................45 5.2 Original Angles ..................................................................................................................46 5.2.1
Angular ROMs .......................................................................................................46
5.2.2
Angular Coefficient of Variation ...........................................................................50
5.3 Instrumentation Error .........................................................................................................52 5.4 Marker Misplacement Error ...............................................................................................55
v
vi
5.5 Skin Movement Artifacts ...................................................................................................58 6 Discussion .................................................................................................................................62 6.1 Angular ROMs and Inter-subject Variability of ROM ......................................................62 6.2 The Effect of instrumentation error ...................................................................................63 6.3 The Effect of Marker Misplacement ..................................................................................64 6.4 The Effect of Skin Movement Artifacts.............................................................................66 6.5 Limitations and Future Directions .....................................................................................69 7 Conclusion ................................................................................................................................71 References ......................................................................................................................................73 Appendices .....................................................................................................................................86
vi
vii
List of Tables Table 4.1. The maximum displacement between the two markings of representative anatomical landmarks in the upright and flexed postures; for two representative directions…….………….40 Table 5.1. Subject characteristics………………………………………………………………...45 Table 5.2. The average angular ROM of the inter-segmental joints in the sagittal, coronal, and transverse planes during trunk bending in five directions. The inter-segmental joints are defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments. The results are presented as the mean ROM (deg) over all subjects. …………………………………...……….48 Table 5.3. Coefficient of variation of ROMs (=100SD/mean) in percentage; in the sagittal, coronal, and transverse planes during trunk bending in five directions. The inter-segmental joints are defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments………………………………………………………………………………………….51 Table 5.4. Relative errors in inter-segmental joint angles' ROM due to instrumentation error during trunk bending in five directions. The results are expressed in percentages as median (inter-quartile range) over all subjects. The inter-segmental joints were defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments………………………………53 Table 5.5. Relative errors in inter-segmental joint angles' ROM due to marker misplacement error during trunk bending in five directions. The results are expressed in percentages as median (inter-quartile range) over all subjects. The inter-segmental joints were defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments………………………………56
vii
viii
Table 5.6. Relative errors in inter-segmental joint angles' ROM due to skin artifacts error during trunk bending in five directions. The results are expressed in percentages of the original ROM as median (inter-quartile range) over all subjects. The inter-segmental joints are defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments………………………..59
viii
ix
List of Figures Figure 1. Two views of the human trunk from The Anatomy of Human Body by W. Cheselden, 1763. University of Toronto libraries, online collections. P. 128-124. .......................................... 1 Figure 2. Schematic diagram of the three levels of biomechanics assessment and analysis of human movement. Figure (a) represents measuring of the raw body kinematics and kinetics, (b) represents processes in which raw data are transformed into body segments and joints’ kinematics, and (c) represents the process of inverse dynamics calculations used to determine joint torques that produce the movement of interest. ...................................................................... 5 Figure 3. The Vertebral column consisting of cervical region (vertebrae C1-C7), Thoracic region (vertebrae T1-T12), Lumbar region (vertebrae L1-L5), sacral region (S1-S5) and the coccyx (Gray, 1893)........................................................................................................................ 7 Figure 4. The position vector of a point of interest in a global frame of reference frame of reference
and a local
denoted as Pg and Pl, respectively. Og, is the position vector of the origin of
the local frame with respect to global frame of reference. ........................................................... 11 Figure 5. Three-dimensional data points of the markers (
,
and
in the global frame
,
which are used to determine the local frame . ............................................................................ 12 Figure 6. The 3-dimensional space in anatomical terms: sagittal, coronal and transverse planes. The rostral-caudal directional axis of the body. The segments in the trunk are referred to with respect to their direction: proximal if towards rostral direction; distal if towards caudal direction. ....................................................................................................................................................... 14 Figure 7. Illustration of a proximal vertebral coordinate system (XYZ), a distal vertebral coordinate system (xyz), and the corresponding joint coordinate system. (Adopted from (Wu et al., 2002)) ...................................................................................................................................... 16 Figure 8. Flowchart of the methodology for sensitivity analyis of inter-segmental joint angles. 27
ix
x
Figure 9. Kinematic model of the trunk. Segments rostral to caudal: upper thoracic (UT), midupper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC). The anatomical Landmark in each segment: Seventh cervical vertebra (C7), third thoracic vertebra (T3), sixth thoracic vertebra (T6), ninth thoracic vertebra (T9), twelfth thoracic vertebra (T12), third lumbar vertebra (L3), fifth lumbar vertebra (L5), first sacral vertebra (S1) which is the midpoint between the left and right posterior superior iliac spines (PSIS) and the left and right iliac crest (IC). ..................................................................... 29 Figure 10. Top view of the layout of setup for optoelectronic stereophotogrammetry. Six cameras each placed at 1.5-2 m distance from the seating apparatus. .......................................... 30 Figure 11. a) Target placements. Left (L), Anterior Left (AL), Anterior (A), Anterior right (AR), Right (R). b) The bending task to reach each target is so that the trunk made a 45⁰ angle with respect to the upright position. ...................................................................................................... 31 Figure 12. The place of the supporting strap: 75% of the distance from the greater trochanter to the lateral epicondyle of the femur. .............................................................................................. 32 Figure 13. A segment of a vertebral column in anterior bending movement. Proximal and distal segments are the two segments each identified by three markers. The proximal and distal local frames are denoted by X, Y, Z and x, y, z, set of axes, respectively. Joint coordinate system is the set of axes for defining the angular motion between the two local frames. Sagittal, coronal and transverse planes are the three anatomical reference planes. ........................................................ 34 Figure 15. The anthropometric features measured for the experiment population. Depth of Base: the buttock popliteal length. The width of base: the hip breadth. The trunk height: hip to base of the neck length. ............................................................................................................................. 45 Figure 16. Inter-segmental joint angle motion (degrees) in the sagittal, coronal and transverse planes during anterior direction bending for the representative subject along the six intersegmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT),
x
xi
lower thoracic (LT), upper lumbar (UL), lower lumbar (LL), and sacral (SC). The time of bending and returning to the upright sitting position is in seconds. ............................................. 47 Figure 17. Angular ROM (median SD over all the subjects) in degrees for all the six intersegmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC); each in five bending directions: Left (L), Anterior Left (AL), Anterior (A), Anterior Right (AR), and Right (R). ................................................................................................................................................ 49 Figure 18. The relevant error in ROM (%) caused by instrumentation error. The bars are medians and standard deviation among subjects and the triangles show the respective Coefficient of variation (CV %). The six inter-segmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC). The five bending directions: Left (L), Anterior Left (AL), Anterior (A), Anterior Right (AR), and Right (R). ........................................................................................................... 54 Figure 19. The relative error in ROM (%) caused by marker misplacement error. The bars are medians among subjects and the triangles show the respective coefficient of variation. The six inter-segmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC). The five bending directions: Left (L), Anterior Left (AL), Anterior (A), Anterior Right (AR), and Right (R). ................................................................................................................................................ 57 Figure 20. The relevant error in ROM (%) caused by skin movement artifacts. The bars are medians among subjects and the triangles show the respective coefficient of variation. The six inter-segmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC). The five bending directions: Left (L), Anterior Left (AL), Anterior (A), Anterior Right (AR), and Right (R). ................................................................................................................................................ 60
xi
xii
List of Appendices Appendix A: RMS error tables for inter-segmental ROMs ……………………………………..86 Appendix B: Figures of inter-segmental angle curves for a representative subject…………….89 Appendix C: Table of maximum skin displacement over anatomical landmarks across the trunk, for five bending directions…………………………………………………………...…………119
xii
1
Introduction
1.1 Problem Statement and Motivation for the Study Human motion analysis produces quantitative information about the mechanics of the musculoskeletal system during the execution of a motor task. This information is related to either kinematics of the body (i.e., the instantaneous position of the body center of mass or the relative movement between adjacent body parts), or to the kinetics of the body (i.e., the constraint forces, joint torques, or the loads transmitted across body segments). This analysis can be performed for the whole body or for a particular segment(s) or part(s) of the body. Trunk is a part of the human body defined by segments/parts that are located between the base of the neck (the line between the cervical vertebra No.7 and thoracic vertebra No.1) and the hips (Leardini, Biagi, Belvedere, & Benedetti, 2009). The trunk does not include upper limbs (Figure1).
Figure 1. Two views of the human trunk from The Anatomy of Human Body by W. Cheselden, 1763. University of Toronto libraries, online collections. P. 128-124. In the case of the trunk, the motion analysis has been performed in the past to investigate a wide range of clinical conditions such as scoliosis (Engsberg et al., 2003; Fortin, Nadeau, & Labelle,
1
2008; Scherrer et al., 2013), low back pain (D. R. Collins, Engsberg, Gombatto, Sahrmann, & Van Dillen, 2007; Gombatto, Klaesner, Minor, Norton, & van Dillen, 2008; Ochia, Inoue, Takatori, Andersson, & An, 2007; Passias et al., 2011; Van Dillen, Gombatto, Collins, Engsberg, & Sahrmann, 2007), and spinal cord injury (Gauthier et al., 2013). Upper body kinetics data, i.e., system dynamics, is also widely used in ergonomics, biomechanics, and rehabilitation research to study the neuro-musculo-skeletal system interactions needed to produce and maintain movements that ensure postural stability. Such research has been executed to study intrinsic trunk stability (Cholewicki & McGill, 1996; Granata & Wilson, 2001; Kavcic, Grenier, & McGill, 2004; M. A. N. O. H. A. R. Panjabi, Abumi, Duranceau, & OXLAND, 1989); to understand the mechanisms of spinal response to impact (King Liu & von Rosenberg, 1974; Orne & Liu, 1971); and to investigate the effects of sudden displacements on the spine (Garcia & Ravani, 2003; M. M. Panjabi, Pearson, Ito, Ivancic, & Wang, 2004). One of the emerging applications of quantifying the spine motion is to provide a sitting posture representation for the purpose of controlling the neuroprosthesis for sitting balance (Lambrecht, Audu, Triolo, & Kirsch, 2009; Vanoncini, Holderbaum, & Andrews, 2008; Wilkenfeld, Audu, & Triolo, 2006). The neuroprosthesis for sitting balance is envisioned as a system that will enable a severely paralyzed individual, who is not able to sit on his/her own, to do so by artificially contracting the paralyzed muscles of the trunk. For this device to work effectively it has to have an accurate and real-time representation of the trunk posture, that is provided by the motion analysis system. At the present time kinetic variables cannot be measured directly in humans, as such measurements would require implantation of sufficiently small and minimally invasive transducers to measure the forces/torques exerted by the muscles, which are not yet available. Therefore, these variables have to be calculated indirectly using mathematical models and subject-specific kinematic and anthropometric data. The method for estimating joint forces and torques through inverse dynamics calculations is called linked-segment model. This approach has become the preferred method for determining joint dynamics in humans. Therefore, having accurate kinematic measurement of the trunk is necessary, as these measurements are used either directly to describe the movement of the trunk or as the basis for calculating forces and torques of the different trunk segments. Thus, assessing the reliability and accuracy of the kinematic
2
measurements of the trunk is the critical element that determines the success in conducting either kinematic or dynamic analysis of the trunk. Due to the unique and complex structure of human trunk, potentially highly accurate techniques for measuring trunk kinematic, such as radiographic imaging (Passias et al., 2011; Scherrer et al., 2013) or percutaneous skeletal trackers (Lundgren et al., 2008; Nester et al., 2007; Reinschmidt et al., 1997; Rozumalski et al., 2008), are not appropriate. Any measurement that involves surgery and insertion of pins into the vertebra is associated with risks of injury as well as with risks of infection. The techniques involving X-rays imaging are also not the most appropriate due to their potential to cause accumulated X-ray exposure. Therefore, the only method that is currently available to record trunk kinematics and at the same time it presents no risk to the subject is optoelectronic stereophotogrammetry, or better known as motion capture system (Andriacchi & Alexander, 2000; Cappozzo, Della Croce, Leardini, & Chiari, 2005). This measurement technique is widely used and it currently represents a gold-standard tool for performing movement analysis that can be used for clinical decision making purposes as well as in research. Optoelectronic stereophotogrammetry uses passive or active skin-mounted markers and infrared cameras to track and record body movements. One challenge with the optoelectronic stereophotogrammetry is that it requires one to place the markers on the skin surface. When markers are placed on the skin surface, they are subject to three possible sources of measurement errors, namely, instrumentation errors, marker misplacement errors and skin movement artifacts (Cappozzo et al., 2005). It is currently unclear whether the calculated kinematics of the multi-segment trunk using the optoelectronic stereophotogrammetry is sufficiently reliable, and as such, can be used for clinical evaluations and clinical decision making. Due to the nonlinear nature of the relationship between the marker coordinates (input) and the three dimensional (3D) joint angles (output), one can only experimentally evaluate the magnitude of the error of the 3D joint angles due to the above mentioned three measurement errors (Della Croce et al., 2005). The effect of these types of errors on the 3D joint angles of the lower limbs has been discussed and analyzed in the past, such as in Ramakrishnan and Kadaba, (1991), Della Croce et al. (1999), Chèze, (2000), Piazza and Cavanagh, (2000), and others. However, to date a study that has investigated how marker errors
3
impact the 3D inter-segmental joint angle calculations of the multi-segment trunk was not carried out. Hence, there is no agreement in the biomechanical community about the value of trunk kinematic measurements through stereophotogrammetry. Therefore, the goal of this study is to assess the sensitivity of trunk kinematics to most common experimental errors that may occur during optoelectronic stereophotogrammetry. In particular, this study intends to analyze the sensitivity of 3D inter-segmental joint angles to experimental errors that may occur due to instrumentation errors, marker misplacement errors and skin movement artifacts (Cappozzo et al., 2005). By doing that, this study will for the first time offer guidelines pertinent to marker placement and what kind of accuracies one should expect when 3D
inter-segmental
angles
of
the
trunk
are
calculated
using
optoelectronic
stereophotogrammetry. The study will also suggest which angles of which inter-segmental joints are more susceptible to errors, and which are calculated with higher degree of accuracy. For the purpose of this analysis we will estimate relative angle accuracy (i.e., the error relative to the measured range of motion, ROM) comparing it with the inter-subject variability.
1.2 Outline of the Thesis The thesis is organized in five chapters: Chapter 1 introduces the trunk motion analysis; the applications and necessaity of trunk kinematics; challenges of using the noninvasive technologies, and the goal and contribution of this thesis. Chapter 2 brings an overview of kinematic analysis, kinematic modeling of the trunk and rigid body mechanics methodology when using stereophotogrammetry. A review of the literature that investigated the three experimental sources of error are provided. Objectives and hypothesis of this study are stated at the end. Chapter 3 describes the methodology used for trunk modeling, 3D angle measurement, and error simulation and analysis. Chapter 4 discuss the results and limitations of this study. Chapter 5 summarizes the findings and provides concluding remarks and recommendations for future work.
4
2
Background
2.1 The Biomechanics of Human Movement Biomechanics of human movement is a field of study that uses complex processes such as mechanics and biophysics to convert raw measurements into descriptive data that allows one to analyze and assess the movements of the musculoskeletal system (Winter, 2005). Any quantitative assessment of human movement starts with the measuring of the raw data, which captures and tracks the 3D coordinates of selected points on the body (Error! Reference source not found..a). The data has to be processed to extract kinematic variables that describe the movement, such as linear displacements, velocities, and accelerations of each body segment, as well as angular displacements, velocities and accelerations (e.g., joint angles, angular velocities and accelerations) (Error! Reference source not found..b). Once the kinematics of different joints and body segments is available, these datasets can be used to calculate the torques and forces that the joints need to produce to generate the measured body kinematics. This is accomplished using inverse dynamics (Error! Reference source not found..c). Once kinematic and dynamic data pertinent to a movement of interest is available, further analysis an interpretation of the movement is possible. For example, many orthopedic surgeons use such analyses to decide if knee surgery is required. Similarly, neuroscientists and kinesiologists use them to investigate the neural control of movements and how the neuromuscular system compensates for external perturbations.
Describe/ Analyze
Measure
(a)
(b)
Assessment
(c)
Figure 2. Schematic diagram of the three levels of biomechanics assessment and analysis of human movement. Figure (a) represents measuring of the raw body kinematics and kinetics, (b) represents processes in which raw data are transformed into body segments and joints’
5
kinematics, and (c) represents the process of inverse dynamics calculations used to determine joint torques that produce the movement of interest. The initial measurements are acquired by imaging techniques such as cinematography, stereophotogrammetry, roentgen stereophotogrammetry, and fluroscoopy (Ochia et al., 2007; Passias et al., 2011) each of which can utilize different types of markers, e.g. bone- mounted intra-cortical pins (Lundgren et al., 2008; Nester et al., 2007; Okita, Meyers, Challis, & Sharkey, 2009; Rozumalski et al., 2008; Wolf et al., 2008) or skin- mounted optical trackers. Optoelectronic stereophotogrammetry, the technique that is widely used nowadays, is a noninvasive imaging system that uses infra-red cameras and reflective markers mounted on the skin and the output of which is the instantaneous positions of the markers. The kinematic and kinetic variables are then obtained through mathematical calculations based on an anthropomorphic model of the body. This model consists of a chain of links, where each link represents a rigid portion of the human body. The number of links or segments in the model contributes to its faithfulness to reality, affecting the final goal of achieving an accurate assessment and interpretation of the human musculoskeletal structure.
2.2 Trunk Kinematic Model Different link segment settings can be defined for the trunk based on the desired degree of accuracy of reconstruction of trunk movement. Nevertheless, all models are based on the anatomical characteristics of the structures in the trunk region: the vertebral column, and the sacrum.
2.2.1
Anatomy of the Vertebral Column and Sacrum
The vertebral column (Figure 3), or the spine, is located toward the posterior of the trunk and consists of 33 vertebrae. Twenty-four of these vertebrae are not firmly attached to other vertebrae but are mutually connected with soft tissue and muscles that span the entire vertebral column. The combination of solid vertebrae and elastic connective tissue and muscles allows the spine to be both flexible when exposed to bending and fairly strong when exposed to vertical loading. The twenty-four vertebrae that provide this flexibility are seven vertebrae of the cervical spine, twelve vertebrae of the thoracic spine, and five vertebrae of the lumbar spine. The
6
remaining vertebrae, i.e., the vertebrae of the sacral and coccygeal regions, are fused (Gray, 1893)
Figure 3. The Vertebral column consisting of cervical region (vertebrae C1-C7), Thoracic region (vertebrae T1-T12), Lumbar region (vertebrae L1-L5), sacral region (S1-S5) and the coccyx (Gray, 1893).
2.2.2
Whole Trunk Models
The simplest model for the trunk is to consider it as a single rigid body. This approach is common in gait analysis studies (Davis III, Õunpuu, Tyburski, & Gage, 1991a). This model is only considering the angel of the whole trunk, defined as an inverted pendulum, with respect to the hip. The advantage of this model is that with only three to four markers the entire trunk
7
movement can be captured. However, this is done at the expense of ignoring the role of movements across different levels of the trunk during locomotion or standing, which limits our ability to understand how trunk contributes to gait or standing balance. More detailed analysis of the trunk movement usually divides the trunk into two large segments, which has been applied in the protocols to analyze spine motion (Fortin et al., 2008; Leardini et al., 2009) and studies assessing post-surgery improvements for scoliosis (Engsberg et al., 2003). The benefit of such a model is that the interactions between the segments of the trunk itself can be studied. However, these large segments are regarded as rigid body segments and their relative movement is analyzed in two dimensions and often neglects transverse motion (Syczewska, Öberg, & Karlsson, 1999; Troke, Moore, Maillardet, Hough, & Cheek, 2001).
2.2.3
Multi-Segment Model of the Trunk
The trunk has more degrees of freedom than 2 or 3 that were described with the above models. As discussed above trunk has 33 vertebrae, each of which may have up to 3 degrees of freedom. However, monitoring each intervertebral motion is not easy and it would require an invasive approach. With optoelectronic stereophotogrammetry, the common non-invasive approach, single units of intervertebral motion are hard to be tracked in three-dimensions. This is because the spinous processes are small and do not allow to place the required number of markers on each of them to capture their actual movements (Konz et al., 2006). Therefore, the best next thing to measuring movements of individual vertebrae, which is any way impossible to do, is to group few vertebrae together and consider them jointly as a single rigid body segment. In this arrangement, one would partition 33 vertebrae into a chain of links, each consisting of 2-3 or more vertebrae and represented as a single ridged body. Each newly defined trunk segment could be then represented by a set of markers whose motion can be measured, tracked and later analyzed (Konz et al., 2006). As the next step, Vette et al. (Vette, Yoshida, Thrasher, Masani, & Popovic, 2011; Vette, Yoshida, Thrasher, Masani, & Popovic, 2012) developed comprehensive kinematic and dynamic models for the trunk with all 33 the vertebrae and all available degrees of freedom that these vertebrae have. They determined the masses and moments of inertia associated with each
8
vertebra individually. To do that they used the Visible Human project and calculate the messes and moments of inertia for each vertebrae using a male individual described in the Visible Human project (Vette et al., 2011). In this approach, by tracking only segments of the trunk it is possible to calculate kinematics of each vertebral joint in a hierarchical manner by applying the pre-determined set of parameters and relationships between the joints. The benefit of this approach is that finally we have very detailed and comprehensive kinematic and dynamic models for the trunk that can be used to better understand how trunk moves and how these movements are controlled. For these models to demonstrate their full potential the accuracy of monitoring and assessment of the inter-segmental rotations should be assured, since in these hierarchical models potential errors propagate downstream. With the advances in motion capture systems more segments across the trunk can be defined and monitored. The first multi-segment model of the trunk, that defines more than two segments across the trunk, and where each segment is composed of a group of vertebrae and their surrounding soft tissue, was proposed by Preuss and Popovic (Preuss & Popovic, 2010a). They showed that more detailed multi-segment model, which has 7 segments, was able to provide detailed reconstruction of the trunk movements during forward and sideways bending. They compared a multi-segment trunk model with both the whole trunk model and the two-segment model. Their multi-segment model allowed them to measure with the higher degree of accuracy how the selected seven trunk segments were being displaced in able-bodied individuals during forward and sideways bending. From these results one can conclude that the segmentation of the trunk is necessary when one is trying to measure and analyze trunk function and spinal abnormalities. The selection of the number of trunk segments used in the analysis and/or modeling is important since by measuring more segments the validity of the inverse dynamic models, such as the model proposed by Vette et al. (Vette et al., 2012) is enhanced. This study clearly demonstrated the limitations of whole trunk model and the two-segment model, and the necessity of using multi-segment models as means to analyze and describe spine motion.
9
2.3 Rigid Body Mechanics The goal of human kinematics is to reconstruct the movement of a body segment in space in successive steps of time during the execution of a task. Each segment is identified by a cluster of markers affixed to the body segment to be tracked by motion capture systems. These segments are considered to be non-deformable and hence can be represented as rigid bodies. Tracking segment’s markers allows for reconstruction of the trajectory of each body segment throughout the task. Then the mechanics of rigid bodies provides the means to calculate the position and orientation of segments in 6D space (3D orientation and 3D position). For this purpose frames of reference should be introduced first:
2.3.1
Global and Local Frames
To reconstruct the position in space of any point of interest a position vector in a global frame of reference, Pg, is provided by the stereophotogrammetry system. This global frame of reference
{ } is constructed by an orthogonal set of axes (Xg, Yg, Zg) in which 3D coordinates of the point of interest are captured by the cameras of the stereophotogrammetry system. The global frame is defined through the calibration procedure. Nevertheless, the point of interest can also be represented with respect to any observer; one of which can be with respect to a local frame. So the point of interest can also be represented with a position vector, Pl, relative to a local frame {
} that is defined by (Xl, Yl, Zl) (Figure 4).
10
Figure 4. The position vector of a point of interest in a global frame of reference { } and a local frame of reference { } denoted as Pg and Pl, respectively. Og, is the position vector of the origin of the local frame with respect to global frame of reference. The local frame of each segment is rigidly associated with the segment. It is reconstructed using a cluster of non-aligned markers (at least three) that are placed on that segment. These superficial markers are positioned in an invariant configuration with respect to the underlying anatomical landmarks and thus they are called bone-embedded anatomical frames (BAF). The anatomical landmarks are usually the bony prominences that their position is determined by palpation and are located by a marker (Winter, 2005). However, not all the markers in the cluster constituting a BAF need to locate an anatomical landmark. It suffices to have one marker allocating an anatomical landmark and a geometric rule between the markers in the cluster (Jenkyn & Nicol, 2007; Leardini et al., 2007). With this approach the frame is identifiable in a repeatable manner and hence meets the requirements for intra- and inter-subject repeatability of the kinematics descriptions (Cappozzo et al., 2005). The local frame is reconstructed using the instantaneous three-dimensional position of the segment’s markers given in global coordinates (Cappozzo et al., 2005). The procedure of describing a vector in the local frame in terms of a rotation matrix with respect to the global frame is obtained via coordinate transformation principle described below.
11
2.3.2
Coordinate Transformation
Figure 5. Three-dimensional data points of the markers ( ⃗ , ⃗ and ⃗ which are used to determine the local frame{
in the global frame{
},
}.
⃗ , ⃗ and ⃗ are position vectors of the three markers that define the local frame of reference, where each vector gives the global coordinates of a marker (Figure 5). The set of orthogonal unit coordinates defining the orientation of each local frame axis with respect to the global frame is calculated as follows:
(2.1)
⃗
⃗ ‖⃗
⃗ ⃗ ‖
⃗
⃗ ‖⃗
⃗ ⃗ ‖
⃗
⃗
⃗
⃗
⃗
⃗
These unit vectors, also called the direction cosines, constitute the columns of the matrix that defines the orientation of the local frame of reference relative to the global frame of reference; that is the time-varying rotation matrix of a given segment denoted as
12
:
(2.2)
[ ⃗ ⃗ ⃗]
[
]
where each of the nine s is the angle between two pairs of the axes in the global and local frames. It should be noted that the elements in the matrix are not independent since the axes they define are mutually orthogonal. Thus, the number of independent elements is reduced to three by the six scalar equations between orthogonal axes. Therefore, the transformation between the two representations of a point of interest on the segment under consideration, i.e., with respect to global and local frame, would be as follows. At any point during the execution of a motor task, the position vector in the global frame of reference is obtained via stereophotogrammetry. To obtain the position vector in the local frame of reference, we should use the position of the point is in the global frame, Pg. Then we need to find out what is the vector that is connecting the origin on the local frame of reference and the global frame of reference Og. The transformation matrix of the segment allows one to transform the orientation of the object from the local frame of reference into the global frame of reference. Using orientation matrix gRl, and Og vector, the formula describing the relationship between the point of interest in the local frame of reference Pl and the position of the point of interest in the global frame of reference, as follows: (2.3)
Pg =
Pl + Og
2.4 Kinematic Description 2.4.1
Fundamental Definitions
In order to explain the human kinematics it is first necessary to discuss key definitions of standard anatomical terms. Similar to other body parts, trunk’s motion is considered in the three reference planes that are used to describe human anatomy: Sagittal, Coronal (Frontal) and Transverse planes. The sagittal plane divides the trunk into left and right “symmetric” parts, the coronal plane divides the trunk
13
into posterior (back) and anterior (front) parts, and the transverse plane divides the trunk into rostral (closer to the head) and caudal (closer to the tailbone) parts (Figure 6). Any two adjacent segments in the trunk can be called in terms of their distance to the head, as the proximal and distal; the proximal being the rostral segment or the segment closer to the head and distal being the caudal segment or the segment more distant from head (Figure 6).
Figure 6. The 3-dimensional space in anatomical terms: sagittal, coronal and transverse planes. The rostral-caudal directional axis of the body. The segments in the trunk are referred to with respect to their direction: proximal if towards rostral direction; distal if towards caudal direction.
14
2.4.2
Joint Coordinate System
The relative rotational motion between any two vertebral segments can be described according to the Joint Coordinate System (JCS) the standard recommended by the International Society of Biomechanics (Wu et al., 2002). It can be applied either to an intervertebral motion or for segmental spinal motion, i.e., for rotation between two segments of the spine rather than between two vertebrae. There are three steps in the JCS procedure. The first step is to define a Cartesian coordinate system for each of the two adjacent segments, denoted as XYZ and xyz for the proximal and distal segments, respectively (Figure 7). Next, a coordinate system, defined by e1, e2, and e3 axes, is established to describe the three-dimensional joint angular position. As shown in Figure 7, two of the JCS axes, e1 and e3, are embedded in the segments: e1 is the Z-axis of the proximal segment; and e3 is the y-axis of the distal segment. These are called the body-fixed axes. The third axis, e2, is the common perpendicular to the two body-fixed axes, referred to as the floating axis (Equation 2.4) Three rotations about these axes, denoted as ,
and , define the relative
angular motion between the two adjacent segments. To calculate the three angular rotations, two of the relative rotations between segments can be described as the spin of each segment about its own fixed axis when the other segment is stationary, and the third rotation occurs about the floating axis. The angle in the sagittal plane, , whose anatomical designation is flexion-extension, occurs about e1; it lies between the floating axis and the Y-axis (in the proximal segment) (Equation 2.5). The angle in the frontal plane, whose anatomical designation is side bending, occurs about the floating axis; it lies between the two body-fixed axes (Equation 2.6). The angle in the transverse plane, , clinically called axial rotation, occurs about e3; it lies between the floating axis and the z-axis (in the distal segment) (Equation 2.7).
15
Figure 7. Illustration of a proximal vertebral coordinate system (XYZ), a distal vertebral coordinate system (xyz), and the corresponding joint coordinate system. (Adopted from (Wu et al., 2002))
2.4.3
Calculating 3D Angles based on Joint Coordinate System
If the proximal and distal segments’ rotation matrixes are [
]
e1 = [ e2 =
] , [
]
[
]
‖[
]
[
] ‖
e3 = [
(2.7)
=
,
]
(2.5) (2.6)
]
and
=
respectively, the calculations for the 3D angles would be as follows (Grood & Suntay,
1983): (2.4)
=[
(
[
]
(
[
]
(
16
When, as described in section 2.4.2, e1, e2, and e3 are the axes of the defined joint coordinate system, and
is the flexion/extension angle in the sagittal plane,
the coronal plane, and
is the side-bending angle in
is the axial rotation in the transverse plane.
In conclusion, with a segmental kinematic model of the trunk we can obtain inter-segmental joint kinematics during the execution of a motor task using optoelectronic stereophotogrammetry systems. This state of the art method has been utilized vastly in the scientific and clinical communities; however as any instrumentation examining a biological system, still has its own limitations.
The
limitations
in
human
movement
analysis
using
optoelectronic
stereophotogrammetry arise from instrumentation errors, marker misplacement errors, and skin movement artifacts that exist when using motion capture systems.
2.5 Experimental Errors in Human Motion Analysis 2.5.1
Instrumentation Errors
When the kinematic measurements are performed using optoelectronic stereophotogrammetry systems, it is observed that even in static conditions, reconstructed marker positions in the global frame are not always stationary (Chiari, Croce, Leardini, & Cappozzo, 2005). There are many studies that have investigated this error, the measurement error on 3D marker coordinates, and how it propagates to the kinematic calculations of the observed movement. The instrumentation error is of two types: systematics and random errors. Previous studies have shown that the systematic errors are caused by improper lens and camera assembly (Burton, 1992) or stereo set up of the cameras (Chiari et al., 2005); Stereo set-up refers to configuration of the cameras surrounding the subject. Stereo set-up of the capture volume determines the distance between the centers of projection of the cameras, the field of view and the depth of field, which all contribute to the systematic error (Gazzani, 1993). The random errors are associated with electronic noise, marker flickering, digitizing process, partially obscured marker images, and merging of markers with each other or with strobe illumination of another camera (Della Croce & Cappozzo, 2000; Furnée, 1997).
17
With the advances in motion capture technology the inherent systematic errors are attenuated with the improved calibration procedures. Calibration techniques determine the location of the cameras with respect to each other (i.e., external parameters), and optical characteristics of the cameras (i.e., internal parameters). These parameters identify a camera model that is used to compensate for the linear and non-linear distortions (Ji & Zhang, 2001). Today self-calibration techniques that are based on a planar calibration object with a grid of fixed points are utilized as an important step before the experiment is carried out and enable researchers to achieve high accuracies by eliminating systematic errors (Borghese, Cerveri, & Rigiroli, 2001). The random error is compensated with the use of filters and smoothing protocols, such as finite difference techniques, approximations with least squares, generalized cross-validation with splines (Woltring, 1997), and different time-frequency analyses and filtering (Chau, 2001; Georgakis, Stergioulas, & Giakas, 2002). Most of these compensation techniques are now integrated in the motion capture software. The software also takes care of the marker image processing and missing markers. It is well known that in common motor tasks the human movement has low-frequency content with additive, wide-band noise. Therefore in such experiments a low-pass filtering of the data is a routine procedure (Winter, 2005). Overall, nowadays sophisticated correction algorithms are incorporated by manufacturers in the calibration procedures. Also filtering and smoothing of marker position data and image processing techniques are integrated into motion capture software. Nevertheless, the accuracy reported by the manufacturer doesn’t account for inadequate capture volume set-up and handling of calibration procedure by the user, therefore it is recommended that an ad hoc estimation of actual accuracy is performed before any study. This investigation is important as the error in marker coordinates propagates unpredictably to the estimation of body segment kinematics (Chiari et al., 2005).
2.5.2
Marker Misplacement Errors
As discussed earlier, human motion analysis by means of multi segment modeling and stereophotogrammetry measurements requires one to have local frames associated with each segment of interest. These local frames consist of a system of axes that is derived from the global
18
coordinates of a cluster of markers. When these markers are placed over anatomical landmarks they form anatomical frames and hence allow one to reconstruct the position of human skeleton structure. But, determining the location of anatomical landmarks to place the markers on may lack precision, as the anatomical landmarks are not always sharp bony protuberances but frequently relatively large and curved bony regions. Anatomical landmarks can also be internal or small subcutaneous bones, or be relatively fused together shaping large surfaces, which are not easily palpable. Three main reasons for incorrectly locating anatomical landmarks are reported: (1) the shape of the anatomical landmarks (e.g., they are not pointed but rather flat surfaces); (2) the relative movements of the soft tissue covering the landmark prevents the examiner from identifying the exact point of the anatomical landmarks during different trials; and (3) the palpation procedure and the level of expertise of the examiner (Cappozzo, Catani, Croce, & Leardini, 1995a; Rabuffetti, Baroni, Ferrarin, Ferrigno, & Pedotti, 2002). Therefore, the identification of anatomical landmarks is subject to both intra- and inter-examiner variability. The precision of the examiner in finding the anatomical landmark and placing the markers over the landmark affects the position and orientation of the anatomical frames and consequently the calculation of joint kinematics (Donati, Camomilla, Vannozzi, & Cappozzo, 2008). This effect is not predictable because the dependency of kinematics to the anatomical frame’s orientation is nonlinear. Therefore, no compensation technique can be devised post-recording to correct for these errors, and only reduction techniques can be implemented by improving the anatomical landmark identification procedures (Della Croce, Leardini, Chiari, & Cappozzo, 2005). Studies have found that this erroneous orientation of the segment’s local frame (bone-embedded anatomical frame) creates an offset in joint kinematics curves. The relevant error pattern, though, remains unaffected throughout the gait cycle (Kadaba, Ramakrishnan, & Wootten, 1990). Previous studies that investigated the kinematics of lower limbs have given quantitative description of the precision with which the markers are placed with respect to the anatomical landmarks. (Piazza & Cavanagh, 2000) reported an average of 10 mm of error in locating the medial and lateral femoral epicondyles by ten examiners. The intra-examiner error in palpating
19
the left and right posterior superior iliac spines (PSIS) for six trials has been reported to be 11.5 and 13 mm, respectively. The error was reported as the root mean square (RMS) of the deviation from the mean (Croce, Cappozzo, & Kerrigan, 1999). The inter-examiner error among six registered physical therapists, for the same anatomical landmark, for example PSIS, has been reported to be 20.5 and 24.8 mm for left and right PSIS, respectively (Croce et al., 1999). Such errors were shown to affect the orientation of the anatomical frame that is developed from those landmarks, and consequently that these errors propagate into the calculations of the 3D angles describing relative movements of two segments. For example, in the case of the hip’s local frame of reference the intra-examiner errors propagated into joint angle errors to produce errors of 3.9 , 2.5 , and 5.3 in the sagittal, coronal and transverse planes, respectively. Similarly, the intra-examiner errors propagated into joint angle errors to produce errors of 5 , 5.2 and 5.6 in the sagittal, coronal and transverse planes, respectively (Croce et al., 1999). These values show that such errors critically distort the reported angles of the hip in the coronal and transverse planes as they are comparable to the range of motion (ROM) of hip joint in those planes (The ROMs of hip joint at level walking at a natural cadence are 50°, 10° and 12° in the sagittal, coronal and transverse planes, respectively). Overall, such results indicate that anatomical misplacement errors propagate into 3D joint angle estimations, which for the joints with ranges of motion less than 10° is a critical factor in limiting the interpretations of their relative angular movement.
2.5.3
Skin Movement Artifacts
Skin artifacts are defined as the displacements of skin-mounted markers relative to their underlying bone caused by the soft tissue and skin that is between them. These displacements prevent the markers to be an accurate representative of the anatomical landmark of interest (Leardini, Chiari, Croce, & Cappozzo, 2005). Many studies have been carried out to investigate the effects of skin artifacts on lower limb kinematic assessment, mainly the knee joint, i.e., thigh and shank movements (Fuller, Liu, Murphy, & Mann, 1997; Manal, McClay, Stanhope, Richards, & Galinat, 2000; Okita et al.,
20
2009; Reinschmidt et al., 1997; Taylor et al., 2005). These studies investigated the error that skin artifacts induce in the kinematic analysis of the joint by comparing the measurements obtained using skin-mounted markers with those obtained from an artifact-free method. These methods, often called gold standard, are usually invasive. For example, with intra-cortical pins a metal rod is surgically screwed into the bone, leaving the rod head protruding from the body (Benoit et al., 2006). Markers are put on these heads and measurement is performed using motion capture systems. A less invasive method is to measure skin-mounted metal markers with fluoroscopy that exposes the subject to x-rays (Stagni, Fantozzi, Cappello, & Leardini, 2005). The magnitude of the skin artifacts is reported in more detail. It has been shown that in lower limb segments, skin artifacts are greatest at the thigh (Peters, Galna, Sangeux, Morris, & Baker, 2010), reaching magnitudes of 30 mm or greater, and up to 15 mm on the tibia. Another study (Reinschmidt et al., 1997) showed that for hip, knee and ankle joints, only motion about the flexion/extension axis can be determined reliably. Motion about other axes (abduction/adduction and interior/exterior) has spurious effects with magnitudes comparable to the amount of motion actually occurring in those joints. (Stagni et al., 2005) reported that the displacement magnitudes reported for skin markers placed on the thigh were around 31 mm and up to 21 mm for the shank. These errors propagate into the estimated kinematic data and cause root mean square errors of up to 192% and 117% of the corresponding range, respectively. Other studies also reported the propagation of skin movement into the kinematics and angle calculation. (Tranberg & Karlsson, 1998) showed that internal/external rotation of the knee, when measured with the bone-screwed markers, had a range of about 20 while the same measurement with the skin-mounted markers revealed to be about 50 . (Benoit et al., 2006) reported average rotational errors between 4.4 and 13.1 in knee joint angle during walking. Another study measured the abduction/adduction rotations, root mean square error ranged 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 (Leardini et al., 2005). Discrepancies between the values reported by different authors may be justified by the different techniques used, and also by the large variability in the subjects analyzed and in the tasks performed, but mainly by the different locations of the skin-mounted markers.
21
(Manal et al., 2000) adopted a less invasive technique and investigated fixing the markers to the body by wrappings (underwrap/overwrap). They also included other factors such as several sets of markers that differ in terms of the position of the markers (proximal/distal) on the shank and tibia; and the characteristics (constrained/unconstrained) for tracking the motion of the tibia during natural walking. The walking cadence of each subject was recorded for all the marker sets and the estimated angular rotations were compared to the rotations estimated in terms of a set of percutaneous skeletal trackers pinned to the bone. The relative angle gives the deviation in the estimate of the tibia’s orientation from the true value. For the entire stance phase, the root mean square of the deviations was calculated, and it represents the total error. The results showed that when the markers are attached to a rigid shell (constrained) under wrapped to the distal lateral shank, the optimal estimate of the tibia’s rotation during walking is obtained. However, error cannot be avoided even with this optimal marker set. There where two deviations, 2 deviation in sagittal and frontal planes and 4 deviations in transverse plane. The significance of these error magnitudes becomes evident when they are compared to the tibia’s ROM (relative to the femur) in different planes. The relative errors then would be 3% in the sagittal plane, 25% in the frontal plane, and 40% in the transverse plane. The ROM in the frontal plane is 8 , and 10 in the transverse plane. This shows that the error in the transverse plane is the major contributor to error in estimating the shank motion. (Rosario, Page, Besa, Mata, & Conejero, 2012) also adopted similar approach. Typically, skin movement artifacts were defined as a field of marker displacements relative to the underlying bone. These errors can be decomposed into two components: (1) deformation of the marker cluster and (2) rigid movement; both strongly associated with the movement of the bone and therefore was defined as functions of relative movement. The results showed that both components are greater than the instrumentation error, and within the three coordinates, skin movement artifact was greater in the Y-axis, which confirms that the error is a function of bone movement. (Taylor et al., 2005) have investigated the effect of skin artifacts adopting a numerical approach and simulating the error. The advantage of their approach is that the exact joint position is known, but the limitation is that the numbers used for noise simulation were not taken from
22
actual clinical data. A specific configuration of the markers was simulated, and then perturbed by noise representing the marker artifacts during movement. The new configuration was subjected to movement, and the position of the center of rotation was estimated. As soft tissue artifacts involve both elastic distortion and synchronous shift, the noise was selected to have isotropic, independent, and identically distributed Gaussian distribution. This noise was first applied to each marker position, representing the elastic distortion component. Next, a similar Gaussian noise was applied to all the markers on the segment simultaneously to represent the synchronous shift of the entire marker set. Then, both noise components were applied to the marker positions. Each simulation of a movement was repeated 1,000 times, and the root mean square error in estimating the center of rotation over the 1,000 repetitions was reported as a measure of performance. When the simultaneous noise was superimposed on all the marker positions in the set, all they could reach reasonably accurate determinations of the center of rotation position. However, when the noise was applied to the marker positions individually, the center of noise estimate in all the methods exhibited on average an error of 5cm. To the best of author’s knowledge to date not a single study investigated the effect of skin artifacts on the trunk kinematics, where trunk was described as a multi-segment system/model. (Vergara, Page, & Sancho, 2006) have studied the effect of soft tissue and skin movement on identification of anatomical landmarks in lumbar flexion for ergonomic analysis. Their focus was on lumbar region movements and they have evaluated only C7, L4 (upper points of the iliac crest) and L5 (the dimples of Venus). They have also recognized that non-invasive methods are based on identifying the positions of markers on the skin, so they emphasized that the accuracy of these methods depends on the accuracy of the palpation and the identification of spinous processes on which to place the markers and also on the measurement of the skin displacement associated with the spine movements. Therefore, Vergara et al. compared the movement of the skin-mounted metal markers on the three mentioned spinous processes with the actual movements of the spine by taking two lateral view radiographs, one with the subject in an upright sitting posture, and the other with the subject in a flexed posture. They measured the change in the distance between the spinous process and the external marker. It was determined that at the lumbar level the average change in the distance between markers and underlying
23
anatomical landmarks was up to 5 mm. Accordingly, it was concluded that the lumbar angle calculated based on skin markers should not be interpreted in an absolute manner, as it might not represent the internal angle between spinous processes. Overall, skin movement artifacts are the main limitation in the analysis of human motion by video photogrammetry. All studies have reported that skin artifacts cause an error that is task dependent, greater than the instrumentation error, hard to filter as it has a frequency content similar to the actual bone movement, and is not predictable since it is not reproducible among subjects (Leardini et al., 2005).
2.6 Summary In summary, any human motion analysis using non-invasive technique of optoelectronics stereophotogrammetry is subject to three types of experimental errors: the instrumentation error, the marker misplacement error and skin movement artifacts. For some body segments, such as legs, there is sufficient information in the literature describing how these errors influence the kinematic measurements of these body parts, and which measurements can be considered reliable and clinically useful, and which not. Similar kind of analysis was not yet carried out for human trunk. As the biomechanics of the trunk is becoming increasingly relevant field of investigation, it is prudent to determine with what accuracy one can measure kinematics of the trunk, considering the above errors. Therefore, there is a need to determine how the instrumentation errors, the marker misplacement errors and skin movement artifacts influence the optoelectronics stereophotogrammetry of the trunk and its segments. The present study investigated the effect of the above-mentioned experimental errors on the calculated 3D intersegmental angles in a multi-segmental model of the trunk, and it provides a new insight into utility of these measurements and the ability of this approach to generate clinically relevant information.
24
3
Study Objectives
The overall goal of this study was to assess the impact of experimental errors on the kinematic analysis of the multi-segment trunk model during bending movements in a seated position. Three distinct tasks were undertaken to address this goal: 1. To find the expected range of experimental error associated with (i) instrumentation error, (ii) marker misplacement, and (iii) skin movement artifacts in the evaluation of trunk kinematics. 2. To evaluate the sensitivity of inter-segmental trunk angles to each type of experimental error in individual anatomical planes, i.e., coronal, sagittal and transverse planes. 3. To determine the trunk segments/levels with high sensitivity to experimental errors in the multi-segment trunk model.
25
4
Methods
To investigate the impact of experimental errors in the kinematic measurement of the trunk we first captured trunk motion in with the standard stereophotogrammetry equipment in combination with applying a multi-segment model of the trunk. Then, we simulated the three sources of error inherent in such kinematic analysis and incorporated each error into the captured data separately. The uncertainty or random error in the marker trajectories is represented by a Gaussian noise, with different weighing and temporal characteristics for each error source. Previous studies have used Gaussian noise to model fluctuations in kinematic observation functions (Cerveri, Pedotti, & Ferrigno, 2004; Chèze, Fregly, & Dimnet, 1995; Rouhani, Favre, Crevoisier, Jolles, & Aminian, 2011). The trunk motion was described via six inter-segmental joint angles, according to the multi-segment trunk model developed by (Preuss & Popovic, 2010b). The 3D angles were calculated from the marker coordinates data according to joint coordinate system convention. The angles were obtained once with the original captured data, and once with corrupted data for each error type separately. The two results, erroneous and original, were compared to provide analysis on the impact of each source of error. An overview of the sensitivity analysis of 3D inter-segmental joint angles is presented in the flowchart in Figure 8.
26
Figure 8. Flowchart of the methodology for sensitivity analyis of inter-segmental joint angles.
4.1 The Kinematic Model of the Trunk The 7-segment model of the trunk developed by (Preuss & Popovic, 2010b) was investigated in this study. In this model the vertebral column was modeled as seven segments (Fig. 1B): upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments (Figure.9). Each segment includes three vertebrae (except the sacral segment (SC) that marks the sacrum), which allows for the most detailed analysis of the trunk movement, as tracking individual vertebrae is not presently possible (Preuss & Popovic, 2010b). Except for SC, each segment was defined based on three markers: a centrally placed marker on the caudal spinous processes and two markers
27
placed at least 50 mm lateral to the rostral spinous processes. UT segment was defined by C7 and T3 vertebrae as anatomical landmarks, MUT segment has T3 and T6 as anatomical landmarks, MLT has T6 and T9 vertebrae, LT includes T9 and T12, UL has T12 and L3, LL has L3 and L5 as anatomical landmarks (Figure.9). Markers for the SC segment were one virtual marker at the mid-point between two markers placed on the posterior superior iliac spines (PSIS) and two on both iliac crests (IC) (Figure.9). This set of anatomical landmarks is a modified Helen Hayes set first proposed by Davis et al. (Davis III, Õunpuu, Tyburski, & Gage, 1991b) for sacral region, and since has been the base for the majority of marker sets defined for clinical use (T. D. Collins, Ghoussayni, Ewins, & Kent, 2009). These particular landmarks for sacral region are also recommended by (Cappozzo, Catani, Croce, & Leardini, 1995b). The International Society of Biomechanics has published recommendations for bone-embedded anatomical frame for each vertebra (Wu et al., 2002). To authors’ knowledge, however, there is no widely-approved standard anatomical frame for segments composed of 2-3 vertebrae, based on anatomical landmarks. Therefore, anatomical frame definitions were chosen to obtain axes approximating the International Society of Biomechanics recommendations (Wu and Cavanagh, 1995; Wu et al., 2002). The Z-axis was defined by the two rostral markers (or the two ICs for SC segment), towards right, and the YZ-plane was formed by the three markers of each segment, such that the Y-axis was upwards and the X-axis was anterior. A similar approach for defining trunk segments frames based on marker triads was used by AlEisa et al. (2006), Preuss and Fung (2008), and Preuss and Popovic (2010). Other anatomical frame axes definitions, based on these three markers, are expected to obtain similar results to this sensitivity analysis (Rouhani et al., 2011; Rouhani et al., 2012). Inter-segmental angles between two successive segments (rostral segment with respect to caudal segment) were calculated in the sagittal (flexion-extension), frontal (side-bending), and transverse (axial-rotation) planes based on the joint coordinate system (JCS) recommended by the International Society of Biomechanics (Grood and Suntay, 1983; Wu and Cavanagh, 1995). This produced 3D inter-segmental angle time series for the six trunk levels, for each of the five target-directed trunk bending movements.
28
Y
X
C7
Z
Upper Thoracic (UT)
T3
Mid-Upper Thoracic (MUT)
T6
Mid-Lower Thoracic (MLT)
T9
Lower Thoracic (LT)
T12
Upper Lumbar (UL)
L3
Lower Lumbar (LL)
S1
Sacral (SC)
IC PSIS
Seat Figure 9. Kinematic model of the trunk. Segments rostral to caudal: upper thoracic (UT), midupper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC). The anatomical Landmark in each segment: Seventh cervical vertebra (C7), third thoracic vertebra (T3), sixth thoracic vertebra (T6), ninth thoracic vertebra (T9), twelfth thoracic vertebra (T12), third lumbar vertebra (L3), fifth lumbar vertebra (L5), first sacral vertebra (S1) which is the midpoint between the left and right posterior superior iliac spines (PSIS) and the left and right iliac crest (IC).
4.2 Data Acquisition Twenty-one reflective markers, each 10 mm in diameter, were placed in groups of three, so that they divided the trunk into seven segments as discussed in Section 4.1: sacral (SC), lower lumbar (LL), upper lumbar (UL), lower thoracic (LT), mid-lower thoracic (MLT), mid-upper thoracic (MUT), and upper thoracic (UT) (Figure 9). Markers were tracked by an optoelectronic stereophotogrammetry comprising of six Vicon-512 cameras (Oxford, UK) and motion analysis system that uses sampling frequency of 120 Hz. The configuration of the cameras is shown in
29
Figure 10. Each camera was placed at 1.5 m to 2 m distance from the seating apparatus to maximize the field of view of the sensors for the designed experiment. From the six cameras, four cameras were arranged behind and to the sides of the subjects. Two were high, around 2 m off the ground and two lower down, around 1 m off the ground. The two other were in front and both high up (~ 2m). Cortex software was used to calibrate the system before recording, and to perform post processing on the recorded data (e.g., rectifying and refining trajectories, and modifying tracks). The marker trajectories were low-pass filtered with an 8th order Butterworth filter with a cut-off frequency of 2 Hz. The experimental data in (Preuss and Popovic, 2010) was used in this study.
Figure 10. Top view of the layout of setup for optoelectronic stereophotogrammetry. Six cameras each placed at 1.5-2 m distance from the seating apparatus.
30
4.3 Experimental Task The experiments involved seated subjects bending in five directions to touch a target in front with the head (Figure 11.a). The five bending directions were anterior, anterior right, anterior left, right, and left (Figure 11.a). The five targets were placed relative to the trunk length of each subject, so that he/she had to have 45 bending posturer to reach the target (Figure 11.b). The seat was a rigid surface with a support for the thighs that was provided by the strap placed at the 75% of the distance from the greater trochanter to the lateral epicondyle of the femur (Figure. 12). No other support or constraints to movement were implemented.
Target: Anterior Target: AnteriorLeft
Target: Left
Seat
Target: AnteriorRight
Target: Right
a)
b) Figure 11. a) Target placements. Left (L), Anterior Left (AL), Anterior (A), Anterior right (AR), Right (R). b) The bending task to reach each target is so that the trunk made a 45⁰ angle with respect to the upright position.
31
The support strap
Greater trochanter
Lateral epicondyle of the femur
Figure 12. The place of the supporting strap: 75% of the distance from the greater trochanter to the lateral epicondyle of the femur.
The task in the experiment was to look and see the target in front and then lean towards it to touch it with the head and return to the upright sitting position. It should be noted that the subjects were instructed not to keep looking at the target throughout the movement so that they have natural bending without artificially constraining movement of the trunk to allow them to see the target. Each subject performed the task in three trials for each of the five bending directions in a random order.
4.4 Kinematic Evaluation After recording marker coordinates the kinematic variables are calculated. In this study the kinematic variable of interest were the inter-segmental joint angles, which are usually analyzed by their range of motion (ROM). The method of evaluating inter-segmental angles and the angular ROMs of these segments are described in the following sections.
32
4.4.1
Inter-segmental Joint Angles
Although International Society of Biomechanics has recommendations for bone-embedded anatomical frame definition for each vertebra (Wu et al., 2002), there is no widely-approved bone-embedded anatomical frame standard of segments composed of two to three vertebrae. Therefore, we adopted the same definitions of local bone-embedded anatomical frames recommended by International Society of Biomechanics for individual vertebrae (Wu and Cavanagh, 1995; Wu et al., 2002). The axis system was created for each trunk segment; the Zaxis is parallel to a line between the two upper markers running from left to right (Figure 13); the Y-axis is parallel to a line between the caudal marker and the mid-point between the two rostral markers as shown in Figure 13, and the X-axis is orthogonal to Z and Y-axes running from posterior to anterior. For the sacrum that is defined by four markers, the midpoint between the two left and right posterior superior iliac spines is considered as the caudal marker and the same procedure for defining the axes was followed. Similar approach for defining trunk segments technical frame based on markers on a triangle was used by AlEisa et al. (2006), Preuss and Fung (2008), and Preuss and Popovic (2010). Then, the relative movement between adjacent segments was described in terms of three angular displacements according to the joint coordinate system convention (Grood and Suntay, 1983; Wu and Cavanagh, 1995). 3D angles between two successive segments (rostral segment with respect to caudal segment) equivalent to the Cardan angles were calculated based on the sequence of rotations around three axes: one from the proximal local frame (e1), one from the distal local frame (e3) and a floating axis perpendicular to the first two (e2) (Figure 13). The mathematical calculation to derive 3D joint angles was thoroughly reviewed in Chapter 2. The angles are flexion-extension around the ⃗ axis on the sagittal plane, side-bending around the ⃗ axis in the coronal plane, and axial rotation around the ⃗ axis in the transverse plane.
33
Figure 13. A segment of a vertebral column in anterior bending movement. Proximal and distal segments are the two segments each identified by three markers. The proximal and distal local frames are denoted by X, Y, Z and x, y, z, set of axes, respectively. Joint coordinate system is the set of axes for defining the angular motion between the two local frames. Sagittal, coronal and transverse planes are the three anatomical reference planes.
4.4.2
Angular Range of Motion of Inter-segmental Joints
The angular ROM of each inter-segmental joint was calculated from quiet-sitting to the maximum trunk bending position, in all the three planes and for each trial. The ROM of an intersegmental joint indicates the range in which angular rotation occurs between the two adjacent segments during the execution of the bending task. In addition, the inter-subject variability of each original ROM for the eleven subjects was calculated based on the definition of the coefficient of variation (CV) as follows:
34
(4.1)
CV =
where
and
are the standard deviation and the mean of original ROM over the number of
subjects enrolled in the study. Hence, the coefficient of variation of each angle’s ROM shows the extent of variability of ranges of motion for that angle among subjects in relation to the mean for population.
4.5 Sensitivity Analysis The next step in the study was to simulate each of the three experimental errors (namely, instrumentation error, marker misplacement error, and skin movement artifact) and determine how much they distort the measured marker locations with respect to the anatomical landmarks that they represent.
4.5.1 As
Simulation of the instrumentation error
discussed
in
chapter
two,
in
recent
commercially
available
optoelectronic
stereophotogrammetry systems, different correction techniques have been incorporated into the calibration procedures, which are now a routine practice in all motion analysis laboratories. Also, proper filtering and smoothing techniques have been integrated into the motion capture software to minimize the instrumentation error. Assuming that camera calibration has been performed and the proper tools in the capture software are used, the performance of the system, i.e. accuracy of the measurements, is still affected by the set-up in the laboratory: including the location and number of the cameras, the size of the capture volume, and the quality in executing the calibration by the user. The typical accuracy that manufacturers provide nowadays is 1:5,000 of the diagonal of the capture volume. These general figures can change with different set-ups, and can even be enhanced for volumes captured with sufficient number of cameras and with careful calibration procedures. For example, accuracy of 1:15,000 was reported using 36 cameras (Chiari et al., 2005) . (Schmid, 2001) has achieved root mean square errors of 0.19 mm, and Rouhani et al., (2011) has also reported accuracies around 0.2 mm. Therefore, the actual accuracy in any experiment set-up is recommended to be assessed and several tests have been recommended in the literature (Chiari et al., 2005).
35
The accuracy of the Vicon512 motion capture systems is reported by the manufacturer to be between 1:5,000 and 1:2,000 of the diagonal of the capture volume, depending on the focal length of the lenses. We also followed the procedure suggested by (Thornton, Morrissey, & Coutts, 1998) and estimated the actual accuracy in our set-up by measuring the distance between two markers placed at the two ends of a wand with 100 mm distance (similar as the distance in of the markers on the trunk). This wand was moved in the capture volume and the accuracy of around 0.2 mm was measured. During the experiment, marker reconstruction residuals were observed to be less than 0.5 mm. Therefore, the perturbation in coordinate reconstruction of each of the 22 markers was modeled with a Gaussian variable with a standard deviation of 0.2 mm and was truncated to have a maximum of two times the standard deviation (0.4 mm). (4.2)
( | |
where
is the error (perturbation) in the anatomical landmark trajectory at each time step in the
course of the bending for each
{
(
It should be noted that t is dropped from the notation to eliminate ambiguity, and the equation applies at every point in the course of the movement. This error function was then added as random noise to the marker coordinates of all markers in all three axes for each time step through the execution of the motor task.
4.5.2
Simulation of the Marker Misplacement Induced Error
For the marker misplacement error, we conducted a preliminary experiment where we observed the precision of our examiners in palpating anatomical landmarks and in placing the markers. Based on these findings, marker misplacement error was represented as a Gaussian function with a standard deviation of 6 mm, and truncated to a maximum value of 12 mm. Since the markers
36
were affixed on the back plane of the trunk and the examiner palpated and identified the spinous process of vertebrae on the back of the trunk, the precision in identifying the anatomical landmarks (i.e., marker misplacement error) occurred in the coronal plane (YZ plane) of the trunk. Therefore, the Gaussian error distribution was applied to both the Y and Z coordinates of the local frame of each spine segment. For the SC segment, however, since the two right and left IC (iliac crest) markers were located on the sides of the trunk along the sagittal plane, the marker misplacement error could have had a component across the X axes of the plane of the local frame. Therefore, the Gaussian error was applied to all the three coordinates of sacral local frame.
Marker misplacement error was modeled as time-invariant during each trial. We
assumed, however, that the landmark palpation and marker placement was repeated before each trial, and therefore let the modeled errors vary among the three trials of each subject, in order to model the inter-session variability of the error for each subject. This protocol took into account both intra-examiner and inter-examiner errors, i.e., the precision of the examiner in palpating in each trial and the difference between the expertise of examiners in landmark palpation and identification. The modeled marker misplacement error values were similar to those previously observed for marker misplacement errors in the lower limbs for anatomical landmarks in foot that are similar to vertebrae regarding their palpability (Favre et al., 2010; Rouhani et al., 2012). To formulate, the initial dislocation error in anatomical landmark placement model would be:
(
(4.3)
(
, | |
(
For {
This initial dislocation in markers remains constant for the course of the bending movement, hence: (4.4)
(
( (
(It is worth once again noting that for
37
)
4.5.3
Simulation of the Skin Movement Artifacts
The background section reviewed characteristics of skin artifacts that can be used as the basis for simulations. The main characteristic of skin movement artifacts found to be their systematic pattern in relation to motor tasks. We simulated this characteristic in our study and hence the movement of skin-mounted markers’ coordinates with respect to the underlying anatomical landmark was defined based on the three phases of the bending tasks in our experiments. According to the three phases of bending i) to approach the target, ii) reaching the target (the point in which peak trunk motion occurs) and iii) returning to upright sitting posture, the marker coordinate noise was determined as: i) an ascending array of displacements in the ⃗⃗⃗⃗⃗ plane of the local frame of each segment (i.e., anatomical landmark) in correlation with the bending movement; ii) reaching a maximum displacement at the point of peak trunk motion; and iii) a descending array of displacements proportionate to the subject’s return to upright sitting posture. The rate of the movement was derived based on the projection of the height of the trunk on the transverse plane of the global frame; where the height of the trunk was defined as the distance between markers C7 and S1. Therefore, the point of peak trunk motion was measured as the point at which the projected vector has reached its maximum length. Therefore, skin displacement with respect to the initial posture increased to the maximum value at the point of peak trunk motion and decrease as the subject returned back to upright sitting posture. The maximum displacement between the skin-mounted marker and the anatomical landmarks varied at different levels of the trunk and also between subjects. For lower limbs, as mentioned in chapter three, studies investigating skin artifacts propagation to kinematics have each used different ranges of random amplitudes as an estimate for this displacement. The current study intended to estimate the range of the maximum displacement between skin-mounted markers and anatomical landmarks for the trunk region. The study consisted of three distinct phase. In Phase 1 a preliminary experiment was conducted to obtain an expected range of the maximum displacements. In Phase 2, the maximum displacement for each skin-mounted marker was simulated for each subject as a random noise defined in the range obtained from Phase 1. Then, in Phase 3, marker displacements throughout the course of the bending task were determined.
38
Phase 1: Determining the expected range of the maximum displacements Five able-bodied subjects participated in this experiment and all provided written consent (University Health Network Research Ethics Board approval 10-035). Each subject was asked to assume two postures. First the reference upright sitting posture and second the flexed posture at 45 degrees. At each posture selected anatomical landmarks of the multi-segment model were palpated and marked by an expert. The selected anatomical landmarks were spinous processes at vertebral levels C7, T3, T6, L4, and S1. In addition the two lateral marker sites each 5cm to the left and right of the spinous processes were measured and marked. The steps followed were: 1) With the subject seated in the reference posture the spinous processes and the left and right points were palpated and marked with a pen on the skin by a qualified examiner, a registered physiotherapist. 2) The subject bent in each of the five directions (Figure 11.a) to the point of maximum trunk bending (Figure 11.b). 3) While in the flexed posture the qualified examiner palpated anatomical landmarks and marked them with a different colour pen. 4) The distance between these two marks was measured and called maximum displacement. In order to limit the interference of marker misplacement errors in determining the vertebrae in the two postures, the selection of vertebrae was based on anatomical features that ensured the highest degree of accuracy and feasibility of palpation. Each of the five vertebrae selected have relatively prominent spinous processes as well as other auxiliary landmarks that improve the accuracy of identification: C7 is located at approximately shoulder level; T3 is approximately aligned with the root of the scapular spine (edge of the shoulder blade); T6 with the inferior edge of the scapula; L3 with the superior level of iliac crest (upper edge of hip bones); and S1 with the posterior superior iliac spines. For the other two thoracic vertebrae (T9, T12), dislocations were estimated with values calculated for T6. The maximum distance for each of the anatomical landmarks was measured for the anterior bending and left bending directions and was used as the basis of estimation for the other directions (i.e., right bending, anterior left bending and anterior right bending). Based on the task-related and symmetrical nature of skin movements, the maximum displacements for other
39
directions were determined based on the relationship between movement patterns of various directions. Hence, the maximum distances in marker movements for the right direction were estimated to have the same value obtained for the left direction, but in opposite direction in the relative anatomical frame. For the anterior left direction, the maximum distance in marker movements was determined so that the orientation of the anatomical frame was the midpoint of the left direction and the anterior direction. The same procedure was performed for anterior right direction. This preliminary experiment provided an estimate of the maximum displacement between each of the skin-mounted markers and the underlying anatomical landmarks at the point of peak trunk motion for the five bending directions. This displacement is a vector in the ⃗⃗⃗⃗⃗ plane of the anatomical frame (i.e., local frame) of the relative segment. Table 4.1 shows the mean and standard deviation of the measured values obtained for population for each of the selected anatomical landmarks (C7, T3, T6, L4, and S1) for two representative bending movements: anterior bending and left bending. The full table is presented in Appendix C.
Table 4.1. The maximum displacement between the two markings of representative anatomical landmarks in the upright and flexed postures; for two representative directions. Maximum displacement in the ⃗⃗⃗⃗⃗ plane of the anatomical frame Mean Spinous Process
SD ( mm )
Anterior Bending ⃗
Left Bending
⃗
⃗
⃗
0.0 0.0
0.0 0.0
0.0 0.0
C7
1.4
T3
-5.0
T6
-8.9
0.0 0.0
5.0
L3
16.0
0.0 0.0
9.8 17.8
-3.6 5.1
S1
-1.0
0.0
5.0 14.3
-2.0
.9
-1.0 2.0
40
.0
-10
21.0 .7
0.0 -1.0
.0
.1
Phase 2: The maximum displacement simulation Based on the expected maximum displacements obtained in Phase 1, we simulated maximum displacements caused by potential skin movement artifacts for the data obtained from the original experiment (Section 4.2). For each of the given bending tasks, the maximum displacement of each marker at the point of peak trunk motion was derived from a random variable with Gaussian distribution whose mean and standard deviation were obtained from the estimated data for the same marker from the experiment in Phase 1. The random variable represented the variation in skin artifacts between subjects and conditions, and the estimated mean and standard deviation provided the expected range. The derived maximum displacement for each subject was preserved invariant through the three trials since the characteristics of skin movement artifacts of a given subject were not expected to change if the experimental condition was not altered. Phase 3: Anatomical landmark dislocation throughout the trajectory The skin movement artifact was not exclusive to the flexed posture at the point of peak trunk motion but was present and changing throughout the course of the bending task. Therefore, to simulate the error between the skin-mounted marker trajectory and the corresponding anatomical landmark trajectory, marker coordinates were submitted to displacement in each time step. The time series of displacements were calculated as an ascending array that started from zero and reached the maximum displacement determined in Phase 2 with the same rate as the bending movement, and with a descending order array in the time frame that the subject was returning to upright sitting posture. Thus, the anatomical landmark dislocation error model defined as the measurement error due to the displacements of the skin-mounted markers with respect to the anatomical landmarks, were as follows: (4.5)
(
(
41
where
(
is the anatomical landmark trajectory error due to skin movement artifacts in the
course of the bending for each
{
(
where
is the displacement error in the point of the peak trunk motion. This maximum
error was modeled as a Gaussian noise:
(
(4.6)
, | |
with its
assigned from the table of data obtained in Phase 1 for coordinate j of marker i
in the bending direction d. C(t) is the coefficient which modulates (
(
between the initial value in quiet-sitting and
in point of peak trunk motion, and proportional to the movement pattern
during the bending task:
(4.7)
⃗⃗⃗⃗⃗⃗(
(
⃗⃗⃗⃗⃗⃗(
where ⃗⃗⃗⃗⃗ is the vector defining the distance between C1 and S1 (trunk’s height) in the global frame;
⃗⃗⃗⃗⃗(
is the projection of the ⃗⃗⃗⃗⃗ vector in the transverse frame (T) at any time
during the bending task; and ⃗⃗⃗⃗⃗(
is the distance at the point of peak trunk motion. Note:
Since in the experimental conditions subjects have an initial degree of bending the ⃗⃗⃗⃗⃗ vector was normalized with its initial value to obtain
⃗⃗⃗⃗⃗(
= 0.
Finally, the displacement array was added to the trajectory of marker coordinates, and the erroneous coordinates for markers were obtained. The next section describes how the erroneous inter-segmental angles were calculated from the perturbed marker coordinates.
42
4.5.4
Calculating Noisy Angles
After simulations for the duration of the execution of the motor task were run for instrumentation error, marker misplacement error, and skin movement artifacts; they were individually added to each marker trajectory. Then the erroneous 3D inter-segmental angles over the duration of each trunk bending trial were calculated with the same method as the original angles were calculated according to JCS convention. Therefore, for each error type, 2970 time series were computed: 3 angle dimensions
4.5.5
6 inter-segmental joints
3 trial
5 direction
11 subjects.
The Relative Error in ROMs
For each inter-segmental joint, its range of motion (ROM) was calculated from quiet sitting to the maximum trunk bending position, first for the original captured data and then for the corrupted angles. The relative error induced in the ROM was calculated to be the absolute value of the difference between erroneous and original ROM values, over the original ROM, represented in percentage. Relative Error in ROM =
|
|
The whole procedure of simulating error, adding the error to marker trajectories and calculating relative error in ROM was repeated 1,000 times. The 95th percentile of the 1,000 values of the obtained relative error for each trial was determined as the standard experimental error (Besier, Sturnieks, Alderson, & Lloyd, 2003; Cerveri et al., 2004). This estimated experimental error was then averaged over the three trials of each bending direction, for each subject. At the end, the median and inter-quartile range of the results for the eleven subjects was determined.
4.6 Summary Measurements with opoelectronic stereophptogrammetry gives the time series of marker trajectories in global frame. Three types of experimental errors were simulated and added to the marker trajectories. Similar approach of estimating the sensitivity to experimental errors by adding simulated errors to the original kinematic data was previously used in literature (Kadaba et al., 1990; Ramakrishnan and Kadaba, 1991; Chèze, 2000; Manal et al., 2002). At the end,
43
kinematic description of all the inter-segmental joints was calculated in joint coordinate system as original 3D angles and errounous 3D angles. The two were compared and the propagation of error to kinematics was analysed.
44
5
Results
5.1 Subjects Eleven able-bodied subjects in the age range of 24 to 34 were recruited for the experiment. The subjects had no history of back pain or neurological condition as well as a previous diagnosis of any musculoskeletal condition affecting the spine. The age and anthropometric data of the population is presented in Table 5.1. The anthropomorphic measures include: trunk height, depth of base and width of base, according to Figure 15.
Figure 15. The anthropometric features measured for the experiment population. Depth of Base: the buttock popliteal length. The width of base: the hip breadth. The trunk height: hip to base of the neck length. Table 5.1. Subject characteristics Trunk height Age (m) 30 0.76 30 0.76 29 0.71 28 0.72 24 0.72 24 0.75 26 0.79 34 0.71 26 0.76 32 0.82 31 0.80 Mean 28.5 0.75 St. dev. 3.3 0.04
Depth of base (m) 0.43 0.45 0.45 0.45 0.45 0.48 0.49 0.48 0.46 0.48 0.52 0.47 0.03
45
Width of base (m) 0.42 0.43 0.43 0.46 0.39 0.44 0.43 0.38 0.42 0.43 0.49 0.43 0.03
All subjects provided written informed consent prior to participation. The rest of the chapter discusses the results, first in terms of the original inter-segmental angles, and their range of motion (ROM) for the bending tasks in the experiment. Then the relative error in the distorted ROMs due to each of the three experimental errors is discussed.
5.2 Original Angles From the original captured data, the marker coordinates given in the global frame, the intersegmental angles were calculated for the course of the bending movements in the experiment. The range of motion of each trunk level (inter-segmental angle) was derived as well as the coefficient of variation that described the inter-subject variability.
5.2.1
Angular ROMs
Original inter-segmental joint angles comprise 2970 time series. Therefore, as a representative sample, the time series of the angles of all the inter-segmental joints from trial number two of subject number five in anterior (A) bending task is presented in Figure 16. The angle time series of the other 4 directions (AL, AR, L, and R) of the same subject and trial are presented in the appendix through Figures B.1.c to B.1.e. The range of angles in the sagittal plane is relatively larger than that of angles in the coronal and transverse planes. Therefore, in order for the angular curve patterns to be visible in the two latter planes, the plots are not uniformly scaled.
46
Figure 16. Inter-segmental joint angle motion (degrees) in the sagittal, coronal and transverse planes during anterior direction bending for the representative subject along the six intersegmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL), and sacral (SC). The time of bending and returning to the upright sitting position is in seconds.
47
The angular range of motion (ROM) for each inter-segmental joint indicates the range in which the angular rotation occurs between the two adjacent segments comprising the joint, from quietsitting to the maximum trunk bending position. The mean range of angular ROM among all subjects for the joints between adjacent trunk segments, UT-MUT, MUT-MLT, MLT-LT, LTUL, UL-LL, and LL-SC, in the sagittal, coronal, and transverse planes and for all five bending directions are shown in Table 5.2. The mean and standard deviation of the angular ROM of all 3D inter-segmental joint angles is shown in Figure 17. Table 5.2. The average angular ROM of the inter-segmental joints in the sagittal, coronal, and transverse planes during trunk bending in five directions. The inter-segmental joints are defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments. The results are presented as the mean ROM (deg) over all subjects. UT-MUT Sagittal Coronal Transverse
Sagittal Coronal Transverse
Sagittal Coronal Transverse
4.14 1.34 1.93
MUT-MLT MLT-LT Anterior 4.51 4.26 1.27 1.21 1.84 2.30
LT-UL
UL-LL
LL-SC
7.52 1.86 2.30
15.15 1.82 2.21
13.11 1.63 1.60
4.52 1.95 3.03
Anterior Left 3.56 4.74 1.93 3.43 4.10 7.58
7.63 7.07 6.82
15.92 6.02 4.40
10.11 2.98 2.86
4.60 2.02 4.06
Anterior Right 3.65 4.46 2.32 3.58 3.77 7.63
6.79 5.66 7.16
13.63 5.39 4.51
10.52 3.09 2.80
5.44 5.33 10.84
7.44 9.35 8.93
11.83 6.33 6.68
5.27 3.78 3.25
5.02 5.04 10.06
7.52 7.83 9.05
12.09 6.43 6.81
4.58 3.83 3.07
Left Sagittal Coronal Transverse
3.66 3.07 5.42
4.41 3.47 5.27 Right
Sagittal Coronal Transverse
4.64 2.93 6.14
3.84 3.33 5.63
48
Sagittal
L AL A AR R
20 15 10 5 UT-MUT
MUT-MLT
MLT-LT
LT-UL
UL-LL
LL-SC
MUT-MLT
MLT-LT
LT-UL
UL-LL
LL-SC
MUT-MLT
MLT-LT
LT-UL
UL-LL
LL-SC
Coronal
L AL A AR R
0 20 15 10 5 0
UT-MUT
Transverse
L AL A AR R
20
15 10 5 0
UT-MUT
Figure 17. Angular ROM (median SD over all the subjects) in degrees for all the six intersegmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC); each in five bending directions: Left (L), Anterior Left (AL), Anterior (A), Anterior Right (AR), and Right (R).
5.2.1.1
Analysis on ROMs in the Three Dimensions
In all the three planes, the mean of the angular ROM of the trunk inter-segmental joints did not exceed 16 . The angular rotation in the sagittal plane ranged from 4 to 14 for anterior, anterior right and anterior left bending directions, and ranged between 3.5 and 12 for right and left bending directions. In comparison, for anterior, anterior right and anterior left bending, the coronal and transverse rotations were between 1 and 7 and between 2.5 to 10.5 for left and right bending directions. This shows that when the motor task involves some degree of anterior bending (e.g. anterior bending, anterior left bending, and anterior right bending of this experiment), trunk rotation occurs mainly about the Z-axis or the mediolateral axis of the body
49
(i.e., in the sagittal plane). However, when the task involves side bending (e.g. left and right bending of this experiment) the trunk rotation occurs mainly about Y-axis and X-axis in the coronal and transverse planes, respectively.
5.2.1.2
Analysis on ROMs in the Six Inter-segmental Joints
The lumbar inter-segmental joints (UL-LL and LL-SC) showed large angular ranges in the sagittal plane, for all bending directions. The average ROMs for sagittal lumbar angles are up to 15.92°, while thoracic level joints (UT-MUT, MUT-MLT, MLT-LT) had average ROMs less than 5.44°. The comparison of the thoracic and lumbar levels indicates that lumbar segments made the major contribution to the movement in the sagittal plane, which is consistent in all directions (≈73%). In the coronal plane, as well, the joint between lumbar and thoracic regions, LT-UL joint, has the largest ROMs. This indicates that this joint is the main level in the trunk in which trunk’s side bending occurs during movements.
The MLT-LT joint has the largest ROM in the transverse plane, in all the trunk bending directions that involved a lateral movement, i.e., anterior right, anterior left, right and left directions (average ROM up to 10.84°). This suggests that this joint is the main level in the trunk in which trunk’s horizontal rotation occurs during movements.
It should be noted that for anterior bending, all inter-segmental joints similarly have small angular ROMs in the coronal and transverse planes with average values between 1.2° and 2.3°; which is expected as anterior bending doesn’t involve side bending or axial rotations.
5.2.2
Angular Coefficient of Variation
The coefficient of variation table shows the inter-subject variability of each inter-segmental joint angle (Table 5.3). The results show that the overall coefficient of variation is relatively high with values no less than 20.9% and up to 60%. The thoracic inter-segmental joints (UT-MUT, MUTMLT, MLT-LT) are the joints in which the highest coefficient of variations are shown, in the coronal plane. This indicates that subjects have the most difference in their angular ranges of motion in thoracic levels of the trunk. For lumbar inter-segmental joints, although generally less
50
than thoracic levels, the inter-subject variability is again higher in coronal and transverse planes than in the sagittal plane. Overall, the coefficients of variation values suggest that the angles in the coronal and transverse planes have more variability among subjects than the angles in the sagittal plane. In the following stages of the study, the coefficient of variation or inter-subject variability is used in the sensitivity analysis of inter-segmental joint angles for different errors. The error in the reported angle can be neglected until it is less than the inter-subject variability value in that joint. Errors higher than the inter-subject variability, however, are corrupting the reported angles. Table 5.3. Coefficient of variation of ROMs (=100SD/mean) in percentage; in the sagittal,
coronal, and transverse planes during trunk bending in five directions. The inter-segmental joints are defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments. UT-MUT Sagittal Coronal Transverse
31.0 60.1 57.1
MUT-MLT MLT-LT Anterior 38.3 35.4 58.6 29.4 31.6 31.8
LT-UL
UL-LL
LL-SC
43.6 39.3 40.2
34.7 36.7 29.1
45.5 44.6 25.9
Sagittal Coronal Transverse
29.2 31.8 41.2
Anterior Left 21.2 32.9 23.2 36.0 33.5 30.0
38.4 34.8 41.4
31.7 36.4 32.8
46.4 54.9 33.6
Sagittal Coronal Transverse
28.9 29.0 35.0
Anterior Right 30.9 25.3 20.9 41.5 36.8 40.7
35.4 30.4 41.1
32.0 30.8 37.3
50.7 53.9 37.5
Sagittal Coronal Transverse
36.2 47.3 27.6
22.3 23.6 36.4
20.8 29.1 29.7
37.1 28.9 41.4
32.9 36.3 35.7
35.1 47.5 48.1
26.9 53.0 43.0
40.4 24.9 38.8
40.5 26.7 33.2
36.3 40.1 43.9
Left
Right Sagittal Coronal Transverse
36.1 53.8 33.2
35.1 24.6 39.5
51
5.3 Instrumentation Error The relative error in calculated angular ROMs of inter-segmental joints of the trunk is presented in Table 5.4. The reported erroneous angles were the 95th percentile over 1,000 simulations calculated for each trial. Each erroneous angle time series was low-pass filtered with an 8th order Butterworth filter with a cut-off frequency of 6 Hz since in human movement 99.7% of the signal power is contained in the frequency bandwidth lower 6 Hz (Winter, 2005). The angular ROM reported for each subject is the average of the three trials of that subject. The error represented in the table is the median over the eleven subjects; with inter-quartile range in the parenthesis. The induced ROM errors were smaller than 9% in all inter-segmental joint angles and all bending directions, except for the coronal rotations of the Thoracic inter-segmental joints and only during bending in anterior direction, which average relative error was 11.2%, 12.6% and 12.4% for UT-MUT, MUT-MLT and MLT-LT joints, respectively. According to Figure 18, these values were below the inter-subject variability, as the error margin. All the relative ROM errors are shown in Figure 18 together with the coefficient of variation of that ROM among subjects. Only in MUT-MLT joint the error was close to the coefficient of variation among subjects. For the rest of the inter-segmental joint angles the coefficient of variation, being overall more than 20%, were higher than the range of errors, being overall less than 10%. Therefore, in order for the error bars to be visible in the graph, the scale of the plot was not enlarged to show the coefficient of variation values.
52
Table 5.4. Relative errors in inter-segmental joint angles' ROM due to instrumentation error during trunk bending in five directions. The results are expressed in percentages as median (inter-quartile range) over all subjects. The inter-segmental joints were defined between upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC) segments. UT-MUT
MUT-MLT
MLT-LT
LT-UL
UL-LL
LL-SC
Anterior Sagittal
4.3(2.4)
4.9 (1.8)
5.5 (2.6)
3.4 (2.3)
1.3 (0.9)
1.0 (1.0)
Coronal
11.2 (6.1)
12.6 (5.0)
12.4 (6.3)
8.5 (4.0)
8.2 (2.9)
6.5 (2.2)
Transverse
8.3 (4.6)
7.9 (3.6)
8.8 (2.9)
7.7 (6.6)
8.1 (4.5)
6.9 (2.3)
Anterior-Left Sagittal
4.1 (3.2)
4.8 (1.9)
3.6 (1.8)
2.6 (1.5)
1.1 (0.8)
1.4 (1.3)
Coronal
7.8 (3.4)
6.3 (1.9)
4.3 (2.4)
1.6 (0.5)
1.6 (1.4)
4.0 (2.2)
Transverse
7.0 (3.9)
4.1 (2.1)
2.7 (2.0)
2.7 (3.0)
3.5 (1.0)
3.3 (2.3)
Anterior-Right Sagittal
3.4 (2.1)
5.0 (2.8)
3.7 (1.4)
2.8 (2.5)
1.3 (1.0)
1.5 (1.8)
Coronal
5.3 (1.7)
4.5 (2.6)
3.8 (2.4)
2.0 (1.0)
2.0 (1.0)
3.7 (1.4)
Transverse
3.6 (1.2)
4.2 (2.8)
2.2 (1.2)
2.5 (1.7)
3.6 (3.1)
4.2 (2.8)
Left Sagittal
5.3 (2.4)
3.7 (1.9)
3.2 (0.7)
2.5 (1.7)
2.2 (1.2)
3.4 (2.2)
Coronal
4.1 (1.9)
2.9 (1.0)
2.3 (1.2)
1.2 (0.7)
1.6 (0.9)
3.0 (1.2)
Transverse
2.6 (1.2)
2.5 (1.1)
1.3 (0.6)
1.5 (0.6)
1.9 (1.8)
3.4 (1.5)
Right Sagittal
5.4 (2.6)
5.4 (1.9)
3.9 (1.3)
2.1 (1.3)
1.5 (1.2)
3.8 (1.7)
Coronal
4.6 (2.3)
4.3 (3.0)
2.8 (2.0)
1.5 (0.3)
1.5 (1.0)
2.2 (0.7)
Transverse
2.9 (2.0)
3.0 (1.7)
1.4 (1.1)
1.9 (1.4)
1.7 (0.8)
3.1 (1.9)
53
Sagittal
L AL A AR R
60
40
20
0
UT-MUT
MUT-MLT
MLT-LT
LT-UL
UL-LL
LL-SC
UT-MUT
MUT-MLT
MLT-LT
LT-UL
UL-LL
LL-SC
UT-MUT
MUT-MLT
MLT-LT
LT-UL
UL-LL
LL-SC
Coronal
60
40
20
0
Transverse
60
40
20
0
Figure 18. The relevant error in ROM (%) caused by instrumentation error. The bars are medians and standard deviation among subjects and the triangles show the respective Coefficient of variation (CV %). The six inter-segmental joints: upper thoracic (UT), mid-upper thoracic (MUT), mid-lower thoracic (MLT), lower thoracic (LT), upper lumbar (UL), lower lumbar (LL) and sacral (SC). The five bending directions: Left (L), Anterior Left (AL), Anterior (A), Anterior Right (AR), and Right (R).
54
In general, the results suggest that the propagated instrumentation error that distorts intersegmental joint angles is small when it is less than 5.5% in the sagittal plane, less than 12.6% in the coronal plane and less than 8.8% in the transverse plane. When comparing with the CV or the inter-subject variability that is above 20.8% for all the joints it was confirmed that the instrumentation error was not large enough to affect the repeatability of the ROM measurement among subjects.
5.4 Marker Misplacement Error Relative errors induced in the sagittal rotations due to marker misplacement error were less than 11% (except for MLT-LT inter-segmental joint: 30%), these relative marker misplacement errors were small. As such, marker misplacement errors are not expected to affect the reliability of ROM measures in the sagittal plane, when compared among clinical populations. For bending in the left and right directions, the relative marker misplacement errors for measures of coronal plane ROM were also small (less than 14%). For the other bending directions, however, the relative marker misplacement errors for coronal plane ROM were often large enough that caution should be used when interpreting these findings. For trunk bending in the anterior direction, relative marker misplacement errors for coronal plane ROM at the MLT-LT, LL-SC, and LT-UL levels (50.4%, 49.0%, 32.6%) were comparable to the inter-subject variability (29.4%, 44.6%, 39.3%). Marker misplacement error at the MUT-MLT level was also large (36%), although it was smaller than the inter-subject variability (58.6%). For bending in anterior-left and anterior-right directions, the relative marker misplacement errors for coronal plane ROM at the MUT-MLT level (19.6% and 19.7%) were also comparable to the inter-subject variability (23.2% and 20.9%). The relative marker misplacement errors for coronal plane ROM at the other trunk levels were smaller than the inter-subject variability, and thus their reliability for clinical evaluations should not be of concern. The relative marker misplacement errors for measures of transverse plane ROM were also largest for trunk movements in the anterior direction where transverse plane ROM was small and smallest for trunk movements to the left and right where transverse plane ROM was larger.
64
These errors were largest at the UL-LL and LL-SC levels, where the relative marker misplacement errors for transverse plane ROM were 57% and 52% during bending in anterior direction. For the UT-MUT, MUT-MLT, MLT-LT, and LT-UL levels, however, these errors were smaller than 20% during trunk bending in anterior direction, and smaller than 10% in the other bending directions. Furthermore, these marker misplacement errors, for transverse plane ROM, were only comparable to the inter-subject variability at the UL-LL and LL-SC level during trunk bending in anterior direction, and for the UL-LL level alone for trunk bending in the anterior-left and anterior-right directions. Therefore, whenever any anterior trunk bending is involved, the lumbar spine movements in the transverse plane, during anterior bending, are likely to be small, and may therefore be affected by marker misplacement errors. Marker misplacement errors, similar to those described above, would be expected for any multisegmental trunk model where the anatomical frame of the segments is defined based on anatomical landmarks. One reason why these errors will tend to be smallest for the sagittal plane ROM is that marker misplacement was not introduced to the X-axis for anatomical frame of each segment except sacral segment anatomical frame in the simulations performed in this study. Since YZ plane was taken to approximate the plane of the skin, the marked misplacement would occur in the YZ plane and would not occur in the X-axis. Therefore, the effect of this error is to rotate the Y-axis and Z-axis of each anatomical frame inside the YZ-plane, which then remains constant during the course of bending. Such Y-axis and Z-axis rotation results in the introduction of a constant offset to the calculated inter-segmental angle in the coronal and transverse planes, with a minimal effect to the ROM. This offset error is reported by RMS difference between the original and erroneous angular curves in Table A.2, in appendix A. However, the instantaneous value of the induced error in the coronal and transverse planes, also partially depends on the instantaneous inter-segmental angle in the sagittal plane. This dependency changes the inter-segmental angles pattern in the coronal and transverse planes and induces error in the ROMs in these two planes. Figure B.2 (a-e) in appendix B, depicts the original and erroneous angular curves, for a representative trial and subject, where both offset error and pattern error can be observed. Other researchers observed the induced errors as both
65
offset and angle pattern error for lower limbs joints (Kadaba et al., 1990; Della Croce et al., 1999; Della Croce et al., 2005). This study indicates that the error induced by marker misplacement is likely to be negligible for measured inter-segmental ROM in the sagittal plane. High inter-subject variability for the coronal and transverse plane ROM, combined with high relative marker misplacement errors for many trunk levels, suggests that measures in these planes should be viewed with caution for any movements with an anterior component. For the multi-segmental model used in our study, we recommend particular caution for the coronal plane ROM at the MUT-MLT, MLT-LT, LT-UL, and LL-SC levels and for the transverse plane ROM at the UL-LL and LL-SC levels.
6.4 The Effect of Skin Movement Artifacts Skin artifacts are the main source of error in the kinematic measurement of human motion, according to previous research that assessed this error in the lower limbs. Studies examining the effect of this type of error on kinematic evaluation of the trunk are limited to investigating a few specific spinous processes and the linear displacement of a single marker over these bony landmarks. The current study is the first that investigated a multi-segment model of the trunk and the propagation of error from skin artifacts to the inter-segmental joint angle calculations. During trunk bending in the five directions of the experiment, anterior bending, anterior left bending, anterior right bending, right bending, and left bending, the relative ROM error for rotations in sagittal plane caused by skin artifacts were generally small for all inter-segmental joints. Comparing the errors in the sagittal plane for different directions reveals that the errors in ROM evaluation relatively increase with more lateral bending tasks. The increase in errors while bending to left and right, especially in thoracic levels, correspond with the fact that muscles on thoracic region are more engaged. Overall, with the small ranges of error in the sagittal plane we can conclude that the error caused by skin movement artifacts in the sagittal plane is not expected to affect the reliability of the ROM. This may be mainly because the skin movement artifacts across the back profile distort the ⃗⃗⃗⃗⃗ plane of the anatomical frame and therefore the sagittal plane angles are not affected.
66
The results showed that the error propagated to angle measurements due to skin artifacts significantly affects the angles in the coronal plane. The relative error propagated to the ROM of the coronal angles ranged between 75% and 500%. This means that the angles may be erroneously reported to be 6 times larger than the original ROM. Such large errors were expected because of the pattern of soft tissue deformation and stretch across the coronal plane of the posterior trunk. It should be added that the angular ROM of the coronal plane angles were very small, between 1.2 and 9.35 Therefore, the results indicate that angles that have small ROM are the angles that are seriously affected by skin artifacts. The errors that propagated to the coronal rotations may be large enough to mask the actual movements of the underlying bony anatomical landmarks. These observations are comparable to previous studies examining lower limb joints that concluded the joints with smaller ROM are markedly affected by soft tissue artifacts (Leardini et al., 2005; Schwartz, Trost, & Wervey, 2004). Likewise, in the transverse plane, the inter-segmental joint angles had small ROMs ranging from 1.84 to 7.63 , especially in the movements containing an anterior bending component (i.e., anterior, anterior right, anterior left). However, the errors in the ROM in the transverse plane are relatively small (
