Accepted for publication in Medical Engineering & Physics
A Complete, Non-Lumped, and Verifiable Set of Upper Body Segment
Parameters for Three-Dimensional Dynamic Modeling
Running Head: Upper Body Segment Parameters for 3D Dynamic Modeling
Authors:
Albert H. Vette , Takashi Yoshida , T. Adam Thrasher3, Kei Masani2, and Milos R. Popovic1,2
1,2
1,2
Affiliations:
1
Institute of Biomaterials and Biomedical Engineering, University of Toronto,
164 College Street, Toronto, Ontario, M5S 3G9, Canada
2
Lyndhurst Centre, Toronto Rehabilitation Institute,
520 Sutherland Drive, Toronto, Ontario, M4G 3V9, Canada
3
Center for Neuromotor and Biomechanics Research, University of Houston,
2450 Holcombe Boulevard, Houston, Texas 77021-2040, USA
September 21, 2010
Corresponding Author:
Albert H. Vette, Dipl.-Ing.
Rehabilitation Engineering Laboratory, Lyndhurst Centre
Toronto Rehabilitation Institute
520 Sutherland Drive, Toronto, Ontario, M4G 3V9, Canada
Phone: +1-416-964-7145 / Fax: +1-416-425-9923
Email: a.vette@utoronto.ca
www.toronto-fes.ca
Upper Body Segment Parameters for 3D Dynamic Modeling
ABSTRACT
Dynamic models of the human trunk have been extensively used to investigate the biomechanics
of lower back pain and postural instability in different populations. Despite their diverse
applications, previous models rely on intrinsic upper body segment parameters (UBSP), e.g.,
each segment’s mass-inertia characteristics. However, a comprehensive UBSP set allowing stateof-the-art, three-dimensional (3D) dynamic modeling does not exist to date. Therefore, our
objective was to establish a UBSP set of all vertebral trunk segments that is accurate and
complete. Based on high-resolution, transverse color images, anatomical structures of the Male
Visible Human (MVH) were digitally reconstructed via commercial software. Subsequently, we
identified the 3D spinal joint and 3D center of mass coordinates, the mass, and the moment of
inertia tensor for 24 vertebral trunk segments and 4 upper limb segments (two segments per
arm). Since the MVH images are public domain, the parameters are uniquely verifiable and
expandable to also include lower limb parameters. To demonstrate the UBSP set’s practicality,
the parameters were finally implemented in a previously proposed inverse dynamics model of
the upper body. Our findings reveal that an accurate and complete UBSP set has been obtained
that will be beneficial to: (1) systemize thinking in postural control studies; (2) quantify the
effect of impact forces on the head and trunk (e.g., during whiplash); (3) suggest populationspecific experiments based on theoretical insights into trunk dynamics (e.g., regarding lower
back pain); or (4) assess the feasibility of new surgical techniques (e.g., spinal fusion) and
neuroprostheses (e.g., after spinal cord injury).
INDEX TERMS – Biomechanics; center of mass; dynamic modeling; mass; moment of inertia;
spinal joints; the Visible Human Project; trunk; upper limbs.
2
Upper Body Segment Parameters for 3D Dynamic Modeling
1. INTRODUCTION
Trunk instability is a major problem for people with spinal cord injury (SCI): it severely
compromises their independence in daily life [1] and frequently leads to secondary health
complications such as kyphosis [2,3], pressure sores [4], and respiratory dysfunction [5,6]. In
fact, a representative survey revealed that people with quadriplegia and paraplegia prioritize the
recovery of trunk stability over the recovery of walking function [7]. Furthermore, trunk stability
is a key factor in human balance control and mobility – regardless of the population and task.
This can be ascribed to the fact that over half of the body’s mass is located above the pelvis [8];
as such, the ability to balance the trunk is critical for maintaining stability of the entire body [9].
In exploring mechanisms that may compromise postural stability, linked-segment models
have proven very useful [10]. Interest in mathematical modeling of the upper body arose in the
context of studies on pilot ejection procedures [11,12] that came to the foreground with the
advent of high speed aircrafts [13]. More recently, biomechanical trunk models were employed
to study intrinsic spine stability [14-20] or the kinetics of vertebral trunk segments during various
movements and tasks (e.g., bending or lifting) [21-29]. Other efforts utilized trunk models to
predict spinal or head injuries caused by sudden seat displacements [30-33] or to evaluate the
feasibility of controlling seated posture after SCI via functional electrical stimulation [34-36].
In spite of their diverse applications, all linked-segment models commonly rely on
intrinsic upper body segment parameters (UBSP). For three-dimensional (3D) dynamic
modeling, these UBSP consist of the 3D joint coordinates as well as each segment’s mass, 3D
center of mass (COM) location, and moment of inertia tensor [37-39]. Since even small
deviations from the true parameter values can, however, lead to substantial errors in the output
measures (joint torques or kinematics) [40,41], a dynamic model of the trunk is only as good as
the UBSP defining it [42]. Hence, implementing accurate UBSP is of great importance.
3
Upper Body Segment Parameters for 3D Dynamic Modeling
Many studies have quantified select UBSP using different subject matter (i.e., cadaver
versus
living)
and
techniques
[37,38,43-53].
Applied
methods
include
volumetric,
photogrammetric, and mechanical torsion techniques [43-46], but more recently also medical
diagnostic technologies such as magnetic resonance imaging (MRI) [37], computer tomography
(CT) [38,47], gamma ray scanning [48,49,52,53], and X-ray absorptiometry [50,51]. While a few
studies identified UBSP for some of the vertebral trunk segments [38,45,46,53], most of the
studies reported UBSP for lumped trunk portions such as ‘upper trunk’ and ‘lower trunk’
[37,43,44,47-52].
All of these efforts offer valuable information for mathematical modeling; none of the
studies, however, provide a complete set of UBSP that is needed for 3D dynamic modeling. In
fact, complete 3 × 3 inertia tensors of the upper body segments and complete 3D coordinates of
the underlying joints cannot be found in the literature [37,38,43-53]. Moreover, some reports did
not include the location of the segment COM [43,50,53] or reported it in only one dimension
[37,49,51]. These shortcomings may be due to the fact that previous studies may not have been
driven by 3D dynamic modeling (e.g., [47,50,53]), or that the applied methodology did not allow
for identifying such a comprehensive set of 3D parameters (e.g., [45,46]). Besides, only the everincreasing computer power of recent years has made the implementation and simulation of more
realistic and complex 3D models possible [54]. In any case, researchers are still bound to
implement UBSP from multiple sources (e.g., [34,35]) and following pre-defined body
segmentations (e.g., [8,37,49]), which could potentially compromise the significance of their
studies.
To resolve these limitations, the objective of this study was to use publicly available,
high-resolution transverse photographs from the Visible Human Project [55] to identify a
comprehensive set of UBSP for 3D dynamic modeling of the upper body. Particular
4
Upper Body Segment Parameters for 3D Dynamic Modeling
requirements were that the obtained parameters are: (1) accurate and complete; (2) specified for
each vertebral level independently; and (3) entirely verifiable and expandable for complete body
modeling. To demonstrate the practicality of the UBSP, they were finally implemented in a
complex 3D dynamic model of the upper body to predict spinal joint torques during perturbed
sitting (inverse dynamics). The use of such models will be beneficial to: (1) systemize thinking
in postural control studies; (2) quantify the effect of impact forces on the head and trunk (e.g.,
during whiplash); (3) suggest population-specific experiments based on theoretical insights into
trunk dynamics (e.g., regarding lower back pain); or (4) assess the feasibility of new surgical
techniques (e.g., spinal fusion) and neuroprostheses (e.g., after spinal cord injury).
5
Upper Body Segment Parameters for 3D Dynamic Modeling
2. MATERIALS AND METHODS
2.1. Image Properties and Segment Definition
The Visible Human Project was initiated by the National Institutes of Health (NIH, USA) in
1988 [55]. Five years later, the Male Visible Human (MVH) was obtained from the body of a 38
year old white male [55]. Having a height of 1.80 m and a weight of 90 kg [55], the subject was
centered between the 50th and 75th height and weight percentiles of the general male population
[56]. As such, also the overall anthropometrics of the subject should not significantly differ from
the average anthropometrics of the general male population [8].
After the frozen body was sectioned with a cryomacrotome at 1 mm intervals, the
resulting 1871 transverse body slices were photographed [55,57] with a 70-mm film and
digitized at a resolution of 4096 × 2700 pixels [57,58]. Due to this pixilation and the 1-mm
spacing of the body slices, each voxel has the size of 0.144 × 0.144 × 1 mm3 [58]. The 24-bit
RGB images (8 bits for Red, 8 bits for Green, and 8 bits for Blue colors) were obtained from the
National Library of Medicine and converted to high-resolution JPEG (Joint Photographic
Experts Group) images for convenient processing.
Using the JPEG images, a complete set of UBSP was identified for 24 vertebral trunk
segments and 4 upper limb segments (two segments per arm). In particular, the trunk was
divided into five lumbar segments (L1 to L5), twelve thoracic segments (T1 to T12), six cervical
segments (C2 to C7), and the head portion adjacent to the C2 segment (HD)1. Note that cervical
and head segment parameters are needed for studying whiplash [31-33] as well as the
coordination and control of head-trunk dynamics during external perturbations [60-62]. The
upper limbs were divided into upper arm segments and forearm-hand segments.
1
Based on the kinematic analysis of the upper cervical spine by White and Panjabi [59], the neck portion
defined by the first cervical vertebra (C1 segment) was included in the head segment HD.
6
Upper Body Segment Parameters for 3D Dynamic Modeling
2.2. UBSP Identification
2.2.1. Images Pre-Processing and Reference Frame Definition
949 images from the vertex to the most distal point of the ischium (94.9 cm in height) were preprocessed using a commercial 3D reconstruction software (3D-Doctor, Able Software
Corporation, USA). First, anatomical structures were sharpened and their edges enhanced using a
high-pass filter whose pixel radius and opacity were based on the image features. To obtain a set
of planes that is geometrically accurate, the sharpened images were then realigned across the
entire stack. Specifically, neighboring planes were oriented to each other by applying a
maximum likelihood algorithm to a central alignment region of 10 × 10 cm2 that featured strong
contrasts, visible patterns, and large variations2. These features were ensured by choosing a
cross-section of a large number of different anatomical structures.
To dissociate the MVH images from the external reference frame of the digitized
photographs {FVH} (Fig. 1), a world reference frame {FWD} internal to the MVH anatomy was
established. As shown in Fig. 1, {FWD} was fixed to the right anterior superior iliac spine (ASIS)
of the MVH and oriented as to approximate the ‘natural’ axes of the human body [63]: The Ycoordinate (YWD) pointed medially from the right to the left ASIS; the X-axis (XWD) was
perpendicular to the plane defined by the two ASIS and the midpoint between the pubic tubercles
(pointing anteriorly); and the Z-coordinate (ZWD) was the common perpendicular to the first two
axes (pointing superiorly) [63]. These conventions resulted in a translation vector
a rotation matrix
WD
VH
WD
PVHorg and
ROT that transformed any given point from {VH} to {WD}:
2
The neck and head images demanded smaller alignment regions to avoid including pixels outside the
body shell boundary.
7
Upper Body Segment Parameters for 3D Dynamic Modeling
WD Px
WD
Py
WD
Pz
1
VH Px
VH
WD
Py VH ROT
WD
VH T
VH
Pz 0 0 0
1
VH Px 0.056 0.998 0.028 240.558 VH Px
WD
PVHorg VH Py 0.998 0.056 0.034 146.654 VH Py
(1)
VH
1
Pz 0.032 0.030 0.999 811.980 VH Pz
0
0
1 1
1 0
2.2.2. Spinal Joint Centers
In order to identify the spinal joint centers, 3D geometric models were obtained for all spinal
discs between the first cervical (C1) and the first sacral vertebrae (S1). Using 3D-Doctor, we
traced the disc boundaries on the MVH images and stacked them for geometric volume
reconstruction. Since the resulting 3D disc models did not show any undesired artifacts such as
protruding edges, only a low level of smoothing was applied to the 3D models that increased the
number of face triangles by 20 % (smoothing factor of 0.2 in 3D-Doctor). The obtained models
were then used to calculate the 3D COM of each spinal disc, which was assumed to represent the
joint about which neighboring vertebral trunk segments could articulate.
The anterior-posterior COM coordinate (APCOM) of a given spinal disc was identified by
evaluating the mass-weighted COM coordinates of all 1-mm disc slices via
APCOM m Disc VH APi mi ,
N
VH
(2)
i 1
where mDisc is the mass of the disc, N the number of the disc’s transverse images,
VH
APi the AP
COM coordinate of the i-th disc slice in {VH}, and mi the mass of the i-th disc slice. As we
assume that the density of each spinal disc is uniformly distributed, Equation (2) can be written
as
VH
APCOM h Ai VH APi h Ai
N
N
i 1
i 1
8
Upper Body Segment Parameters for 3D Dynamic Modeling
N
VH
APCOM
i 1
VH
APi Ai
A
N
i 1
,
(3)
i
where Δh = 1 mm is the thickness of the disc slices and Ai the transverse area of the i-th disc
slice. While Equation (3) was also used to identify the superior-inferior coordinate of each spinal
disc’s COM, the medial-lateral (ML) COM coordinate was assumed to lie in the body’s sagittal
plane. This plane was perpendicular to YWD and passed through the midpoint between the pubic
tubercles (Fig. 1). Lastly, the obtained 3D coordinates were transformed into {WD}. To verify
the validity of the tracing procedure, three spinal discs (C3-C4, T3-T4, and L3-L4) were traced
and stacked by an additional researcher. The resulting volume and COM coordinates had an
average discrepancy of 0.07 ± 0.06 % with respect to the values identified by the main
researcher.
2.2.3. Mass and COM of Vertebral Trunk Segments
The MVH images were also used to create 3D geometric models of the vertebral trunk segments.
First, a volumetric representation of the MVH was obtained by tracing and stacking the body
shell boundaries of all transverse images in 3D-Doctor. Following, the smoothed body shell
model (smoothing factor of 0.2) was divided into vertebral trunk segments using transverse
planes that intersected with the COM of the spinal discs [38].
Since the density of the trunk varies substantially along its length [64], the mass of the
thoracic and lumbar segments (T1 to L5) was identified via a continuous trunk density function
[64]. The densities of the remaining segments (HD and C2 to C7), which were assumed to be
uniformly distributed within each segment, were taken from Winter [8]. Accordingly, the mass
of a given vertebral trunk segment ( mSegment ) was calculated as
9
Upper Body Segment Parameters for 3D Dynamic Modeling
mSegment Segment VSegment i h Ai ,
N
i 1
(4)
where N is the number of the segment’s transverse images, Δh = 1 mm the thickness of the
segment slices, δi the density, and Ai the transverse area of the i-th segment slice.
The AP COM coordinate (APCOM) of a given vertebral trunk segment was again found by
evaluating the mass-weighted COM coordinates of each 1-mm segment slice:
APCOM m Segment VH APi mi ,
N
VH
i 1
(5)
where VHAPi is the AP COM coordinate of the i-th segment slice in {VH}, and mi the mass of the
i-th segment slice. Utilizing the continuous density variation of the trunk along its length [64],
Equation (5) yields
VH
APCOM i h Ai VH APi i h Ai
N
N
i 1
i 1
N
VH
APCOM
i 1
VH
APi i Ai
N
i 1
i
Ai
.
(6)
While Equation (6) was also used to identify the superior-inferior COM coordinate of each
segment, the ML COM coordinate was again assumed to lie in the body’s sagittal plane. Lastly,
the obtained 3D coordinates were transformed into {WD}. To verify the validity of the tracing
procedure, three trunk segments (C3, T3, and L3) were traced and stacked by an additional
researcher. The resulting volume and COM coordinates had an average discrepancy of 0.11 ±
0.08 % with respect to the values identified by the main researcher.
10
Upper Body Segment Parameters for 3D Dynamic Modeling
2.2.4. Moment of Inertia of Vertebral Trunk Segments
In order to accurately identify the moment of inertia tensor for each vertebral trunk segment
about its COM, the total volume of each segment was dissolved into cubic sub-volumes of VS =
1 mm3. This was done by applying Jordan’s curve theorem to the polygons of the trunk segment
boundaries, i.e., by determining the cube centers that lie within the boundaries of each segment.
Taking the continuous density variation of the trunk along its length into account [64], the mass
of each cube was then approximated by a point mass ranging between 0.77 and 1.11 mg [8,64].
Using these point masses and their spatial distribution, the principal moments of inertia and
products of inertia were calculated as
N
VH
2
2
I
V
Jt xx S i ( yi zi )
i 1
N
VH
2
2
Jt I yy VS i ( xi zi )
i 1
N
VH
2
2
I
V
Jt zz S i ( xi yi )
i 1
VH
VH
Jt I xy Jt I yx VS i xi yi
i 1
N
VH
VH
I
I
V
Jt xz Jt zx
S i xi zi
i 1
N
VH
VH
I
I
V
Jt yz Jt zy
S i yi zi
i 1
(7)
N
In Equation (7), xi, yi, and zi identify the location of a particular point mass in {VH} with respect
to the segment’s COM. The moment of inertia tensors of the vertebral trunk segments were
finally transformed from {VH} to {WD} using
WD
Jt
WD
WD
I Segment VH
ROT VHJt I Segment VH
ROT T
(8)
11
Upper Body Segment Parameters for 3D Dynamic Modeling
2.2.5. Segment Parameters for Upper Limbs
Upper limb parameters were identified for the upper arm (UA) and the forearm-hand segments
(FA-H). The upper arm was defined as the portion between the glenohumeral joint center (GHJ)
and the midpoint between the humeroulnar and humeroradial joint centers (HURJ). While the 3D
joint centers of the upper limbs where directly taken from the MVH images, all other parameters
(mass, 3D COM location, and moment of inertia tensor) were calculated as for the trunk
segments. As only uniform estimates of the upper limb densities exist [8], we decided to assign
different density values to different tissues: (1) bone tissue: 1.90 g/cm3 [65]; (2) muscle tissue:
1.06 g/cm3 [66]; and (3) adipose tissue: 0.90 g/cm3 [67]. For all remaining tissues (mostly blood
vessels), a value of 1.00 g/cm3 was assigned based on the density of water.
2.3. Example Application: Inverse Dynamics for Perturbed Sitting
To demonstrate the completeness of the UBSP and their independence from lumped trunk
portions, the identified set was implemented in a previously proposed 3D dynamic model of the
upper body that focuses on the actions of the lumbar spine [34]. The model consisted of six rigid
bodies, representing five lumbar segments (L1 to L5) and the head-arms-thorax (HAT) complex.
The lowest moving segment, i.e., the L5 segment, was located above the pelvis, which served as
the inertial frame of reference (Fig. 1). The model had three rotational degrees of freedom
between the lowest lumbar segment and the pelvis (L5-S1): flexion-extension, lateral bending,
and axial rotation. The remaining five joints were modeled as 3 × 5 rotational constraints. A
particular constraint’s rotation was defined by: (1) the movement of the ‘free’ L5-S1 joint; and
(2) the ratio between the given joint’s and the L5-S1 joint’s ranges of motion as reported by
White and Panjabi [59].
In order to estimate the lumbar joint torques by applying the inverse dynamics method,
the kinematics of each model segment had to be described in inertial frames of reference. The
12
Upper Body Segment Parameters for 3D Dynamic Modeling
frame assignment of the model followed the Standard Denavit-Hartenberg notation [68] as it
elegantly describes the kinematic relationship between the joint variables of the model. To obtain
the dynamic model of the upper body, we implemented the identified UBSP in a recursive
Newton-Euler formulation of the multi-body dynamics [68]. The model was then used in
combination with experimental data from a subject with MVH anthropometrics to predict the
lumbar joint torques during perturbed sitting [69,70] (Matlab ver. 7.5, Mathworks Inc., USA). In
the experiments, the horizontal force had a Gaussian profile (peak of approximately 200 N), was
applied just inferior to the axillae (T7 segment), and perturbed the subject diagonally in the
anterior-left direction (five trials). The model implementation was finally validated by solving
the same inverse dynamics problem using (1) the Lagrangian formulation [68] and (2) a block
diagram within a commercial simulation environment (Simulink ver. 7.4 & SimMechanics ver.
3.1, The MathWorks Inc.). Note that both the Newton-Euler and Lagrangian formulations are
‘gold standards’ in forward and inverse dynamics calculations [68,71-73]. Block diagram
simulations on the other hand are easy to execute, allowing the user to quickly alternate between
forward and inverse dynamics applications.
13
Upper Body Segment Parameters for 3D Dynamic Modeling
3. RESULTS
The complete UBSP set is available on the worldwide web in form of xls-spreadsheets (Excel),
MAT-files (Matlab), and txt-files (www.toronto-fes.ca/upper-body-segment-parameters). The
webpage also presents some detailed examples of how to combine the UBSP for models with
lumped trunk segments.
3.1. 3D Joint Coordinates and Upper Body Segmentation
The 3D coordinates of the MVH joint centers are listed in Table I. The locations of the vertex
and the spinal joint centers from HD-C2 to L4-L5 are expressed in {WD} and given with respect
to the subjacent joint in order to capture the joint distances as needed in kinematic modeling. The
joint centers of L5-S1 and the upper limb joints are expressed in {WD} and given with respect to
{FWD}. Note that all spinal joint centers were assumed to lie in the body’s sagittal plane,
resulting in zero ML offsets between the joints (y = 0 in Table I).
Fig. 2 depicts the surface reconstructions of the MVH body shell and spine. The joint
centers listed in Table I were used to define the vertebral trunk and upper limb segments, for
which respective mass-inertia characteristics were calculated. Note that the segment border
between the upper arm and the forearm-hand complex was rotated with respect to the transverse
planes to account for the flexion angle of the forearm (Fig. 2).
3.2. Segment Masses, COM Coordinates, and Moment of Inertia Tensors
The utilized segment densities as well as the calculated masses and COM coordinates of all
upper body segments are listed in Table II. The COM coordinates of the vertebral trunk segments
are expressed in {WD} and given with respect to the subjacent spinal joint center; the COM
coordinates of the upper limb segments are expressed in {WD} and given with respect to {FWD}.
14
Upper Body Segment Parameters for 3D Dynamic Modeling
Note that all COM of the vertebral trunk segments were again assumed to lie in the body’s
sagittal plane (y = 0 in Table II).
Fig. 3 depicts the distribution of the cubic sub-volumes that were used to calculate the
moment of inertia tensor for each upper body segment. Note that the sub-volumes are
represented by 1-point dots that are positioned at every cube center. Table III shows each
segment’s principal moments of inertia and products of inertia about the COM with respect to
the axes of the world reference frame {FWD} (see Fig. 1).
3.3. Lumbar Joint Torques during Perturbed Sitting
Fig. 4 depicts the inverse dynamics results for perturbed sitting. Shown are the average
perturbation force, the average HAT angles (AP and ML), and the calculated joint torques (AP
and ML) for an anterior-left diagonal perturbation. The output torques from the three different
inverse dynamics methods are plotted on top of each other. The dashed gray lines in the torque
plots mark the predictions for the highest joint (HAT-L1), whereas the dashed black lines mark
the predictions for the lowest joint (L5-S1). The torques at the four joints in-between (L1-L2 to
L4-L5) are marked by thin and solid gray lines. The vertical line across the subplots indicates the
onset of the perturbation force.
A simple visual inspection of Fig. 4 suggests that the joint torque estimations for the three
different inverse dynamics formulations coincide. As this observation was supported by an R2 of
over 99.9999 % for different time intervals, the internal validity of the inverse dynamics routines
is confirmed. Fig. 4 finally reveals that the AP torque traces are clearly affected by the AP
curvature of the spine.
15
Upper Body Segment Parameters for 3D Dynamic Modeling
4. DISCUSSION AND CONCLUSIONS
The present paper takes advantage of the Visible Human Project to identify a complete set of
upper body segment parameters as needed for state-of-the-art, 3D dynamic modeling. The
created UBSP set is particularly useful as its parameters are: (1) accurate and complete; (2)
specified for each vertebral level independently; and (3) entirely verifiable and expandable for
complete body modeling. In what follows, we elaborate on these advantages in comparison to
previously reported UBSP and discuss the implications of the inverse dynamics example.
4.1. Characteristics of UBSP Set
Due to the availability of high-resolution color photographs of the MVH, we could obtain highly
accurate 3D surface models of the body shell and spine. The voxels on which the 3D surface
reconstructions were based had a size of 0.144 × 0.144 × 1 mm3 [58]. This resolution, which is
significantly higher than in previous reports [37,38,43,44,47,50,51,53], allowed us to minimize
errors in boundary tracing and to acquire an accurate stack along the longitudinal body axis.
Since all identified UBSP are based on the 3D surface models, the models’ quality was essential
for identifying accurate parameters for the MVH. In addition, the present study obtained a
complete set of UBSP (3D joint coordinates, segment mass, 3D COM location, and moment of
inertia tensor) as needed for 3D dynamic modeling.
One of the main objectives of the present study was to obtain a flexible set of parameters
that is independent of any pre-defined body segmentations. This goal was accomplished by
identifying the parameters for all 24 vertebral trunk segments (HD to L5) and 4 upper limb
segments. Since the acquired parameters can be easily combined for different model
segmentations (see www.toronto-fes.ca/upper-body-segment-parameters for detailed procedure),
they should become an important resource for researchers in different fields. For example, in our
inverse dynamics application (see Section 2.3.), we used the obtained parameters in a model that
16
Upper Body Segment Parameters for 3D Dynamic Modeling
features five lumbar and a HAT segment [34]. Additional models for which the UBSP set could
be harvested have been used to study spinal loads during various tasks [22,24,25,27], whiplash
injuries [31-33], and the coordination of head-trunk dynamics [60,62].
Another advantage of the obtained dataset is its verifiability: Since the UBSP were
derived from a public domain resource (NIH, USA), other researchers can verify our parameters
using the outlined identification procedure. Note that this property is unique as the data used in
other UBSP reports (e.g., CT [38,47], MRI [37], or cadaver data [45,46]) are study-specific and
generally inaccessible to the scientific community. Moreover, the public domain MVH images
allow researchers to expand the UBSP set to include respective parameters of the lower body.
4.2. Comparison with Previous Studies on UBSP
Also other studies identified select inertial parameters of vertebral trunk segments: Liu and
Wickstrom used seven segmented cadavers to identify the masses and AP COM coordinates of
the segments as well as their principal moments of inertia [46]. In a study by Pearsall et al. [38],
CT images of four adults were used to obtain the same parameters. For both studies, the vertebral
trunk segment masses and AP COM coordinates exhibited the same profiles along the length of
the trunk as in the present study. While the masses were a bit larger for the MVH, the AP COM
coordinates with respect to the segments’ joints were mostly centered between those reported in
[38] and [46]. Finally, the principal moments of inertia were slightly larger in the present study
and had a dissimilar profile for the thoracic segments T1 to T4. While the differences in mass
and inertia size can be partially explained by differences in subject height and weight, the
dissimilar profiles of the thoracic moments of inertia may result from different segmentation
boundaries at the glenohumeral joint.
In this context, it has to be emphasized that the discussed studies did not identify
complete 3D spinal joint coordinates, 3D COM coordinates, and 3 × 3 moment of inertia tensors
17
Upper Body Segment Parameters for 3D Dynamic Modeling
[38,46]. Moreover, parameters were calculated for the thoracic and lumbar trunk segments (T1 to
L5), but not for the cervical trunk or upper limb segments [38,46]. Finally, the obtained
parameters in [38] were based on a voxel size of 0.16 × 0.16 × 1 cm3, resulting in an overall
resolution that was more than 1000 times lower than in the present study. Especially the image
spacing of 1 cm must at least partially result in erroneous body segmentations that are not always
bounded by the actual spinal disc centers; as a result, respective mass-inertia characteristics must
be skewed as well. Considering these shortcomings, the present study is the first to report a set of
UBSP that is based on highly accurate surface models and at the same time complete with
respect to: (1) the upper body segment definitions; and (2) the parameters needed for 3D
dynamic modeling.
4.3. Implications of Inverse Dynamics Application
The inverse dynamics application demonstrated that the identified UBSP can be easily
implemented in a 3D model with pre-defined body segments. The example also reveals that the
AP curvature of the spine has a distinct effect on the AP torques during body (re-)stabilization.
In fact, the static upright posture requires lumbar AP torques of different sign (Fig. 4, before 0
seconds) – a property that is dependent on the AP location of joint centers and segment COM.
Moreover, the intersecting of the AP torque traces (Fig. 4, around 0.25 seconds) implies that the
lower joints do not necessarily carry larger loads, but that the relative magnitudes depend on the
actual trunk kinematics. These are important kinetic observations that are masked in trunk
models ignoring the spinal curvature [27,34,35].
4.4. Potential Limitations and their Justification
Since the present study was limited to a single cadaver, we did not establish regression equations
for estimating parameters for different subject anthropometrics. Although such scaling rules are
18
Upper Body Segment Parameters for 3D Dynamic Modeling
beneficial, their identification was not our objective. Instead, the MVH database represented the
ideal resource for disseminating an accurate, complete, and verifiable UBSP set of all vertebral
trunk segments3. The main purpose of the UBSP is to use them independent of subject-specific
data,
i.e.,
without
the
objective
of
gaining
insights
into
a
sample’s
particular
characteristics/conditions. Models implementing the UBSP in forward or inverse dynamics
methods will rather represent the human ‘per se’ to address more basic questions. Such studies
are beneficial to: (1) systemize thinking in postural control studies that oftentimes require only a
single coherent set of UBSP (e.g., characterization of active & passive control mechanisms); (2)
quantify the effect of impact forces on the head and trunk (e.g., during whiplash); (3) suggest
population-specific experiments based on theoretical insights into trunk dynamics with and
without loads (e.g., regarding lower back pain); or (4) assess the feasibility of new surgical
techniques (e.g., spinal fusion) and neuroprostheses (e.g., after spinal cord injury). Studies of this
nature are especially important in the context of head and trunk dynamics as technical difficulties
either preclude experimental measurements of joint torques or make experiments very time
consuming, cumbersome, and error prone [41,76].
The densities within each vertebral trunk segment were assumed to be uniformly
distributed along two or three anatomical axes. One reason for this choice was that it is difficult
to assign appropriate values to complex connective tissue and organs such as the intestines, the
lungs, the kidneys, or the liver. While the chosen approximation may affect the accuracy of
respective parameters, the utilized density estimates are still more differentiated than in all
previous reports on UBSP. This is the case as we used a recently proposed density function that
describes the continuously varying density of the trunk along its length [64]. Moreover, Wicke et
3
It should be emphasized that strong evidence exists that there is no gender difference in postural stability
[74,75]. Nevertheless, we acknowledge a potential gender effect on the UBSP; therefore, having a UBSP
set for the Female Visible Human may be beneficial as well.
19
Upper Body Segment Parameters for 3D Dynamic Modeling
al. revealed that mass-inertia estimates of the trunk are most sensitive to the volume function
(which is highly accurate for the MVH), but not very sensitive to the density function [77].
In agreement with previous reports on trunk models [34,35,78], ML asymmetries in the
spinal joint centers and trunk segment COM were eliminated during the parameter identification.
Unlike other anatomical features that have been retained (such as the AP curvature of the spine
or products of inertia entries), these attributes are MVH-specific and not representative for larger
samples. Actual ML displacements away from the body’s sagittal plane had an average value of
1.7 mm (SD: 1.2 mm) for both the spinal joint centers and trunk segment COM. Using the ML
width of the body at different joint and COM heights as a benchmark, this resulted in an overall
average error of 0.7 % (SD: 0.5 %). Note that the observed displacement of the spinal joint
centers can be mostly attributed to the ML curvature of the spine (minor scoliosis), whereas the
displacement of the trunk segment COM is also affected by spine-independent ML body
asymmetries.
20
Upper Body Segment Parameters for 3D Dynamic Modeling
ACKNOWLEDGEMENT
The authors thank Alan Morris, Vivian Sin, and Roger Xu for their assistance in data acquisition
and processing. This work was supported by the Canadian Institutes of Health Research (#86427,
#94018, and #97953), the Natural Sciences and Engineering Research Council of Canada, the
Ontario Rehabilitation Research Advisory Network, the Ontario Ministry of Health and LongTerm Care, the University of Toronto, and the Toronto Rehabilitation Institute.
CONFLICT OF INTEREST STATEMENT
There are no conflicts of interest for the authors of this study.
LIST OF ABBREVIATIONS
{FVH}
{FWD}
{VH}
{WD}
3D
AP
ASIS
COM
CT
FA-H
GHJ
HAT
HURJ
JPEG
ML
MRI
MVH
NIH
RGB
SCI
UA
UBSP
External Reference Frame (internal to digitized MVH photographs)
World Reference Frame (internal to MVH anatomy)
External Reference System
World Reference System
Three-Dimensional
Anterior-Posterior
Anterior Superior Iliac Spine
Center Of Mass
Computer Tomography
Forearm-Hand Segment
Glenohumeral Joint Center
Head-Arms-Thorax
Midpoint between the Humeroulnar and Humeroradial Joint Centers
Joint Photographic Experts Group
Medial-Lateral
Magnetic Resonance Imaging
Male Visible Human
National Institutes of Health
Red-Green-Blue
Spinal Cord Injury
Upper Arm Segment
Upper Body Segment Parameters
21
Upper Body Segment Parameters for 3D Dynamic Modeling
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26
Upper Body Segment Parameters for 3D Dynamic Modeling
Table I. MVH joint centers for all spinal and upper limb joints. The 3D coordinates are expressed in
{WD} with respect to the subjacent spinal joint center (spinal joints except L5-S1) or with respect to
{FWD} (L5-S1 and upper limb joints). All spinal joint centers were assumed to lie in the body’s sagittal
plane.
Joint
x [mm]
y [mm]
z [mm]
Vertex
HD-C2
C2-C3
C3-C4
C4-C5
C5-C6
C6-C7
C7-T1
T1-T2
T2-T3
T3-T4
T4-T5
T5-T6
T6-T7
T7-T8
T8-T9
T9-T10
T10-T11
T11-T12
T12-L1
L1-L2
L2-L3
L3-L4
L4-L5
L5-S1
rGHJ
rHURJ
lGHJ
lHURJ
-5.801
0.948
1.616
-0.213
1.552
4.907
9.527
9.803
9.494
7.467
6.810
4.234
2.572
-0.144
-2.197
-4.160
-3.679
-3.750
-9.400
-9.704
-11.932
-8.878
-4.886
3.249
-56.683
-89.198
-117.901
-80.030
-106.983
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
123.551
-34.148
-127.199
280.416
356.487
172.656
20.039
19.096
18.051
18.067
17.106
18.239
19.289
21.273
21.199
23.195
23.120
24.098
25.100
24.998
25.934
24.923
29.902
32.740
35.808
35.755
38.780
38.913
39.054
40.279
488.119
200.176
486.762
205.168
Expressed in
{WD}, with
respect to
subjacent spinal
joint center
{FWD}
{FWD}
27
Upper Body Segment Parameters for 3D Dynamic Modeling
Table II. Densities, masses, and COM coordinates for all upper body segments. The COM coordinates
are expressed in {WD} with respect to the subjacent spinal joint center (HD to L5) or with respect to
{FWD} (upper limb segments). All COM of the vertebral trunk segments were assumed to lie in the body’s
sagittal plane.
COM
Segment
Density [g/cm3]
Mass [kg]
HD
C2
C3
C4
C5
C6
C7
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
L1
L2
L3
L4
L5
rUA
rFA-H
lUA
lFA-H
1.11 [8]
1.11 [8]
1.11 [8]
1.11 [8]
1.11 [8]
1.11 [8]
1.11 [8]
f(z)={1.00-1.01} [64]
f(z)={0.97-1.00} [64]
f(z)={0.92-0.97} [64]
f(z)={0.86-0.92} [64]
f(z)={0.80-0.86} [64]
f(z)={0.77-0.80} [64]
f(z)={0.77-0.78} [64]
f(z)={0.78-0.81} [64]
f(z)={0.81-0.86} [64]
f(z)={0.86-0.91} [64]
f(z)={0.91-0.96} [64]
f(z)={0.96-1.00} [64]
f(z)={1.00-1.01} [64]
f(z)={0.96-1.00} [64]
f(z)={0.91-0.96} [64]
f(z)={0.89-0.91} [64]
f(z)={0.89-0.93} [64]
0.90-1.90 [65-67]
0.90-1.90 [65-67]
0.90-1.90 [65-67]
0.90-1.90 [65-67]
3.752
0.514
0.459
0.434
0.532
0.696
1.029
1.247
1.584
1.410
1.434
1.349
1.332
1.533
1.572
1.700
1.694
2.113
2.403
2.621
2.541
2.624
2.520
2.588
3.051
1.823
2.998
1.785
x [mm]
y [mm]
z [mm]
-0.090
5.380
3.578
-3.262
-20.076
-29.729
-23.228
-14.056
-2.656
6.901
17.616
27.803
35.851
39.643
41.575
39.873
38.440
37.827
33.825
30.324
22.478
13.168
7.678
5.982
-97.131
-11.144
-87.783
-10.007
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-97.277
-56.979
338.120
300.026
70.718
10.257
9.759
8.760
7.986
7.064
7.883
8.788
10.240
10.877
12.153
12.378
13.284
13.766
13.697
14.144
13.610
16.046
17.450
19.021
18.844
20.094
19.826
19.380
339.645
93.938
333.170
96.554
Expressed
in {WD},
with
respect to
subjacent
spinal joint
center
{FWD}
28
Upper Body Segment Parameters for 3D Dynamic Modeling
Table III. Principal moments of inertia (left) and products of inertia (right) for all upper body segments.
The moments of inertia are expressed in {WD} and given for rotations about the segment’s COM.
Principal Moments of Inertia
Segment
IXX
IYY
Products of Inertia
IZZ
IXY =IYX
2
HD
C2
C3
C4
C5
C6
C7
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
L1
L2
L3
L4
L5
rUA
rFA-H
lUA
lFA-H
120.673
7.602
6.295
6.489
16.235
48.401
114.159
174.195
246.231
187.651
186.822
189.944
195.278
141.048
139.368
143.337
134.204
158.157
169.439
174.895
167.440
182.594
183.898
198.149
197.754
130.280
158.132
119.798
155.404
12.315
10.506
9.749
10.774
10.634
17.631
25.937
39.634
51.707
67.763
77.123
88.820
72.025
76.841
84.103
83.833
106.230
123.855
136.548
130.985
133.226
125.476
126.160
211.134
162.556
169.848
153.203
[kg cm
139.038
19.538
16.491
15.959
26.637
58.573
130.978
198.975
284.122
237.662
252.498
264.927
281.643
211.093
214.164
225.089
215.857
260.745
288.430
305.256
292.390
308.557
302.358
317.040
48.401
117.193
45.751
96.517
IXZ =IZX
IYZ =IZY
1.555
-0.356
-0.334
-0.367
-0.478
-0.274
-0.374
-0.526
-0.781
-1.127
-1.484
-1.711
-2.026
-1.642
-1.872
-2.110
-2.102
-2.503
-2.780
-3.077
-3.375
-3.622
-3.510
-4.018
-4.581
71.102
-7.394
67.181
-2.050
0.248
0.198
0.251
0.623
1.581
3.643
5.654
8.047
6.178
6.086
6.056
6.358
4.560
4.527
4.700
4.408
5.113
5.487
5.600
5.396
5.939
6.063
6.337
-12.318
51.912
6.111
-43.011
]
1.373
0.175
0.051
0.410
0.639
-1.931
-4.045
-5.235
-6.887
-5.244
-6.774
-6.732
-7.388
-5.415
-5.024
-4.417
-4.489
-6.166
-6.813
-6.477
-3.528
-2.436
-0.947
-2.007
-6.452
-54.761
5.177
39.119
29
Upper Body Segment Parameters for 3D Dynamic Modeling
Fig. 1. Anterior view of the pelvis and three bony landmarks that define the world reference
frame {FWD}. The bony landmarks were the right and left anterior superior iliac spines (ASIS)
and the midpoint between the pubic tubercles (marked as ‘×’).
30
Upper Body Segment Parameters for 3D Dynamic Modeling
Fig. 2. Surface models of the MVH body shell and spine. The joint centers listed in Table I were
used to define the upper body segments for which respective mass-inertia characteristics were
calculated.
31
Upper Body Segment Parameters for 3D Dynamic Modeling
Fig. 3. Distribution of the cubic sub-volumes for all upper body segments. The sub-volumes are
represented by 1-point dots that are positioned at every cube center.
32
Upper Body Segment Parameters for 3D Dynamic Modeling
Fig. 4. Inverse dynamics results for perturbed sitting. Shown are the average perturbation force,
the average HAT angles (AP and ML), and the calculated joint torques (AP and ML) for an
anterior-left diagonal perturbation. The output torques from the three different inverse dynamics
methods are plotted on top of each other (not distinguishable). The dashed gray lines in the
torque plots mark the predictions for the highest joint (HAT-L1), whereas the dashed black lines
mark the predictions for the lowest joint (L5-S1). The torques at the four joints in-between (L1L2 to L4-L5) are marked by thin and solid gray lines. The vertical line across the subplots
indicates the onset of the perturbation force.
33
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