Joseph E. Barton1
Research and Development Service,
VA Maryland Health Care Center,
Baltimore VA Medical Center,
Baltimore, MD 21201;
Department of Neurology,
University of Maryland School of Medicine,
Baltimore, MD 21201;
Department of Physical Therapy & Rehabilitation Science,
University of Maryland School of Medicine,
Baltimore, MD 21201
e-mail: mailto:jbarton@som.umaryland.edu
Valentina Graci
Research and Development Service,
VA Maryland Health Care Center,
Baltimore VA Medical Center,
Baltimore, MD 21201;
Department of Neurology,
University of Maryland School of Medicine,
Baltimore, MD 21201
e-mail: vgraci@som.umaryland.edu
Charlene Hafer-Macko
Geriatric Research Education and Clinical Center,
VA Maryland Health Care Center,
Baltimore VA Medical Center,
Baltimore, MD 21201;
Department of Neurology,
University of Maryland School of Medicine,
Baltimore, MD 21201
e-mail: cmacko@grecc.umaryland.edu
John D. Sorkin
Geriatric Research Education and Clinical Center,
VA Maryland Health Care Center,
Baltimore VA Medical Center,
Baltimore, MD 21201;
Division of Gerontology and Geriatric Medicine,
Department of Medicine,
University of Maryland School of Medicine,
Baltimore, MD 21201
e-mail: jsorkin@grecc.umaryland.edu
Richard F. Macko
Geriatric Research Education and Clinical Center,
VA Maryland Health Care Center,
Baltimore VA Medical Center,
Baltimore, MD 21201;
Department of Neurology,
University of Maryland School of Medicine,
Baltimore, MD 21201
e-mail: rmacko@grecc.umaryland.edu
1
Dynamic Balanced Reach:
A Temporal and Spectral
Analysis Across Increasing
Performance Demands
Standing balanced reach is a fundamental task involved in many activities of daily living
that has not been well analyzed quantitatively to assess and characterize the multisegmental nature of the body’s movements. We developed a dynamic balanced reach test
(BRT) to analyze performance in this activity; in which a standing subject is required to
maintain balance while reaching and pointing to a target disk moving across a large projection screen according to a sum-of-sines function. This tracking and balance task is
made progressively more difficult by increasing the disk’s overall excursion amplitude.
Using kinematic and ground reaction force data from 32 young healthy subjects, we
investigated how the motions of the tracking finger and whole-body center of mass (CoM)
varied in response to the motion of the disk across five overall disk excursion amplitudes.
Group representative performance statistics for the cohort revealed a monotonically
increasing root mean squared (RMS) tracking error (RMSE) and RMS deviation (RMSD)
between whole-body CoM (projected onto the ground plane) and the center of the base of
support (BoS) with increasing amplitude (p < 0.03). Tracking and CoM response delays
remained constant, however, at 0.5 s and 1.0 s, respectively. We also performed detailed
spectral analyses of group-representative response data for each of the five overall excursion amplitudes. We derived empirical and analytical transfer functions between the
motion of the disk and that of the tracking finger and CoM, computed tracking and CoM
responses to a step input, and RMSE and RMSD as functions of disk frequency. We found
that for frequencies less than 1.0 Hz, RMSE generally decreased, while RMSE normalized
to disk motion amplitude generally increased. RMSD, on the other hand, decreased
monotonically. These findings quantitatively characterize the amplitude- and frequencydependent nature of young healthy tracking and balance in this task. The BRT is not subject to floor or ceiling effects, overcoming an important deficiency associated with most
research and clinical instruments used to assess balance. This makes a comprehensive
quantification of young healthy balance performance possible. The results of such analyses could be used in work space design and in fall-prevention instructional materials, for
both the home and work place. Young healthy performance represents “exemplar” performance and can also be used as a reference against which to compare the performance
of aging and other clinical populations at risk for falling. [DOI: 10.1115/1.4034506]
Keywords: balance, balance disorders, balanced reach test, internal model
Introduction
Bipedal standing balance is inherently unstable and must be
actively controlled to prevent falling. This involves coordinated
interactions between the sensorimotor and multisegment musculoskeletal systems that are difficult to characterize and not fully
understood. Falls typically occur in a larger perturbational context
than simply maintaining balance. Standing reach, for example,
consists of three subtasks: fixing gaze, reaching to acquire an
object, and maintaining balance. These subtasks must be coordinated and sensorimotor resources properly allocated between
1
Corresponding author.
Manuscript received February 18, 2016; final manuscript received August 18,
2016; published online November 3, 2016. Assoc. Editor: Zong-Ming Li.
This material is declared a work of the U.S. Government and is not subject to
copyright protection in the United States. Approved for public release; distribution is
unlimited.
Journal of Biomechanical Engineering
them. While young individuals maintain balance across a wide
range of perturbational challenges, sensorimotor and musculoskeletal systems gradually deteriorate with aging [1,2], predisposing
some to an increased risk of falls. Certain disease and neurological
conditions (e.g., peripheral neuropathy, stroke, Parkinson’s disease) can also impair balance, magnifying the deleterious effects
of aging [3]. An integral part of coordination and resource allocation is the ability to adapt to these sensorimotor and musculoskeletal deficits.
A variety of clinical instruments have been developed to assess
balance and fall risk (e.g., Berg Balance Scale [4], Timed Up and
Go Test [5], Single Leg Stance Test [6]), but these have proven to
be of limited usefulness, or applicable only to select populations.
Some employ subjective ordinal scales that do not lend themselves to quantitative analysis. Some lack hierarchical structure
and/or include redundant items that artificially inflate scores.
Some are relevant only for a narrow range of subject performance,
DECEMBER 2016, Vol. 138 / 121009-1
exhibiting floor or ceiling effects when performance falls outside
that range [7]. Finally, reports regarding reliability in predicting
fall risk are inconsistent [8–12]. These fall short of the practice
needs of rehabilitation professionals [13], or provide only limited
information beyond that obtained through direct clinical observation [14,15]. Three recent balance instruments (Physiological Profile Assessment [16], Protective Stepping Test [17], and Balance
Evaluation Systems Test (BESTest) [18]) begin to address these
shortcomings by taking a systems-oriented approach. Sensorimotor functions and biomechanical measures judged important for
balance are assessed and scored independently, then combined
into an overall score. Overall scores correlate better with fall risk,
while component scores provide qualitative indices of the nature
of the increased risk. These instruments are still limited in that
they cannot specify how performance in any of the component
tests will affect balance and fall risk. It can only be said that performance in these tests covaries to some degree with an ability to
control and maintain balance.
A comprehensive understanding of balance requires quantitative models with sufficient sensorimotor and biomechanical complexity to enable mathematical characterization of balance
control. Movement scientists have long employed engineering
concepts such as system identification [19] and feedback control
[20] to study balance. While not all (e.g., Refs. [21] and [22]),
most have employed simplified balance dynamics to study small
perturbations in a single plane for which the standing body is represented by a linear, two-dimensional, single link inverted pendulum rotating about the ankles, controlled by a generic
proportional-integral-derivative (PID) controller. While such
models convey overall movement mechanics, they are largely limited to cause-and-effect behavior, and lack the complexity to
probe the neurophysiological and musculoskeletal bases for balance and falls.
Our long-term objective is to develop an engineering control
system model of balance (CSMB) that represents the sensorimotor
and musculoskeletal determinates of performance, and quantifies
the manner in which performance changes as a function of task
difficulty. To accomplish this, we are proceeding along two
complimentary lines. The first is to develop the CSMB [23],
which simulates performance in an experimental protocol, the balanced reach test (BRT), whose development and validation constitute the second line. The BRT constitutes a complex reaching and
tracking task in three-dimensional space that is relevant to daily
function. Our goal is that it be sensitive enough to detect differences in the ability of different population groups (e.g., young
healthy, older high fall risk, stroke) to maintain balance under different levels of task difficulty. This report presents the BRT protocol and the analytical methods to quantify performance in
tracking and balance maintenance for 32 young healthy subjects
(YHSs) across a range of task difficulty.
2
Methods
2.1 The Balanced Reach Test. During the BRT (Fig. 1), subjects stand on a platform with each foot directly underneath its
respective shoulder joint and supported by an AMTI Optima
series triaxial force plate (AMTI, Watertown, MA). A 60 100
reverse-projection screen (Da-Lite, Eden Prairie, MN) is located
one arm’s length in front of the subject, aligned perpendicular to
the anterior–posterior (AP) (z) axis and parallel to the subject’s
frontal plane. An image of a disk is projected on the screen by a
BenQ SP 890 high resolution digital projector (BenQ, Costa
Mesa, CA). Subjects are instructed to point with the dominant
hand index finger to the center of the disk as it moves, lightly
touching the screen, with their hand in the neutral position with
respect to wrist pronation/supination. (With either upper arm
hanging alongside the trunk and the elbow flexed at 90 deg, the
palm of the hand faces medially (toward the body). This is done
to ensure consistency of movement in a natural fashion, and also
to ensure that the motion detection markers attached to the forearm always remains in view of the motion detection system.)
The medial–lateral (ML) (x) and superior–inferior (SI) (y)
positions of the disk at time t are determined by a sum of 14 sine
functions, given by
xd ðtÞ ¼
14
X
1
sinð2pfi tÞ ;
2pf
i
i¼1
yd ðtÞ ¼
14
X
1
sinð2pfi t þ /i Þ
2pf
i
i¼1
(1)
Such a stimulus appears random to the observer, but because only
discrete frequencies are contained in the stimulus, it produces a
Fourier transform with very sharply defined frequency spectra,
Table 1
Disk motion parameters
Predictable frequency set
Fig. 1 During the balanced reach test, subjects stand on force
platforms, fix gaze and point to the projected disk as it moves
around the screen. The locations of two landmarks on each foot
are used to compute the perimeter of the BoS at each sampling
instant. This computation is robust enough to accurately represent the perimeter should the subject shift their stance or
momentarily raise up on the ball of one foot (as shown in the
figure).
121009-2 / Vol. 138, DECEMBER 2016
Unpredictable frequency set
#
fi (Hz)
Period (s)
/i (deg)
fi (Hz)
Period (s)
/i (deg)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0.024
0.048
0.096
0.192
0.288
0.336
0.48
0.576
0.72
0.816
0.912
1.416
2.184
2.928
41.67
20.83
10.42
5.21
3.47
2.98
2.08
1.74
1.39
1.23
1.10
0.71
0.46
0.34
90
76
192
238
99
145
261
30
168
284
215
307
330
122
0.024
0.056
0.104
0.184
0.296
0.344
0.488
0.584
0.712
0.824
0.904
1.432
2.104
2.936
41.67
17.86
9.62
5.43
3.38
2.91
2.05
1.71
1.40
1.21
1.11
0.70
0.48
0.34
90
284
76
215
122
99
330
145
261
238
168
192
30
53
Note: Overall excursion amplitudes: 0.5000, 0.6563, 0.8125, 0.9688,
1.1250 arm lengths (ALs).
Transactions of the ASME
easing subsequent frequency response analysis and interpretation
of results. We use ten frequencies (fi, Table 1) that lie within a
range (0.05 fi 3.0 Hz) that can be visually tracked by healthy
subjects [24], and four additional frequencies in the vicinity of 1
Hz where we find tracking gain (Sec. 2.2.2) changes most rapidly.
Amplitudes of individual sinusoids are scaled by the inverse of
their respective frequencies so that each sinusoid has the same
peak velocity. A randomly selected phase shift (/i, Table 1) is
then applied to each term of the vertical sum-of-sines, yd(t), so
that the vertical component of the disk’s motion does not appear
correlated with the horizontal component. At the beginning of
each experiment, arm length (AL) is measured as the distance
from the tip of the pointing index finger to the acromion process.
Five multiples of arm length ranging from 0.5 to 1.125 (Table 1,
bottom) are then computed. Once the disk’s overall trajectory is
computed, its maximum excursions in the ML and SI directions
are normalized to unity, and then multiplied by one of these multiples, depending on the test condition. Increasing the overall excursion amplitude of the disk increases its velocity and thus, task
difficulty, since for sinusoidal motion velocity is directly proportional to amplitude. Task difficulty also increases with amplitude
in that as the disk moves farther outside the limits of the subject’s
base of support (BoS), the subject must assume increasingly less
stable body poses with respect to the BoS to maintain contact.
When the sinusoidal frequencies are integer multiples of one
another (Table 1, predictable frequency set), the overall motion is
periodic and in theory predictable by the subject [25]. When the
frequencies are not integer multiples of one another (Table 1,
unpredictable frequency set), the motion of the disk is not periodic, and thus not predictable. The protocol incorporates both frequency sets to determine subjects’ ability to predict the disk’s
motion. Each trial’s duration is 90 s, allowing capture of two or
more complete cycles of each frequency sinusoid. All combinations of frequency set and disk excursion amplitude (ten in total,
15 min total testing time) are presented to each subject.
To accurately represent movements during the BRT, a triangular “rigid body” is attached to each of the 13 body segments listed
in Table 2. Subjects’ hands are placed in rigid splints to prevent
movement of the hand with respect to the forearm (not shown in
Fig. 1); thus subjects’ hands are assumed rigidly connected to
their respective forearms. Infrared emitting diodes (IREDs) placed
at the rigid bodies’ vertices (Fig. 1) are sensed by an OptoTrak
Certus motion capture system (Northern Digital, Waterloo,
Ontario, Canada), allowing construction of a local coordinate system for each body segment. The locations of the joint centers of
rotation (CoRs) defining each body segment’s endpoints (and thus
length) are obtained relative to these local coordinate systems
using the motion capture system’s digitizing stylus. This
Table 2
Segment index
1
2
3
4
5
6
7
8
9
10
11
12
13
Body segments and joints
Segment
Joint
Right foot
Right shank
Right thigh
Left foot
Left shank
Left thigh
Lower trunk
Trunk
Head
Right upper arm
Right forearm and hand
Left upper arm
Left forearm and hand
Right ankle
Right knee
Right hip
Left ankle
Left knee
Left hip
L5/S1a
C7/T1b
Right shoulder
Right elbow
Left shoulder
Left elbow
a
Intervertebral disk between the fifth lumbar and first sacral vertebrae.
Intervertebral disk between the seventh cervical and first thoracic
vertebrae.
b
Journal of Biomechanical Engineering
information and the subject’s height and weight are used to calculate each body segment’s mass and the location of its center of
mass (CoM) using sex-specific anthropometric data [26,27]. After
the experiment, the positions and orientations of each body segment are computed with respect to the global coordinate system
for each sampling instant from the measured positions and orientations of the local coordinate systems. Whole-body CoM is computed as the weighted mean of the positions of the body
segments’ CoMs, where the weighting is the ratio of body segment mass to total mass. The 13 segment representation thus
incorporates actual body segment lengths and CoR locations, as
well as any asymmetries (e.g., unequal right/left femur lengths)
and other unique aspects of musculoskeletal anatomy.
The positions of the tracking fingertip and other significant
landmarks relative to the local coordinate system fixed to the
body segment containing those landmarks are recorded. Stable
upright balance requires that the projection of the body’s CoM
onto the ground plane be maintained within the area of its BoS,
delimited by the feet [28,29]. The boundaries of the BoS are identified by the positions of the fifth metatarsal joint and the lateral
outside of the heel. Projection of these four points onto the ground
plane comprises the vertices of a quadrilateral used to compute
the center and boundaries of the BoS. Variations in the position of
the BoS are minimized by instructing subjects to move their feet
as little as possible, and to maintain ground contact with both feet.
Occasionally, some subjects shift the position of their feet slightly
or raise up on the ball of a foot (Fig. 1). In such cases, resulting
changes to the BoS are accounted for since its center and boundaries are computed at each sampling instant. A test is also incorporated in the calculation to determine if the front or back of either
foot is off the ground. If so, the associated landmark is excluded
and the computed perimeter of the BoS becomes triangular
shaped. Shifting stance or raising up on the ball of the foot was
observed to occur infrequently, and for only brief periods. Hence,
the positions of the center and vertices of the BoS remained very
nearly constant throughout each test.
At the end of setup, the projection screen and projector are positioned so that the horizontal limits of the screen’s projection area
are located approximately 11=2 arm lengths from the dominant
shoulder joint. Four calibration points are projected onto the
screen at known positions (in projector coordinates; pixels) and
their global coordinate locations (meter) recorded using the digitizing stylus. Using this data, a function is derived to map the
disk’s position from projector coordinates to global coordinates,
so that the disk’s trajectory during each trial can be compared to
the subject’s movements.
In addition to kinematic data, the subject’s weight and the
forces and moments applied by each foot are measured by the
force plates. Eye motion relative to head is captured using an EyeLink II eye tracking system (SR Research, Ottawa, Ontario,
Canada). Electromyographs (EMGs) of certain muscles (Table 3)
used while pointing and responding to the self-induced balance
perturbations are recorded using a wireless EMG system (Noraxon, Scottsdale, AZ). Force plate and motion detection data are
sampled at 60 Hz, eye tracking data at 250 Hz, and EMG data at
3000 Hz. EMG data are down-sampled to 60 Hz and eye tracking
data are interpolated to 60 Hz using a third-order spline interpolation polynomial; so that combined analyses with the force plate
Table 3 Measured muscle activations
Right and left soleus
Right and left tibialis anterior
Right and left pectoralis major (caudal head)
Right and left anterior deltoid
Right and left middle deltoid
Right and left sternocleidomastoid
Right and left paraspinal
DECEMBER 2016, Vol. 138 / 121009-3
and motion detection data can be carried out. Measurement data
from the force plates and the motion capture, eye tracking, and
EMG systems are synchronized and consolidated by a Motion
Monitor system (Innovative Sports Training, Chicago, IL). The
Motion Monitor also establishes a global coordinate (x0, y0, z0)
system whose origin is located between the subject’s feet (Fig. 1)
and approximately coincident with the center of the BoS. In this
system, þx0 points to the subject’s left, þy0 in subject’s superior
direction, and þz0 in subject’s anterior direction. All quantities
are referred to the global coordinate system. The current analysis
is based on kinematic and kinetic data obtained during the BRT.
Eye motion and EMG analyses are ongoing and will be reported
in subsequent articles.
2.2 Analytical Methods. Overall performance is characterized by analyzing the tracking fingertip and whole body CoM
motion relative to the projected target disk. AP (z) motion of the
finger is not included, as it is constrained by the planar projection
screen aligned perpendicularly to the AP axis. AP CoM motion is
also affected (though not to as great a degree) by the presence of
the projection screen, but it remains an important aspect of balance in this task and is included where appropriate. Finally, SI
motion of the CoM is not included because it does not have a
direct bearing on the primary measure of balance considered here,
CoM–BoS deviation, which is the deviation between the projection of the CoM onto the ground plane (resulting in an SI component of zero) and the center of the BoS. A more complete
description of the factors affecting AP tracking and CoM motion
is provided in Appendix A, which is available under the
“Supplemental Materials” tab for this paper on the ASME Digital
Collection.
Finger tracking, CoM, and BoS trajectories (xyz position versus
time) for each trial are visually inspected to identify and remove
spurious spikes in the data caused by intermittent noise in the
OptoTrak electronics, or abrupt shifts in the location of wholebody CoM that result when a marker falls out of view of the
motion detection system, causing the rigid body segment that it
was attached to to “disappear.” Since the location of whole body
CoM is the weighted average of the locations of the individual
body segment CoMs, the disappearance of a body segment
removes its contribution to the calculation, bringing about an
abrupt shift in the result. Notwithstanding the constraints imposed
by the projection screen, subjects engaged in a continuum of complex motions and body positions performing the tracking task.
This presented a particular challenge for motion capture: as body
segments twisted and turned to track the disk, the IRED’s attached
to any particular body segment could assume positions that were
not visible to the sensors, leaving brief gaps in the data. Because
of the strong observed correlation between the motions of the
tracking finger and CoM and the sum-of sines motion of the disk,
we employed spectral methods [30] to estimate missing data
caused by both removal of outliers and out-of-view IRED’s. Subsequently, “clean data” refers to measured test data with outliers
removed and gaps due to out-of-view IRED’s. We used clean data
to compute overall performance measures (see Sec. 2.2.1), as
these data represent the unaltered tracking and balance performance of each subject, and the calculations can be made with missing data. In no case was missing data extensive enough to
compromise validity of the calculations. Group representative performance (see Sec. 2.2.2), however, requires complete data sets
and for this, we used “estimated data,” which refers to the result
of the spectral estimation process.
2.2.1 Overall Performance Measures. For each subject and
condition clean data is used to calculate root mean squared error
(RMSE) in the ML and SI directions. This is defined for the ML
(x) direction as
121009-4 / Vol. 138, DECEMBER 2016
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
uP
2
u nx ð Þ
xd i xf ðiÞ
u
t
RMSEx ¼ i¼1
nx
(2)
where xd(i) is the x component of the disk’s position at sampling
instant i, xf(i) is the corresponding position of the tracking finger, and nx is the number of data points associated with the x
direction. For the SI (y) direction, the tracking errors are defined
similarly. The composite error RMSExy is also computed
according to
RMSExy
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
uP
ny
2
2 P
u nx ð Þ
yd ðiÞ yf ðiÞ
xd i xf ðiÞ
u
ti¼1
þ i¼1
¼
ny
nx
(3)
RMSE can range from zero toþ1. A value of zero represents perfect tracking.
Similarly, we computed RMS CoM-BoS deviation (RMSD) to
quantify balance performance
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
uP
u nx ½
2
x ðiÞ xCoM ðiÞ
u
ti¼1 BoS
;
RMSDx ¼
nx
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
uP
nz
P
u nx ½
2
½zBoS ðiÞ zCoM ðiÞ2
xBoS ðiÞ xCoM ðiÞ
u
ti¼1
RMSDxz ¼
þ i¼1
nx
nz
(4)
where xCoM(i) and xBoS(i) are the x components of the CoM’s and
the center of the BoS’s position at sampling instant i. Deviations
in the AP (z) direction are defined similarly. The deviations presented in Eq. (4) can range from zero to values corresponding to
the boundaries of the BoS, at which point a step or fall would
ensue. Beyond this, there is no measure or definition of “perfect”
control of the CoM within the boundaries of the BoS (see Sec. 4).
These quantities are averaged over the entire cohort of young
healthy subjects for each disk excursion amplitude.
Clean data is also used to compute the overall correlation coefficient q and response delay s between the target disk trajectories
and the tracking finger and CoM response trajectories. q is
obtained by identifying the maximum correlation coefficient
between the response trajectory and numerous lagged versions of
the corresponding target disk trajectory. s is the lag (s) corresponding to this maximum value of q. Correlation coefficients and
response delays are computed for the disk/tracking finger and
disk/CoM, then averaged across the entire cohort of young healthy
subjects for each disk excursion amplitude.
2.2.2 Group Representative Disk and Response Trajectories.
We next undertook a detailed analysis of the cohort’s performance
in both the temporal and spectral domains. It is not possible in this
analysis to obtain group-representative temporal or spectral
response data simply by averaging individual subject responses
(in either domain) for each condition. The overall amplitude of
the disk’s motion and the prescribed distance of the projection
screen from the subject varies across subjects. Further, it is not
possible to position the high resolution projector and projection
screen in exactly the same position relative to each other and the
subject for each experiment. If, as an initial review of the experimental data revealed, subjects respond approximately linearly to
the disk’s motion, then it is possible to compute an empirical
transfer function (ETF) [31] for each subject/condition and
average these to arrive at a group-representative ETF. GroupTransactions of the ASME
representative responses are then obtained by applying an
appropriate input to the ETF.
Fourier transforms of the disk, tracking finger, and CoM–BoS
deviation trajectories are computed for each subject and condition.
This requires complete data sets, and we employ the method of
Ferreira [30] to estimate missing data and compute Fourier transforms in one step. The ETF for each response (Fourier coefficients
of the response, divided frequency by frequency by the corresponding Fourier coefficients of disk motion [31]) is then computed. The ETF’s corresponding to each overall disk excursion
amplitude are averaged together, frequency by frequency, and
standard errors computed to obtain group-representative ETF’s
for each excursion amplitude and associated upper and lower 95%
confidence limits. Because the disk’s motion is made up of a 14term sum of sines (Table 1), its Fourier transform is zero for every
frequency but those included in the sum (hereafter, referred to as
the disk motion frequencies). As a result, the corresponding ETF’s
are undefined (set to zero) at all nondisk motion frequencies; and
the resulting group-representative response trajectories are also
composed of only the disk motion frequencies. This calculation
serves to “filter out” noise and nonlinear aspects of subjects’
responses, leaving only the linear portion. To gauge how much
information is lost in the calculation, we estimated missing data
and response Fourier transforms for each subject only at the disk
motion frequencies, then took the inverse Fourier transforms of
the results and compared these estimated response trajectories
with the original clean data, using the measure %Fit, given by
%Fit ¼
!
P
ðri r^i Þ
i
100
1 P
Þ
i ðri r
(5)
Here, r is the actual response given by clean data, r is its mean,
and r^ is the estimated response. Fit can range from zero to 100%,
with 100% indicating that r^ ¼ r, i.e., that the estimated trajectory
retains all of the information contained in the clean data
trajectory.
Representative disk trajectories for each amplitude are computed using average arm length for the group (76.5 cm), and
assuming the projector screen is placed exactly perpendicular to
the global z-axis (Fig. 1). Under these conditions, the AP position
of the disk is constant throughout the disk’s motion. The assumed
locations of the projector and projection screen with respect to the
global coordinate system are such that the positions of the four
calibration dots used to map the disk’s motion to global coordinates are averages of the actual calibration points measured for
each subject (see Sec. 2.1). By multiplying the Fourier transforms
of these trajectories by their corresponding group-representative
ETF for each disk excursion amplitude, a group-representative
Fourier transform and (by taking its inverse) temporal trajectory
of the tracking finger and CoM–BoS deviation response for each
disk excursion amplitude are obtained. Because AP CoM motion
is a function of disk motion in all three dimensions (Appendix A,
which is available under the “Supplemental Materials” tab for this
Fig. 2 Group-average RMSEs, RMSDs, and response delays for 32 young healthy subject
Journal of Biomechanical Engineering
DECEMBER 2016, Vol. 138 / 121009-5
paper on the ASME Digital Collection), the ETF’s for AP
CoM–BoS deviation responses are computed with respect to overall (xyz) disk motion instead of AP disk motion. ETF’s are also
used to compute group-representative transfer function gain and
phase shift relationships. To gain greater insight into human
tracking and balance performance in this task, analytical transfer
functions (in the Laplace variable s) are fit to the discrete ETF
gain and phase data points, and unit step responses computed.
Finally, group-representative data are used to compute RMSE
and RMSD as a function of disk motion frequency. In this analysis, we compute one additional tracking error measure, normalized root mean squared error (NRMSE), defined for the ML
direction as
NRMSEx; i ¼
RMSEx; i
ax; i ðfi Þ
(6)
where ax,i is the amplitude of the ith harmonic of disk motion.
NRMSEy,i in the SI direction is defined similarly. All data analyses are performed using MATLAB (The MathWorks, Inc., Natick,
MA).
2.2.3 Statistical Methods. A nonparametric sign test [32] is
used to determine whether overall RMSE and RMSD increase
monotonically with amplitude. A standard t-test of the difference
between means [32] is employed to determine significance of differences between individual quantities. Group-averaged ETF’s are
obtained by computing frequency-by-frequency averages of individual subject ETF’s for each amplitude. Frequency-by-frequency
standard errors are computed, and 95% confidence intervals
defined. All subsequent group-averaged quantities and confidence
limits are calculated from these group-averaged EFT’s and confidence limits.
3
Results
Performance tracking a disk whose movement is governed by
the predictable frequency set is analyzed for 32 young healthy
subjects (nine male/23 female, 28 right/four left handed, age:
25.7 6 3.3 yr, arm length: 76.5 6 10.0 cm, height: 166.2 6 10.8 cm,
weight: 67.3 6 12.0 kg, BMI: 23.0 6 5.0 kg/m2 (mean 61 standard
deviation)].
3.1 Overall Performance Measures. Figure 2 plots average
ML, SI, and composite RMSE (Fig. 2(a)), ML, AP, and composite
RMSD (Fig. 2(b)), tracking response delays (Fig. 2(c)), and
CoM–BoS deviation response delays (Fig. 2(d)) for this group, for
each of the five excursion amplitudes tested. Component and composite RMSEs and RMSDs all increase monotonically with
increasing amplitude, and a nonparametric sign test shows that
these trends are significant (p 0.03). Further, a standard t-test of
the difference of means shows that ML RMSE is significantly
greater than SI RMSE for all amplitudes (p 0.05); and ML
RMSD is significantly greater than AP RMSD for all amplitudes
(p 0.001). In contrast, delays associated with the tracking finger
remain constant over the range of amplitudes. ML CoM–BoS
deviation response delays decrease monotonically with amplitude
(p 0.03), but AP and composite CoM–BoS deviation delays
remain constant with amplitude. Averaging across disk excursion
Fig. 3 Temporal trajectories (a) and frequency spectra (b) of the disk (gray), tip of the tracking finger (black, top two panels)
and CoM–BoS deviation (black, bottom two panels). Dotted lines indicate 95% confidence intervals. Tracking fingertip and
CoM–BoS deviation ordinates are along the left hand side of the plots, disk ordinates are along the right-hand side. All trajectories have been shifted along their respective ordinate axes so that the overall excursion amplitude of each can be read
directly (e.g., 54.5 cm for the tracking fingertip in the x-direction, 47.6 cm in the y-direction). Movements in the positive xdirection are to the subject’s left, those in the positive y-direction are up, and movements in the positive z-direction are forward
with respect to the subject (see global coordinate axis orientation in Fig. 1). Due to the scale, tracking finger confidence intervals are barely discernable, so their mean “width” is indicated. This shows that all confidence intervals are approximately the
same. The reduced ranges of the AP CoM–BoS deviation in the plot “magnifies” this trajectory, making it appear “noisier”
than the other trajectories. 1.1250 arm lengths overall excursion amplitude.
121009-6 / Vol. 138, DECEMBER 2016
Transactions of the ASME
amplitude gives an overall composite tracking finger delay of
0.51 6 0.06 s (mean6standard error), and an overall composite
CoM–BoS deviation delay of 0.92 6 0.04 s.
3.2 Group Representative Disk and Response Trajectories. The algorithm employed to estimate missing data (Sec. 2.2)
produces tracking finger response trajectories that are very close
to the corresponding clean data trajectories. For the ML (x) and SI
(y) directions, the %Fit is 93% and 94%, respectively, across all
conditions. The ML CoM–BoS deviation %Fit is lower, 78%, but
still captures a majority of the response dynamics. AP CoM–BoS
deviation %Fit is lower yet at 36%, indicating that significant
noise and/or other nonlinearities are associated with CoM motion
in this direction. In Fig. 3, we plot group-representative performance maintaining balance and tracking the disk according to the
predictable frequency set with amplitude 1.125 AL. Performance
for all amplitudes is tabulated in Appendix B, which is available
under the “Supplemental Materials” tab for this paper on the
ASME Digital Collection. Finger tracking trajectories (position
versus time) in the ML and SI directions (Fig. 3(a), upper two
panels, black solid lines) indicate very close tracking of the disk
(gray lines). These tracking trajectories are nearly identical in
shape to those of the disk movement itself (q ¼ 0.998, 0.996,
respectively), though modest attenuation and delay are present.
The shape of the ML CoM–BoS deviation trajectory (Fig. 3(a),
third panel, black solid line) is also quite similar to that of the disk
(q ¼ 0.936), but with substantially more attenuation and delay
than that of the corresponding finger tracking motion. AP CoMBoS deviation is not as well correlated with overall disk motion
(q ¼ 0.417).
Figure 3(b) details the frequency spectra (amplitude versus frequency) corresponding to the temporal plots of Fig. 3(a). Table
B5 in Appendix B (available under the “Supplemental Materials”
tab for this paper on the ASME Digital Collection) lists the
amplitudes of these spectra versus frequency. For the ML and SI
tracking fingertip motions (Fig. 3(b), upper two panels, black
lines), the spectra corresponding to the disk motion frequencies
have amplitudes approximately 90% as great as the corresponding
disk motion amplitudes (gray lines) for the six lowest frequency
components. Note the difference between the right and left-hand
scales in Fig. 3(b). The spectra for ML CoM–BoS deviation
(Fig. 3(b), third panel, black lines) is also similar to the corresponding disk spectra, but attenuation is much greater (approximately 20% for the six lowest frequency components). This
complimentary view of the temporal plots of Fig. 3(a) again indicates that these stimulus and response waveforms are similarly
shaped. The spectra of AP CoM–BoS deviation (Fig. 3(b), bottom
panel, black lines) is dissimilar to that of overall disk motion and
highly attenuated, indicating the low correlation previously noted
between these two motions.
3.3 Group Representative Gain and Phase Relationships.
Empirical transfer functions relating these responses to corresponding disk motion are computed by dividing the tracking and
CoM–BoS deviation frequency spectra by their corresponding
disk motion frequency spectra. Gains and phase shifts computed
from these transfer functions are presented in the Bode diagrams of
Fig. 4 (discrete dots). Note that the gain is reported as the transfer
function’s amplitude characteristic (dimensionless) for clarity,
rather than converted to decibel. Analytical transfer functions (in
the Laplace variable s, solid lines in Fig. 4) are fit to the empirical
transfer function data. The lowest order stable transfer functions that
fit this data are listed in Table 4 (upper three rows). Note that the fitted transfer functions are mixed phase, since they contain zeros in
the right-half s-plane. The corresponding minimum phase transfer
functions are listed in the lower three rows of Table 4, and appear as
dashed lines in Fig. 4. Because the minimum phase transfer functions have identical gain characteristics as their nonminimum phase
Fig. 4 Gain/phase diagram of ML(y) and SI (z) components of tracking finger motion and ML
CoM-BoS deviation. Dots denote the empirical transfer function gain computed at each disk
motion frequency. Solid lines denote the analytical transfer functions fit to the empirical data
(upper three rows in Table 4). Dotted lines denote the fitted transfer functions’ 95% confidence
intervals. Dashed lines denote the minimum phase transfer functions (lower three rows in
Table 4). Because minimum phase transfer functions have identical gain characteristics as fitted transfer functions only their phase relationships are visible in the figure. 1.1250 arm
lengths overall excursion amplitude. Bode diagrams for other amplitudes are shown in Appendix C, which is available under the “Supplemental Materials” tab for this paper on the ASME
Digital Collection.
Journal of Biomechanical Engineering
DECEMBER 2016, Vol. 138 / 121009-7
Table 4 Best-fit and minimum phase transfer functions for the tracking fingertip and
CoM–BoS (i 5 冑21) 1.1250 arm lengths overall excursion amplitude
System (num/den order)
Fitted transfer function
ML finger tracking
(num/den ¼4 /6)
½s þ 0:5871½s 10:59½s ð6:933610:52iÞ
½s þ 0:5821½s þ 5:598½s þ ð5:492614:61iÞ½s þ ð5:51968:035iÞ
SI finger tracking
(num/den ¼ 4/6)
½s þ 2:958½s 6:995½s ð6:024611:69iÞ
½s þ ð3:37561:614iÞ½s þ ð3:674614:16iÞ½s þ ð4:4368:427iÞ
ML CoM–BoS
(num/den ¼ 4/6)
½s þ 0:04346½s þ 5:752½s ð2:57066:710iÞ
½s þ 0:04558½s þ 1:945½s þ ð1:68865:470iÞ½s þ ð2:08163:066iÞ
Minimum phase transfer function
ML finger tracking
(num/den ¼ 4/6)
½s þ 1:233½s þ 13:06½s þ ð6:356611:23iÞ
½s þ 1:213½s þ 6:372½s þ ð5:346614:63iÞ½s þ ð5:74768:68iÞ
SI finger tracking
(num/den ¼ 4/6)
½s þ 2:54½s þ 9:346½s þ ð5:488611:87iÞ
½s þ ð3:569614:16iÞ½s þ ð3:72760:9775iÞ½s þ ð4:44468:765iÞ
ML CoM–BoS
(num/den ¼ 4/6)
½s þ 0:04484½s þ 5:114½s þ ð2:67166:817iÞ
½s þ 0:04706s þ 1:908½s þ ð1:73565:432iÞ½s þ ð2:09363:011iÞ
counterparts, only their phase characteristics are visible in the figure.
Bode diagrams for the other disk excursion amplitudes are given in
Appendix C, which is available under the “Supplemental Materials”
tab for this paper on the ASME Digital Collection.
The fitted transfer function plots (solid and dotted lines in
Fig. 4) indicate that the finger tracks the disk closely with a gain
of approximately 0.9 and a phase lag of less than 32 deg for the
lowest four frequencies. At this point, the gain characteristics
begin to diverge, with the ML gain decreasing steadily to approximately 0.8 at 1 Hz, while the SI gain gradually increases to a resonant peak of approximately 1.0 at 1 Hz. The phase lags associated
with both movement directions remain very close to one another
throughout the frequency range. By the fifth frequency, 0.288 Hz,
the lags are approximately 50 deg, large enough to seriously compromise tracking accuracy. In contrast, CoM–BoS deviation
tracks the disk in the ML direction with a gain of approximately
0.2 for the lowest six frequencies before its response quickly falls
off to zero. The response gain and phase characteristics for all five
disk excursion amplitudes are plotted together in Fig. 5. These are
nearly the same for all amplitudes, indicating that the system is
linear with respect to amplitude. Therefore, earlier observations
regarding performance at 1.1250 AL amplitude apply to these
other amplitudes as well.
The responses of the tracking finger and CoM–BoS deviation to
a unit step function (computed using the transfer functions listed
in Table 4) are shown in Fig. 6. Fitted transfer function step
responses are shown with heavy lines while minimum phase transfer function step responses are represented by the thinner lines.
These plots indicate that ML CoM-BoS deviation exhibits the
most heavily damped response, followed by ML motion of the
tracking finger. SI motion of the tracking finger exhibits the least
damping. The dots in the figure locate points at which each
response settles to within 5% of its final, steady state value. Based
on these data, the tracking finger reaches steady state in the ML
direction in 0.30–0.66 s, and in the SI direction in 0.54–0.89 s. ML
CoM–BoS deviation reaches steady state in 1.02–1.54 s. The
tracking finger settling times are comparable to the response
delays determined by correlation analysis and shown in Fig. 2
(ML lag: 0.48 s, SI lag: 0.51 s), while the CoM–BoS deviation settling time is somewhat larger than the previous result (0.73 s).
3.4 Group Representative Tracking Error and CoM–BoS
Deviation as Functions of Disk Frequency. To understand how
the response at each individual frequency contributes to overall
121009-8 / Vol. 138, DECEMBER 2016
response, the motions of the disk, tracking finger, and CoM–BoS
deviation are decomposed into their sinusoidal components, and
RMSEs and RMSDs calculated for each frequency component.
These are shown in Fig. 7. The odd-looking variation of these
errors with frequency is explained in Appendix D, which is available under the “Supplemental Materials” tab for this paper on the
ASME Digital Collection, which shows that the tracking errors
are given by equations of the form
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ g2i 2gi cos vi
;
2rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
RMSEðfi Þ
1 þ g2i 2gi cos vi
NRMSEðfi Þ ¼
¼
ai
2
RMSEðfi Þ ¼ ai
(7)
where ai is the amplitude of the ith disk harmonic (frequency fi)
and gi and vi are the associated gain and phase lag. As frequency
increases, RMSE generally decreases since gain decreases with
frequency (Fig. 4), but it fluctuates due to the cosvi term. NRMSE
shows the same general trend but is not as distorted due to the normalizing effect of division by ai. For frequencies less than 1.0 Hz,
RMSE generally decreases, while NRMSE increases. These
observations do not apply to RMSD because that calculation does
not involve the stimulus trajectory (Eq. (4)). In this case, both ML
and AP RMSD decrease approximately according to k1 fik2 þ k3 ,
where the ki are fitted constants.
4
Discussion
These experimental and analytical results demonstrate that the
BRT can quantify young healthy performance in the combined
tracking and balance task, and that it has the sensitivity to detect
changes in performance based on task difficulty (disk motion
amplitude). In particular, they further reveal that the tracking
and balance systems respond linearly under these conditions,
and that performance in the SI direction is superior to that in the
ML direction. The BRT is also able to quantify tracking and balance performance without floor or ceiling effects in this young
population, indicating thus far that it is a valid platform for
ongoing comparisons to aging and neurological disability
populations.
Transactions of the ASME
The results presented in this article illuminate several noteworthy aspects of young healthy tracking and balance performance.
The lower tracking error (Fig. 2), tighter confidence intervals (Fig.
3), and different gain characteristics between the two tracking finger directions (Fig. 4) suggest that subjects are better able to track
the disk, and track it at higher frequencies, in the SI direction than
in the ML direction. Moreover, the presence of a resonant frequency associated with SI tracking (Fig. 4) indicates that the “SI
tracking system” has less damping and is more responsive than
the “ML tracking system,” which can also be discerned from the
step responses shown in Fig. 6. For this test subjects oriented their
reaching arm with the palm faced medially (toward the center of
the body). In such a configuration movement of the tracking finger
in the SI direction involves movement of the humerus and forearm/hand in the Sagittal plane. Tracking in the ML direction
involves movement of the humerus and forearm/hand in the horizontal and frontal planes, respectively.
Tracking in the SI direction involves elbow flexion/extension,
shoulder flexion/extension, and shoulder elevation/depression;
which are produced by the elbow, glenohumeral joint, acromioclavicular joint, and the sternoclavicular joint. ML tracking involves
shoulder abduction/adduction and internal/external rotation, produced by just the glenohumeral joint. Thus, four joints with their
associated degrees-of-freedom and musculature participate in SI
tracking while only one joint participates in ML tracking. Moreover, the size, proportion of fibers recruited, and lines of action of
muscles involved in SI motion produce more powerful synergy
patterns than strictly ML motion. Though neither the tracking task
nor the action of the shoulder and elbow can be strictly divided
into SI and ML motion (as we have done for illustrative purposes),
our findings suggest that more degrees-of-freedom and more
powerful movements are likely available for SI tracking than ML
tracking, which contributes to the superiority of performance in
the SI direction. Elbow and shoulder flexion/extension are
employed in ballistic movements of the hand, as in striking,
“clubbing,” and throwing objects. It is widely accepted that the
body and particularly the hand, arm, and shoulder evolved, beginning with early hominins, to facilitate such movements [33]. This
would have conferred a strong selective benefit to these early
hunters [34]. The evolutionary development of the shoulder and
arm is most evident in high performance sports that involve overhand throwing, such as baseball pitching [35]. Movements requiring shoulder abduction/adduction and internal/external shoulder
rotation typically do not involve high levels of force or speed. At
frequencies below the SI resonant peak, ML tracking system performance is equal to SI performance, which might facilitate precision tasks such as manipulation of objects, writing, or drawing on
a vertical surface such as a blackboard.
There is no reason to expect the CoM, which is a function of
whole-body orientation, to track the disk’s motion very closely.
For this task, the CoM is located approximately within the pelvic
region, separated from the center of the target disk by several segments of the reaching body (trunk, upper arm, and forearm/hand).
The CoM’s position in space is determined primarily by the positions and orientations of the legs, pelvis, and trunk. Substantial
CoM movement entails accelerating these more massive body
segments in order to change their position and orientation—an
energy-intensive proposition. Moreover, moving the CoM too far
from the center of the BoS could result in a fall. A conservative
strategy (with respect to both energy expenditure and safety)
would involve fixing the legs and pelvis, and then employing
smaller trunk movements to the point that still smaller movements
of the substantially less massive upper arm and forearm/hand are
all that are required to place the tracking finger in contact with the
disk’s center. This is largely what is observed in the experiment.
Like the motion of the tracking finger, ML CoM motion is highly
correlated with ML disk motion, but greatly attenuated. The CoM
responds much differently in the AP direction, due at least in part
Fig. 5 Gain/phase diagrams of ML(y) and SI (z) components of tracking finger motion and ML CoM–BoS deviation for all five
disk excursion amplitudes. The individual characteristics are nearly the same across amplitude, indicating that these systems
respond linearly under these conditions.
Journal of Biomechanical Engineering
DECEMBER 2016, Vol. 138 / 121009-9
to the constraining placement of the projection screen. This, however, is not an unrealistic movement environment. Reaching for
objects in overhead or under-counter kitchen shelves, for example,
involves just such environments. AP motion of the CoM is not
solely predicated upon AP motion of the disk. As the disk moves
in the ML and SI directions toward the outer boundaries of the
projection screen, subjects must shift forward to maintain contact
with the disk. When the disk moves back to the center of the
screen, the subjects must shift back to provide room for the arm
and hand moving directly in front. AP motion of the CoM
(61 cm, Fig. 3(a)) is quite small compared to ML CoM motion
(612 cm) or tracking motion (648–55 cm), due not only to the
placement of the projection screen but also to the BoS’s smaller
AP dimension (17 cm) relative to its ML dimension (30 cm).
We noted that the analytical transfer functions which best fit
the ETF data (Table 4) are not minimum phase transfer functions.
Of all transfer functions with the same gain characteristic, the one
with the minimum phase characteristic exhibits the shortest group
delay, hence the fastest response time. In this regard, they represent an upper limit on the system’s performance (see Fig. 6). Not
only do the minimum phase transfer functions exhibit substantially shorter response times than their fitted counterparts, they
also do not exhibit the initial fluctuations that the best-fit, nonminimum phase tracking transfer functions do. Analysis of tracking
errors (Fig. 7) also reveals that for both ML and SI directions
RMSE decreases with frequency, while NRMSE increases for
frequencies below 1 Hz. Since the amplitude of each sinusoidal
component is inversely proportional to its frequency, the lowest
frequency components of motion have the highest amplitudes, and
vice versa. At the same time, lower frequency components are
easier to track than higher frequency components. Thus, the subject tracks the lower frequency components more accurately than
the higher frequency components (as indicated by NRMSE), but
the magnitudes of the tracking errors are greater due to the greater
amplitudes (as indicated by RMSE). We also saw that subjects
exhibit better high frequency tracking performance (i.e., higher
gains) in the SI direction than in the ML direction. This
superiority is also reflected both in the lower overall tracking
errors (Fig. 2), and lower frequency-specific tracking errors
(Fig. 7).
A physical limitation of the experiment is the presence of the
projection screen in front of the subject. Though this represents an
important reaching environment encountered in ADL’s, it nonetheless constrains AP motion of the CoM and limits our ability to
fully challenge balance in this direction. To address this work has
begun on a second generation BRT, which employs a virtual reality environment instead of a projection screen. A second limitation concerns the assumption that the measured responses are
substantially linear, and that linear portions can be separated from
nonlinear portions and analyzed to give a meaningful characterization of overall response dynamics. This follows the work of
McRuer et al. [36], Kleinman et al. [37], and Baron et al. [38],
who separated human tracking responses into a linear component
and a nonlinear “remnant.” We were able to verify that the tracking system responses and ML CoM–BoS deviation response were
substantially linear. The %Fit for the tracking system responses
was greater than 93%, and for the ML CoM–BoS deviation
response it was 78%. Further, Fig. 5 shows that for these
responses the gain and phase characteristics did not vary with
amplitude, a second test of linearity. An analysis of the nonlinear
aspects of performance in this task is not presented in this first
article, but will be addressed in a subsequent one.
A number of tracking studies have been undertaken to assess
human tracking performance (e.g., Refs. [36–40]). However, these
have focused exclusively on performance in the tracking task
itself. Performance in a secondary task such as balance has not
been considered. Likewise, balance studies generally focus exclusively on the maintenance of balance when subjected to externally
applied disturbances of the BoS, visual surround, etc. (e.g., Refs.
[19], [20], and [22]). To our knowledge, no prior studies have
assessed balance maintenance while performing some other task
involving volitional, perturbing movements of the whole body
and/or its parts. Nonetheless, prior studies reveal similar control
patterns. McRuer et al. [36] found that for a given set of test
Fig. 6 Step responses of ML(y) and SI (z) components of tracking finger motion and ML CoMBoS deviation. Thick lines represent fitted transfer function step responses (upper three rows
in Table 4), while thin lines represent minimum phase transfer function responses (lower three
rows in Table 4). Dots indicate time to settle to within 5% of response final value. 1.1250 arm
lengths overall excursion amplitude.
121009-10 / Vol. 138, DECEMBER 2016
Transactions of the ASME
conditions, healthy adult subjects adaptively alter tracking
response dynamics to respond linearly to an input. Kleinman et al.
[37] and Baron et al. [38] also found that healthy subjects respond
linearly to a tracking input, and further found evidence that subjects were capable of developing a predictive model of this input
to aid in the tracking task. That human movement control employs
adaptive and predictive algorithms together implies the existence
of internal models [41–43]: highly adaptable neural structures
[44] that represent the kinematics and dynamics of the body and
its parts, and the forces and constraints imposed by the external
environment. The CSMB that we are developing incorporates a
controller based on this concept. Paterka [19], Mergner [20], and
others have found that the balance system exhibits at least a quasilinear response to unexpected disturbances. We are inclined to
rule this out for the tracking system, given the high %Fit measures
associated with it, but we do not rule it out for the balance system,
given its lower %Fit measures. It is important to note, though, that
while these earlier studies employed unexpected balance disturbances, our study employs expected disturbances caused by volitional movements of the body and its parts. The response to each
is generated by distinctly different regions of the brain (at least
initially). Responses to unexpected disturbances are generated by
lower level brain stem and spinal cord processes after the disturbance is sensed. Responses to expected disturbances are generated
by suprabrainstem (cortex, cerebellum, and basal ganglia) predictive and motor planning processes in advance of the disturbance
[23]. These latter regions are also where reaching and tracking
motor commands are generated. Responses to the expected balance disturbances encountered in this study are closely predicated
upon the tracking motions for which they are designed to compensate, and so we posit that these responses exhibit greater linearity
than those associated with unexpected balance disturbances.
The BRT was designed to challenge balance and to bring subjects with and without balance impairments to the limits of their
balance (without substantially moving their feet), just short of
inducing a fall. Young healthy subjects do not have appreciable
fall risk and are able to perform the test with relative ease because
their uncompromised sensorimotor and musculoskeletal systems
are able to anticipate expected, impending balance perturbations
and execute compensatory actions far enough in advance of the
disturbance to eliminate any threat of falling. Their performance
still has limits, however, and it is important to characterize and
quantify them. Moreover, even though this population is free from
the confounding effects of age and disease, we still cannot (yet)
determine even young healthy response to a particular balance
disturbance from “first principles,” given the high degree of complexity and redundancy associated with the sensorimotor and musculoskeletal systems and our limited knowledge of their functions
and interactions. Our approach to this goal lies in measuring and
quantifying young healthy performance both to advance our
knowledge of normal function and as a reference against which to
compare and assess high fall risk populations. Young healthy performance data has a number of more immediate applications. It
can inform work space design, for example, in the home and on
the job. Many athletic and job-related activities involve reaching.
It is important not only to know when to step to prevent a fall, but
also how to stand or step when at the limits of balance in order to
provide an optimal base of support for the upper extremity to
achieve maximal performance. Finally, given its sensitivity, variants of the BRT could be useful for movement training whose
goal is to achieve high fidelity and optimal human performance
within a prescribed movement or sequence of movements. We are
currently using the results reported here as a reference against
which to compare the performance of healthy older adults, otherwise healthy older adults with a history of falls, and older adults
whose balance has been further compromised by stroke. We
hypothesize that such comparisons will enable us to better characterize the multisegmental nature of functional balance in health,
Fig. 7 RMS (solid lines) and NRMS (dashed lines) finger tracking errors and CoM–BoS deviations (solid lines) with 95% confidence intervals (dotted lines). For tracking errors (Figs. 7(a)
and 7(b)), dots (RMS error) and stars (NRMS error) correspond to errors computed from the
ETF gains and phase lags (dots in Figs. 4(a) and 4(b)), while the solid and dashed lines correspond to those computed by the fitted analytical transfer function gains and phase lags (solid
lines in Figs. 4(a) and 4(b)). For CoM–BoS deviations (panels C and D), dots correspond to
deviations computed from the ETF gains and phase lags (dots in Figs. 4(c) and 4(d)), and solid
lines represent fitted equations of the form k1 fik2 1k3 . The lower 95% confidence bound for AP
CoM–BoS deviation is zero. 1.1250 arm lengths overall excursion amplitude.
Journal of Biomechanical Engineering
DECEMBER 2016, Vol. 138 / 121009-11
aging, and disease to enhance diagnostic specificity, better target
movement therapy, and quantify treatment response, including
changes in balance, referenced against young healthy controls.
Acknowledgment
This study (PI: Joseph Barton) was supported by a Veterans
Administration Career Development Award, CDA Grant No.
B7160-W (PI: Joseph Barton), a Pepper Center Development Project (PI: Joseph Barton) supported by NIA Grant No. P30AG028747 (PI: Andrew Goldberg), the Baltimore Veterans
Administration Medical Center Geriatric Research, Education and
Clinical Center (GRECC), and the Baltimore VA Maryland Exercise and Robotics Center of Excellence (VA Grant No. B9215-C),
PI: Richard Macko.
The authors thank Dr. Vincent Conroy and Dr. Douglas Savin
of the University of Maryland Physical Therapy and Rehabilitation Science Department for their expert advice on shoulder anatomy and motion.
Nomenclature
ai ¼ amplitude of the ith disk frequency
harmonic
f ¼ sum of sines frequency (Hz)
fi ¼ ith frequency harmonic
G ¼ transfer function gain
gi ¼ transfer function gain at the ith frequency
harmonic
p
ffiffiffiffiffiffiffi
i ¼ 1
ki ¼ fitted constants
r ¼ mean of clean data trajectory
ri ¼ ith element of clean data response
trajectory
r^i ¼ ith element of estimated data response
trajectory
s ¼ Laplace variable
t ¼ time (s)
x ¼ ML (x) position relative to global coordinate system
xd(t) ¼ horizontal trajectory of disk
y ¼ SI (y) position relative to global coordinate system
yd(t) ¼ vertical trajectory of disk
z ¼ AP (z) position relative to global coordinate system
%Fit ¼ percent fit
q ¼ correlation coefficient
s ¼ response lag
/ ¼ sum of sines phase shift
vi ¼ transfer function phase lag at the ith frequency harmonic
Abbreviations
ADL ¼
AL ¼
AP ¼
BoS ¼
BRT ¼
CoM ¼
CoM–BoS deviation ¼
CoR ¼
CSMB ¼
C7/T1 ¼
EMG ¼
activities of daily living
arm length
anterior–posterior
base of support
balanced reach test
center of mass
deviation between the projection of the
CoM onto the ground plane and the center
of the BoS
center of rotation
control system model of balance
intervertebral disk between the seventh
cervical and first thoracic vertebrae
electromyography
121009-12 / Vol. 138, DECEMBER 2016
ETF ¼ empirical transfer function
IRED ¼ infrared emitting diode
L5/S1 ¼ intervertebral disk between the fifth lumbar and first sacral vertebrae
ML ¼ medial–lateral
NRMSE ¼ normalized root mean squared finger
tracking error
PID ¼ proportional-integral-derivative
RMS ¼ root mean squared
RMSD ¼ root mean squared CoM–BoS deviation
RMSE ¼ root mean squared finger tracking error
SI ¼ superior–inferior
YHS ¼ young healthy subject
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