The 15th International Conference on Advanced Robotics
Tallinn University of Technology
Tallinn, Estonia, June 20-23, 2011
Foot Bone Kinematics at Half and Three Quarters Body Weight:
A Robotic Cadaveric Simulation of Stance Phase
Patrick M. Aubin, Member, IEEE, Eric C. Whittaker, and William R. Ledoux
attaching marker clusters to individual bones of interest [3].
This technique is more accurate but also a highly invasive
procedure with associated surgical risks. These limitations
have motivated the development of dynamic robotic
cadaveric models of the stance phase of gait [2],[4-8]. A
cadaveric model is advantageous because invasive bone pins
can be used to accurately measure bone kinematics without
the ethical considerations associated with living subjects.
Dynamic robotic cadaveric gait simulators animate a
lower limb cadaveric specimen with the same motion,
tendon forces, and vertical ground reaction force (vGRF)
that occurs in vivo. Simulating a full body weight (BW)
vGRF has proved difficult however due to challenges
associated with building high force robotic devices and
because the acquired cadaveric specimens from older donors
often fail easily due to their low bone density.
Previous studies have measured the bony motion of the
foot and ankle when the applied vGRF was reduced to a BW
of approximately 31 kg to 54 kg [7], or in some cases simply
50% BW [5],[9]. Other investigators have simulated 100%
BW but used very light weight donors, i.e., BWs ranging
from 35 to 50 kg [2]. It is unknown however how a reduced
BW simulation affects foot kinematics. The purpose of this
study therefore is to determine if the range of motion (ROM)
of the bones in the foot is significantly different between
50% BW and 75% BW simulations of the stance phase of
gait.
Abstract—Lower limb cadaveric robotic gait simulators have
been employed to model foot bone kinematics during the stance
phase of gait. Often the simulations are performed at reduced
body weight (BW) but the effect of this limitation on foot bone
kinematics has not been quantified. In this study we utilized the
robotic gait simulator (RGS) to measure in vitro foot bone
kinematics at different applied ground reaction forces (GRFs)
(50% BW and 75% BW). The RGS simulated gait by
replicating in vivo tibial kinematics, GRFs, and tendon forces.
A six-camera motion analysis system recorded the in vitro
motion of ten bones in the foot. Linear mixed effects regression
was used to test for differences in range of motion (ROM) by
BW (75% vs. 50%) for 12 bone-to-bone relationships.
Statistically significantly (p < 0.05) differences in ROM by BW
were found for six of the 12 angles investigated. On average the
ROM for the 75% BW simulations were systematically higher
than that for the 50% BW simulations (p < .0001), but the
magnitude of the difference was small (1.2˚). These results
indicate that reduced BW in vitro simulations approximately
model the ROM and temporal characteristic of foot bone
kinematics.
I. INTRODUCTION
U
nderstanding foot bone kinematics during the stance
phase of gait is useful to further our knowledge of foot
function, disease etiology, and surgical intervention efficacy.
Accurately measuring foot bone kinematics in vivo is
difficult however, and each method has its limitations.
Motion capture of retro-reflective markers adhered to the
skin is one approach but often results in grouping several
bones together into one “rigid” body. For example, A.
Leardini et al. grouped the navicular, lateral, middle and
medial cuneiforms, and the cuboid bones into a single midfoot segment resulting in an inability to measure the motion
that occurs between these bones [1]. Surface marker
techniques also suffer from skin movement artifact where
motion of the underlying bone can differ from the soft tissue
covering it [2]. Surgical bone pins avoid these limitations by
II. METHODS
A. Living Subject Gait Analysis
Ten healthy subjects were recruited and asked to perform
five gait trails each after providing informed consent for this
institutional review board approved study. A 12-camera
motion analysis system (Vicon, Lake Forest, CA) sampling
at 120 or 250 Hz recorded the motion of the three retroreflective markers attached to the tibia and fibula while a
force plate (Bertec Corporation; Columbus, Ohio) sampling
at 600 or 1500 Hz recorded the GRF. Rigid body motion of
the tibia (i.e., TIB, a coordinate system constructed from
anatomical landmarks of the tibia and fibula consistent with
the proposed ISB standards [10]) with respect to the
laboratory ground (i.e., GND, a coordinate system parallel to
the force plate reference frame but with an origin located
underneath the medial malleolus at heel strike) was
calculated and decomposed into sagittal, frontal and
transverse plane fixed angles and translations.
In vivo tendon forces during stance phase were estimated
Manuscript received March 21, 2011. This work was funded in part by
the VA RR&D, grants A3923 and A4843C.
P. M. Aubin was with the VA RR&D Center of Excellence for Limb
Loss Prevention and Prosthetic Engineering, Seattle, WA 98108 USA and
the Department of Electrical Engineering, University of Washington,
Seattle, WA 98195 USA. He is now with the Department of Biomechanics,
Vilnius Gediminas Technical University, Vilnius, Lithuania LT-03224.
Eric Whittaker is with the VA RR&D Center of Excellence for Limb
Loss Prevention and Prosthetic Engineering, Seattle, WA 98108 USA.
William R. Ledoux is with the VA RR&D Center of Excellence for
Limb Loss Prevention and Prosthetic Engineering, Seattle, WA 98108 USA
and the Departments of Orthopaedics & Sports Medicine, and Mechanical
Engineering, University of Washington, Seattle, WA 98195 USA. e-mail:
wrledoux@u.washington.edu; phone: (1) 206-768-5347; fax (1) 206-2773963.
978-1-4577-1159-6/11/$26.00 ©2011 IEEE
653
from literature values of each muscle’s physiological cross
sectional area (PCSA cm2), maximum specific isometric
tension (MST N/cm2), and electromyography activity during
gait (EMG % of maximum voluntary contraction) [11-14].
Muscle EMG to excitation (E) electromechanical delay
dynamics were modeled by a second-order discrete linear
difference equation given by (1):
E(t ) EMG(t d ) 1E(t 1) 2 E(t 2)
analyzed from the kinematics of the ten segment foot model.
We focused on twelve clinically important angles - six in the
sagittal plane, three in the frontal plane, and three in the
transverse plane. For these angles, the bone-to-bone ROM
was calculated as the difference between their maximum and
minimum value from heel strike to toe off.
(1)
with coefficients, α = 0.9007, β1 = -0.0982, β2 = -0.0012,
and electromechanical delay (d) = 42 ms [15]. Tendon force
(FT) was calculated as the product of E, MST, PCSA, and a
gain (G) equal to one (2).
FT (t ) G PCSA MST E(t )
(2)
B. In Vitro Kinematic Foot Model
Six cadaveric specimens transected approximately 10 cm
proximal to the malleoli were acquired for this study. The
Achilles (Ach), tibialis anterior (TA), extensor hallucis
longus (EHL), extensor digitorum longus (EDL), peroneus
brevis (PB), peroneus longus (PL), posterior tibialis (PT),
flexor hallucis longus (FHL) and flexor digitorum longus
(FDL) tendons were dissected two cm proximal to the
malleoli and their proximal ends were attached to tendon
clamps. A 40-marker kinematic foot model, which has been
previously described [8], was attached to the cadaveric foot
(Fig. 1). Briefly, retro-reflective markers (6.4 mm) placed at
specific sites with bone pins where used to create anatomical
coordinate systems for the tibia (TIB), calcaneus (CAL),
first metatarsal (MET1), third metatarsal (MET3), fifth
metatarsal (MET5), and hallux (HAL). Quad clusters of
retro-reflective markers were attached to bone pins and
secured to the talus (TAL), navicular (NAV), cuboid (CUB),
and medial cuneiform (CUN), with screws. For these four
bones a four-marker digitizing wand was used to create
embedded anatomical coordinate systems by registering the
location of bony anatomical land marks to their respective
quad clusters coordinate systems.
During the simulation the motion of the retro-reflective
markers was recorded with a six-camera motion analysis
system (Vicon, Lake Forest, CA). A custom Body Builder
(Vicon, Lake Forest, CA) program was written to calculate
the zxy fixed angle pose of each child-segment (bone) with
respect to (wrt) their parent-segment (bone) from the retroreflective marker positions, e.g., the angular pose of the
HAL wrt the MET1. The kinematic data was filtered with a
10 Hz zero phase low pass Butterworth filter.
A large number of bone-to-bone relationships can be
Fig. 1. A cadaveric foot with the 40 marker kinematic foot model attached.
Four retro-reflective markers were attached to the tibia (TIB), talus (TAL),
calcaneus (CALC), navicular (NAV), medial cuneiform (CUN), first
metatarsal (MET1), third metatarsal (MET3), fifth metatarsal (MET5),
cuboid (CUB), and hallux (HAL) in order to track their motion via a 6camera motion analysis system during the in vitro simulation of stance
phase.
C. The Robotic Gait Simulator
The RGS consists of a 6-DOF parallel robot (the R2000,
Mikrolar Inc., Hampton, NH), nine brushless DC linear
tendon force actuators (SR21 & GSX40, Exlar Corp.,
Chanhassen, MN), a force plate (model 9281CA, Kistler
Instrument Corp.; Amherst, NY), a 6-camera motion
analysis system (Vicon; Lake Forest, CA), a real time
embedded controller (PXI, National Instruments Corp.;
Austin, TX), and a PC with a graphical user interface (Fig.
2). To simulate gait the TIB was held fixed in space while
the R2000 moved a mobile “ground” in order to recreate the
relative tibia to ground motion.
The R2000 is a 6-DOF parallel robot similar to a Stewart
platform with six legs that actuate a mobile platform (Fig. 2,
top right inset). The robot has a 2.4 m by 1.7 m footprint
and net weight of 1450 kg. The mobile platform has an
asymmetric working volume of roughly ± 100 mm
translation in the x-, y-, and z-axis and ± 15° rotation around
the x-, and y-axis and ± 360° rotation around the z-axis. The
manufacturer specified accuracy and repeatability are
approximately 50 μm and 25 μm, respectively. Its parallel
construction provides high stiffness and allows for a 227 kg
payload. A robust steel frame surrounding the R2000
mechanically grounds the base of the robot to the laboratory
floor and also acts as a rigid support for the tibial mounting
frame.
Attached to the mobile platform via a
654
Fig. 2. The robotic gait simulator with surrounding frame (A), R2000 parallel robot (top right inset), R2000 motor (B, one of six), mobile force plate (C),
cadaveric foot (D), mobile top plate (E), tibia mounting device (F), force control tendon actuators (G), 6-camera motion analysis system (H, only one
camera shown), tendon pull control cable (I), and tendon freeze clamp (J).
custom steel frame is a force plate that acts as the “ground”
and moves relative to the static cadaveric TIB. Six brushless
DC motors control the pose of the mobile platform. Unlike
a traditional Stewart platform, the R2000’s legs have a fixed
length; the position and orientation of the mobile platform
are controlled by the legs rotating around a circular steel rim
attached to the base of the robot.
Tendon force was provided by a nine axis tendon
actuation system which consists of nine linear actuators
(SR21 & GSX40, Exlar Corp., Chanhassen, MN) in series
with nine load cells (Transducer Techniques Inc., Temecula,
CA). Control cables were routed from the load cells to
custom tendon clamps (Fig. 2). The tendon actuation system
operated in force control mode. A PID controller operating
on the PXI controller measured tendon force in real time and
made appropriate adjustments to the motor current in order
to track the target tendon forces.
The in vitro vGRF was controlled by a fuzzy logic
controller (FLC) which has been previously described in
detail [16]. Briefly, the FLC made adjustments to the R2000
kinematics, Ach tendon force, and TA tendon force in order
to track the desired vGRF. The FLC had three inputs:
percent stance phase, vGRF error, and the integral of the
vGRF error. The outputs of the FLC were a change in Ach
force, a change in TA force, and a change in the mobile
force plate translational kinematics. Adjustments to the
target tendon forces were performed in real time while
adjustments to the R2000 kinematics were done iteratively,
similarly to a previously developed iterative learning vGRF
controller [17].
clamps were used for the other tendons. The motion
analysis system was used to measure the pose of the tibia wrt
the R2000 base frame. An optimization algorithm was used
to determine the optimum tibial pose which would minimize
the required R2000 motor velocity during the simulation
[16]. The optimization allowed the simulation to occur in the
desired 2.782 s, or 4 times slower than in vivo gait. Several
initial simulations were performed at a reduced vGRF to
verify proper system operation. The vGRF was then
manually increased iteratively by increasing the tendon force
gain G in (2) and by adjusting a translational superiorinferior offset parameter in the trajectory until the vGRF was
within approximately ± 10% of the target vGRF. Manual
control of the vGRF was then halted and the FLC was
enabled for subsequent simulations in order to track the
target vGRF with high fidelity.
Each cadaveric specimen was tested at both 50% BW and
75% BW. At each BW three quartets of simulations were
performed.
Each quartet consisted of four iterative
simulations, where the first three simulations of the quartet
allowed the FLC to iteratively improve the vGRF tracking.
During the fourth and final simulation of the quartet the
motion of the retro-reflective markers were recorded at 200
Hz and saved for post analysis.
E. Statistical Analysis
Linear mixed effects regression was used to test for
differences in ROM by BW (75% vs. 50%) for twelve
important bone-to-bone relationships.
ROM was the
dependent variable, BW was the independent fixed effect
and cadaveric foot and cadaveric foot x BW interaction were
random effects. To assess the effect of BW on ROM for all
angles (17 bone-to-bone relationships in three planes each or
51 angles) together, linear mixed effects models were carried
out combining all 51 angles into one model, as above, with
D. Cadaveric Gait Simulation
Each cadaveric specimen was mounted into the RGS via
the tibia mounting device. A freeze clamp [18] was used to
attach the Ach tendon to its actuator while non-freezing
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TABLE I. MEAN RANGE OF MOTION (ROM) AND THE STANDARD ERROR
(SE) OF THE MEAN FOR 12 BONE-TO-BONE RELATIONSHIPS. STATISTICALLY
SIGNIFICANT DIFFERENCES IN ROM (P < 0.05) ARE SHOWN IN BOLD.
50% BW
75% BW
difference
ROM
ROM
bone
½–¾
mean
mean
with respect to (-)
[SE]
[SE]
bone
p-value
[SE]
the addition of joint/plane as fixed effects covariates, and
random effects foot, joint/plane within foot, and joint/plane
x BW interaction. Analyses were carried out using R 2.11.1
[19].
III. RESULTS
Sagittal plane
The RGS was able to recreate the physiological
characteristics of gait. The mean tibia wrt ground angles in
the sagittal, frontal, and transverse planes were entirely
within ± 1 SD of the target in vivo tibia angles for both the
50% BW and 75% BW simulations. The in vitro vGRF also
closely match that of the living subjects. For the 50% BW
simulations the average RMS error between the target in
vivo and actual in vitro vertical, medial/lateral and
anterior/posterior GRF was 5.1% BW, 1.8% BW and 3.7 %
BW, respectively. The 75% BW simulations had similar
GRF tracking results with RMS tracking errors of 5.9% BW,
3.6% BW, and 4.0% BW for the vertical, medial/lateral and
anterior/posterior GRF, respectively. The average RMS
tracking error for all tendons except for the fuzzy logic
controlled TA and Ach was 3.6 N and 3.9 N for the 50%
BW and 75% BW simulations, respectively.
The mean and the standard error (SE) of the mean ROM
for 12 bone-to-bone relationships was calculated for both the
50% BW and 75% BW simulations (Table I, Fig. 3 - 4). The
difference (75% BW - 50% BW) in the mean ROM ranged
from 0.7° for the TAL wrt the TIB in the sagittal plane to a
maximum of 6.7° for the HAL wrt the MET1 in the sagittal
plane. The linear mixed effects regression found statistically
significant differences in ROM by BW for six of the 12
angles investigated (Table I).
In the sagittal plane
statistically significant differences were found for the MET1
wrt the TAL (3.7° ROM difference; p=.0002) and for the
HAL wrt the MET1 (6.7° ROM difference; p=.0061). In the
frontal plane statistically significant differences were found
for the CALC wrt the TAL (1.4° ROM difference; p=.016)
and NAV wrt the TAL (2.9° ROM difference; p=.0056). In
the transverse plane, statistically significant differences in
ROM were found for the MET1 wrt TAL (3.1° ROM
difference; p=.0059) and for the NAV wrt the TAL (2.7°
ROM difference; p=.014).
The model combining ROM measures for all 51 bone-tobone relationships (1707 individuals ROM measurements)
found that on average the ROM for the 75% BW simulations
was systematically higher than that for the 50% BW
simulations (p < .0001), although the magnitude of the
difference was small (1.2˚) (Table I).
CALC - TIB
22.0 [3.0]
23.6 [2.9]
1.6 [0.8]
.057
TAL - TIB
22.5 [2.0]
23.2 [1.9]
0.7 [0.7]
.3
NAV - TAL
8.4 [1.8]
9.6 [1.9]
1.2 [0.7]
.094
CUN - NAV
11.0 [1.2]
12.2 [0.9]
1.2 [0.6]
.062
MET1 - TAL
18.9 [2.6]
22.6 [2.7]
3.7 [0.6]
.0002
HAL - MET1
55.2 [3.0]
61.9 [2.8]
6.7 [1.9]
.0061
CALC - TIB
8.2 [0.9]
9.2 [1.3]
1.0 [0.6]
.11
CALC – TAL
7.1 [0.7]
8.6 [1.1]
1.4 [0.5]
.016
NAV –TAL
15.9 [1.9]
18.8 [2.1]
2.9 [0.8]
.0056
Frontal plane
Transverse plane
CALC - TAL
5.4 [0.7]
6.2 [0.9]
0.8 [0.4]
.086
NAV – TAL
12.2 [1.7]
14.9 [2.4]
2.7 [0.9]
.014
MET1 – TAL
16.3 [1.3]
19.4 [1.6]
3.1 [0.9]
.0059
1.2 [0.2]
<.0001
All angles combined
In general the temporal joint motions patterns were
similar between the 50% BW and 75% BW conditions. For
example, motion of the talotibial joint (TAL wrt the TIB) in
the sagittal plane plantar flexed at heel strike then
dorsiflexed during midstance and finally plantar flexed again
during push off for both the 50% BW and 75% BW tests
(Fig. 5, top plot). CALC wrt the TAL in the frontal plane
and MET1 wrt the TAL in the transverse plane are also
representative, with minimal changes in the kinematics
between the 50% BW and the 75% BW simulations (Fig. 5,
middle and bottom plot).
Fig. 3. Mean ± 1 SE sagittal plane range of motion (ROM) for the 50%
body weight (BW) (empty squares) and 75% BW (black circles)
simulations.
656
associated with walking and the fragility of cadaveric
specimens has resulted in routinely testing specimens at
reduced BWs, the effects of which are unknown. For this
study, we sought to determine if foot bone kinematics during
the stance phase of gait differ between a 50% BW and a
75% BW simulation. Our study results suggest that
differences in foot bone kinematics between the BW
simulations are small and often less than a couple of degrees.
This implies that reduced BW simulations of the stance
phase of gait are able to approximately model in vivo foot
kinematics.
The inability to test the cadaveric feet at 100% BW is one
limitation of this study. Ideally we would have been able to
test the cadaveric feet at 100%, 75% and 50% BW. While
the RGS is able to deliver the force required to test at 100%
BW, we instead tested at lower forces because one of the
earlier tested specimens failed at 100% BW. Our results,
however, still provide new insight into how scaling the
vGRF affects foot kinematics. The differences between 75%
and 100% BW are likely similar to the minimal differences
discovered between 50% and 75%. Furthermore, our results
facilitate other research groups trying to weigh the
advantages and disadvantages of testing at large or small
BWs which until now have been unknown.
Another limitation of this study is the accuracy and
precision to which the joint angles were measured. The 40marker foot model employed in this study pushes the
boundary of what is currently possible for in vitro foot
models. Many of the bone measured are in close proximity
to one another, have small feature sizes, and have minimal
angular movement. Camera settings (position, alignment
focal length, aperture and infrared strobe intensity), bone pin
rigidity, retro-reflective marker size, and anatomical
coordinate system construction all affect the accuracy and
precision of the recorded kinematics.
Some of the
variability in the results is likely due to these limitations.
The ROM of HAL wrt MET1 in the sagittal plane for both
the 50% BW and 75% BW simulations was greater than the
42° ROM previously reported by Nawoczenski et al. [20].
Interestingly, HAL wrt the MET1 also had the largest
difference in ROM between 50% BW and 75% BW. Two
reasons may explain these findings. First, the TIB wrt GND
kinematics were held constant and equal to the in vivo TIB
kinematics for all cadaveric specimens even though interspecimen foot size differences were present, as were size
differences between the cadaveric feet and the living
subject’s feet. Thus, a smaller than average cadaveric foot
would have had greater ankle plantar flexion to maintain
contact with the ground during late stance which would have
led to greater HAL dorsiflexion. Secondly, and perhaps
more importantly, the intrinsic musculature of the foot was
not actuated in this study. The flexor hallucis brevis, for
example, is a plantar flexor of HAL, and if actuated it would
have likely stabilized and limited the sagittal plane ROM of
the great toe. An important implication of this finding is that
joints that are not actively articulated by intrinsic muscles,
Fig. 4. Mean ± 1 SE frontal and transverse plane range of motion (ROM)
for the 50% body weight (BW) (empty squares) and 75% BW (black
circles) simulations.
Fig. 5. Joint motion from one cadaveric foot for the three 50% BW (black
lines) and three 75% BW (gray lines) simulations. The plots shown are the
talotibial joint (TAL wrt TIB) in the sagittal plane (top), the subtalar joint
(CALC wrt TAL) in the frontal plane (middle), and the first metatarsal with
respect to the talus (MET1 wrt TAL) in the transverse plane (bottom).
These representative figures demonstrate the similarity of the joint’s motion
between different BW simulations indicating that the kinematics of the joint
are well modeled at reduced BW.
IV. DISCUSSION
Cadaveric robotic gait simulators are useful to investigate
the biomechanics of the foot and ankle. The large forces
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[5]
such as the naviculo-cuneiform joint, are better modeled by,
and less sensitive to, the limitations associated with dynamic
cadaveric gait simulators as compared to other segments
articulated by intrinsic musculature such as the
metatarsophalangeal joints.
The results of this study can be used to facilitate the
design and development of future robotic cadaveric
simulators. Designing a high force system is often more
complex and expensive than a comparable low force system.
These results can aid future investigators in performing a
cost benefit analysis for their designs. The utility of robotic
technologies was also demonstrated. Specifically, the robotic
methodology we used allowed for precise and accurate
kinematic control, complex force control, and good
experimental repeatability.
The implications of this study should be use cautiously.
While joint kinematics have been shown to have low
sensitivity to the applied vGRF, that is not to say that scaling
the vGRF is in general not a limitation of dynamic cadaveric
robotic gait simulation studies. Many investigators have
used cadaveric robotic gait simulators to investigate a
variety of parameters ranging from bone strain [21] to
midfoot joint pressure [4] to plantar fascia strain [22]. It is
important to keep in mind that other biomechanical
properties may be more sensitive to vGRF than foot bone
kinematics.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
V. CONCLUSION
[14]
Differences in foot bone kinematics during the stance
phase of gait at 50% BW and 75% BW were quantified
using a robotic cadaveric gait simulator. While some
statistically significant differences in ROM were found, in
general the differences were small and are likely comparable
to the accuracy of many kinematic foot models. When
designing their experimental protocols, investigators can use
these results to evaluate the advantages and disadvantages of
testing at reduced BW.
[15]
[16]
[17]
[18]
ACKNOWLEDGMENT
The authors would like to thank Jane Shofer for her
generous help with the statistical analysis of the ROM data.
[19]
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